一般稀疏线性方程组的因子组合型并行预条件研究

基于因子组合给出一般稀疏线性方程组的一种新并行预条件。在该方案中,应用基于邻接图的重叠区域分解,形成一串相互重叠的子区域。对每个子区域,可以采用任何不完全LU分解。之后,利用全局三角因子与全局下三角因子的乘积作为全局的并行预条件,其中全局三角因子利用限制加性Schwarz思想对每个局部上三角因子的逆进行组合得到。分析表明,提出的预条件优于经典加性Schwarz和限制加性Schwarz,且能保持对称正定性。对混凝土细观数值模拟中线性方程组的实验再次表明,新方案优于经典加性Schwarz。

GENERAL SPARSE LINEAR SYSTEM FACTOR COMBINED PARALLEL PRECONDITION RESEARCH

Based on factor combination,the thesis introduces a new parallel precondition for general sparse linear systems.The scheme applies adjacent graph based overlapping domain decomposition to create a sequence of mutually overlapping sub-domains.For each sub-domain,any incomplete LU factorization can be applied.Then the multiplied value by the global triangular factor and the global lower triangular factor,the former of which is obtained by combining the inverse of every local upper triangle factor by restrictive additive Schwarz,as global parallel precondition.Analyses show that the proposed precondition is superior to classical additive Schwarz and restricted additive Schwarz while still preserves its symmetric positive definite property.Experiments with linear equations in concrete microscopic numerical value simulation once again demonstrates that the new scheme is better than classical additive Schwarz.