A High-Order Close Evaluation Scheme of Laplace and Helmholtz Layer Potentials in 3D

We present an efficient high-order discretization scheme for the evaluation of Laplace and Helmholtz layer potentials on smooth surfaces in three dimensions. The scheme is panel based and applies an analytical surface to line integral conversion on each panel to evaluate single layer, double layer, and their normal derivatives accurately. A new basis approximation scheme tailed for these layer potential kernels is proposed. Both nearly singular and singular cases are supported via a unified recursive framework. The Laplace part of the scheme is joint work with Shravan Veerapaneni, and the Helmholtz part is joint work with Shidong Jiang.