An element agglomeration nonlinear additive Schwarz preconditioned Newton method for unstructured finite element problems

Xiao-Chuan Cai; Leszek Marcinkowski; Vassilevski, Panayot S.

Applications of Mathematics (2005)

  • Volume: 50, Issue: 3, page 247-275
  • ISSN: 0862-7940

Abstract

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This paper extends previous results on nonlinear Schwarz preconditioning (Cai and Keyes 2002) to unstructured finite element elliptic problems exploiting now nonlocal (but small) subspaces. The nonlocal finite element subspaces are associated with subdomains obtained from a non-overlapping element partitioning of the original set of elements and are coarse outside the prescribed element subdomain. The coarsening is based on a modification of the agglomeration based AMGe method proposed in Jones and Vassilevski 2001. Then, the algebraic construction from Jones, Vassilevski and Woodward 2003 of the corresponding non-linear finite element subproblems is applied to generate the subspace based nonlinear preconditioner. The overall nonlinearly preconditioned problem is solved by an inexact Newton method. A numerical illustration is also provided.

How to cite

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Cai, Xiao-Chuan, Marcinkowski, Leszek, and Vassilevski, Panayot S.. "An element agglomeration nonlinear additive Schwarz preconditioned Newton method for unstructured finite element problems." Applications of Mathematics 50.3 (2005): 247-275. <http://eudml.org/doc/33220>.

@article{Cai2005,
abstract = {This paper extends previous results on nonlinear Schwarz preconditioning (Cai and Keyes 2002) to unstructured finite element elliptic problems exploiting now nonlocal (but small) subspaces. The nonlocal finite element subspaces are associated with subdomains obtained from a non-overlapping element partitioning of the original set of elements and are coarse outside the prescribed element subdomain. The coarsening is based on a modification of the agglomeration based AMGe method proposed in Jones and Vassilevski 2001. Then, the algebraic construction from Jones, Vassilevski and Woodward 2003 of the corresponding non-linear finite element subproblems is applied to generate the subspace based nonlinear preconditioner. The overall nonlinearly preconditioned problem is solved by an inexact Newton method. A numerical illustration is also provided.},
author = {Cai, Xiao-Chuan, Marcinkowski, Leszek, Vassilevski, Panayot S.},
journal = {Applications of Mathematics},
keywords = {algebraic multigrid; agglomeration; non-linear elliptic problem; nonlinear preconditioning; Newton method; finite elements; algebraic multigrid; agglomeration; nonlinear elliptic problem; nonlinear preconditioning; Newton method; finite elements},
language = {eng},
number = {3},
pages = {247-275},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An element agglomeration nonlinear additive Schwarz preconditioned Newton method for unstructured finite element problems},
url = {http://eudml.org/doc/33220},
volume = {50},
year = {2005},
}

TY - JOUR
AU - Cai, Xiao-Chuan
AU - Marcinkowski, Leszek
AU - Vassilevski, Panayot S.
TI - An element agglomeration nonlinear additive Schwarz preconditioned Newton method for unstructured finite element problems
JO - Applications of Mathematics
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 3
SP - 247
EP - 275
AB - This paper extends previous results on nonlinear Schwarz preconditioning (Cai and Keyes 2002) to unstructured finite element elliptic problems exploiting now nonlocal (but small) subspaces. The nonlocal finite element subspaces are associated with subdomains obtained from a non-overlapping element partitioning of the original set of elements and are coarse outside the prescribed element subdomain. The coarsening is based on a modification of the agglomeration based AMGe method proposed in Jones and Vassilevski 2001. Then, the algebraic construction from Jones, Vassilevski and Woodward 2003 of the corresponding non-linear finite element subproblems is applied to generate the subspace based nonlinear preconditioner. The overall nonlinearly preconditioned problem is solved by an inexact Newton method. A numerical illustration is also provided.
LA - eng
KW - algebraic multigrid; agglomeration; non-linear elliptic problem; nonlinear preconditioning; Newton method; finite elements; algebraic multigrid; agglomeration; nonlinear elliptic problem; nonlinear preconditioning; Newton method; finite elements
UR - http://eudml.org/doc/33220
ER -

References

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