Mathematik und StatistikMathematik und Statistikhttps://kops.uni-konstanz.de/handle/123456789/82023-05-31T04:53:21Z2023-05-31T04:53:21Z5017351(Reflected) Backward Stochastic Differential Equations and Contingent Claims123456789/5872023-02-09T05:51:55Z1999dc.title: (Reflected) Backward Stochastic Differential Equations and Contingent Claims
dc.contributor.author: Kohlmann, Michael
dc.description.abstract: Abstract. We review the relations between adjoints of stochastic control problems with the derivative of the value function, and the latter with the value function of a stopping problem. These results are applied to the pricing of contingent claims.
1999Kohlmann, Michael330Abstract. We review the relations between adjoints of stochastic control problems with the derivative of the value function, and the latter with the value function of a stopping problem. These results are applied to the pricing of contingent claims.WORKINGPAPERurn:nbn:de:bsz:352-opus-3197engCoFE-Diskussionspapiere / Zentrum für Finanzen und Ökonometrie1999/102011-03-22T18:45:09+01:00123456789/392011-03-22T17:45:09Z3D-2D Stokes-Darcy Coupling for the Modelling of Seepage with an Application to Fluid-Structure Interaction with ContactVermolen, Fred J.Vuik, Cornelis123456789/560372023-02-07T06:12:56Z2021dc.title: 3D-2D Stokes-Darcy Coupling for the Modelling of Seepage with an Application to Fluid-Structure Interaction with Contact
dc.contributor.author: Burman, Erik; Fernández, Miguel A.; Frei, Stefan; Gerosa, Fannie M.
dc.description.abstract: In this note we introduce a mixed dimensional Stokes-Darcy coupling where a d dimensional Stokes’ flow is coupled to a Darcy model on the d − 1 dimensional boundary of the domain. The porous layer introduces tangential creeping flow along the boundary and allows for the modelling of boundary flow due to surface roughness. This leads to a new model of flow in fracture networks with reservoirs in an impenetrable bulk matrix. Exploiting this modelling capability, we then formulate a fluid-structure interaction method with contact, where the porous layer allows for mechanically consistent contact and release. Physical seepage in the contact zone due to rough surfaces is modelled by the porous layer. Some numerical examples are reported, both on the Stokes’-Darcy coupling alone and on the fluid-structure interaction with contact in the porous boundary layer.
2021Burman, ErikFernández, Miguel A.Frei, StefanGerosa, Fannie M.510In this note we introduce a mixed dimensional Stokes-Darcy coupling where a d dimensional Stokes’ flow is coupled to a Darcy model on the d − 1 dimensional boundary of the domain. The porous layer introduces tangential creeping flow along the boundary and allows for the modelling of boundary flow due to surface roughness. This leads to a new model of flow in fracture networks with reservoirs in an impenetrable bulk matrix. Exploiting this modelling capability, we then formulate a fluid-structure interaction method with contact, where the porous layer allows for mechanically consistent contact and release. Physical seepage in the contact zone due to rough surfaces is modelled by the porous layer. Some numerical examples are reported, both on the Stokes’-Darcy coupling alone and on the fluid-structure interaction with contact in the porous boundary layer.SpringerVermolen, Fred J.Vuik, CornelisINPROCEEDINGSeng10.1007/978-3-030-55874-1_20Lecture Notes in Computational Science and Engineering978-3-030-55873-41439-73582197-7100215223Numerical Mathematics and Advanced Applications ENUMATH 20192021-12-23T11:45:53+01:00123456789/39Numerical Mathematics and Advanced Applications ENUMATH 2019 / Vermolen, Fred J.; Vuik, Cornelis (Hrsg.). - Cham : Springer, 2021. - (Lecture Notes in Computational Science and Engineering). - S. 215-223. - ISSN 1439-7358. - eISSN 2197-7100. - ISBN 978-3-030-55873-4Egmond aan Zee2019-09-30ChamNumerical Mathematics and Advanced Applications ENUMATH 20192019-10-042021-12-23T10:45:53ZA 2n<sup>2</sup>-log<sub>2</sub>(n)-1 lower bound for the border rank of matrix multiplication123456789/532332023-02-07T06:12:22Z2018dc.title: A 2n<sup>2</sup>-log<sub>2</sub>(n)-1 lower bound for the border rank of matrix multiplication
dc.contributor.author: Landsberg, Joseph M.; Michalek, Mateusz
dc.description.abstract: Let M<sub>⟨n⟩</sub> ∈ C<sup>n2</sup>⊗C<sup>n2</sup>⊗C<sup>n2</sup> denote the matrix multiplication tensor for n×n matrices. We use the border substitution method [2, 3, 6] combined with Koszul flattenings [8] to prove the border rank lower bound R(M<sub>⟨n,n,n⟩</sub>)≥2n<sup>2</sup>−⌈log<sub>2</sub>(n)⌉−1.
2018Landsberg, Joseph M.Michalek, Mateusz510Let M<sub>⟨n⟩</sub> ∈ C<sup>n2</sup>⊗C<sup>n2</sup>⊗C<sup>n2</sup> denote the matrix multiplication tensor for n×n matrices. We use the border substitution method [2, 3, 6] combined with Koszul flattenings [8] to prove the border rank lower bound R(M<sub>⟨n,n,n⟩</sub>)≥2n<sup>2</sup>−⌈log<sub>2</sub>(n)⌉−1.Oxford University Press (OUP)JOURNAL_ARTICLEeng10.1093/imrn/rnx0251073-79281687-024747224733201815International Mathematics Research Notices2021-03-23T10:44:04+01:00123456789/39International Mathematics Research Notices ; 2018 (2018), 15. - S. 4722-4733. - Oxford University Press (OUP). - ISSN 1073-7928. - eISSN 1687-0247true2021-03-23T09:44:04ZtrueA Baer-Krull theorem for quasi-ordered groups123456789/407132023-02-09T13:28:16Z2018-07dc.title: A Baer-Krull theorem for quasi-ordered groups
dc.contributor.author: Kuhlmann, Salma; Lehéricy, Gabriel
dc.description.abstract: We give group analogs of two important theorems of real algebra concerning convex valuations, one of which is the Baer-Krull theorem. We do this by using quasi-orders, which gives a uniform approach to valued and ordered groups. We also recover the classical Baer-Krull theorem from its group analog.
2018-07Kuhlmann, SalmaLehéricy, Gabriel510We give group analogs of two important theorems of real algebra concerning convex valuations, one of which is the Baer-Krull theorem. We do this by using quasi-orders, which gives a uniform approach to valued and ordered groups. We also recover the classical Baer-Krull theorem from its group analog.JOURNAL_ARTICLEurn:nbn:de:bsz:352-2-1pisj4or0mdtc4eng10.1007/s11083-017-9432-50167-80941572-9273283291352Order2017-11-22T16:04:43+01:00123456789/39Order ; 35 (2018), 2. - S. 283-291. - ISSN 0167-8094. - eISSN 1572-9273unknown2017-11-22T15:04:43ZA Branch-and-Bound Approach to Mixed-Integer Optimal Control Using POD123456789/439342023-02-09T13:27:19Z2017dc.title: A Branch-and-Bound Approach to Mixed-Integer Optimal Control Using POD
dc.contributor.author: Bachmann, Freya
dc.description.abstract: In this thesis we consider a mixed-integer optimal control problem motivated by energy-efficient building operations. The aim is to choose suitable insulation materials for outer walls from a set of integer values and determine an underfloor heating strategy to maintain a desired temperature in a room while keeping the costs reasonably low. Mathematically, this translates into a mixed-integer optimal control problem that combines two major fields, mixed-integer programming (for which we will present the branch-and-bound algorithm) and optimal control (which we will speed-up by a reduced-order model approach). The branch-and-bound algorithm performs a tree-search by iteratively solving relaxed problems (without integrality constraint, i.e. restricted linear-quadratic optimal control problems) for various lower and upper bounds on the boundary control. Consequently, many state and adjoint equations have to be solved which is time-consuming as their finite element discretizations lead to large degrees of freedom. Therefore, we apply a model reduction technique using proper orthogonal decomposition providing a significant speed-up alongside small errors as few specific ansatz functions can capture the main characteristics of the system dynamics. We discuss strategies for branching decisions and node selection in the branch-and-bound algorithm and present numerical experiments for different scenarios.
