Trefftz discontinuous Galerkin methods for time-harmonic electromagnetic and ultrasound transmission problems

An efficient strategy is described for the solution of time-harmonic electromagnetic and elastic wave problems. The strategy is based on the framework of the discontinuous Galerkin (DG) method, thereby using approximation bases that are locally conservative. Additionally, in the Trefftz DG method each approximation function satisfies the underlying partial differential equation in each finite element. The Trefftz DG method is similar to the ultra weak variational formulation (UWVF) but the local bases are constructed differently. Electromagnetic wave, eddy current and elastic wave problems are solved in order to analyze the performance of the method. The ultrasonic testing (UT) example is a two-dimensional elastic wave model of the Inconel welding area in reactor vessels.