79 citations · 258 across the 61 of their papers we have counts for
46 papers · 1 filter
Efficient localised model reduction for multiscale PDEs via Grassmannian interpolation
Christian Alber, Markus Bachmayr, Robert Scheichl +1
Multiscale, parameter-dependent partial differential equations (PDEs) pose severe computational challenges due to strong coefficient heterogeneity and high-dimensional parameter sp…
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 construct…
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…
Exploiting Inexact Computations in Multilevel Monte Carlo and Other Sampling Methods
Josef Martínek, 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…
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…