6 papers
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…
Multiscale Spectral Generalized Finite Element Methods for Discontinuous Galerkin Schemes
Christian Alber, Lukas Holbach
We propose a multiscale spectral generalized finite element method (MS-GFEM) for discontinuous Galerkin (DG) discretizations. The method builds local approximations on overlapping…
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…
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…
A Mixed Multiscale Spectral Generalized Finite Element Method
Christian Alber, Chupeng Ma, Robert Scheichl
We present a multiscale mixed finite element method for solving second order elliptic equations with general -coefficients arising from flow in highly heterogeneous por…
Wavenumber explicit convergence of a multiscale generalized finite element method for heterogeneous Helmholtz problems
Chupeng Ma, Christian Alber, Robert Scheichl
In this paper, a generalized finite element method (GFEM) with optimal local approximation spaces for solving high-frequency heterogeneous Helmholtz problems is systematically stud…