We develop a boundary integral equation solver for elliptic partial differential equations on complex 3D 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, hedgehog: a simple extrapolation of the solution along a line to the boundary. We present a series of geometry-processing algorithms required for hedgehog 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.

我们为复杂 3D 几何上的椭圆偏微分方程开发了一个边界积分方程求解器。我们的方法高效、高阶准确并且可以稳健地处理复杂的几何形状。一个关键组成部分是我们的奇异和接近奇异的层电位评估方案，刺猬：沿着一条线到边界的解决方案的简单外推。我们提出了一系列几何处理算法，刺猬在任意几何上的精度保证下高效运行，以及基于正交误差的无迭代启发式的自适应上采样方案。我们通过一系列数值测试验证准确性和性能，并将我们的方法与竞争性本地评估方法进行比较。