高阶稠密矩阵的并行求逆与应用

Parallel Highorder Dense Matrix Inversion and Applications

采用基于列交换的Ｇａｕｓｓ－Ｊｏｒｄａｎ并行算法来解决空气动力学中超音速高阶面元法的稠密矩阵求逆问题，该方法采取了块循环数据分配方式，尤其对超立方体结构的并行机系统来说具有通讯优势。在４台ＳＧＩ工作站构成的２×２网格上进行的实验表明，对秩为１０００左右的矩阵可得到５７％～６４％的效率。

In this paper we propose GaussJordan algorithm using column interchanges for computing a highorder dense matrix inverse produced by the highorder panel method in aerodynamics. The algorithm implements the block cyclic data distribution,which especially has communication advantages for the hypercube network.Results are achieved when running this program on the 4 SGI workstations configured as a 2×2 processor grid. It shows that 57%～64% efficiency can be gained when solving a matrix is about 1000 order.