Iterative solution methods
On a Two-Level Parallel MIC(0) Preconditioning of Crouzeix-Raviart Non-conforming FEM Systems
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
Parallel incomplete factorization of 3D NC FEM elliptic systems
NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
Parallel DD-MIC(0) Preconditioning of Nonconforming Rotated Trilinear FEM Elasticity Systems
Large-Scale Scientific Computing
Locally optimized MIC( 0) preconditioning of Rannacher--Turek FEM systems
Applied Numerical Mathematics
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
| Hi-index | 0.09 |
Novel parallel algorithms for the solution of large FEM linear systems arising from second order elliptic partial differential equations in 3D are presented. The problem is discretized by rotated trilinear nonconforming Rannacher-Turek finite elements. The resulting symmetric positive definite system of equations Ax=f is solved by the preconditioned conjugate gradient algorithm. The preconditioners employed are obtained by the modified incomplete Cholesky factorization MIC(0) of two kinds of auxiliary matrices B that both are constructed as locally optimal approximations of A in the class of M-matrices. Uniform estimates for the condition number @k(B^-^1A) are derived. Two parallel algorithms based on the different block structures of the related matrices B are studied. The numerical tests confirm theory in that the algorithm scales as O(N^7^/^6) in the matrix order N.