Investigation of conformal Mappings for the Approximation of Faber Polynomial based Propagators

Time domain dependent exponential integrators for solving Maxwell's equations in an explicit manner can be approximated by the use of Faber polynomial based expansions. The expansion is based on the contour comprising the eigenvalue spectrum of the system matrix, which occurs after performing a spatial discretization onto Maxwell's equations. The contour has a substantial impact on computational efficiency and accuracy as it should comprise the eigenvalue spectrum tightly. Different suitable polygons defining the contour are investigated with respect to these criteria and to their potential for a possible optimization.