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

Abstract

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.

On the creation of parallelizing compilers for distributed memory computing systems

“…В [16] показано, что эти компиляторы плохо оптимизируют код, имеют большой неиспользованный потенциал оптимизирующих преобразований. Эти результаты частично подтверждаются в [17], [18]. Можно полагать, что для микросхем supercomputer-on-chip этот потенциал оптимизаций значительно больше.…”