Boundary Value Problems (BVPs) are ubiquitous in scientific and engineering applications. The Boundary Integral Equation Method is a robust and accurate method for solving BVPs, which has the great advantage of dimensionality reduction: all of the unknowns reside on the boundary surface instead of in its enclosing volume. A key challenge when solving integral equations is that special quadrature methods are required to discretize the underlying singular and near-singular integral operators. Accurate discretization of these operators is of essential importance in problems that involve close interacting components. In this talk, we present a simple singular quadrature method that is based on the trapezoidal rule with error corrections. This quadrature method is high-order accurate, fast, robust, and easy to extend to a variety of applications.
