Informatica

Three parallel algorithms for solving the 3D problem with nonlocal boundary condition are considered. The forward and backward Euler finite-difference schemes, and LOD scheme are typical representatives of three general classes of parallel algorithms used to solve multidimensional parabolic initial-boundary value problems. All algorithms are modified to take into account additional nonlocal boundary condition. The algorithms are implemented using the parallel array object tool ParSol, then a parallel algorithm follows semi-automatically from the serial one. Results of computational experiments are presented and the accuracy and efficiency of the presented parallel algorithms are tested.

The conjugate gradient method is an iterative technique used to solve systems of linear equations. The paper analyzes the performance of parallel preconditioned conjugate gradient algorithms. First, a theoretical model is proposed for estimation of the complexity of PPCG method and a scalability analysis is done for three different data decomposition cases. Computational experiments are done on IBM SP4 computer and some results are presented. It is shown that theoretical predictions agree well with computational results.

This work describes a realistic performance prediction tool for the parallel block LU factorization algorithm. It takes into account the computational workload, communication costs and the overlapping of communications by useful computations. Estimation of the tool parameters and benchmarking are also discussed. Using this tool we develop a simple heuristic for scheduling LU factorization tasks. Results of numerical experiments are presented.

This paper presents a parallel version of a Generalized Conjugate Gradient algorithm proposed by Liu and Story in which the search direction considers the effect of the inexact line search. We describe the implementation of this algorithm on a parallel architecture and analyze the related speedup ratios. Numerical results are given for a shared memory computer (Cray C92).

In this paper we consider the problem of solving 3D diffusion problems on distributed memory computers. We present a parallel algorithm that is suitable for the number of processors less or equal 8. The pipelining method is used to enlarge the number of processors till 64. The computational grid decomposition method is proposed for heterogenous clusters of workstations which preserves the load balancing of computers. The numerical results for two clusters of workstations are given.