Efficient multigrid based solvers for B-spline MPM

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Abstract

The Material Point Method (MPM) has been applied successfully to problems in engineering which involve large deformations and history-dependent material behavior. However, the classical method suffers from some shortcomings which influence the quality of the numerical solution significantly. High-order B-spline basis functions solve the problem of so-called ‘grid crossing errors’ completely due to their higher continuity at inter-element boundaries. Adopting a consistent mass matrix instead of its lumped counterpart, which is common practice in standard MPM, further improves the convergence properties of the MPM. However, solving a linear system of equations resulting from a B-spline discretization is considered a challenging task. In this paper, we present a solution technique using p-multigrid methods to efficiently solve linear systems arising in B-spline MPM.
Original languageEnglish
Title of host publicationProceedings of the Second International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction
Subtitle of host publication8 – 10 January 2019, University of Cambridge, United Kingdom
Pages161-165
Number of pages5
Publication statusPublished - 2019
EventMPM 2019: 2nd International Conference on the Material Point Method for Modelling Soil–Water–Structure Interaction - Cambridge, United Kingdom
Duration: 8 Jan 201910 Jan 2019
Conference number: 2
http://mpm2019.eu/home

Conference

ConferenceMPM 2019: 2nd International Conference on the Material Point Method for Modelling Soil–Water–Structure Interaction
Abbreviated titleMPM 2019
CountryUnited Kingdom
CityCambridge
Period8/01/1910/01/19
Internet address

Keywords

  • B-spline Material Point Method
  • Iterative solvers
  • p-Multigrid

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