7 papers · 1 filter
Robust spectral preconditioning for high-Péclet number convection-diffusion
Lukas Holbach, Peter Bastian, Robert Scheichl
We introduce a two-level hybrid restricted additive Schwarz (RAS) preconditioner for heterogeneous steady-state convection-diffusion equations at high Péclet numbers. Our construc…
Multigrid Monte Carlo Revisited: Theory and Bayesian Inference
Yoshihito Kazashi, Eike H. Müller, Robert Scheichl
Gaussian random fields play an important role in many areas of science and engineering. In practice, they are often simulated by sampling from a high-dimensional multivariate norma…
Exploiting Inexact Computations in Multilevel Monte Carlo and Other Sampling Methods
Josef MartÃnek, Erin Carson, Robert Scheichl
Multilevel sampling methods, such as multilevel and multifidelity Monte Carlo, multilevel stochastic collocation, or delayed acceptance Markov chain Monte Carlo, have become standa…
Optimal Spectral Approximation in the Overlaps for Generalized Finite Element Methods
Christian Alber, Peter Bastian, Moritz Hauck +1
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approxim…
A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems
Niklas Baumgarten, Robert Kutri, Robert Scheichl
We present a high-performance budgeted multi-level Monte Carlo method for estimates on the entire spatial domain of multi-PDE problems with random input data. The method is designe…
Two-level Restricted Additive Schwarz preconditioner based on Multiscale Spectral Generalized FEM for Heterogeneous Helmholtz Problems
Chupeng Ma, Christian Alber, Robert Scheichl +1
We present and analyze a two-level restricted additive Schwarz (RAS) preconditioner for heterogeneous Helmholtz problems, based on a multiscale spectral generalized finite element…