Solving Maxwell's equations using the ultra weak variational formulation
This paper is concerned with the development and validation of the ultra weak variational formulation (UWVF) for Maxwell's equations. This method is based on a volume mesh and uses plane wave solutions of the Maxwell system on each element in the grid in the discretization procedure. It is also shown that the method can solve scattering problems such as scattering in a layered medium and scattering from a sphere where exact solutions are available. Potential future developments of the UWVF include: (i) theoretical estimates for the error and condition number for the UWVF; (ii) reduction in the number of directions in the plane wave basis; (iii) a better parametrization of surfaces and interfaces in the computational mesh; (iv) to improve the accuracy of the UWVF near singularities.
scientific article; zbMATH DE number 5156474