2017Bachmann, Freya510In this thesis we consider a mixed-integer optimal control problem motivated by energy-efficient building operations. The aim is to choose suitable insulation materials for outer walls from a set of integer values and determine an underfloor heating strategy to maintain a desired temperature in a room while keeping the costs reasonably low. Mathematically, this translates into a mixed-integer optimal control problem that combines two major fields, mixed-integer programming (for which we will present the branch-and-bound algorithm) and optimal control (which we will speed-up by a reduced-order model approach). The branch-and-bound algorithm performs a tree-search by iteratively solving relaxed problems (without integrality constraint, i.e. restricted linear-quadratic optimal control problems) for various lower and upper bounds on the boundary control. Consequently, many state and adjoint equations have to be solved which is time-consuming as their finite element discretizations lead to large degrees of freedom. Therefore, we apply a model reduction technique using proper orthogonal decomposition providing a significant speed-up alongside small errors as few specific ansatz functions can capture the main characteristics of the system dynamics. We discuss strategies for branching decisions and node selection in the branch-and-bound algorithm and present numerical experiments for different scenarios.MSC_THESISurn:nbn:de:bsz:352-2-1m16ohd67jnfs7eng2018-11-21T11:12:38+01:00123456789/392018-11-21T10:12:38ZA causal formulation of dissipative relativistic fluid dynamics with or without diffusion123456789/664692023-03-28T09:42:16Z2023dc.title: A causal formulation of dissipative relativistic fluid dynamics with or without diffusion
dc.contributor.author: Freistühler, Heinrich
2023Freistühler, Heinrich510American Mathematical Society (AMS)JOURNAL_ARTICLEeng10.1090/qam/16560033-569X1552-4485Quarterly of Applied Mathematics2023-03-28T11:41:12+02:00123456789/39Quarterly of Applied Mathematics ; 2023. - American Mathematical Society (AMS). - ISSN 0033-569X. - eISSN 1552-4485true2023-03-28T09:41:12ZA class of Hadamard well-posed five-field theories of dissipative relativistic fluid dynamics123456789/492452023-02-07T06:20:22Z2020-03-01dc.title: A class of Hadamard well-posed five-field theories of dissipative relativistic fluid dynamics
dc.contributor.author: Freistühler, Heinrich
dc.description.abstract: This paper proposes a class of causal formulations for dissipative relativistic fluid dynamics as a hyperbolic five-field system of second-order partial differential equations. The argumentation continues lines of thinking developed in the author’s earlier papers with Temple and generalizes a four-field description that was recently given by Bemfica, Disconzi, and Noronha [Phys. Rev. D 98, 104064 (2018)] for the case of the pure radiation fluid. The Navier–Stokes–Fourier-like models are constructed as perturbations of auxiliary “involutory augmentations” of the Euler equations and shown to be Hadamard well-posed at least at the level of their linearization.
2020-03-01Freistühler, Heinrich510This paper proposes a class of causal formulations for dissipative relativistic fluid dynamics as a hyperbolic five-field system of second-order partial differential equations. The argumentation continues lines of thinking developed in the author’s earlier papers with Temple and generalizes a four-field description that was recently given by Bemfica, Disconzi, and Noronha [Phys. Rev. D 98, 104064 (2018)] for the case of the pure radiation fluid. The Navier–Stokes–Fourier-like models are constructed as perturbations of auxiliary “involutory augmentations” of the Euler equations and shown to be Hadamard well-posed at least at the level of their linearization.American Institute of Physics (AIP)JOURNAL_ARTICLEeng10.1063/1.51357040022-24881089-7658613Journal of Mathematical Physics2020-04-21T15:34:46+02:00123456789/39Journal of Mathematical Physics ; 61 (2020), 3. - 033101. - American Institute of Physics (AIP). - ISSN 0022-2488. - eISSN 1089-7658true2020-04-21T13:34:46ZA class of uniformly dissipative symmetric hyperbolic-hyperbolic systems123456789/537482023-02-07T06:25:18Z2021dc.title: A class of uniformly dissipative symmetric hyperbolic-hyperbolic systems
dc.contributor.author: Freistühler, Heinrich; Sroczinski, Matthias
dc.description.abstract: Motivated by applications in relativistic fluid dynamics, this paper studies a general class of linear systems of partial differential equations in which a second-order symmetric hyperbolic part and a first-order symmetric hyperbolic part interact dissipatively. It shows that corresponding algebraic properties of the two operators induce decay in natural Sobolev spaces, and discusses examples which demonstrate the logical interplay between associated conditions referring to small, large, and all wave numbers, respectively.
2021Freistühler, HeinrichSroczinski, Matthias510Motivated by applications in relativistic fluid dynamics, this paper studies a general class of linear systems of partial differential equations in which a second-order symmetric hyperbolic part and a first-order symmetric hyperbolic part interact dissipatively. It shows that corresponding algebraic properties of the two operators induce decay in natural Sobolev spaces, and discusses examples which demonstrate the logical interplay between associated conditions referring to small, large, and all wave numbers, respectively.ElsevierJOURNAL_ARTICLEeng10.1016/j.jde.2021.04.0050022-03961090-27324061288Journal of Differential Equations2021-05-26T08:54:36+02:00123456789/39Journal of Differential Equations ; 288 (2021). - S. 40-61. - Elsevier. - ISSN 0022-0396. - eISSN 1090-2732true2021-05-26T06:54:36ZA Cluster-Based Outlier Detection Scheme for Multivariate Data123456789/294132023-02-07T06:24:28Z2015dc.title: A Cluster-Based Outlier Detection Scheme for Multivariate Data
dc.contributor.author: Jobe, J. Marcus; Pokojovy, Michael
dc.description.abstract: Detection power of the squared Mahalanobis distance statistic is significantly reduced when several outliers exist within a multivariate data set of interest. To overcome this masking effect, we propose a computer-intensive cluster-based approach that incorporates a reweighted version of Rousseeuw’s minimum covariance determinant method with a multi-step cluster-based algorithm that initially filters out potential masking points. Compared to the most robust procedures, simulation studies show that our new method is better for outlier detection. Additional real data comparisons are given.
2015Jobe, J. MarcusPokojovy, Michael510Detection power of the squared Mahalanobis distance statistic is significantly reduced when several outliers exist within a multivariate data set of interest. To overcome this masking effect, we propose a computer-intensive cluster-based approach that incorporates a reweighted version of Rousseeuw’s minimum covariance determinant method with a multi-step cluster-based algorithm that initially filters out potential masking points. Compared to the most robust procedures, simulation studies show that our new method is better for outlier detection. Additional real data comparisons are given.JOURNAL_ARTICLEeng10.1080/01621459.2014.9832310162-14591537-274X15431551110512Journal of the American Statistical Association2014-12-10T13:56:04+01:00123456789/39Journal of the American Statistical Association ; 110 (2015), 512. - S. 1543-1551. - ISSN 0162-1459. - eISSN 1537-274X2014-12-10T12:56:04ZA cohomological interpretation of the Grothendieck-Teichmüller group123456789/233102023-02-07T06:17:59Z1997dc.title: A cohomological interpretation of the Grothendieck-Teichmüller group
dc.contributor.author: Lochak, Pierre; Schneps, Leila; Scheiderer, Claus
1997Lochak, PierreSchneps, LeilaScheiderer, Claus510JOURNAL_ARTICLEurn:nbn:de:bsz:352-233109eng10.1007/s0022200501310020-99101432-12975716001273Inventiones mathematicae2013-05-15T11:55:16+02:00123456789/39Inventiones mathematicae ; 127 (1997), 3. - S. 571-600. - ISSN 0020-9910. - eISSN 1432-12972013-05-15T09:55:16ZA COKOSNUT code for the control of the time-dependent Kohn–Sham model123456789/412262023-02-07T06:13:16Z2017-05dc.title: A COKOSNUT code for the control of the time-dependent Kohn–Sham model
dc.contributor.author: Sprengel, Martin; Ciaramella, Gabriele; Borzì, Alfio
dc.description.abstract: Optimal control of multi-electron systems is considered in the framework of the time-dependent density functional theory. For this purpose, the MATLAB package COKOSNUT is presented that aims at solving optimal quantum control problems governed by the Kohn–Sham equation. This package includes a robust globalized nonlinear conjugate gradient scheme and an efficient splitting procedure for the numerical integration of the nonlinear Kohn–Sham equations in two dimensions. Results of numerical experiments demonstrate the ability of the COKOSNUT code in computing accurate optimal controls.
2017-05Sprengel, MartinCiaramella, GabrieleBorzì, Alfio510Optimal control of multi-electron systems is considered in the framework of the time-dependent density functional theory. For this purpose, the MATLAB package COKOSNUT is presented that aims at solving optimal quantum control problems governed by the Kohn–Sham equation. This package includes a robust globalized nonlinear conjugate gradient scheme and an efficient splitting procedure for the numerical integration of the nonlinear Kohn–Sham equations in two dimensions. Results of numerical experiments demonstrate the ability of the COKOSNUT code in computing accurate optimal controls.JOURNAL_ARTICLEeng10.1016/j.cpc.2017.01.0200010-46551879-2944231238214Computer Physics Communications2018-02-05T14:48:14+01:00123456789/39Computer Physics Communications ; 214 (2017). - S. 231-238. - ISSN 0010-4655. - eISSN 1879-29442018-02-05T13:48:14ZA combined lattice BGK/level set method for immiscible two-phase flows123456789/8312023-02-07T06:27:42Z2009dc.title: A combined lattice BGK/level set method for immiscible two-phase flows
dc.contributor.author: Becker, Jürgen; Junk, Michael; Kehrwald, Dirk; Thömmes, Guido; Yang, Zhaoxia
dc.description.abstract: We present a lattice Boltzmann method (LBM) for simulating immiscible multi-phase flows which is based on a coupling of LBM with the level set method. The computation of immiscible flows using the LBM with BGK collision operator is done separately in each of the fluid domains and coupled at the interface by an appropriate boundary condition. In this way we preserve sharp interfaces between different fluid phases. We apply a new interface condition that represents the fluid mechanical jump conditions at the interface in the kinetic LBM framework. The level set method is applied to compute the evolution of the interface between fluids. Numerical results demonstrate the applicability of the method even in the presence of large viscosity and density ratios.
