Differentiation of Approximate Solutions of the Helmholtz Equation

Abstract

Two procedures are described for accurate derivative computation based on Green's second identity and applicable to approximate solutions of the scalar Helmholtz equation. One applies a technique previously developed for Poisson equation: the k²ϕ term of the Helmholtz operator is transposed to the source side and integrated with the Green's function for the Laplace operator. The second method uses the Green's function for the Helmholtz operator; it is particularly suitable for the homogeneous case. Performance data and analytic verification are given for both methods. These techniques are suited to postprocessing of finite element solutions, or may be applied to other numerical approximate solutions.

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