Search results for "Minimization of integral functional"

showing 3 items of 3 documents

A spectral approach to a constrained optimization problem for the Helmholtz equation in unbounded domains

2014

We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains (Ciraolo et al. in J Comput Phys 246:78–95, 2013) where the index of refraction is not required to be constant at infinity. The approach is based on the minimization of an integral functional, which arises from an integral formulation of the radiation condition at infinity. In this paper, we implement a Fourier–Chebyshev collocation method to study some convergence properties of the numerical algorithm; in particular, we give numerical evidence of some convergence estimates available in the literature (Ciraolo in Helmholtz equation in unbou…

Helmholtz equationApplied MathematicsMathematical analysisTransparent boundary conditionComputational mathematicsFOS: Physical sciencesNumerical Analysis (math.NA)Mathematical Physics (math-ph)Electric-field integral equationComputational MathematicsCollocation methodConvergence (routing)Computational MathematicFOS: MathematicsMathematics - Numerical AnalysisBoundary value problemHelmholtz equationMinimization of integral functionalSpectral methodSpectral methodConstant (mathematics)Mathematical PhysicsMathematics
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Helmholtz equation in unbounded domains: some convergence results for a constrained optimization problem

2016

We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we prove some estimates on the rate of convergence to the exact solution.

Optimization problemHelmholtz equationDomain (software engineering)Constrained optimization problemExact solutions in general relativityMathematics - Analysis of PDEsRate of convergenceBounded functionConvergence (routing)FOS: MathematicsHelmholtz equation Transparent boundary conditions Minimization of integral functionals.Applied mathematicsMathematicsAnalysis of PDEs (math.AP)
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A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional

2012

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.

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)
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