Mixed finite element methods—reduced and selective integration techniques: a unification of concepts
Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Iterative solution methods
Computers & Mathematics with Applications
Parallel performance evaluation of MIC(0) preconditioning algorithm for voxel µFE simulation
PPAM'09 Proceedings of the 8th international conference on Parallel processing and applied mathematics: Part II
Parallel MIC(0) preconditioning for numerical upscaling of anisotropic linear elastic materials
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
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A new parallel preconditioning algorithm for 3D nonconforming FEM elasticity systems is presented. The preconditioner is constructed in two steps. First, displacement decomposition of the stiffness matrix is used. Then MIC(0) factorization is applied to a proper auxiliary M-matrix to get an approximate factorization of the obtained block-diagonal matrix. The auxiliary matrix has a special block structure -- its diagonal blocks are diagonal matrices themselves. This allows the solution of the preconditioning system to be performed efficiently in parallel. Estimates for the parallel times, speedups and efficiencies are derived. The performed parallel tests are in total agreement with them. The robustness of the proposed algorithm is confirmed by the presented experiments solving problems with strong coefficient jumps.