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On the immersed interface method for solving time-domain Maxwell's equations in materials with curved dielectric
1Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223-0001, USA.
Computer Physics Communications
|September 28, 2011
Summary
This study introduces an enhanced numerical method for simulating Maxwell's equations, improving long-time stability for electromagnetic wave scattering problems with curved interfaces.
Area of Science:
- Computational Electromagnetics
- Numerical Analysis
- Applied Mathematics
Background:
- Accurate numerical simulation of Maxwell's equations is crucial for understanding electromagnetic phenomena.
- Handling curved dielectric interfaces in structured numerical schemes presents a significant challenge.
- Existing methods may suffer from long-time stability issues in time-domain simulations.
Purpose of the Study:
- To develop and validate a novel, accurate numerical scheme for two-dimensional time-domain Maxwell's equations.
- To effectively incorporate curved dielectric interfaces into structured numerical grids.
- To enhance the long-time stability of numerical solutions for electromagnetic wave propagation and scattering.
Main Methods:
- Hybridization of the Immersed Interface Method (IIM) with the Lax-Wendroff scheme.
- Extension of IIM, originally for acoustic wave equations, to Maxwell's equations using a least squares procedure.
- Development of a fully second-order accurate numerical scheme for spatial and temporal discretization.
Main Results:
- The proposed augmented IIM demonstrates significantly improved long-time stability compared to the original IIM.
- Numerical simulations of electromagnetic scattering by a dielectric circular cylinder validate the scheme's accuracy.
- The method effectively handles curved geometries in time-domain simulations of Maxwell's equations.
Conclusions:
- The hybridized IIM with least squares fitting provides a robust and stable numerical solution for Maxwell's equations with curved interfaces.
- This approach offers a significant advancement in the accurate simulation of electromagnetic scattering problems.
- The developed scheme is suitable for long-time simulations in computational electromagnetics.
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