Scalable multigrid methods for immersed finite element methods and immersed isogeometric analysis

Frits de Prenter (Corresponding author), Clemens Verhoosel, Harald van Brummelen, John Evans, Christian Messe, Joseph Benzaken, Kurt Maute

Research output: Contribution to journalArticleAcademic

11 Downloads (Pure)

Abstract

Ill-conditioning of the system matrix is a well-known complication in immersed finite element methods and trimmed isogeometric analysis. Elements with small intersections with the physical domain yield problematic eigenvalues in the system matrix, which generally degrades efficiency and robustness of iterative solvers. In this contribution we investigate the spectral properties of immersed finite element systems treated by Schwarz-type methods, to establish the suitability of these as smoothers in a multigrid method. Based on this investigation we develop a geometric multigrid preconditioner for immersed finite element methods, which provides mesh-independent and cut-element-independent convergence rates. This preconditioning technique is applicable to higher-order discretizations, and enables solving large-scale immersed systems in parallel, at a computational cost that scales linearly with the number of degrees of freedom. The performance of the preconditioner is demonstrated for conventional Lagrange basis functions and for isogeometric discretizations with both uniform B-splines and locally refined approximations based on truncated hierarchical B-splines.
Original languageEnglish
Article numberarXiv:1903.10977 [math.NA]
Number of pages43
JournalarXiv
Issue numberarXiv:1903.10977 [math.NA]
Publication statusPublished - 26 Mar 2019

Fingerprint Dive into the research topics of 'Scalable multigrid methods for immersed finite element methods and immersed isogeometric analysis'. Together they form a unique fingerprint.

  • Cite this

    de Prenter, F., Verhoosel, C., van Brummelen, H., Evans, J., Messe, C., Benzaken, J., & Maute, K. (2019). Scalable multigrid methods for immersed finite element methods and immersed isogeometric analysis. arXiv, (arXiv:1903.10977 [math.NA]), [arXiv:1903.10977 [math.NA]]. https://arxiv.org/abs/1903.10977