论文标题
3D复合物几何形状中椭圆pdes的强大求解器
A robust solver for elliptic PDEs in 3D complex geometries
论文作者
论文摘要
我们开发了一个在复合\三几何形状上的椭圆形部分微分方程的边界积分方程求解器。我们的方法是有效，高阶准确且坚固的处理复杂几何形状。一个关键的组成部分是我们的奇异和近乎单位的潜在评估方案\ qbkix：沿线向边界的简单推断溶液。我们提供了\ qbkix有效运行所需的一系列几何处理算法，并根据任意几何形状的准确性保证，并且基于无迭代的启发式启发式误差，可以对任意几何形状和自适应上采样方案进行保证。我们通过一系列数值测试来验证准确性和性能，并将我们的方法与竞争的本地评估方法进行比较。
We develop a boundary integral equation solver for elliptic partial differential equations on complex \threed geometries. Our method is efficient, high-order accurate and robustly handles complex geometries. A key component is our singular and near-singular layer potential evaluation scheme, \qbkix: a simple extrapolation of the solution along a line to the boundary. We present a series of geometry-processing algorithms required for \qbkix to run efficiently with accuracy guarantees on arbitrary geometries and an adaptive upsampling scheme based on a iteration-free heuristic for quadrature error. We validate the accuracy and performance with a series of numerical tests and compare our approach to a competing local evaluation method.