2009Becker, JürgenJunk, MichaelKehrwald, DirkThömmes, GuidoYang, Zhaoxia510We present a lattice Boltzmann method (LBM) for simulating immiscible multi-phase flows which is based on a coupling of LBM with the level set method. The computation of immiscible flows using the LBM with BGK collision operator is done separately in each of the fluid domains and coupled at the interface by an appropriate boundary condition. In this way we preserve sharp interfaces between different fluid phases. We apply a new interface condition that represents the fluid mechanical jump conditions at the interface in the kinetic LBM framework. The level set method is applied to compute the evolution of the interface between fluids. Numerical results demonstrate the applicability of the method even in the presence of large viscosity and density ratios.JOURNAL_ARTICLEurn:nbn:de:bsz:352-opus-106489eng10.1016/j.camwa.2009.02.0050097-49430898-1221950964585Computers & Mathematics with Applications2011-03-22T18:49:02+01:00123456789/39Computers & Mathematics with Applications ; 58 (2009), 5. - S. 950-964. - ISSN 0097-4943. - eISSN 0898-12212011-03-22T17:49:02ZA computational approach to an alternative working environment for the constructible universeLöwe, BendiktSoskov, Ivan123456789/415732023-02-07T06:29:32Z2011dc.title: A computational approach to an alternative working environment for the constructible universe
dc.contributor.author: Carl, Merlin
dc.description.abstract: We exhibit aspects of fine structure theory related to infinitary computations and describe a new approach to fine structure based on it, the F-hierarchy, and its refinement, the hyperings. As a sample application, we prove a variant of a theorem of Magidor.
2011Carl, Merlin510We exhibit aspects of fine structure theory related to infinitary computations and describe a new approach to fine structure based on it, the F-hierarchy, and its refinement, the hyperings. As a sample application, we prove a variant of a theorem of Magidor.SpringerLöwe, BendiktSoskov, IvanINPROCEEDINGSeng10.1007/978-3-642-21875-0_3Lecture Notes in Computer Science6735978-3-642-21875-00302-97431611-33492130Models of Computation in Context : 7th Conference on Computability in Europe, CiE 2011, Sofia, Bulgaria, June 27 - July 2, Proceedings2018-02-23T11:00:00+01:00123456789/39Models of Computation in Context : 7th Conference on Computability in Europe, CiE 2011, Sofia, Bulgaria, June 27 - July 2, Proceedings / Löwe, Bendikt; Soskov, Ivan (Hrsg.). - Berlin : Springer, 2011. - (Lecture Notes in Computer Science ; 6735). - S. 21-30. - ISSN 0302-9743. - eISSN 1611-3349. - ISBN 978-3-642-21875-0Sofia, Bulgaria2011-06-27Berlin7th Conference on Computability in Europe, CiE 20112011-07-022018-02-23T10:00:00ZA dyadic model on a tree123456789/452982023-02-07T06:12:21Z2013dc.title: A dyadic model on a tree
dc.contributor.author: Barbato, David; Bianchi, Luigi Amedeo; Flandoli, Franco; Morandin, Francesco
dc.description.abstract: We study an infinite system of non-linear differential equations coupled in a tree-like structure. This system was previously introduced in the literature and it is the model from which the dyadic shell model of turbulence was derived. It mimics 3d Euler and Navier-Stokes equations in a rough approximation of a wavelet decomposition. We prove existence of finite energy solutions, anomalous dissipation in the inviscid unforced case, existence and uniqueness of stationary solutions (either conservative or not) in the forced case.
2013Barbato, DavidBianchi, Luigi AmedeoFlandoli, FrancoMorandin, Francesco510We study an infinite system of non-linear differential equations coupled in a tree-like structure. This system was previously introduced in the literature and it is the model from which the dyadic shell model of turbulence was derived. It mimics 3d Euler and Navier-Stokes equations in a rough approximation of a wavelet decomposition. We prove existence of finite energy solutions, anomalous dissipation in the inviscid unforced case, existence and uniqueness of stationary solutions (either conservative or not) in the forced case.JOURNAL_ARTICLEeng10.1063/1.47924880022-24881089-7658542Journal of Mathematical Physics2019-03-05T11:18:12+01:00123456789/39Journal of Mathematical Physics ; 54 (2013), 2. - 021507. - ISSN 0022-2488. - eISSN 1089-7658true2019-03-05T10:18:12ZtrueA dynamical systems approach to constrained minimization123456789/7082023-02-09T13:27:49Z1999dc.title: A dynamical systems approach to constrained minimization
dc.contributor.author: Schropp, Johannes
dc.description.abstract: We present an ordinary differential equations approach to solve general smooth minimization problems including a convergence analysis. Generically often the procedure ends up at a point which fulfills sufficient conditions for a local minimum. This procedure will then be rewritten in the concept of differential algebraic equations which opens the route to an efficient implementation. Furthermore, we link this approach with the classical SQP-approach and apply both techniques onto two examples relevant in applications.
1999Schropp, Johannes510We present an ordinary differential equations approach to solve general smooth minimization problems including a convergence analysis. Generically often the procedure ends up at a point which fulfills sufficient conditions for a local minimum. This procedure will then be rewritten in the concept of differential algebraic equations which opens the route to an efficient implementation. Furthermore, we link this approach with the classical SQP-approach and apply both techniques onto two examples relevant in applications.PREPRINTurn:nbn:de:bsz:352-opus-20597engKonstanzer Schriften in Mathematik und Informatik892011-03-22T18:45:35+01:00123456789/392011-03-22T17:45:35ZA Family of 2{alef}1 Logarithmic Functions of Distinct Growth Rates123456789/127542023-02-07T06:18:34Z2010dc.title: A Family of 2{alef}1 Logarithmic Functions of Distinct Growth Rates
dc.contributor.author: Kuhlmann, Salma
dc.description.abstract: We construct a totally ordered set Γ of positive infinite germs (i.e. germs of positive real-valued functions that tend to +∞), with order type being the lexicographic product ℵ1 × ℤ2. We show that Γ admits 2N1 order preserving automorphisms of pairwise distinct growth rates.
2010Kuhlmann, Salma510We construct a totally ordered set Γ of positive infinite germs (i.e. germs of positive real-valued functions that tend to +∞), with order type being the lexicographic product ℵ1 × ℤ2. We show that Γ admits 2N1 order preserving automorphisms of pairwise distinct growth rates.JOURNAL_ARTICLEurn:nbn:de:bsz:352-127548eng10.2478/s11533-010-0070-z1895-10741026102886Central European Journal of Mathematics2011-09-07T09:21:58+02:00123456789/39Central European Journal of Mathematics ; 8 (2010), 6. - S. 1026-1028. - ISSN 1895-10742011-09-07T07:21:58ZA Fenchel-Moreau Theorem for L<sup>0</sup>-Valued Functions123456789/493572023-02-07T06:12:19Z2019dc.title: A Fenchel-Moreau Theorem for L<sup>0</sup>-Valued Functions
dc.contributor.author: Drapeau, Samuel; Jamneshan, Asgar; Kupper, Michael
2019Drapeau, SamuelJamneshan, AsgarKupper, Michael510Heldermann VerlagJOURNAL_ARTICLEeng0944-6532593603262Journal of Convex Analysis2020-04-30T10:51:57+02:00123456789/39Journal of Convex Analysis ; 26 (2019), 2. - S. 593-603. - Heldermann Verlag. - ISSN 0944-6532true2020-04-30T08:51:57ZtrueA Finite Difference Interpretation of the Lattice Boltzmann Method123456789/254302023-02-07T06:19:48Z2001dc.title: A Finite Difference Interpretation of the Lattice Boltzmann Method
dc.contributor.author: Junk, Michael
dc.description.abstract: Compared to conventional techniques in computational fluid dynamics, the lattice Boltzmann method (LBM) seems to be a completely different approach to solve the incompressible Navier–Stokes equation. The aim of this article is to correct this impression by showing the close relation of LBM to two standard methods: relaxation schemes and explicit finite difference discretizations. As a side effect, new starting points for a discretization of the incompressible Navier–Stokes equation are obtained.
2001Junk, Michael510Compared to conventional techniques in computational fluid dynamics, the lattice Boltzmann method (LBM) seems to be a completely different approach to solve the incompressible Navier–Stokes equation. The aim of this article is to correct this impression by showing the close relation of LBM to two standard methods: relaxation schemes and explicit finite difference discretizations. As a side effect, new starting points for a discretization of the incompressible Navier–Stokes equation are obtained.JOURNAL_ARTICLEurn:nbn:de:bsz:352-254309eng10.1002/num.10180749-159X1098-2426383402174Numerical Methods for Partial Differential Equations2013-12-12T21:25:41+01:00123456789/39Numerical Methods for Partial Differential Equations ; 17 (2001), 4. - S. 383-402. - ISSN 0749-159X. - eISSN 1098-24262013-12-12T20:25:41ZA Forward Scheme for Backward SDEs123456789/6642023-02-09T13:25:01Z2005dc.title: A Forward Scheme for Backward SDEs
dc.contributor.author: Bender, Christian; Denk, Robert
dc.description.abstract: We introduce a forward scheme to simulate backward SDEs. Compared to existing schemes, we avoid high order nestings of conditional expectations backwards in time. In this way the error, when approximating the conditional expectation, in dependence of the time partition is significantly reduced. Besides this generic result, we present an implementable algorithm and provide an error analysis for it. Finally, we demonstrate the strength of the new algorithm by solving some financial problems numerically.
