Adaptively enriched coarse space for the discontinuous Galerkin multiscale problems
For computational scientists solving multiscale elliptic PDEs with high contrast, this method offers a robust preconditioner that maintains efficiency regardless of heterogeneity.
The authors propose a two-level overlapping additive Schwarz preconditioner for discontinuous Galerkin methods on highly heterogeneous elliptic problems, using adaptively enriched coarse spaces from generalized eigenvalue problems. Numerical results confirm that the condition number becomes independent of coefficient contrast with sufficient enrichment.
In this paper, we propose a two-level overlapping additive Schwarz domain decomposition preconditioner for the symmetric interior penalty discontinuous Galerkin method for the second order elliptic boundary value problem with highly heterogeneous coefficients. A specific feature of this preconditioner is that it is based on adaptively enriching its coarse space with functions created by solving generalized eigenvalue problems on thin patches covering the subdomain interfaces. It is shown that the condition number of the underlined preconditioned system is independent of the contrast if an adequate number of functions are used to enrich the coarse space. Numerical results are provided to confirm this claim.