A Fast Algorithm for Quadrature by Expansion in Three Dimensions
This work provides a rigorous and efficient algorithm for singular kernel evaluation in 3D, benefiting computational scientists in electromagnetics, acoustics, and fluid dynamics.
The paper presents an accelerated quadrature scheme combining Quadrature by Expansion (QBX) with a modified Fast Multipole Method (FMM) for evaluating layer potentials in 3D, achieving high order accuracy and scalability. Numerical experiments on Laplace and Helmholtz equations demonstrate accuracy and performance.
This paper presents an accelerated quadrature scheme for the evaluation of layer potentials in three dimensions. Our scheme combines a generic, high order quadrature method for singular kernels called Quadrature by Expansion (QBX) with a modified version of the Fast Multipole Method (FMM). Our scheme extends a recently developed formulation of the FMM for QBX in two dimensions, which, in that setting, achieves mathematically rigorous error and running time bounds. In addition to generalization to three dimensions, we highlight some algorithmic and mathematical opportunities for improved performance and stability. Lastly, we give numerical evidence supporting the accuracy, performance, and scalability of the algorithm through a series of experiments involving the Laplace and Helmholtz equations.