Expansion of random boundary excitations for elliptic PDEs

DOI10.1515/mcma.2007.022zbMath1158.60027OpenAlexW2003849651MaRDI QIDQ5443553

K. K. Sabel'fel'd

Publication date: 21 February 2008

Published in: Monte Carlo Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/mcma.2007.022

zbMATH Keywords

white noiseLaplacePoisson integral formulageneralized random processesKarhunen- Lòev expansionrandom boundary excitations

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items

Simulation of Gaussian random field in a ball, Stochastic analysis of an elastic 3D half-space respond to random boundary displacements: exact results and Karhunen-Loève expansion, Influence functions, integral formulas, and explicit solutions for thermoelastic spherical wedges, Elastic half-plane under random displacement excitations on the boundary, Stokes flows under random boundary velocity excitations, On solving stochastic differential equations, New Poisson's type integral formula for thermoelastic half-space, Elastostatics of a half-plane under random boundary excitations

Cites Work

• Unnamed Item
• On the hidden beauty of the proper orthogonal decomposition
• Eigenvalues of positive definite integral operators on unbounded intervals
• A multiscale stochastic finite element method on elliptic problems involving uncertainties
• Representation of kernels of integral operators by bilinear series
• The analysis of the Neumann and the oblique derivative problem: the theory of regularization and its stochastic version.
• Multidimensional reaction-diffusion equations with white noise boundary perturbations
• Comparative analysis of multiscale Gaussian random field simulation algorithms
• Convergence study of the truncated Karhunen–Loeve expansion for simulation of stochastic processes
• Random Walk on Fixed Spheres for Laplace and Lamé equations
• Stochastic Spectral and Fourier-Wavelet Methods for Vector Gaussian Random Fields