Exact integration of polynomial-exponential products with application to wave-based numerical methods

Wave-based numerical methods often require to integrate products of polynomials and exponentials. With quadrature methods, this task can be particularly expensive at high frequencies as large numbers of integration points are required. This paper presents a set of closed-form solutions for the integrals of polynomial-exponential products in two and three dimensions. These results apply to arbitrary polygons in two dimensions, and for arbitrary polygonal surfaces or polyhedral volumes in three dimensions. Quadrature methods are therefore not required for this class of integrals that can be evaluated quickly and exactly