On the effect of boundary conditions on the scalability of Schwarz methods

Ciaramella, Gabriele; Mechelli, Luca

On the effect of boundary conditions on the scalability of Schwarz methods

Files

There are no files associated with this item.

Date

2021

Publication type

Preprint

Publication status

Published

Abstract

In contrast with classical Schwarz theory, recent results have shown that for special domain geometries, one-level Schwarz methods can be scalable. This property has been proved for the Laplace equation and external Dirichlet boundary conditions. Much less is known if mixed boundary conditions are considered. This short manuscript focuses on the convergence and scalability analysis of one-level parallel Schwarz method and optimized Schwarz method for several different external configurations of boundary conditions, i.e., mixed Dirichlet, Neumann and Robin conditions.

Subject (DDC)

510 Mathematics

Cite This

ISO 690

CIARAMELLA, Gabriele, Luca MECHELLI, 2021. On the effect of boundary conditions on the scalability of Schwarz methods

BibTex

@unpublished{Ciaramella2021-03-27T09:12:19Zeffec-55637,
  year={2021},
  title={On the effect of boundary conditions on the scalability of Schwarz methods},
  author={Ciaramella, Gabriele and Mechelli, Luca}
}

RDF

<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/55637">
    <dc:rights>terms-of-use</dc:rights>
    <dcterms:issued>2021-03-27T09:12:19Z</dcterms:issued>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-11-24T10:31:28Z</dc:date>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:creator>Mechelli, Luca</dc:creator>
    <dcterms:title>On the effect of boundary conditions on the scalability of Schwarz methods</dcterms:title>
    <dc:contributor>Ciaramella, Gabriele</dc:contributor>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <dc:creator>Ciaramella, Gabriele</dc:creator>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/55637"/>
    <dcterms:abstract xml:lang="eng">In contrast with classical Schwarz theory, recent results have shown that for special domain geometries, one-level Schwarz methods can be scalable. This property has been proved for the Laplace equation and external Dirichlet boundary conditions. Much less is known if mixed boundary conditions are considered. This short manuscript focuses on the convergence and scalability analysis of one-level parallel Schwarz method and optimized Schwarz method for several different external configurations of boundary conditions, i.e., mixed Dirichlet, Neumann and Robin conditions.</dcterms:abstract>
    <dc:language>eng</dc:language>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-11-24T10:31:28Z</dcterms:available>
    <dc:contributor>Mechelli, Luca</dc:contributor>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
  </rdf:Description>
</rdf:RDF>

Bibliography of Konstanz

Yes