Keywords: OOSol library, domain decomposition methods, distributed data structures, parallel scalability, large scale problems, multibody contact problems.

During recent years, our research team at the Department of Applied Mathematics has been focused on the development of scalable algorithms for finite element analysis of problems in engineering. These algorithms are typically based on domain decomposition techniques such as a family of finite element tearing and interconnecting (FETI) methods which are well known for their parallel and numerical scalability. Solution of the most technical problems is reduced to the solution of a system of the elliptic partial differential equations with boundary conditions. It has to be discretized for the numerical solution and transformed to the quadratic programming problem with a special matrix of large dimension. The computation demands of the solution of large systems of equations is the motivation for development of effective algorithms. These algorithms can be effectively implemented on massively parallel computers.

The first aim of this paper is to present our system of distributed data structures, mainly matrices, that are either sparse or full. A suitable tool has been created especially for parallel communication that incorporates mainly initialization of parallel environment, data distribution to particular processors, and the final gathering of the results data. The second aim is to present parallel iteration solvers which have been implemented in an object oriented solvers (OOSol) library [1]. The focus is on domain decomposition methods for the solution of variational equalities and inequalities. Special effort has been devoted to optimize the parallel code so as to have low memory requirements and short run times.

We have generated a two-dimensional model problem of two membranes as the benchmark. This problem has been used for the parallel scalability testing of the distributed data structures implemented and the BLAS algorithms. Their performance has been tested on a standard conjugate gradient (CG) algorithm. The model problem has been decomposed with respect to the decomposition parameter H and discretized with discretization parameter h. Decreasing the decomposition parameter H with fixed number of primal variables, we can observe the decreasing of solution time, i.e. the speed-up is proportional to the number of CPUs used.

1

V. Vondrák, P. Kabelíková, M. Merta, M. Stachon, T. Kozubek, "OOSol library", VŠB-Technical University of Ostrava, 2010. http://www.am.vsb.cz/oosol

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