TY - JOUR
T1 - The approximate component mode synthesis special finite element method in two dimensions
T2 - Parallel implementation and numerical results
AU - Heinlein, A.
AU - Hetmaniuk, U.
AU - Klawonn, A.
AU - Rheinbach, O.
PY - 2015
Y1 - 2015
N2 - Abstract A special finite element method based on approximate component mode synthesis (ACMS) was introduced in Hetmaniuk and Lehoucq (2010). ACMS was developed for second order elliptic partial differential equations with rough or highly varying coefficients. Here, a parallel implementation of ACMS is presented and parallel scalability issues are discussed for representative examples. Additionally, a parallel domain decomposition preconditioner (FETI-DP) is applied to solve the ACMS finite element system. Weak parallel scalability results for ACMS are presented for up to 1024 cores. Our numerical results also suggest a quadratic-logarithmic condition number bound for the preconditioned FETI-DP method applied to ACMS discretizations.
AB - Abstract A special finite element method based on approximate component mode synthesis (ACMS) was introduced in Hetmaniuk and Lehoucq (2010). ACMS was developed for second order elliptic partial differential equations with rough or highly varying coefficients. Here, a parallel implementation of ACMS is presented and parallel scalability issues are discussed for representative examples. Additionally, a parallel domain decomposition preconditioner (FETI-DP) is applied to solve the ACMS finite element system. Weak parallel scalability results for ACMS are presented for up to 1024 cores. Our numerical results also suggest a quadratic-logarithmic condition number bound for the preconditioned FETI-DP method applied to ACMS discretizations.
KW - Component mode synthesis
KW - Domain decomposition
KW - Eigendecomposition
KW - FETI-DP
KW - Finite elements
KW - Multiscale
UR - http://www.scopus.com/inward/record.url?scp=84939462185&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2015.02.053
DO - 10.1016/j.cam.2015.02.053
M3 - Article
AN - SCOPUS:84939462185
SN - 0377-0427
VL - 289
SP - 116
EP - 133
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
M1 - 10049
ER -