Exact nonreflecting boundary conditions for exterior wave equation problems
Exact nonreflecting boundary conditions for exterior wave equation problems
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DOI：
10.2298/pim1410103f
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
S. Falletta;G. Monegato
中科院分区：
文献类型：
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作者：
S. Falletta;G. Monegato
我们考虑定义在有界二维空间域外部的经典波动方程问题，可能具有远场源。我们在时域和频域都考虑这个问题。对于它的解，我们提出将边界积分方程（BIE）与它联系起来，边界积分方程定义在感兴趣区域周围的人工边界上。这个边界条件对于传出和传入的波都是不反射的（或透明的），它不一定要包括问题基准支持。问题的物理域甚至可以是一个多域，由几个不相交的域的并定义。这些域可以是凸域，也可以是非凸域。这种透明边界条件被施加于所选的人工边界上；因此，它的（空间配置）离散化可以与（空间）有限差分或有限元方法相结合来求解相关的偏微分方程问题。在时域情况下，还使用了经典的（显式或隐式）时间积分器。我们提出了BIE离散化的一致性结果和我们进行的密集数值测试的样本。
We consider the classical wave equation problem defined on the exterior of a bounded 2D space domain, possibly having far field sources. We consider this problem in the time domain, but also in the frequency domain. For its solution we propose to associate with it a boundary integral equation (BIE) defined on an artificial boundary surrounding the region of interest. This boundary condition is nonreflecting (or transparent) for both outgoing and incoming waves and it does not have to include necessarily the problem datum supports. The problem physical domain can even be a multi-domain, defined by the union of several disjoint domains. These domains can be convex or nonconvex. This transparent boundary condition is imposed pointwise on the chosen artificial boundary; therefore, its (space collocation) discretization can be coupled with a (space) finite difference or finite element method for the associated PDE problem. In the time-domain case, a classical (explicit or implicit) time integrator is also used. We present a consistency result for the BIE discretization and a sample of the intensive numerical testing we have performed.