A fourth–order orthogonal spline collocation method for two‐dimensional Helmholtz problems with interfaces

Abstract

AbstractOrthogonal spline collocation is implemented for the numerical solution of two‐dimensional Helmholtz problems with discontinuous coefficients in the unit square. A matrix decomposition algorithm is used to solve the collocation matrix system at a cost of O(N2 log N) on an N × N partition of the unit square. The results of numerical experiments demonstrate the efficacy of this approach, exhibiting optimal global estimates in various norms and superconvergence phenomena for a broad spectrum of wave numbers.