Abstract
| Language | English |
|---|---|
| Pages | n/a |
| Number of pages | 30 |
| Journal | Numerische Mathematik |
| Volume | n/a |
| Issue number | n/a |
| Early online date | 15 Aug 2013 |
| DOIs | |
| Publication status | Published - 2013 |
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Keywords
- coarse spaces
- overlapping Schwarz method
- two-level methods
- generalized eigenvectors
- large coefficient variation
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Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps. / Spillane, N.; Dolean Maini, Victorita; Hauret, P.; Nataf, F.; Pechstein, C.; Scheichl, R.
In: Numerische Mathematik, Vol. n/a, No. n/a, 2013, p. n/a.Research output: Contribution to journal › Article
TY - JOUR
T1 - Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps
AU - Spillane, N.
AU - Dolean Maini, Victorita
AU - Hauret, P.
AU - Nataf, F.
AU - Pechstein, C.
AU - Scheichl, R.
PY - 2013
Y1 - 2013
N2 - Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities in the PDE coefficients, especially for systems of PDEs. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems in the overlaps of subdomains that isolate the terms responsible for slow convergence. We prove a general theoretical result that rigorously establishes the robustness of the new coarse space and give some numerical examples on two and three dimensional heterogeneous PDEs and systems of PDEs that confirm this property.
AB - Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities in the PDE coefficients, especially for systems of PDEs. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems in the overlaps of subdomains that isolate the terms responsible for slow convergence. We prove a general theoretical result that rigorously establishes the robustness of the new coarse space and give some numerical examples on two and three dimensional heterogeneous PDEs and systems of PDEs that confirm this property.
KW - coarse spaces
KW - overlapping Schwarz method
KW - two-level methods
KW - generalized eigenvectors
KW - large coefficient variation
UR - http://link.springer.com/journal/211
U2 - 10.1007/s00211-013-0576-y
DO - 10.1007/s00211-013-0576-y
M3 - Article
VL - n/a
SP - n/a
JO - Numerische Mathematik
T2 - Numerische Mathematik
JF - Numerische Mathematik
SN - 0029-599X
IS - n/a
ER -