A shape calculus based method for a transmission problem with a random interface

DOI10.1016/j.camwa.2015.06.021zbMath1443.65401arXiv1402.6748OpenAlexW1582915135MaRDI QIDQ2006447

Yanyan Li

Publication date: 11 October 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.6748

zbMATH Keywords

boundary integral equationsmoment equationstransmission problemshape derivativespectral discretizationrandom domain

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Structured surfaces and interfaces, coexistent phases (74A50) Waves and radiation in optics and electromagnetic theory (78A40) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items

Hierarchical matrix approximation for the uncertainty quantification of potentials on random domains, Helmholtz Scattering by Random Domains: First-Order Sparse Boundary Element Approximation, Exterior Dirichlet and Neumann problems in domains with random boundaries

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications
• Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs
• Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients
• Boundary integral equations
• Sparse second moment analysis for elliptic problems in stochastic domains
• Sparse finite element methods for operator equations with stochastic data.
• Approximation theory in tensor product spaces
• Sparse tensor product spectral Galerkin BEM for elliptic problems with random input data on a spheroid
• Karhunen-Loève approximation of random fields by generalized fast multipole methods
• Identification of a discontinuous source in the heat equation
• An adaptive stochastic Galerkin method for random elliptic operators
• A polynomial chaos approach to stochastic variational inequalities
• ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S
• Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs
• Numerical Approximation Methods for Elliptic Boundary Value Problems
• A shape calculus analysis for tracking type formulations in electrical impedance tomography
• On output functionals of boundary value problems on stochastic domains
• The domain derivative and two applications in inverse scattering theory
• The determination of a discontinuity in a conductivity from a single boundary measurement
• First order $k$-th moment finite element analysis of nonlinear operator equations with stochastic data
• First order second moment analysis for stochastic interface problems based on low-rank approximation
• Abstract Sensitivity Analysis for Nonlinear Equations and Applications
• Boundary Element Methods
• A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data