Large deformation shape uncertainty quantification in acoustic scattering

DOI10.1007/s10444-018-9594-8zbMath1402.35321OpenAlexW2792017407MaRDI QIDQ1633009

Christoph Schwab, Ralf Hiptmair, Claudia Schillings, Laura Scarabosio

Publication date: 18 December 2018

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-018-9594-8

zbMATH Keywords

Helmholtz equationhigh-dimensional approximationuncertainty quantificationstochastic parametrizationrandom interfacedimension-adaptive Smolyak quadrature

Mathematics Subject Classification ID

Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs (65N75) Particle methods and lattice-gas methods (76M28) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Hydro- and aero-acoustics (76Q05) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35)

Related Items

Least-squares Padé approximation of parametric and stochastic Helmholtz maps ⋮ Inverse Source Problems for the Stochastic Wave Equations: Far-Field Patterns ⋮ Extrapolated Polynomial Lattice Rule Integration in Computational Uncertainty Quantification ⋮ Deep Neural Network Surrogates for Nonsmooth Quantities of Interest in Shape Uncertainty Quantification ⋮ Explicit bounds for the high-frequency time-harmonic Maxwell equations in heterogeneous media ⋮ Polynomial Collocation for Handling an Inaccurately Known Measurement Configuration in Electrical Impedance Tomography ⋮ Wavenumber-Explicit Parametric Holomorphy of Helmholtz Solutions in the Context of Uncertainty Quantification ⋮ Multilevel domain uncertainty quantification in computational electromagnetics ⋮ Uncertainty quantification for random domains using periodic random variables ⋮ Convergence rates of high dimensional Smolyak quadrature ⋮ An Adaptive Stochastic Galerkin Tensor Train Discretization for Randomly Perturbed Domains ⋮ Shape Holomorphy of the Stationary Navier--Stokes Equations ⋮ Acoustic transmission problems: Wavenumber-explicit bounds and resonance-free regions ⋮ Rapid computation of far-field statistics for random obstacle scattering ⋮ Non-intrusive double-greedy parametric model reduction by interpolation of frequency-domain rational surrogates ⋮ Low-dimensional spatial embedding method for shape uncertainty quantification in acoustic scattering by 2D star shaped obstacles ⋮ A note on the domain mapping method with rough diffusion coefficients ⋮ Stochastic phase-field modeling of brittle fracture: computing multiple crack patterns and their probabilities ⋮ A stochastic collocation approach for parabolic PDEs with random domain deformations ⋮ Efficient Distribution Estimation and Uncertainty Quantification for Elliptic Problems on Domains with Stochastic Boundaries ⋮ Mesh quality preserving shape optimization using nonlinear extension operators ⋮ The Helmholtz Equation in Random Media: Well-Posedness and A Priori Bounds ⋮ Shape holomorphy of the Calderón projector for the Laplacian in \(\mathbb{R}^2\) ⋮ Isogeometric multilevel quadrature for forward and inverse random acoustic scattering ⋮ A Continuous Perspective on Shape Optimization via Domain Transformations ⋮ Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM ⋮ Linear Parabolic Problems in Random Moving Domains ⋮ Tensor train based isogeometric analysis for PDE approximation on parameter dependent geometries ⋮ CAS4DL: Christoffel adaptive sampling for function approximation via deep learning

Uses Software

• ALEA
• gMLQMC

Cites Work

• Unnamed Item
• Unnamed Item
• On tensor product approximation of analytic functions
• Analysis of the domain mapping method for elliptic diffusion problems on random domains
• High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs
• Adaptive stochastic Galerkin FEM
• Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs
• Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs
• Sparse second moment analysis for elliptic problems in stochastic domains
• Optimal a priori estimates for higher order finite elements for elliptic interface problems
• A perfectly matched layer for the absorption of electromagnetic waves
• On the existence and convergence of the solution of PML equations
• Dimension-adaptive tensor-product quadrature
• Elliptic partial differential equations of second order
• A level-set method for shape optimization.
• On the Lebesgue constant of Leja sequences for the complex unit disk and of their real projection
• Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations
• A fictitious domain approach to the numerical solution of PDEs in stochastic domains
• Stochastic analysis of transport in tubes with rough walls
• An extended stochastic finite element method for solving stochastic partial differential equations on random domains
• Lagrange interpolation at real projections of Leja sequences for the unit disk
• Sparse, adaptive Smolyak quadratures for Bayesian inverse problems
• Computational Higher Order Quasi-Monte Carlo Integration
• Multilevel higher-order quasi-Monte Carlo Bayesian estimation
• Sparse Tensor Discretization of Elliptic sPDEs
• ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S
• Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs
• Higher-Order Quasi-Monte Carlo for Bayesian Shape Inversion
• Numerical Methods for Differential Equations in Random Domains
• Computing quantities of interest for random domains with second order shape sensitivity analysis
• The Perfectly Matched Layer in Curvilinear Coordinates
• The Adaptive Computation of Far-Field Patterns by A Posteriori Error Estimation of Linear Functionals
• Electromagnetic wave scattering by random surfaces: Shape holomorphy
• Shape Holomorphy of the Stationary Navier--Stokes Equations
• Sparsity in Bayesian inversion of parametric operator equations
• First order second moment analysis for stochastic interface problems based on low-rank approximation
• The Mathematical Theory of Finite Element Methods
• High-Order Collocation Methods for Differential Equations with Random Inputs
• A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
• Inverse acoustic and electromagnetic scattering theory
• Acoustic and electromagnetic equations. Integral representations for harmonic problems
• Moving mesh methods in multiple dimensions based on harmonic maps
• Level set methods: An overview and some recent results