An adaptive multigrid solver for DPG methods with applications in linear acoustics and electromagnetics. (1st April 2021)

• Record Type: Journal Article
• Authors: Petrides, Socratis; Demkowicz, Leszek
• Is Part Of: Computers & mathematics with applications. Volume 87(2021)
• Page Start: 12
• Page End: 26
• Publication Date: 2021-04-01
• Subjects: Preconditioners for high-frequency wave propagation -- hp-adaptivity -- Multigrid methods -- DPG methods; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.01.017
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We propose an adaptive multigrid preconditioning technology for solving linear systems arising from Discontinuous Petrov–Galerkin (DPG) discretizations. Unlike standard multigrid techniques, this preconditioner involves only trace spaces defined on the mesh skeleton, and it is suitable for adaptive hp-meshes. The key point of the construction is the integration of the iterative solver with a fully automatic and reliable mesh refinement process provided by the DPG technology. The efficacy of the solution technique is showcased with numerous examples of linear acoustics and electromagnetic simulations, including simulations in the high-frequency regime, problems which otherwise would be intractable. Finally, we analyze the one-level preconditioner (smoother) for uniform meshes and we demonstrate that theoretical estimates of the condition number of the preconditioned linear system can be derived based on well established theory for self-adjoint positive definite operators.