A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
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DOI：
10.1016/j.jcp.2006.03.021
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发表时间：
2006-11
期刊：
影响因子：
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通讯作者：
Lexing Ying;G. Biros;D. Zorin
中科院分区：
文献类型：
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作者：
Lexing Ying;G. Biros;D. Zorin
给出了光滑边界域上三维椭圆边值问题的高阶边界积分方程求解器。我们使用Nyström的方法进行离散化，并将其与边界积分中出现的奇异核的特殊正交规则相结合。本文方法的总体渐近复杂度为O(N3/2)，其中N为域边界上离散化点的个数，对应于均匀抽样评价点个数中的线性复杂度。采用与核无关的快速求和算法来加速离散积分算子的求值。我们描述了一种高阶精确的方法，用于计算区域内任意点的解，包括靠近区域边界的点。我们演示了如何将我们的求解器与规则网格谱求解器相结合，应用于具有分布式源的问题。我们给出了Stokes、Navier和Poisson问题的数值结果。
We present a high-order boundary integral equation solver for 3D elliptic boundary value problems on domains with smooth boundaries. We use Nyström’s method for discretization, and combine it with special quadrature rules for the singular kernels that appear in the boundary integrals. The overall asymptotic complexity of our method is O(N3/2), where N is the number of discretization points on the boundary of the domain, and corresponds to linear complexity in the number of uniformly sampled evaluation points. A kernel-independent fast summation algorithm is used to accelerate the evaluation of the discretized integral operators. We describe a high-order accurate method for evaluating the solution at arbitrary points inside the domain, including points close to the domain boundary. We demonstrate how our solver, combined with a regular-grid spectral solver, can be applied to problems with distributed sources. We present numerical results for the Stokes, Navier, and Poisson problems.