TY - GEN
T1 - GenEO Coarse Spaces for Heterogeneous Indefinite Elliptic Problems
AU - Bootland, Niall
AU - Dolean, Victorita
AU - Graham, Ivan G.
AU - Ma, Chupeng
AU - Scheichl, Robert
PY - 2023/3/16
Y1 - 2023/3/16
N2 - For domain decomposition preconditioners, the use of a coarse correction as a second level is usually required to provide scalability (in the weak sense), such that the iteration count is independent of the number of subdomains, for subdomains of fixed dimension. In addition, it is desirable to guarantee robustness with respect to strong variations in the physical parameters. Achieving scalability and robustness usually relies on sophisticated tools such as spectral coarse spaces [4, 5]. In particular, we can highlight the GenEO coarse space [9], which has been successfully analysed and applied to highly heterogeneous positive definite elliptic problems. This coarse space relies on the solution of local eigenvalue problems on subdomains and the theory in the SPD case is based on the fact that local eigenfunctions form an orthonormal basis with respect to the energy scalar product induced by the bilinear form.
AB - For domain decomposition preconditioners, the use of a coarse correction as a second level is usually required to provide scalability (in the weak sense), such that the iteration count is independent of the number of subdomains, for subdomains of fixed dimension. In addition, it is desirable to guarantee robustness with respect to strong variations in the physical parameters. Achieving scalability and robustness usually relies on sophisticated tools such as spectral coarse spaces [4, 5]. In particular, we can highlight the GenEO coarse space [9], which has been successfully analysed and applied to highly heterogeneous positive definite elliptic problems. This coarse space relies on the solution of local eigenvalue problems on subdomains and the theory in the SPD case is based on the fact that local eigenfunctions form an orthonormal basis with respect to the energy scalar product induced by the bilinear form.
UR - http://www.scopus.com/inward/record.url?scp=85151152161&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-95025-5_10
DO - 10.1007/978-3-030-95025-5_10
M3 - Chapter in a published conference proceeding
AN - SCOPUS:85151152161
SN - 9783030950248
T3 - Lecture Notes in Computational Science and Engineering
SP - 117
EP - 125
BT - Domain Decomposition Methods in Science and Engineering XXVI
A2 - Brenner, Susanne C.
A2 - Klawonn, Axel
A2 - Xu, Jinchao
A2 - Chung, Eric
A2 - Zou, Jun
A2 - Kwok, Felix
PB - Springer
CY - Cham, Switzerland
T2 - 26th International Conference on Domain Decomposition Methods, 2020
Y2 - 7 December 2020 through 12 December 2020
ER -