Is Pollution Effect of Finite Difference Schemes Avoidable for Multi-Dimensional Helmholtz Equations with High Wave Numbers? (Communications in Computational Physics, 2018)
This paper presents an approach using the method of separation of variablesapplied to 2D Helmholtz equations in the Cartesian coordinate. The solutionis then computed by a series of solutions resulted from solving a sequence of 1D problems,in which the 1D solutions are computed using pollution free difference schemes.Moreover, non-polluted numerical integration formulae are constructed to handle theintegration due to the forcing term in the inhomogeneous 1D problems. Consequently,the computed solution does not suffer the pollution effect. Another attractive featureof this approach is that a direct method can be effectively applied to solve the tridiagonalmatrix resulted from numerical discretization of the 1D Helmholtz equation. Themethod has been tested to compute 2D Helmholtz solutions simulating electromagneticscattering from an open large cavity and rectangular waveguide.