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**Harvard**

Winges, J. och Rylander, T. (2016) *Higher-order brick-tetrahedron hybrid method for Maxwell's equations in time domain*.

** BibTeX **

@article{

Winges2016,

author={Winges, Johan and Rylander, Thomas},

title={Higher-order brick-tetrahedron hybrid method for Maxwell's equations in time domain},

journal={Journal of Computational Physics},

issn={0021-9991},

volume={321},

pages={698-707},

abstract={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.},

year={2016},

keywords={Brick-tetrahedron hybridization; Explicit-implicit time-stepping; Finite element method; Higher-order method; Maxwell's equations; Nitsche's method},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 239187

A1 Winges, Johan

A1 Rylander, Thomas

T1 Higher-order brick-tetrahedron hybrid method for Maxwell's equations in time domain

YR 2016

JF Journal of Computational Physics

SN 0021-9991

VO 321

SP 698

OP 707

AB 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.

LA eng

DO 10.1016/j.jcp.2016.05.063

LK http://dx.doi.org/10.1016/j.jcp.2016.05.063

OL 30