UNCONDITIONALLY STABLE TIME STEPPING METHOD FOR MIXED FINITE ELEMENT MAXWELL SOLVERS

cient Finite Element Solvers for the Maxwell Equationsin the Frequency

The present paper shows that certain instabilities encountered with Nedelec-type nite element implementations of the vector wave equation can be eliminated by a family of Lagrange multiplier methods. The considered approaches can be interpreted as coupled vector and scalar potential methods, including an ungauged formulation. We advocate the latter form for use with iterative solvers. We discus...

The Gautschi time stepping scheme for edge finite element discretization of the Maxwell equations

For the time integration of edge finite element discretizations of the three-dimensional Maxwell equations, we consider the Gautschi cosine scheme where the action of the matrix function is approximated by a Krylov subspace method. First, for the spacediscretized edge finite element Maxwell equations, the dispersion error of this scheme is analyzed in detail and compared to that of two conventi...

The Gautschi time stepping scheme for edge finite element discretizations of the Maxwell equations

For the time integration of edge finite element discretizations of the three-dimensional Maxwell equations, we consider the Gautschi cosine scheme where the action of the matrix function is approximated by a Krylov subspace method. First, for the spacediscretized edge finite element Maxwell equations, the dispersion error of this scheme is analyzed in detail and compared to that of two conventi...

Unconditionally stable algorithms to solve the time-dependent Maxwell equations.

Based on the Suzuki product-formula approach, we construct a family of unconditionally stable algorithms to solve the time-dependent Maxwell equations. We describe a practical implementation of these algorithms for one-, two-, and three-dimensional systems with spatially varying permittivity and permeability. The salient features of the algorithms are illustrated by computing selected eigenmode...

Unconditionally stable semi-implicit scheme for the monolithic FSI Finite Element method: application to hemodynamics