High-Order Close Evaluation of Laplace Layer Potentials: A Differential Geometric Approach
High-Order Close Evaluation of Laplace Layer Potentials: A Differential Geometric Approach
This paper presents a new approach for solving the close evaluation problem in three dimensions, commonly encountered while solving linear elliptic partial differential equations via potential theory. The goal is to evaluate layer potentials close to the boundary over which they are defined. The approach introduced here converts these nearly …