2-DIMENSIONAL PRIMAL DOMAIN DECOMPOSITION THEORY IN DETAIL

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F15%3A86096468" target="_blank" >RIV/61989100:27240/15:86096468 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61989100:27740/15:86096468

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s10492-015-0095-5" target="_blank" >http://dx.doi.org/10.1007/s10492-015-0095-5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10492-015-0095-5" target="_blank" >10.1007/s10492-015-0095-5</a>

Jazyk výsledku

angličtina

Název v původním jazyce

2-DIMENSIONAL PRIMAL DOMAIN DECOMPOSITION THEORY IN DETAIL

Popis výsledku v původním jazyce

We give details of the theory of primal domain decomposition (DD) methods for a 2-dimensional second order elliptic equation with homogeneous Dirichlet boundary conditions and jumping coefficients. The problem is discretized by the finite element method.The computational domain is decomposed into triangular subdomains that align with the coefficients jumps. We prove that the condition number of the vertex-based DD preconditioner is O((1 + log(H/h))(2)), independently of the coefficient jumps, where H and h denote the discretization parameters of the coarse and fine triangulations, respectively. Although this preconditioner and its analysis date back to the pioneering work J.H.Bramble, J. E.Pasciak, A.H. Schatz (1986), and it was revisited and extendedby many authors including M.Dryja, O.B.Widlund (1990) and A.Toselli, O.B.Widlund (2005), the theory is hard to understand and some details, to our best knowledge, have never been published. In this paper we present all the proofs in deta

Název v anglickém jazyce

2-DIMENSIONAL PRIMAL DOMAIN DECOMPOSITION THEORY IN DETAIL

Popis výsledku anglicky

We give details of the theory of primal domain decomposition (DD) methods for a 2-dimensional second order elliptic equation with homogeneous Dirichlet boundary conditions and jumping coefficients. The problem is discretized by the finite element method.The computational domain is decomposed into triangular subdomains that align with the coefficients jumps. We prove that the condition number of the vertex-based DD preconditioner is O((1 + log(H/h))(2)), independently of the coefficient jumps, where H and h denote the discretization parameters of the coarse and fine triangulations, respectively. Although this preconditioner and its analysis date back to the pioneering work J.H.Bramble, J. E.Pasciak, A.H. Schatz (1986), and it was revisited and extendedby many authors including M.Dryja, O.B.Widlund (1990) and A.Toselli, O.B.Widlund (2005), the theory is hard to understand and some details, to our best knowledge, have never been published. In this paper we present all the proofs in deta

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: Centrum excelence IT4Innovations</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Applications of Mathematics

ISSN

0862-7940

e-ISSN

—

Svazek periodika

60

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

19

Strana od-do

265-283

Kód UT WoS článku

000361346700003

EID výsledku v databázi Scopus

2-s2.0-84941953368