Parallel numerical solution of the time‐harmonic Maxwell equations in mixed form

Abstract

SUMMARYWe develop a fully scalable parallel implementation of an iterative solver for the time‐harmonic Maxwell equations with vanishing wave numbers. We use a mixed finite element discretization on tetrahedral meshes, based on the lowest order Nédélec finite element pair of the first kind. We apply the block diagonal preconditioning approach of Greif and Schötzau (Numer. Linear Algebra Appl. 2007; 14(4):281–297), and use the nodal auxiliary space preconditioning technique of Hiptmair and Xu (SIAM J. Numer. Anal. 2007; 45(6):2483–2509) as the inner iteration for the shifted curl–curl operator. Algebraic multigrid is employed to solve the resulting sequence of discrete elliptic problems. We demonstrate the performance of our parallel solver on problems with constant and variable coefficients. Our numerical results indicate good scalability with the mesh size on uniform, unstructured, and locally refined meshes. Copyright © 2011 John Wiley & Sons, Ltd.