自适应交叉近似压缩的高阶矩量法的并行实现

高阶矩量法在计算电磁学中的应用越来越广泛, 为了进一步提高其计算规模, 引入并行的自适应交叉近似压缩算法(Adaptive Cross Approximation algorithm, ACA).该算法首先采用非均匀有理B样条建模(Non-Uniform Rational B-Splines, NURBS)的方法进行面片分组; 然后利用矩量法中远区阻抗矩阵的低秩特性进行ACA压缩; 最后采用稀疏近似逆预条件(Sparse Pattern Approximate Inverse preconditioning, SPAI)的共轭梯度法(Conjugate Gradient method, CG)快速求解矩阵方程.该算法中的ACA压缩过程和迭代求解过程都特别适合并行计算.数值实验表明, 对于电大尺寸问题, ACA压缩后的矩阵占用的内存远远低于原矩阵, 而预条件的共轭梯度法可以很快收敛.此外该算法在大规模并行时的效率较高.

A parallelized higher order moment method combined with the ACA compressing

The higher order moment method is widely applied in the computational electromagnetics. In order to compute the electrically massive problems, this paper introduces a parallel adaptive cross approximation algorithm(ACA) to accelerate the higher order moment method. At first, the non-uniform rational B-Splines modeling (NURBS) is applied to divide the patches into groups. Then the ACA algorithm is used to compress the impedance matrix in the far zone, which is low in rank. Finally, the conjugate gradient method(CG) combined with the sparse pattern approximate inverse preconditioning(SPAI) is used to solve the matrix equation. Both the ACA compressing and the CG method are suitable for parallel computation. Numerical experiments show that the memory of the compressed matrix is much less than that of the original matrix, and the preconditioned CG method converges very fast. Besides, the massively parallel method often has a high efficiency.