Fast Solvers for Systems of Linear Equations with Block-Band Matrices

This article deals with parallel iterative algorithms for linear systems with block-band matrices. The algorithms can be used in mathematical modeling of the problems involving finite difference and finite element methods. The solvers are adjusted to the problem and to the computing systems, which use special precompilers. Applications of the algorithms to the ACELAN-COMPOS software package focused on the new material modeling, is described. To achieve a high performance, both parallel programming techniques and the optimization of the processor memory hierarchy are used. The results of numerical experiments confirm the efficiency of the methods and algorithms.

Automated summary

This article discusses parallel iterative algorithms for linear systems with block-band matrices, which can be applied to mathematical modeling problems involving finite difference and finite element methods. The solvers are adapted to the problem and computing systems with the use of special precompilers. The article describes the applications of these algorithms to the ACELAN-COMPOS software package for new material modeling and the utilization of parallel programming techniques and processor memory hierarchy optimization to achieve high performance. Numerical experiments confirm the efficiency of the methods and algorithms.