2005Bender, ChristianDenk, Robert004We introduce a forward scheme to simulate backward SDEs. Compared to existing schemes, we avoid high order nestings of conditional expectations backwards in time. In this way the error, when approximating the conditional expectation, in dependence of the time partition is significantly reduced. Besides this generic result, we present an implementable algorithm and provide an error analysis for it. Finally, we demonstrate the strength of the new algorithm by solving some financial problems numerically.PREPRINTurn:nbn:de:bsz:352-opus-22297engKonstanzer Schriften in Mathematik und Informatik2092011-03-22T18:45:26+01:00123456789/392011-03-22T17:45:26ZA Fourier approach to the computation of conditional value-at-risk and optimized certainty equivalents123456789/299472023-02-07T06:31:35Z2014dc.title: A Fourier approach to the computation of conditional value-at-risk and optimized certainty equivalents
dc.contributor.author: Drapeau, Samuel; Kupper, Michael; Papapantoleon, Antonis
2014Drapeau, SamuelKupper, MichaelPapapantoleon, Antonis510JOURNAL_ARTICLEeng10.21314/JOR.2014.281166The Journal of Risk2015-02-23T10:42:20+01:00123456789/39The Journal of Risk ; 16 (2014), 6. - 3292015-02-23T09:42:20ZA Generalized Itô-Ventzell Formula to Derive Forward Utility Models in a Jump Market123456789/237182023-02-07T06:16:45Z2013dc.title: A Generalized Itô-Ventzell Formula to Derive Forward Utility Models in a Jump Market
dc.contributor.author: Kohlmann, Michael; Dewen, Xiong; Siyuan, Li
2013Kohlmann, MichaelDewen, XiongSiyuan, Li51090A09; 60H30; 60G44.JOURNAL_ARTICLEurn:nbn:de:bsz:352-237180eng10.1080/07362994.2013.7990220736-29941532-9356632662314Stochastic Analysis and Applications2013-06-24T19:13:40+02:00123456789/39Stochastic Analysis and Applications ; 31 (2013), 4. - S. 632-662. - ISSN 0736-2994. - eISSN 1532-93562013-06-24T17:13:40ZA geometric inequality for convex free boundary hypersurfaces in the unit ball123456789/395802023-02-07T06:14:44Z2017dc.title: A geometric inequality for convex free boundary hypersurfaces in the unit ball
dc.contributor.author: Lambert, Ben; Scheuer, Julian
2017Lambert, BenScheuer, Julian510JOURNAL_ARTICLEeng10.1090/proc/135160002-99391088-6826400940201459Proceedings of the American Mathematical Society2017-07-13T14:39:19+02:00123456789/39123456789/52Proceedings of the American Mathematical Society ; 145 (2017), 9. - S. 4009-4020. - ISSN 0002-9939. - eISSN 1088-68262017-07-13T12:39:19ZA Globalized Newton Method for the Accurate Solution of a Dipole Quantum Control Problem123456789/8122023-02-07T06:22:41Z2009dc.title: A Globalized Newton Method for the Accurate Solution of a Dipole Quantum Control Problem
dc.contributor.author: Winckel, Greg von; Borzì, Alfio; Volkwein, Stefan
2009Winckel, Greg vonBorzì, AlfioVolkwein, Stefan510JOURNAL_ARTICLEurn:nbn:de:bsz:352-opus-112494eng10.1137/09074961X41764203316SIAM Journal on Scientific Computing2011-03-22T18:48:58+01:00123456789/39SIAM Journal on Scientific Computing ; 31 (2009), 6. - S. 4176-42032011-03-22T17:48:58ZA goodness-of-fit test for time series with long-range dependence123456789/188142023-02-07T06:22:28Z1992dc.title: A goodness-of-fit test for time series with long-range dependence
dc.contributor.author: Beran, Jan
dc.description.abstract: We propose a test statistic for goodness of fit in time series with slowly decaying serial correlations. The asymptotic distribution of the test statistic, originally proposed by Milhoj for time series with smooth spectra, turns out to be the same, under the null hypothesis, even if the spectrum has a pole at 0. In particular, the test is suitable to detect lack of independence in the observations, or estimated residuals, if the first few correlations are small but the decay of the correlations is slow.
1992Beran, Jan510We propose a test statistic for goodness of fit in time series with slowly decaying serial correlations. The asymptotic distribution of the test statistic, originally proposed by Milhoj for time series with smooth spectra, turns out to be the same, under the null hypothesis, even if the spectrum has a pole at 0. In particular, the test is suitable to detect lack of independence in the observations, or estimated residuals, if the first few correlations are small but the decay of the correlations is slow.JOURNAL_ARTICLEurn:nbn:de:bsz:352-188149eng10.2307/2345855749760543Journal of the Royal Statistical Society / B2012-03-20T15:51:00+01:00123456789/39Journal of the Royal Statistical Society / B ; 54 (1992), 3. - S. 749-7602012-03-20T14:51:00ZA HJB-POD Approach to the Control of the Level Set EquationBenner, Peter123456789/426762023-02-07T06:29:00Z2017-09-06dc.title: A HJB-POD Approach to the Control of the Level Set Equation
dc.contributor.author: Alla, Alessandro; Fabrini, Giulia; Falcone, Maurizio
dc.description.abstract: We consider an optimal control problem where the dynamics is given by the propagation of a one-dimensional graph controlled by its normal speed. A target corresponding to the final configuration of the front is given and we want to minimize the cost to reach the target. We want to solve this optimal control problem via the dynamic programming approach but it is well known that these methods suffer from the “curse of dimensionality” so that we can not apply the method to the semi-discrete version of the dynamical system. However, this is made possible by a reduced-order model for the level set equation which is based on Proper Orthogonal Decomposition. This results in a new low-dimensional dynamical system which is sufficient to track the dynamics. By the numerical solution of the Hamilton-Jacobi-Bellman equation related to the POD approximation we can compute the feedback law and the corresponding optimal trajectory for the nonlinear front propagation problem. We discuss some numerical issues of this approach and present a couple of numerical examples.
2017-09-06Alla, AlessandroFabrini, GiuliaFalcone, Maurizio510We consider an optimal control problem where the dynamics is given by the propagation of a one-dimensional graph controlled by its normal speed. A target corresponding to the final configuration of the front is given and we want to minimize the cost to reach the target. We want to solve this optimal control problem via the dynamic programming approach but it is well known that these methods suffer from the “curse of dimensionality” so that we can not apply the method to the semi-discrete version of the dynamical system. However, this is made possible by a reduced-order model for the level set equation which is based on Proper Orthogonal Decomposition. This results in a new low-dimensional dynamical system which is sufficient to track the dynamics. By the numerical solution of the Hamilton-Jacobi-Bellman equation related to the POD approximation we can compute the feedback law and the corresponding optimal trajectory for the nonlinear front propagation problem. We discuss some numerical issues of this approach and present a couple of numerical examples.SpringerBenner, PeterINCOLLECTIONeng10.1007/978-3-319-58786-8_20Modeling, simulation & applications17978-3-319-58785-1317331Model Reduction of Parametrized Systems2018-06-25T11:09:33+02:00123456789/39Model Reduction of Parametrized Systems / Benner, Peter et al. (Hrsg.). - Cham : Springer, 2017. - (Modeling, simulation & applications ; 17). - S. 317-331. - ISBN 978-3-319-58785-1Cham2018-06-25T09:09:33ZA Hybrid Finite-Dimensional RHC for Stabilization of Time-Varying Parabolic Equations123456789/563062023-02-07T06:29:27Z2019dc.title: A Hybrid Finite-Dimensional RHC for Stabilization of Time-Varying Parabolic Equations
dc.contributor.author: Azmi, Behzad; Kunisch, Karl
2019Azmi, BehzadKunisch, Karl510SIAMJOURNAL_ARTICLEeng10.1137/19M12397870363-01291095-713834963526575SIAM Journal on Control and Optimization2022-01-21T14:02:44+01:00123456789/39SIAM Journal on Control and Optimization ; 57 (2019), 5. - S. 3496-3526. - SIAM. - ISSN 0363-0129. - eISSN 1095-7138true2022-01-21T13:02:44ZtrueA hybrid simulation method for radiative transfer equations123456789/254202023-02-07T06:19:39Z2003dc.title: A hybrid simulation method for radiative transfer equations
dc.contributor.author: Junk, Michael; Unterreiter, Andreas; Zingsheim, Frank
dc.description.abstract: We consider heat transfer processes where radiation in a large number of frequency bands plays a dominant role. In the simulation of such processes, the radiative transfer equation has to be solved repeatedly. To obtain an efficient and accurate solution method, we propose a new hybrid algorithm which combines fast solvers for the radiative transfer equation in the low and high absorption regime, respectively. A key role is played by an exact, residual based error formula. The algorithm is applied to a cooling problem of high quality optical glass.
2003Junk, MichaelUnterreiter, AndreasZingsheim, Frank510We consider heat transfer processes where radiation in a large number of frequency bands plays a dominant role. In the simulation of such processes, the radiative transfer equation has to be solved repeatedly. To obtain an efficient and accurate solution method, we propose a new hybrid algorithm which combines fast solvers for the radiative transfer equation in the low and high absorption regime, respectively. A key role is played by an exact, residual based error formula. The algorithm is applied to a cooling problem of high quality optical glass.JOURNAL_ARTICLEurn:nbn:de:bsz:352-254200eng10.1017/S095679250200493X0956-79251469-4425165179142European Journal of Applied Mathematics2013-12-12T14:46:32+01:00123456789/39European Journal of Applied Mathematics ; 14 (2003), 2. - S. 165-179. - ISSN 0956-7925. - eISSN 1469-44252013-12-12T13:46:32ZA kinetic approach to hyperbolic systems and the role of higher order entropiesFreistühler, Heinrichpop55883Warnecke, Gerald123456789/254662023-02-07T06:25:13Z2001dc.title: A kinetic approach to hyperbolic systems and the role of higher order entropies
dc.contributor.author: Junk, Michael
dc.description.abstract: The reformulation of conservation laws in terms of kinetic equations, which parallels the relation between Boltzmann and Euler equation, has been successfully used in the form of kinetic schemes. The central problem in the kinetic approach is the construction of suitable equilibrium distributions which generalize the Maxwellian in the Boltzmann—Euler case. Here, we present a solution to this problem which allows the construction of equilibrium distributions for general systems of hyperbolic conservation laws. The approach leads to the notion of higher order entropies and generalizes several approaches discussed by other authors.
