Additive Schwarz preconditioner for the finite volume element discretization of symmetric elliptic problems

被引：6

作者：

Marcinkowski, L. ^{[1
]}

Rahman, T. ^{[2
]}

Loneland, A. ^{[2
,3
]}

Valdman, J. ^{[4
,5
]}

机构：

[1] Univ Warsaw, Fac Math, Banacha 2, PL-02097 Warsaw, Poland

[2] Bergen Univ Coll, Dept Comp Math & Phys, N-5020 Bergen, Norway

[3] Univ Bergen, Dept Informat, N-5020 Bergen, Norway

[4] Univ South Bohemia, Inst Math & Biomath, Branisovska 31, Ceske Budejovice 37005, Czech Republic

[5] ASCR, Inst Informat Theory & Automat, Pod Vodarenskou Vezi 4, Prague 18208, Czech Republic

来源：

BIT NUMERICAL MATHEMATICS | 2016年 / 56卷 / 03期

关键词：

Domain decomposition; Additive Schwarz method; Finite volume element; GMRES; CROUZEIX-RAVIART ELEMENT; DOMAIN DECOMPOSITION PRECONDITIONERS; ITERATIVE METHODS; ALGORITHMS; ADJOINT; SYSTEMS;

D O I：

10.1007/s10543-015-0581-x

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

A symmetric and a nonsymmetric variant of the additive Schwarz preconditioner are proposed for the solution of a class of finite volume element discretization of the symmetric elliptic problem in two dimensions, with large jumps in the entries of the coefficient matrices across subdomains. It is shown that the convergence of the preconditioned generalized minimal residual iteration using the proposed preconditioners depends polylogarithmically, in other words weakly, on the mesh parameters, and that they are robust with respect to the jumps in the coefficients.

引用

页码：967 / 993

页数：27

共 50 条

[1] Additive Schwarz preconditioner for the finite volume element discretization of symmetric elliptic problems
L. Marcinkowski
T. Rahman
A. Loneland
J. Valdman
BIT Numerical Mathematics, 2016, 56 : 967 - 993
[2] Parallel Preconditioner for the Finite Volume Element Discretization of Elliptic Problems
Marcinkowski, Leszek
Rahman, Talal
PARALLEL PROCESSING AND APPLIED MATHEMATICS (PPAM 2013), PT II, 2014, 8385 : 469 - 478
[3] Additive Average Schwarz Method for a Crouzeix-Raviart Finite Volume Element Discretization of Elliptic Problems
Loneland, Atle
Marcinkowski, Leszek
Rahman, Talal
DOMAIN DECOMPOSITION METHODS IN SCIENCE AND ENGINEERING XXII, 2016, 104 : 587 - 594
[4] Additive average Schwarz method for a Crouzeix–Raviart finite volume element discretization of elliptic problems with heterogeneous coefficients
A. Loneland
L. Marcinkowski
T. Rahman
Numerische Mathematik, 2016, 134 : 91 - 118
[5] Additive average Schwarz method for a Crouzeix-Raviart finite volume element discretization of elliptic problems with heterogeneous coefficients
Loneland, A.
Marcinkowski, L.
Rahman, T.
NUMERISCHE MATHEMATIK, 2016, 134 (01) : 91 - 118
[6] Additive Schwarz Methods for Elliptic Mortar Finite Element Problems
Petter E. Bjørstad
Maksymilian Dryja
Talal Rahman
Numerische Mathematik, 2003, 95 : 427 - 457
[7] A two-level additive Schwarz preconditioner for the Nitsche extended finite element approximation of elliptic interface problems
Chu, Hanyu
Cai, Ying
Wang, Feng
Chen, Jinru
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2023, 147 : 111 - 120
[8] Additive Schwarz methods for elliptic mortar finite element problems
Bjorstad, PE
Dryja, M
Rahman, T
NUMERISCHE MATHEMATIK, 2003, 95 (03) : 427 - 457
[9] Schwarz Methods for a Crouzeix-Raviart Finite Volume Discretization of Elliptic Problems
Marcinkowski, Leszek
Loneland, Atle
Rahman, Talal
DOMAIN DECOMPOSITION METHODS IN SCIENCE AND ENGINEERING XXII, 2016, 104 : 595 - 602
[10] EDGE-BASED SCHWARZ METHODS FOR THE CROUZEIX-RAVIART FINITE VOLUME ELEMENT DISCRETIZATION OF ELLIPTIC PROBLEMS
Loneland, Atle
Marcinkowski, Leszek
Rahman, Talal
ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, 2015, 44 : 443 - 461

← 1 2 3 4 5 →