Optimal Absorption of Acoustic Waves by a Boundary

DOI10.1137/20M1327239zbMath1459.35121arXiv2003.13250MaRDI QIDQ4965184

T. P. K. Nguyen, Anna Rozanova-Pierrat, Frédéric Magoulès, Pascal Omnes

Publication date: 26 February 2021

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.13250

zbMATH Keywords

wave propagationHelmholtz equationshape optimizationRobin boundary conditionsound absorptionabsorbing wall

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Linear equations (linear algebraic aspects) (15A06) First-order hyperbolic systems (35L40)

Related Items

Dirichlet boundary valued problems for linear and nonlinear wave equations on arbitrary and fractal domains ⋮ Boundary value problems on non-Lipschitz uniform domains: stability, compactness and the existence of optimal shapes ⋮ Non-Lipschitz Uniform Domain Shape Optimization in Linear Acoustics ⋮ Mixed boundary valued problems for linear and nonlinear wave equations in domains with fractal boundaries

Cites Work

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• Shape optimization problems with Robin conditions on the free boundary
• A BE-based shape optimization method enhanced by topological derivative for sound scattering problems
• Robin boundary condition on scale irregular fractals
• Optimal design of the damping set for the stabilization of the wave equation
• Asymptotics for mixed Dirichlet-Robin problems in irregular domains
• The trace of Sobolev-Slobodeckij spaces on Lipschitz domains
• The trace to the boundary of Sobolev spaces on a snowflake
• On the existence of a solution in a domain identification problem
• Boundary value problems and Brownian motion on fractals
• Shape optimization for noise radiation problems.
• A transmission problem with a fractal interface.
• Dirichlet-to-Neumann or Poincaré-Steklov operator on fractals described by \(d\)-sets
• Sobolev embeddings, extensions and measure density condition
• Variation and optimization of formes. A geometric analysis
• Optimal Internal Dissipation of a Damped Wave Equation Using a Topological Approach
• An optimized Schwarz method with two-sided Robin transmission conditions for the Helmholtz equation
• Optimization of a photocell
• The rate at which energy decays in a damped String
• The dual of Besov spaces on fractals
• The Spectrum of the Damped Wave Operator for a Bounded Domain inR²
• Magnetostatic Problems in Fractal Domains
• Shape Optimization of Shell Structure Acoustics