2001Junk, Michael510The reformulation of conservation laws in terms of kinetic equations, which parallels the relation between Boltzmann and Euler equation, has been successfully used in the form of kinetic schemes. The central problem in the kinetic approach is the construction of suitable equilibrium distributions which generalize the Maxwellian in the Boltzmann—Euler case. Here, we present a solution to this problem which allows the construction of equilibrium distributions for general systems of hyperbolic conservation laws. The approach leads to the notion of higher order entropies and generalizes several approaches discussed by other authors.Birkhäuser BaselFreistühler, HeinrichWarnecke, GeraldINPROCEEDINGSurn:nbn:de:bsz:352-254669eng10.1007/978-3-0348-8372-6_12978-3-0348-9538-5583592Hyperbolic Problems: Theory, Numerics, Applications2013-12-17T20:48:37+01:00123456789/39Hyperbolic Problems: Theory, Numerics, Applications / Freistühler, Heinrich; Warnecke, Gerald (Hrsg.). - Basel : Birkhäuser Basel, 2001. - S. 583-592. - ISBN 978-3-0348-9538-5Basel2013-12-17T19:48:37ZA kinetic equation for economic value estimation with irrationality and herding123456789/555372023-02-07T06:13:09Z2017dc.title: A kinetic equation for economic value estimation with irrationality and herding
dc.contributor.author: Düring, Bertram; Jüngel, Ansgar; Trussardi, Lara
dc.description.abstract: A kinetic inhomogeneous Boltzmann-type equation is proposed to model the dynamics of the number of agents in a large market depending on the estimated value of an asset and the rationality of the agents. The interaction rules take into account the interplay of the agents with sources of public information, herding phenomena, and irrationality of the individuals. In the formal grazing collision limit, a nonlinear nonlocal Fokker-Planck equation with anisotropic (or incomplete) diffusion is derived. The existence of global-in-time weak solutions to the Fokker-Planck initial-boundary-value problem is proved. Numerical experiments for the Boltzmann equation highlight the importance of the reliability of public information in the formation of bubbles and crashes. The use of Bollinger bands in the simulations shows how herding may lead to strong trends with low volatility of the asset prices, but eventually also to abrupt corrections.
2017Düring, BertramJüngel, AnsgarTrussardi, Lara510A kinetic inhomogeneous Boltzmann-type equation is proposed to model the dynamics of the number of agents in a large market depending on the estimated value of an asset and the rationality of the agents. The interaction rules take into account the interplay of the agents with sources of public information, herding phenomena, and irrationality of the individuals. In the formal grazing collision limit, a nonlinear nonlocal Fokker-Planck equation with anisotropic (or incomplete) diffusion is derived. The existence of global-in-time weak solutions to the Fokker-Planck initial-boundary-value problem is proved. Numerical experiments for the Boltzmann equation highlight the importance of the reliability of public information in the formation of bubbles and crashes. The use of Bollinger bands in the simulations shows how herding may lead to strong trends with low volatility of the asset prices, but eventually also to abrupt corrections.American Institute of Mathematical Sciences (AIMS)JOURNAL_ARTICLEeng10.3934/krm.20170101937-50931937-5077239261101Kinetic & Related Models2021-11-12T15:18:30+01:00123456789/39Kinetic & Related Models ; 10 (2017), 1. - S. 239-261. - American Institute of Mathematical Sciences (AIMS). - ISSN 1937-5093. - eISSN 1937-5077unknown2021-11-12T14:18:30ZtrueA lattice Boltzmann method for immiscible multiphase flow simulations using the level set method123456789/8072023-02-07T06:19:35Z2009dc.title: A lattice Boltzmann method for immiscible multiphase flow simulations using the level set method
dc.contributor.author: Thömmes, Guido; Becker, Jürgen; Junk, Michael; Vaikuntam, Ashok K.; Kehrwald, Dirk; Klar, Axel; Steiner, Konrad; Wiegmann, Andreas
dc.description.abstract: We consider the lattice Boltzmann method for immiscible multiphase flow simulations. Classical lattice Boltzmann methods for this problem, e.g. the colour gradient method or the free energy approach, can only be applied when density and viscosity ratios are small. Moreover, they use additional fields defined on the whole domain to describe the different phases and model phase separation by special interactions at each node. In contrast, our approach simulates the flow using a single field and separates the fluid phases by a free moving interface. The scheme is based on the lattice Boltzmann method and uses the level set method to compute the evolution of the interface. To couple the fluid phases, we develop new boundary conditions which realise the macroscopic jump conditions at the interface and incorporate surface tension in the lattice Boltzmann framework. Various simulations are presented to validate the numerical scheme, e.g. two-phase channel flows, the Young Laplace law for a bubble and viscous fingering in a Hele-Shaw cell. The results show that the method is feasible over a wide range of density and viscosity differences.
2009Thömmes, GuidoBecker, JürgenJunk, MichaelVaikuntam, Ashok K.Kehrwald, DirkKlar, AxelSteiner, KonradWiegmann, Andreas510We consider the lattice Boltzmann method for immiscible multiphase flow simulations. Classical lattice Boltzmann methods for this problem, e.g. the colour gradient method or the free energy approach, can only be applied when density and viscosity ratios are small. Moreover, they use additional fields defined on the whole domain to describe the different phases and model phase separation by special interactions at each node. In contrast, our approach simulates the flow using a single field and separates the fluid phases by a free moving interface. The scheme is based on the lattice Boltzmann method and uses the level set method to compute the evolution of the interface. To couple the fluid phases, we develop new boundary conditions which realise the macroscopic jump conditions at the interface and incorporate surface tension in the lattice Boltzmann framework. Various simulations are presented to validate the numerical scheme, e.g. two-phase channel flows, the Young Laplace law for a bubble and viscous fingering in a Hele-Shaw cell. The results show that the method is feasible over a wide range of density and viscosity differences.JOURNAL_ARTICLEurn:nbn:de:bsz:352-opus-106476eng10.1016/j.jcp.2008.10.032113911562284Journal of Computational Physics2011-03-22T18:48:57+01:00123456789/39Journal of Computational Physics ; 228 (2009), 4. - S. 1139-11562011-03-22T17:48:57ZA limiter based on kinetic theory123456789/254252023-02-07T06:30:43Z2007dc.title: A limiter based on kinetic theory
dc.contributor.author: Banda, Mapundi K.; Junk, Michael; Klar, Axel
dc.description.abstract: In the present paper the low Mach number limit of kinetic equations is used to develop a discretization for the incompressible Euler equation. The kinetic equation is discretized with a first and second order discretization in space. The discretized equation is then considered in the limit of low Mach and Knudsen number which gives rise to an interesting limiter for the convective part in the incompressible Euler equation. Numerical experiments are shown comparing different approaches.
2007Banda, Mapundi K.Junk, MichaelKlar, Axel510In the present paper the low Mach number limit of kinetic equations is used to develop a discretization for the incompressible Euler equation. The kinetic equation is discretized with a first and second order discretization in space. The discretized equation is then considered in the limit of low Mach and Knudsen number which gives rise to an interesting limiter for the convective part in the incompressible Euler equation. Numerical experiments are shown comparing different approaches.JOURNAL_ARTICLEurn:nbn:de:bsz:352-254250eng10.1081/TT-1200155110041-14501532-2424491512314-6Transport Theory and Statistical Physics2013-12-12T21:23:55+01:00123456789/39Transport Theory and Statistical Physics ; 31 (2007), 4-6. - S. 491-512. - ISSN 0041-1450. - eISSN 1532-24242013-12-12T20:23:55ZA local-global principle for linear dependence of noncommutative polynomials123456789/152802023-02-09T13:30:29Z2011dc.title: A local-global principle for linear dependence of noncommutative polynomials
dc.contributor.author: Brešar, Matej; Klep, Igor
dc.description.abstract: Abstract. A set of polynomials in noncommuting variables is called locally linearly dependent if their evaluations at tuples of matrices are always linearly dependent. By a theorem of Camino, Helton, Skelton and Ye, a nite locally<br />linearly dependent set of polynomials is linearly dependent. In this short note an alternative proof based on the theory of polynomial identities is given. The method of the proof yields generalizations to rectional local linear dependence and evaluations in general algebras over elds of arbitrary characteristic. A main feature of the proof is that it makes it possible to deduce bounds on the size of the matrices where the (directional) local linear dependence needs to be tested in order to establish linear dependence.
2011Brešar, MatejKlep, Igor510Abstract. A set of polynomials in noncommuting variables is called locally linearly dependent if their evaluations at tuples of matrices are always linearly dependent. By a theorem of Camino, Helton, Skelton and Ye, a nite locally<br />linearly dependent set of polynomials is linearly dependent. In this short note an alternative proof based on the theory of polynomial identities is given. The method of the proof yields generalizations to rectional local linear dependence and evaluations in general algebras over elds of arbitrary characteristic. A main feature of the proof is that it makes it possible to deduce bounds on the size of the matrices where the (directional) local linear dependence needs to be tested in order to establish linear dependence.WORKINGPAPERurn:nbn:de:bsz:352-152802engKonstanzer Schriften in Mathematik2832011-09-01T13:02:53+02:00123456789/392011-09-01T11:02:53ZA Locally Modified Parametric Finite Element Method for Interface Problems123456789/558192023-02-07T06:28:41Z2014dc.title: A Locally Modified Parametric Finite Element Method for Interface Problems
dc.contributor.author: Frei, Stefan; Richter, Thomas
dc.description.abstract: We present a modified finite element method that is able to approximate interface problems with high accuracy. We consider interface problems where the solution is continuous; its derivatives, however, may be discontinuous across interface curves within the domain. The proposed discretization is based on a local modification of the finite element basis functions using a fixed quadrilateral mesh. Instead of moving mesh nodes, we resolve the interface locally by an adapted parametric approach. All modifications are applied locally and in an implicit fashion. The scheme is easy to implement and is well suited for time-dependent moving interface problems. We show optimal order of convergence for elliptic problems, and further, we give a bound on the condition number of the system matrix. Both estimates do not depend on the interface location relative to the mesh.
