Fast isogeometric solvers for explicit dynamics

Longfei Gao, Victor M. Calo

Research output: Contribution to journalArticlepeer-review

44 Scopus citations

Abstract

In finite element analysis, solving time-dependent partial differential equations with explicit time marching schemes requires repeatedly applying the inverse of the mass matrix. For mass matrices that can be expressed as tensor products of lower dimensional matrices, we present a direct method that has linear computational complexity, i.e., O(N), where N is the total number of degrees of freedom in the system. We refer to these matrices as separable matrices. For non-separable mass matrices, we present a preconditioned conjugate gradient method with carefully designed preconditioners as an alternative. We demonstrate that these preconditioners, which are easy to construct and cheap to apply (O(N)), can deliver significant convergence acceleration. The performances of these preconditioners are independent of the polynomial order (p independence) and mesh resolution (h independence) for maximum continuity B-splines, as verified by various numerical tests. © 2014 Elsevier B.V.
Original languageEnglish (US)
Pages (from-to)19-41
Number of pages23
JournalComputer Methods in Applied Mechanics and Engineering
Volume274
DOIs
StatePublished - Jun 2014

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Mechanics of Materials
  • Mechanical Engineering
  • Computational Mechanics
  • Computer Science Applications

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