A new discontinuous galerkin solution methodology for solving helmholtz problems

Abstract eng:
We propose a new solution methodology for solving Helmholtz problems in the midand high-frequency regime. The proposed method falls in the category of the discontinuous Galerkin methods (DGM) but distinguishes itself from the existing formulations by (a) The discrete spaces for the primal variable (the field) and the dual variable (the Lagrange multiplier) can be chosen independently, and (b) The resulting algebraic linear system is associated with a hermitian positive definite matrix. The latter property allows the use of robust and efficient existing algorithms such as the conjugate gradient. Results will be presented to highlight the salient features of the proposed formulation.

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