An asynchronous spacetime discontinuous Galerkin finite element method for time domain electromagnetics

We present an asynchronous spacetime discontinuous Galerkin (aSDG) method for time domain electromagnetics in which space and time are directly discretized. By using differential forms we express Maxwell's equations and consequently their discontinuous Galerkin discretization for arbitrary doma...

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Bibliographic Details
Published in:Journal of computational physics 2017-12, Vol.351, p.121-144
Main Authors: Abedi, Reza, Mudaliar, Saba
Format: Article
Language:English
Subjects:
Basis functions
Boundary element method
Computational physics
Computer simulation
Differential equations
Differential forms
Discontinuous Galerkin
Discretization
Electromagnetics
Energy dissipation
Finite element analysis
Finite element method
Galerkin method
Mathematical analysis
Maxwell's equations
Simulation
Spacetime
Time domain
Time domain analysis
Unstructured grids (mathematics)
Wave dispersion
Wave fronts
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Summary:We present an asynchronous spacetime discontinuous Galerkin (aSDG) method for time domain electromagnetics in which space and time are directly discretized. By using differential forms we express Maxwell's equations and consequently their discontinuous Galerkin discretization for arbitrary domains in spacetime. The elements are discretized with electric and magnetic basis functions that are discontinuous across all inter-element boundaries and can have arbitrary high and per element spacetime orders. When restricted to unstructured grids that satisfy a specific causality constraint, the method has a local and asynchronous solution procedure with linear solution complexity in terms of the number of elements. We numerically investigate the convergence properties of the method for 1D to 3D uniform grids for energy dissipation, an error relative to the exact solution, and von Neumann dissipation and dispersion errors. Two dimensional simulations demonstrate the effectiveness of the method in resolving sharp wave fronts. •Formulate all Maxwell's equations and spacetime fluxes in differential forms.•Formulate a time domain discontinuous Galerkin method for electromagnetics.•Achieve linear solution complexity and an asynchronous solution structure.•L2, energy, and von Neumann dispersion numerical error analyses.•Numerical results for 2D wave scattering problems with strong discontinuity.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2017.09.001