第二类边界积分方程Nyström解的高精度组合方法

A HIGH PRECISION COMBINATION METHOD OF NYSTR?M APPROXIMATIONS FOR SOLVING THE BOUNDARY INTEGRAL EQUATIONS OF THE SECOND KIND

  • 摘要: 第二类边界积分方程常用配置法或Galerkin法计算,主要困难有:计算积分耗去大量机时;离散方程是满阵且不对称,计算量随剖分精细而急剧增加。本文提出Nyström近似解的高精度组合法能有效克服上述困难。组合方法是并行地解m个具有n个不同结点的方程组,对得到的m个内点值取算术平均就得到了组合近似,本文证明组合近似精度几乎与解mn个结点近似方程达到精度同阶,数值结果表明本文方法简单、有效、并且算法高度并行。

     

    Abstract: A high pricision combination method for solving BIE of the second kind is presented. The combination algorithm is as follows:Step 1. Compute the jth(j=1,…,m) Nyström approximate equation with nodes (nj+j)/(mn)i=1n parallelly. Step 2. Compute the jth(j=1,…,m) interior print value by the jth Nyström solution parallelly. Step 3. Compute the average of m interior point values, which is the combination approximation.It can be proved that the precision of the combination approximation is almost same as the precision of Nyström appximation with mn nodes.

     

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