基于区域分解的大规模并行有限元快速算法

区域分解方法是近来发展迅速的有限元求解方法之一.基于有限元区域分解方法以及多重网格的思想，我们研究了自适应求解以及离散扫频快速算法，并采用自主研发的高性能计算并行框架，将基于区域分解的大规模并行有限元快速算法进行了实现，并行规模能够扩展到数万CPU 核.我们在文中将展示程序的核心架构，以及如何采用多重网格算法的思想实现有效的粗网格校正技术，从而实现有限元线性系统的多次快速求解，加速自适应求解和离散扫频.最后，对算法进行了准确性验证以及大规模并行测试.

Fast Algorithms of Parallel Finite Element Method Based on Domain Decomposition

DDM (Domain Decomposition Method) is one of the most quickly developed methods in recent years.We investigate the fast solving techniques of adaptive refinement and discrete frequency sweep based on DDM.Besides,an in-house developed infrastructure is used to implement the proposed algorithms,which is able to scale to tens of thousands of CPU cores.We demonstrate the architecture and main features of the program.Then,the DDM,p-adaptive strategy and fast frequency sweep techniques are discussed as well to show how to solve the finite element linear systems quickly.Several numerical examples are presented to demonstrate its accuracy,parallel efficiency and capability in electromagnetic applications.