Search results for "shape sensitivity analysis"

showing 2 items of 2 documents

Multi-parameter analysis of the obstacle scattering problem

2022

Abstract We consider the acoustic field scattered by a bounded impenetrable obstacle and we study its dependence upon a certain set of parameters. As usual, the problem is modeled by an exterior Dirichlet problem for the Helmholtz equation Δu + k 2 u = 0. We show that the solution u and its far field pattern u ∞ depend real analytically on the shape of the obstacle, the wave number k, and the Dirichlet datum. We also prove a similar result for the corresponding Dirichlet-to-Neumann map.

integral equationsshape sensitivity analysisassociated exterior Dirichlet problemDirichlet-to-Neumann operatorApplied MathematicsHelmholtz equation; acoustic scattering; associated exterior Dirichlet problem; Dirichlet-to-Neumann operator; shape sensitivity analysis; perturbed domain; integral equationsacoustic scatteringComputer Science ApplicationsTheoretical Computer Scienceperturbed domainMathematics - Analysis of PDEsSettore MAT/05 - Analisi MatematicaSignal ProcessingFOS: Mathematicsacoustic scattering; associated exterior Dirichlet problem; Dirichlet-to-Neumann operator; Helmholtz equation; integral equations; perturbed domain; shape sensitivity analysisHelmholtz equation35J25 35J05 35P25 31B10 45A05Mathematical PhysicsAnalysis of PDEs (math.AP)
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Implementation of sparse forward mode automatic differentiation with application to electromagnetic shape optimization

2011

In this paper, we present the details of a simple lightweight implementation of the so-called sparse forward mode automatic differentiation (AD) in the C++programming language. Our implementation and the well-known ADOL-C tool (which utilizes taping and compression techniques) are used to compute Jacobian matrices of two nonlinear systems of equations from the MINPACK-2 test problem collection. Timings of the computations are presented and discussed. Moreover, we perform the shape sensitivity analysis of a time-harmonic Maxwell equation solver using our implementation and the tapeless mode of ADOL-C, which implements the dense forward mode AD. It is shown that the use of the sparse forward …

muotoherkkyysanalyysishape sensitivity analysismuodon optimointishape optimizationautomatic differentiationautomaattinen derivointi
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