A numerical study of the classical and penalized LDG method applied to vector Helmholtz equation on three dimensional domains is presented. Using a simple numerical flux based on convex combinations classical rates of convergence can be obtained on unstructured meshes while achieving a substantial reduction of the stencil. The superconvergent behaviour of the auxiliary field is investigated on Cartesian meshes. Numerical experiments also suggest convergence of the method for constant approximations on Cartesian meshes. We explore existing scalable preconditioning techniques adapted to the discontinuous Galerkin framework for the low frequency case. Finally the method is tested on examples arising in practical engineering problems with complex valued electric field.

Se presenta un estudio numérico de un precondicionador para la ecuación vectorial de Helmholtz; el cual se deriva de la técnica del Laplaciano desplazado. Se utiliza una nueva versión del método “Local Discontinuous Galerkin” (LDG) como técnica de discretización espacial. Se valida la escalabilidad del precondicionador mediante una serie de experimentos numéricos en dominios poliédricos y aproximaciones de alto orden en problemas de bajas frecuencias en el caso real.