Parallel Numerical Processing of Linear Systems with Irregularly Sparse Coefficient Matrix

点击翻译按钮获取中文摘要

Parallel solution of large-scale linear systems which arise from the discretization of unstructured grid systems with irregular structures is studied. Although preconditioned conjugate gradient (PCG) methods are applicable to positive symmetric equations, the effectiveness of the PCG critically depends on the acceleration of convergence by the preconditioning and the parallelizability of the precontitioning. In this study, an algorithms to generated automatically generate the miltigrid using geometrical structures and to solve the systems of equations given by irregular finite element method for elliptic partial differential equations proposed. We found that although this method is effective for homogeneous problems, the convergence is not fast enough for problems with inhomogeneity. We proposed a kind of automatica semi-coursening method using an algebraic information at the same time for inhomogeneous problems. We have shown that our method gives almost the same performance as the ICCG (Incomplete Cholesky Conjugate Gradient) method. Since the ICCG cannot be parallelized, we believe our method can be applied to practical problems. For problems with the inhomogeneity of 100 or more, our method is inferior to the ICCG.We would like to continue our research toward the AMG, algebraic multi-grid method, and its application as a preconditioning.