2014Frei, StefanRichter, Thomas510We present a modified finite element method that is able to approximate interface problems with high accuracy. We consider interface problems where the solution is continuous; its derivatives, however, may be discontinuous across interface curves within the domain. The proposed discretization is based on a local modification of the finite element basis functions using a fixed quadrilateral mesh. Instead of moving mesh nodes, we resolve the interface locally by an adapted parametric approach. All modifications are applied locally and in an implicit fashion. The scheme is easy to implement and is well suited for time-dependent moving interface problems. We show optimal order of convergence for elliptic problems, and further, we give a bound on the condition number of the system matrix. Both estimates do not depend on the interface location relative to the mesh.Society for Industrial and Applied Mathematics (SIAM)JOURNAL_ARTICLEeng10.1137/1309194890036-14291095-717023152334525SIAM Journal on Numerical Analysis2021-12-09T11:35:14+01:00123456789/39SIAM Journal on Numerical Analysis ; 52 (2014), 5. - S. 2315-2334. - Society for Industrial and Applied Mathematics (SIAM). - ISSN 0036-1429. - eISSN 1095-7170true2021-12-09T10:35:14ZA locally modified second-order finite element method for interface problems123456789/556282023-02-07T06:30:23Z2020-07-27T23:08:48Zdc.title: A locally modified second-order finite element method for interface problems
dc.contributor.author: Frei, Stefan; Judakova, Gozel; Richter, Thomas
dc.description.abstract: The locally modified finite element method, which is introduced in [Frei, Richter: SINUM 52(2014), p. 2315-2334] is a simple fitted finite element method that is able to resolve weak discontinuities in interface problems. The method is based on a fixed structured coarse mesh, which is then refined into sub-elements to resolve an interior interface. In this work, we extend the locally modified finite element method to second order using an isoparametric approach in the interface elements. Thereby we need to take care that the resulting curved edges do not lead to degenerate sub-elements. We prove optimal a priori error estimates in the L<sup>2</sup>-norm and in a modified energy norm, as well as a reduced convergence order of O(h<sup>3</sup>/<sup>2</sup>) in the standard H<sup>1</sup>-norm. Finally, we present numerical examples to substantiate the theoretical findings.
2020-07-27T23:08:48ZFrei, StefanJudakova, GozelRichter, Thomas510The locally modified finite element method, which is introduced in [Frei, Richter: SINUM 52(2014), p. 2315-2334] is a simple fitted finite element method that is able to resolve weak discontinuities in interface problems. The method is based on a fixed structured coarse mesh, which is then refined into sub-elements to resolve an interior interface. In this work, we extend the locally modified finite element method to second order using an isoparametric approach in the interface elements. Thereby we need to take care that the resulting curved edges do not lead to degenerate sub-elements. We prove optimal a priori error estimates in the L<sup>2</sup>-norm and in a modified energy norm, as well as a reduced convergence order of O(h<sup>3</sup>/<sup>2</sup>) in the standard H<sup>1</sup>-norm. Finally, we present numerical examples to substantiate the theoretical findings.PREPRINTeng2021-11-22T16:29:27+01:00123456789/392021-11-22T15:29:27ZA LONE code for the sparse control of quantum systems123456789/412082023-02-07T06:15:31Z2016-03dc.title: A LONE code for the sparse control of quantum systems
dc.contributor.author: Ciaramella, Gabriele; Borzì, Alfio
dc.description.abstract: In many applications with quantum spin systems, control functions with a sparse and pulse-shaped structure are often required. These controls can be obtained by solving quantum optimal control problems with L<sup>1</sup>-penalized cost functionals. In this paper, the MATLAB package LONE is presented aimed to solving L<sup>1</sup>-penalized optimal control problems governed by unitary-operator quantum spin models. This package implements a new strategy that includes a globalized semi-smooth Krylov–Newton scheme and a continuation procedure. Results of numerical experiments demonstrate the ability of the LONE code in computing accurate sparse optimal control solutions.
2016-03Ciaramella, GabrieleBorzì, Alfio510In many applications with quantum spin systems, control functions with a sparse and pulse-shaped structure are often required. These controls can be obtained by solving quantum optimal control problems with L<sup>1</sup>-penalized cost functionals. In this paper, the MATLAB package LONE is presented aimed to solving L<sup>1</sup>-penalized optimal control problems governed by unitary-operator quantum spin models. This package implements a new strategy that includes a globalized semi-smooth Krylov–Newton scheme and a continuation procedure. Results of numerical experiments demonstrate the ability of the LONE code in computing accurate sparse optimal control solutions.JOURNAL_ARTICLEeng10.1016/j.cpc.2015.10.0280010-46551879-2944312323200Computer Physics Communications2018-02-02T11:38:54+01:00123456789/39Computer Physics Communications ; 200 (2016). - S. 312-323. - ISSN 0010-4655. - eISSN 1879-29442018-02-02T10:38:54ZA mechanically consistent model for fluid-structure interactions with contact including seepage123456789/55626.22023-02-07T06:13:04Z2021dc.title: A mechanically consistent model for fluid-structure interactions with contact including seepage
dc.contributor.author: Burman, Erik; Fernández, Miguel A.; Frei, Stefan; Gerosa, Fannie M.
dc.description.abstract: s.We present a new approach for the mechanically consistent modelling and simulation of fluid–structure interactions (FSI) with contact. The fundamental idea consists of combining a relaxation of the contact conditions with the modelling of seepage through a porous layer of co-dimension one during contact. For the latter, a Darcy model is considered in a thin porous layer attached to a solid boundary in the limit of infinitesimal thickness. The resulting computational model is both mechanically consistent and simple to implement. The FSI coupling and the contact conditions are imposed weakly by means of a unified Nitsche approach. We analyse the approach in detailed numerical studies with both thick- and thin-walled solids, within a fully Eulerian and an immersed approach and using fitted and unfitted finite element discretisations.
2021Burman, ErikFernández, Miguel A.Frei, StefanGerosa, Fannie M.510s.We present a new approach for the mechanically consistent modelling and simulation of fluid–structure interactions (FSI) with contact. The fundamental idea consists of combining a relaxation of the contact conditions with the modelling of seepage through a porous layer of co-dimension one during contact. For the latter, a Darcy model is considered in a thin porous layer attached to a solid boundary in the limit of infinitesimal thickness. The resulting computational model is both mechanically consistent and simple to implement. The FSI coupling and the contact conditions are imposed weakly by means of a unified Nitsche approach. We analyse the approach in detailed numerical studies with both thick- and thin-walled solids, within a fully Eulerian and an immersed approach and using fitted and unfitted finite element discretisations.ElsevierJOURNAL_ARTICLEeng10.1016/j.cma.2022.1146370045-78251879-2138392Computer Methods in Applied Mechanics and Engineering2022-05-12T12:21:16+02:00123456789/39Computer Methods in Applied Mechanics and Engineering ; 392 (2021). - 114637. - Elsevier. - ISSN 0045-7825. - eISSN 1879-2138true2022-05-12T10:21:16ZtrueA meeting point of entropy and bifurcations in cross-diffusion herding123456789/555782023-02-07T06:14:18Z2015-04-28T16:19:24Zdc.title: A meeting point of entropy and bifurcations in cross-diffusion herding
dc.contributor.author: Jüngel, Ansgar; Kuehn, Christian; Trussardi, Lara
dc.description.abstract: A cross-diffusion system modeling the information herding of individuals is analyzed in a bounded domain with no-flux boundary conditions. The variables are the species' density and an influence function which modifies the information state of the individuals. The cross-diffusion term may stabilize or destabilize the system. Furthermore, it allows for a formal gradient-flow or entropy structure. Exploiting this structure, the global-in-time existence of weak solutions and the exponential decay to the constant steady state is proved in certain parameter regimes. This approach does not extend to all parameters. We investigate local bifurcations from homogeneous steady states analytically to determine whether this defines the validity boundary. This analysis shows that generically there is a gap in the parameter regime between the entropy approach validity and the first local bifurcation. Next, we use numerical continuation methods to track the bifurcating non-homogeneous steady states globally and to determine non-trivial stationary solutions related to herding behaviour. In summary, we find that the main boundaries in the parameter regime are given by the first local bifurcation point, the degeneracy of the diffusion matrix and a certain entropy decay validity condition. We study several parameter limits analytically as well as numerically, with a focus on the role of changing a linear damping parameter as well as a parameter controlling the cross-diffusion. We suggest that our paradigm of comparing bifurcation-generated obstructions to the parameter validity of global-functional methods could also be of relevance for many other models beyond the one studied here.
