Stability and convergence of collocation schemes for retarded potential integral equations
Stability and convergence of collocation schemes for retarded potential integral equations
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DOI：
10.1137/s0036142901395321
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发表时间：
2004-01-01
影响因子：
2.9
通讯作者：
Duncan, DB
中科院分区：
文献类型：
--
作者：
Davies, PJ;Duncan, DB
瞬态散射问题的时域边界积分公式涉及延迟势积分方程。以数值方式求解此类方程既复杂又需要大量计算，而且数值方法通常被证明是不稳定的。配置方案比完整的有限元公式更容易实现，但对其稳定性和收敛性似乎知之甚少。在这里，我们推导并分析了瞬态声散射单层方程的一些新的稳定配置方案，并使用（空间）傅里叶和（时间）拉普拉斯变换技术来证明这种稳定方案是二阶收敛的。
Time domain boundary integral formulations of transient scattering problems involve retarded potential integral equations. Solving such equations numerically is both complicated and computationally intensive, and numerical methods often prove to be unstable. Collocation schemes are easier to implement than full finite element formulations, but little appears to be known about their stability and convergence. Here we derive and analyze some new stable collocation schemes for the single layer equation for transient acoustic scattering, and use ( spatial) Fourier and ( temporal) Laplace transform techniques to demonstrate that such stable schemes are second order convergent.