A robust solver for elliptic PDEs in 3D complex geometries

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 A key component our singular near-singular layer potential evaluation scheme, hedgehog: simple extrapolation of the solution along line to boundary. present series geometry-processing algorithms required hedgehog run efficiently with accuracy guarantees arbitrary geometries an adaptive upsampling scheme based iteration-free heuristic quadrature error. validate performance numerical tests compare approach competing local method.