2015-04-28T16:19:24ZJüngel, AnsgarKuehn, ChristianTrussardi, Lara510A cross-diffusion system modeling the information herding of individuals is analyzed in a bounded domain with no-flux boundary conditions. The variables are the species' density and an influence function which modifies the information state of the individuals. The cross-diffusion term may stabilize or destabilize the system. Furthermore, it allows for a formal gradient-flow or entropy structure. Exploiting this structure, the global-in-time existence of weak solutions and the exponential decay to the constant steady state is proved in certain parameter regimes. This approach does not extend to all parameters. We investigate local bifurcations from homogeneous steady states analytically to determine whether this defines the validity boundary. This analysis shows that generically there is a gap in the parameter regime between the entropy approach validity and the first local bifurcation. Next, we use numerical continuation methods to track the bifurcating non-homogeneous steady states globally and to determine non-trivial stationary solutions related to herding behaviour. In summary, we find that the main boundaries in the parameter regime are given by the first local bifurcation point, the degeneracy of the diffusion matrix and a certain entropy decay validity condition. We study several parameter limits analytically as well as numerically, with a focus on the role of changing a linear damping parameter as well as a parameter controlling the cross-diffusion. We suggest that our paradigm of comparing bifurcation-generated obstructions to the parameter validity of global-functional methods could also be of relevance for many other models beyond the one studied here.Cambridge University PressJOURNAL_ARTICLEeng10.1017/S09567925160003460956-79251469-4425317356282European Journal of Applied Mathematics2021-11-17T11:09:49+01:00123456789/39European Journal of Applied Mathematics ; 28 (2015), 2. - S. 317-356. - Cambridge University Press. - ISSN 0956-7925. - eISSN 1469-4425unknown2021-11-17T10:09:49ZtrueA Mesh-Free, Physics-Constrained Approach to solve Partial Differential Equations with a Deep Neural Network123456789/533052023-02-09T11:07:57Z2020dc.title: A Mesh-Free, Physics-Constrained Approach to solve Partial Differential Equations with a Deep Neural Network
dc.contributor.author: Kress, Kevin
dc.description.abstract: In this work, we utilized different approaches for solving partial differential equations with a deep neural network. The network respects the given physical laws of the equations by incorporating these constraints in the training process or in the network architecture. Specifically, a deep, feed-forward, and fully-connected neural network is used to approximate the partial differential equation, where the initial and boundary conditions are either hard or soft assigned. The resulting physics-informed surrogate model learns to satisfy the differential operator and the initial and boundary conditions and can be differentiated with respect to all input variables. The accuracy of the methods is demonstrated on multiple equations of different types and compared to either the exact or a finite element solution.
2020Kress, Kevin004Deep LearningPartial Differential EquationIn this work, we utilized different approaches for solving partial differential equations with a deep neural network. The network respects the given physical laws of the equations by incorporating these constraints in the training process or in the network architecture. Specifically, a deep, feed-forward, and fully-connected neural network is used to approximate the partial differential equation, where the initial and boundary conditions are either hard or soft assigned. The resulting physics-informed surrogate model learns to satisfy the differential operator and the initial and boundary conditions and can be differentiated with respect to all input variables. The accuracy of the methods is demonstrated on multiple equations of different types and compared to either the exact or a finite element solution.BSC_THESISurn:nbn:de:bsz:352-2-1pqapp54g26sl0eng2021-03-30T10:27:27+02:00123456789/36123456789/392021-03-30T08:27:27ZA method for solving exact-controllability problems governed by closed quantum spin systems123456789/412062023-02-07T06:21:14Z2015-04-03dc.title: A method for solving exact-controllability problems governed by closed quantum spin systems
dc.contributor.author: Ciaramella, Gabriele; Salomon, Julien; Borzì, Alfio
dc.description.abstract: The Liouville–von Neumann master equation models closed quantum spin systems that arise in nuclear magnetic resonance applications. In this paper, an efficient and robust computational framework to solve exact-controllability problems governed by the Liouville–von Neumann master equation is presented. The proposed control framework is based on a new optimisation formulation of exact-controllability quantum spin problems that allows the application of efficient computational techniques. This formulation results in an optimality system with four differential equations and an optimality condition. The differential equations are approximated with an appropriate modified Crank–Nicholson scheme and the resulting discretised optimality system is solved with a matrix-free Krylov–Newton scheme combined with a cascadic nonlinear conjugate gradient initialisation. Results of numerical experiments demonstrate the ability of the proposed framework to solve quantum spin exact-controllability control problems.
2015-04-03Ciaramella, GabrieleSalomon, JulienBorzì, Alfio510The Liouville–von Neumann master equation models closed quantum spin systems that arise in nuclear magnetic resonance applications. In this paper, an efficient and robust computational framework to solve exact-controllability problems governed by the Liouville–von Neumann master equation is presented. The proposed control framework is based on a new optimisation formulation of exact-controllability quantum spin problems that allows the application of efficient computational techniques. This formulation results in an optimality system with four differential equations and an optimality condition. The differential equations are approximated with an appropriate modified Crank–Nicholson scheme and the resulting discretised optimality system is solved with a matrix-free Krylov–Newton scheme combined with a cascadic nonlinear conjugate gradient initialisation. Results of numerical experiments demonstrate the ability of the proposed framework to solve quantum spin exact-controllability control problems.JOURNAL_ARTICLEeng10.1080/00207179.2014.9714350020-71791366-5820682702884International Journal of Control2018-02-02T11:33:10+01:00123456789/39International Journal of Control ; 88 (2015), 4. - S. 682-702. - ISSN 0020-7179. - eISSN 1366-58202018-02-02T10:33:10ZA method for the verified solution of finite element models with uncertain node locationsFaber, M. H.123456789/186052023-02-07T06:24:20Z2011dc.title: A method for the verified solution of finite element models with uncertain node locations
dc.contributor.author: Smith, Andrew; Garloff, Jürgen; Werkle, Horst
2011Smith, AndrewGarloff, JürgenWerkle, Horst510CRC PressFaber, M. H.INPROCEEDINGSurn:nbn:de:bsz:352-186052eng978-0-415-66986-3141143Applications of statistics and probability in civil engineering : proceedings of the 11 th International Conference on Applications of Statistics and Probability in Civil Engineering2012-02-21T21:32:04+01:00123456789/39Applications of statistics and probability in civil engineering : proceedings of the 11 th International Conference on Applications of Statistics and Probability in Civil Engineering / Faber, M. H. et al. (Hrsg.). - Boca Raton [u.a.] : CRC Press, 2011. - S. 141-143. - ISBN 978-0-415-66986-3Boca Raton [u.a.]2012-02-21T20:32:04ZA method of a-posteriori error estimation with application to proper orthogonal decomposition123456789/184662023-02-09T13:25:05Z2012dc.title: A method of a-posteriori error estimation with application to proper orthogonal decomposition
dc.contributor.author: Kammann, Eileen; Tröltzsch, Fredi; Volkwein, Stefan
dc.description.abstract: We consider the following problem of error estimation for the optimal control of nonlinear parabolic partial differential equations: Let an arbitrary admissible control function be given. How far is it from the next locally optimal control? Under natural assumptions including a second-order sufficient optimality condition for the (unknown) locally optimal control, we estimate the distance between the two controls. To do this, we need some information on the lowest eigenvalue of the reduced Hessian. We apply this technique to a model reduced optimal control problem obtained by proper orthogonal decomposition (POD). The distance between a local solution of the reduced problem to a local solution of the original problem is estimated.
2012Kammann, EileenTröltzsch, FrediVolkwein, Stefan510We consider the following problem of error estimation for the optimal control of nonlinear parabolic partial differential equations: Let an arbitrary admissible control function be given. How far is it from the next locally optimal control? Under natural assumptions including a second-order sufficient optimality condition for the (unknown) locally optimal control, we estimate the distance between the two controls. To do this, we need some information on the lowest eigenvalue of the reduced Hessian. We apply this technique to a model reduced optimal control problem obtained by proper orthogonal decomposition (POD). The distance between a local solution of the reduced problem to a local solution of the original problem is estimated.PREPRINTurn:nbn:de:bsz:352-184660engKonstanzer Schriften in Mathematik2992012-03-05T08:58:33+01:00123456789/392012-03-05T07:58:33ZA minimizing-movements approach to GENERIC systems123456789/555292023-02-09T13:25:02Z2022dc.title: A minimizing-movements approach to GENERIC systems
dc.contributor.author: Jüngel, Ansgar; Stefanelli, Ulisse; Trussardi, Lara
dc.description.abstract: We present a new time discretization scheme adapted to the structure of GENERIC systems. The scheme is based on incremental minimization and is therefore variational in nature. The GENERIC structure of the scheme provides stability and conditional convergence. We show that the scheme can be rigorously implemented in the classical case of the damped harmonic oscillator. Numerical evidence is collected, illustrating the performance of the method and, in particular, the conservation of the energy at the discrete level.
2022Jüngel, AnsgarStefanelli, UlisseTrussardi, Lara510We present a new time discretization scheme adapted to the structure of GENERIC systems. The scheme is based on incremental minimization and is therefore variational in nature. The GENERIC structure of the scheme provides stability and conditional convergence. We show that the scheme can be rigorously implemented in the classical case of the damped harmonic oscillator. Numerical evidence is collected, illustrating the performance of the method and, in particular, the conservation of the energy at the discrete level.AIMS PressJOURNAL_ARTICLEurn:nbn:de:bsz:352-2-4xwta4dbwp3g9eng10.3934/mine.20220052640-350111841Mathematics in Engineering2021-11-12T13:40:55+01:00123456789/39Mathematics in Engineering ; 4 (2022), 1. - S. 1-18. - AIMS Press. - eISSN 2640-3501unknown2021-11-12T12:40:55ZtrueA monotone convergence theorem for strong Feller semigroups123456789/599522023-02-07T06:12:34Z2022dc.title: A monotone convergence theorem for strong Feller semigroups
dc.contributor.author: Budde, Christian; Dobrick, Alexander; Glück, Jochen; Kunze, Markus
dc.description.abstract: For an increasing sequence (Tn) of one-parameter semigroups of sub Markovian kernel operators over a Polish space, we study the limit semigroup and prove sufficient conditions for it to be strongly Feller. In particular, we show that the strong Feller property carries over from the approximating semigroups to the limit semigroup if the resolvent of the latter maps 1 to a continuous function. This is instrumental in the study of elliptic operators on Rd with unbounded coefficients: our abstract result enables us to assign a semigroup to such an operator and to show that the semigroup is strongly Feller under very mild regularity assumptions on the coefficients. We also provide counterexamples to demonstrate that the assumptions in our main result are close to optimal.
