Parallel iterative solver VS1
Solver is designed for solving large linear systems, arising from the finite element analysis of elasticity problems with voxel grid, in particular problems of micromechanics using CT scan input data. The voxel structure of such problems enables straightforward discretization by regular structured grids. The code, based on finite element method, is optimized to take advantage of such meshing for performance and parallelization. Both Dirichlet and Neumann boundary conditions can be applied. In the second case, the arising singular system are efficiently solved making use of projections. The solver is a part of the finite element system GEM, but can be used independently for voxel based problems with a specific voxel format for the finite element matrices.
Download the complete software package VS1 (TAR.GZ). The solver and associated programs are free software distributed under the terms of the GNU General Public License as published by the Free Software Foundation.
Description
The FE mesh is prepared from digital images produced by the industrial X-ray computer tomography, which allows us data acquisition on the inner microstructure of the domain of interest. The discretization divides regular rectangular voxel based elements into six tetrahedra in a way known as the Kuhn’s decomposition and further uses piecewise linear FE approximation.
The solver processes data in accordance with the algorithm of the preconditioned conjugate gradient method. Its paralellization is based on one-dimensional domain decomposition into parallel layers with nearly minimal overlap of adjacent subdomains. Such decomposition allows directly applying additive Schwarz preconditioners with small communication demands, which ensure high performance of the solver. User can choose the preconditioner of one-level or two-level type, in the later case with coarse spaces created by aggressive aggregation.
The system can be singular as a consequence of the used boundary conditions of the Neumann type or presence of finite elements weekly hanged in the void space of the CT images. The latter phenomenon is removed by filling the voids with auxiliary very week elastic material. The former singularity due to nontrivial but known null space of the FE matrices can be solved by equipping the iterations by an orthogonal projection into the space orthogonal to null space vectors.
The program is written in Fortran 77. The communication of parallel processes is realized by message passing implemented according to MPI standard. The descibed solver was successfully tested, beside others at the cluster Anselm of the National supercomputing centre IT4Innovations, and compared with solvers available from the well known library Trilinos.
References
- R. Blaheta, O. Jakl, J. Stary, E. Turan: Parallel solvers for numerical upscaling. Applied Parallel and Scientific Computing. Springer-Verlag Lecture Notes in Computer Science, Vol. 7782, 2013. Pages 375-386. ISSN 0302-9743, ISBN 978-3-642-36802-8.
- R. Blaheta, O. Jakl, J. Stary: Iterative solution of singular systems with applications. Accepted for PPAM proceedings (Springer, LNCS series).
- R. Blaheta, R. Kohut, A. Kolcun, K. Soucek, L. Stas: Micromechanics of geocomposites: CT images and FEM simulations. In: EUROCK 2013, Balkema, 2013. Pages 399-404.