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Time-integration methods for finite element discretisations of the second-order Maxwell equation

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Sármány, D. and Botchev, M.A. and Vegt van der, J.J.W. (2012) Time-integration methods for finite element discretisations of the second-order Maxwell equation. [Report]

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Abstract:This article deals with time integration for the second-order Maxwell equations with possibly non-zero conductivity in the context of the discontinuous Galerkin finite element method DG-FEM) and the $H(\mathrm{curl})$-conforming FEM. For the spatial discretisation, hierarchic $H(\mathrm{curl})$-conforming basis functions are used up to polynomial order $p=3$ over tetrahedral meshes, meaning fourth-order convergence rate. A high-order polynomial basis often warrants the use of high-order time-integration schemes, but many well-known high-order schemes may suffer from a severe time-step stability restriction owing to the conductivity term. We investigate several possible time-integration methods from the point of view of accuracy, stability and computational work. We also carry out a numerical Fourier analysis to study the dispersion and dissipation properties of the semi-discrete DG-FEM scheme as well as the fully-discrete schemes with several of the time-integration methods. The dispersion and dissipation properties of the spatial discretisation and those of the time-integration methods are investigated separately, providing additional insight into the two discretisation steps.
Item Type:Report
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:
Link to this item:http://purl.utwente.nl/publications/79682
Publisher URL:http://www.math.utwente.nl/publications
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