2022Budde, ChristianDobrick, AlexanderGlück, JochenKunze, Markus510For an increasing sequence (Tn) of one-parameter semigroups of sub Markovian kernel operators over a Polish space, we study the limit semigroup and prove sufficient conditions for it to be strongly Feller. In particular, we show that the strong Feller property carries over from the approximating semigroups to the limit semigroup if the resolvent of the latter maps 1 to a continuous function. This is instrumental in the study of elliptic operators on Rd with unbounded coefficients: our abstract result enables us to assign a semigroup to such an operator and to show that the semigroup is strongly Feller under very mild regularity assumptions on the coefficients. We also provide counterexamples to demonstrate that the assumptions in our main result are close to optimal.SpringerJOURNAL_ARTICLEeng10.1007/s10231-022-01293-90373-31141618-1891Annali di Matematica Pura ed Applicata2023-01-26T15:18:56+01:00123456789/39Annali di Matematica Pura ed Applicata ; 2022. - Springer. - ISSN 0373-3114. - eISSN 1618-1891true2023-01-26T14:18:56ZtrueA Multistep, Cluster-Based Multivariate Chart for Retrospective Monitoring of Individuals123456789/8302023-02-07T06:22:38Z2009dc.title: A Multistep, Cluster-Based Multivariate Chart for Retrospective Monitoring of Individuals
dc.contributor.author: Jobe, J. Marcus; Pokojovy, Michael
dc.description.abstract: The presence of several outliers in an individuals retrospective multivariate control chart distorts both the sample mean vector and covariance matrix, making the classical Hotelling's T^2 approach unreliable for outlier detection. To overcome the distortion or masking, we propose a computer-intensive multistep cluster-based method. Compared with classical and robust estimation procedures, simulation studies show that our method is usually better and sometimes much better at detecting randomly occurring outliers as well as outliers arising from shifts in the process location. Additional comparisons based on real data are given.
2009Jobe, J. MarcusPokojovy, Michael310Dichtebasiertes ClusterverfahrenThe presence of several outliers in an individuals retrospective multivariate control chart distorts both the sample mean vector and covariance matrix, making the classical Hotelling's T^2 approach unreliable for outlier detection. To overcome the distortion or masking, we propose a computer-intensive multistep cluster-based method. Compared with classical and robust estimation procedures, simulation studies show that our method is usually better and sometimes much better at detecting randomly occurring outliers as well as outliers arising from shifts in the process location. Additional comparisons based on real data are given.JOURNAL_ARTICLEurn:nbn:de:bsz:352-opus-100868eng10.1080/00224065.2009.119177890022-40652575-6230323339414Journal of Quality Technology2011-03-22T18:49:01+01:00123456789/39Journal of Quality Technology ; 41 (2009), 4. - S. 323-339. - ISSN 0022-4065. - eISSN 2575-62302011-03-22T17:49:01ZA new Algorithm for Overcomplete Tensor Decomposition based on Sums-of-Squares Optimisation123456789/559902023-02-07T06:28:30Z2018dc.title: A new Algorithm for Overcomplete Tensor Decomposition based on Sums-of-Squares Optimisation
dc.contributor.author: Taveira Blomenhofer, Alexander
2018Taveira Blomenhofer, Alexander510MSC_THESISeng2021-12-22T12:53:27+01:00123456789/392021-12-22T11:53:27ZA new approach to Hilbert's theorem on ternary quartics123456789/235062023-02-07T06:17:22Z2004dc.title: A new approach to Hilbert's theorem on ternary quartics
dc.contributor.author: Powers, Victoria; Reznick, Bruce; Scheiderer, Claus; Sottile, Frank
dc.description.abstract: Hilbert proved that a non-negative real quartic form f(x,y,z)f(x,y,z) is the sum of three squares of quadratic forms. We give a new proof which shows that if the plane curve Q defined by f is smooth, then f has exactly 8 such representations, up to equivalence. They correspond to those real 2-torsion points of the Jacobian of Q which are not represented by a conjugation-invariant divisor on Q.
2004Powers, VictoriaReznick, BruceScheiderer, ClausSottile, Frank510Hilbert proved that a non-negative real quartic form f(x,y,z)f(x,y,z) is the sum of three squares of quadratic forms. We give a new proof which shows that if the plane curve Q defined by f is smooth, then f has exactly 8 such representations, up to equivalence. They correspond to those real 2-torsion points of the Jacobian of Q which are not represented by a conjugation-invariant divisor on Q.JOURNAL_ARTICLEurn:nbn:de:bsz:352-235060engUne nouvelle approche du théorème de Hilbert sur les quartiques ternaires10.1016/j.crma.2004.09.0141631-073X6176203399Comptes Rendus Mathematique2013-06-04T12:16:11+02:00123456789/39Comptes Rendus Mathematique ; 339 (2004), 9. - S. 617-620. - ISSN 1631-073X2013-06-04T10:16:11ZA new class of parabolic problems connected with Newton s polygon123456789/6332023-02-09T13:25:01Z2007dc.title: A new class of parabolic problems connected with Newton s polygon
dc.contributor.author: Denk, Robert; Volevič, Leonid R.
dc.description.abstract: A new class of boundary value problems for parabolic operators is introduced. We discuss some linearized free boundary problems not satisfying the classical parabolicity condition. It is shown that they belong to this class and by means of the Newton polygon method the nontrivial two-sided estimates of these problems are found.
2007Denk, RobertVolevič, Leonid R.510A new class of boundary value problems for parabolic operators is introduced. We discuss some linearized free boundary problems not satisfying the classical parabolicity condition. It is shown that they belong to this class and by means of the Newton polygon method the nontrivial two-sided estimates of these problems are found.JOURNAL_ARTICLEurn:nbn:de:bsz:352-opus-49176eng10.3934/proc.2007.2007.294294303Discrete and continuous dynamical systems / S2011-03-22T18:45:18+01:00123456789/39Discrete and continuous dynamical systems / S ; 2007. - S. 294-3032011-03-22T17:45:18ZA new derivation of Jeffery's equation123456789/8022023-02-07T06:30:46Z2007dc.title: A new derivation of Jeffery's equation
dc.contributor.author: Junk, Michael; Illner, Reinhard
2007Junk, MichaelIllner, Reinhard510JOURNAL_ARTICLEurn:nbn:de:bsz:352-opus-95925eng10.1007/s00021-005-0208-045548894Journal of Mathematical Fluid Mechanics2011-03-22T18:48:56+01:00123456789/39Journal of Mathematical Fluid Mechanics ; 9 (2007), 4. - S. 455-4882011-03-22T17:48:56ZA New Discrete Velocity Method for Navier–Stokes Equations123456789/254792023-02-07T06:22:21Z1999dc.title: A New Discrete Velocity Method for Navier–Stokes Equations
dc.contributor.author: Junk, Michael; Rao, S.V. Raghurama
dc.description.abstract: The relation between the lattice Boltzmann method, which has recently become popular, and the kinetic schemes, which are routinely used in computational fluid dynamics, is explored. A new discrete velocity method for the numerical solution of Navier–Stokes equations for incompressible fluid flow is presented by combining both the approaches. The new scheme can be interpreted as a pseudo-compressibility method and, for a particular choice of parameters, this interpretation carries over to the lattice Boltzmann method.
1999Junk, MichaelRao, S.V. Raghurama510The relation between the lattice Boltzmann method, which has recently become popular, and the kinetic schemes, which are routinely used in computational fluid dynamics, is explored. A new discrete velocity method for the numerical solution of Navier–Stokes equations for incompressible fluid flow is presented by combining both the approaches. The new scheme can be interpreted as a pseudo-compressibility method and, for a particular choice of parameters, this interpretation carries over to the lattice Boltzmann method.JOURNAL_ARTICLEurn:nbn:de:bsz:352-254796eng10.1006/jcph.1999.63360021-99911090-27161781981551Journal of Computational Physics2013-12-18T08:36:27+01:00123456789/39Journal of Computational Physics ; 155 (1999), 1. - S. 178-198. - ISSN 0021-9991. - eISSN 1090-27162013-12-18T07:36:27ZA New Perspective on Kinetic Schemes123456789/254682023-02-07T06:29:33Z2000dc.title: A New Perspective on Kinetic Schemes
dc.contributor.author: Junk, Michael
dc.description.abstract: Compared to standard numerical methods for hyperbolic systems of conservation laws, kinetic schemes model propagation of information by particles instead of waves. In this article, the wave and the particle concept are shown to be closely related. Moreover, a general approach to the construction of kinetic schemes for hyperbolic conservation laws is given that summarizes several approaches discussed by other authors.
2000Junk, Michael510Compared to standard numerical methods for hyperbolic systems of conservation laws, kinetic schemes model propagation of information by particles instead of waves. In this article, the wave and the particle concept are shown to be closely related. Moreover, a general approach to the construction of kinetic schemes for hyperbolic conservation laws is given that summarizes several approaches discussed by other authors.JOURNAL_ARTICLEurn:nbn:de:bsz:352-254687eng10.1137/S00361429993628570036-14291095-717016031625385SIAM Journal on Numerical Analysis2013-12-18T07:47:18+01:00123456789/39SIAM Journal on Numerical Analysis ; 38 (2000), 5. - S. 1603-1625. - ISSN 0036-1429. - eISSN 1095-71702013-12-18T06:47:18Z