6533b82afe1ef96bd128c3fe
RESEARCH PRODUCT
A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional
Francesco GarganoVincenzo SciaccaGiulio Ciraolosubject
Physics and Astronomy (miscellaneous)Helmholtz equationBoundary (topology)FOS: Physical sciencesElectric-field integral equationVolume integralMathematics - Analysis of PDEsSettore MAT/05 - Analisi MatematicaConvergence (routing)Refraction (sound)FOS: MathematicsBoundary value problemHelmholtz equationSettore MAT/07 - Fisica MatematicaMathematical PhysicsMathematicsNumerical AnalysisApplied MathematicsMathematical analysisTransparent boundary conditionMinimization of integral functionalsMathematical Physics (math-ph)Computer Science ApplicationsComputational MathematicsModeling and SimulationConstant (mathematics)Analysis of PDEs (math.AP)description
Abstract We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-11-17 |