IEEE Transactions on Microwave Theory and Techniques · 1981 · 75 citations · 7 references
ComputingElectrical EngineeringPhysicsComputational ElectromagneticsElectromagneticsElectromagnetismConvergence AnalysisError EstimationFinite Difference MethodsFinite Difference Time Domain AnalysisMaxwell's EquationsTime IntegrationElectromagnetic Field SolverElectromagnetic Field TheoryFinite Difference ApproximationFinite Difference ModelingFinite Difference SchemesFinite Difference Solution Of Partial Differential EquationsSingularity TreatmentTruncation Error
When the electromagnetic-field equations are solved in a region with a corner, singularities in the field or in its spatial derivatives will be present at these corners. These singularities cause the load truncation error in a finite-difference approximation of the field equations to be unbounded. In this paper it is shown that failing to take these singularities into account leads to large errors in the finite-difference solution of the time-domain electromagnetic-field equations. A simple method is described to account for these singularities while retaining the simplicity of the finite-difference formulation. Numerical results are given that demonstrate the accuracy obtained when our technique is used.
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