TY - JOUR
A1 - Schrader, Kai
A1 - Könke, Carsten
T1 - Hybrid computing models for large-scale heterogeneous 3d microstructures
JF - International Journal for Multiscale Computational Engineering
N2 - Hybrid computing models for large-scale heterogeneous 3d microstructures
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2011
SP - 365
EP - 377
ER -
TY - JOUR
A1 - Schrader, Kai
A1 - Könke, Carsten
T1 - Distributed computing for the nonlinear analysis of multiphase composites
JF - Advances in Engineering Software
N2 - Distributed computing for the nonlinear analysis of multiphase composites
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2013
SP - 20
EP - 32
ER -
TY - CHAP
A1 - Schrader, Kai
A1 - Könke, Carsten
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - SPARSE APPROXIMATE COMPUTATION OF SADDLE POINT PROBLEMS ARISING FROM FETI-DP DISCRETIZATION
N2 - The numerical simulation of microstructure models in 3D requires, due to enormous d.o.f., significant resources of memory as well as parallel computational power. Compared to homogeneous materials, the material hetrogeneity on microscale induced by different material phases demand for adequate computational methods for discretization and solution process of the resulting highly nonlinear problem. To enable an efficient/scalable solution process of the linearized equation systems the heterogeneous FE problem will be described by a FETI-DP (Finite Element Tearing and Interconnecting - Dual Primal) discretization. The fundamental FETI-DP equation can be solved by a number of different approaches. In our approach the FETI-DP problem will be reformulated as Saddle Point system, by eliminating the primal and Lagrangian variables. For the reduced Saddle Point system, only defined by interior and dual variables, special Uzawa algorithms can be adapted for iteratively solving the FETI-DP saddle-point equation system (FETI-DP SPE). A conjugate gradient version of the Uzawa algorithm will be shown as well as some numerical tests regarding to FETI-DP discretization of small examples using the presented solution technique. Furthermore the inversion of the interior-dual Schur complement operator can be approximated using different techniques building an adequate preconditioning matrix and therewith leading to substantial gains in computing time efficiency.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Architektur
KW - Computerunterstütztes Verfahren
KW - Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing
Y1 - 2010
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28874
UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN - 1611-4086
ER -