摘要 陈志明等针对求解时谐声波散射问题提出了波源转移区域分解算法, 并给出了严格的收敛 性分析. 本文将波源转移区域分解算法推广到求解时谐弹性波散射问题. 我们使用谱元法离散时谐 弹性波方程, 将波源转移区域分解算法作为 GMRES 迭代算法的预条件子去求解离散问题. 数值算 例表明波源转移区域分解算法可以作为常波数或变波数时谐弹性波散射问题的有效预条件子. 对于 常波数问题, 当采用适当高阶谱元格式降低离散误差时, 以波源转移区域分解算法作为预条件子的 GMRES 迭代算法只需要非常少的迭代步数即可收敛. 关键词 Helmholtz 方程 时谐弹性波方程 高频波 谱元法 完美匹配层方法 波源转移 1 引言 本文将文献 [1] 中提出的波源转移区域分解算法推广到如下时谐弹性波问题: 其中 ε 是应变张量, 定义如下: Abstract We extend the source transfer domain decomposition method (STDDM) proposed by Chen et al., in order to solve the time-harmonic

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... elastic wave equation that is discretized using the spectral element method. Some numerical examples are presented, demonstrating that STDDM can be applied as an efficient preconditioner in the preconditioned GMRES method for solving the PML equation of the time-harmonic elastic wave equation, with constant and heterogeneous wave numbers. Regarding the problem with constant wave number, the preconditioned GMRES method converges within just a small number of iterations when the discretization error is reduced by high order spectral elements.