Covariance regularity and \(\mathcal {H}\)-matrix approximation for rough random fields

DOI10.1007/s00211-016-0825-yzbMath1362.65124OpenAlexW1599063302MaRDI QIDQ522237

Christoph Schwab, Jürgen Dölz, Helmut Harbrecht

Publication date: 13 April 2017

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-016-0825-y

zbMATH Keywords

linear operator equationRiemannian \(n\)-manifoldelliptic pseudodifferential operator\(\mathcal {H}\)-matrix approximationcovariance regularityrough random fields

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Boundary value problems for PDEs with pseudodifferential operators (35S15) Boundary value problems on manifolds (58J32)

Related Items (16)

Caccioppoli-type estimates and \(\mathcal{H}\)-matrix approximations to inverses for FEM-BEM couplings ⋮ A fast direct solver for nonlocal operators in wavelet coordinates ⋮ Low-Rank Tensor Approximation for High-Order Correlation Functions of Gaussian Random Fields ⋮ \({\mathcal{H}} \)-matrix approximability of inverses of FEM matrices for the time-harmonic Maxwell equations ⋮ Exponential meshes and \(\mathcal{H}\)-matrices ⋮ Hierarchical matrix approximation for the uncertainty quantification of potentials on random domains ⋮ Multilevel approximation of Gaussian random fields: Fast simulation ⋮ On Uncertainty Quantification of Eigenvalues and Eigenspaces with Higher Multiplicity ⋮ On the Best Approximation of the Hierarchical Matrix Product ⋮ QMC integration for lognormal-parametric, elliptic PDEs: local supports and product weights ⋮ Helmholtz Scattering by Random Domains: First-Order Sparse Boundary Element Approximation ⋮ A Higher Order Perturbation Approach for Electromagnetic Scattering Problems on Random Domains ⋮ \({\mathscr{H}} \)-matrix approximability of inverses of discretizations of the fractional Laplacian ⋮ Iterative algorithms for the post-processing of high-dimensional data ⋮ Multilevel Quasi Monte Carlo Methods for Elliptic PDEs with Random Field Coefficients via Fast White Noise Sampling ⋮ $\mathcal{H}$-Matrix Based Second Moment Analysis for Rough Random Fields and Finite Element Discretizations

Uses Software

• hlib
• ALEA

Cites Work

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