Higher-order brick-tetrahedron hybrid method for Maxwell's equations in time domain
Artikel i vetenskaplig tidskrift, 2016

We present a higher-order brick-tetrahedron hybrid method for Maxwell's equations in time domain. Brick-shaped elements are used for large homogeneous parts of the computational domain, where we exploit mass-lumping and explicit time-stepping. In regions with complex geometry, we use an unstructured mesh of tetrahedrons that share an interface with the brick-shaped elements and, at the interface, tangential continuity of the electric field is imposed in the weak sense by means of Nitsche's method. Implicit time-stepping is used for the tetrahedrons together with the interface. For cavity resonators, the hybrid method reproduces the lowest non-zero eigenvalues with correct multiplicity and, for geometries without field singularities from sharp corners or edges, the numerical eigenvalues converge towards the analytical result with an error that is approximately proportional to h^2p, where h is the cell size and p is the polynomial order of the elements. For a rectangular waveguide, a layer of tetrahedrons embedded in a grid of brick-shaped elements yields a low reflection coefficient that scales approximately as h^2p. Finally, we demonstrate hybrid time-stepping for a lossless closed cavity resonator, where the time-domain response is computed for 300,000 time steps without any signs of instabilities.

Higher-order method

Nitsche's method

Brick-tetrahedron hybridization

Maxwell's equations

Finite element method

Explicit-implicit time-stepping

Författare

JOHAN WINGES

Signaler och system, Signalbehandling och medicinsk teknik, Signalbehandling

Thomas Rylander

Signaler och system, Signalbehandling och medicinsk teknik, Signalbehandling

Journal of Computational Physics

0021-9991 (ISSN) 1090-2716 (eISSN)

Vol. 321 698-707

Fundament

Grundläggande vetenskaper

Infrastruktur

C3SE (Chalmers Centre for Computational Science and Engineering)

Ämneskategorier

Elektroteknik och elektronik

Signalbehandling

DOI

10.1016/j.jcp.2016.05.063