Mass lumping and outlier removal strategies for complex geometries in isogeometric analysis

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Voet, Yannis, Sande, Espen, Buffa, Annalisa
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866916511602442240
author Voet, Yannis
Sande, Espen
Buffa, Annalisa
author_facet Voet, Yannis
Sande, Espen
Buffa, Annalisa
contents Mass lumping techniques are commonly employed in explicit time integration schemes for problems in structural dynamics and both avoid solving costly linear systems with the consistent mass matrix and increase the critical time step. In isogeometric analysis, the critical time step is constrained by so-called "outlier" frequencies, representing the inaccurate high frequency part of the spectrum. Removing or dampening these high frequencies is paramount for fast explicit solution techniques. In this work, we propose mass lumping and outlier removal techniques for nontrivial geometries, including multipatch and trimmed geometries. Our lumping strategies provably do not deteriorate (and often improve) the CFL condition of the original problem and are combined with deflation techniques to remove persistent outlier frequencies. Numerical experiments reveal the advantages of the method, especially for simulations covering large time spans where they may halve the number of iterations with little or no effect on the numerical solution.
format Preprint
id arxiv_https___arxiv_org_abs_2402_14956
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Mass lumping and outlier removal strategies for complex geometries in isogeometric analysis
Voet, Yannis
Sande, Espen
Buffa, Annalisa
Numerical Analysis
65M60, 65F15
Mass lumping techniques are commonly employed in explicit time integration schemes for problems in structural dynamics and both avoid solving costly linear systems with the consistent mass matrix and increase the critical time step. In isogeometric analysis, the critical time step is constrained by so-called "outlier" frequencies, representing the inaccurate high frequency part of the spectrum. Removing or dampening these high frequencies is paramount for fast explicit solution techniques. In this work, we propose mass lumping and outlier removal techniques for nontrivial geometries, including multipatch and trimmed geometries. Our lumping strategies provably do not deteriorate (and often improve) the CFL condition of the original problem and are combined with deflation techniques to remove persistent outlier frequencies. Numerical experiments reveal the advantages of the method, especially for simulations covering large time spans where they may halve the number of iterations with little or no effect on the numerical solution.
title Mass lumping and outlier removal strategies for complex geometries in isogeometric analysis
topic Numerical Analysis
65M60, 65F15
url https://arxiv.org/abs/2402.14956