On a bisection algorithm that produces conforming locally refined simplicial meshes

Antti Hannukainen*, Sergey Korotov, Michal Křížek

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

3 Citations (Scopus)

Abstract

First we introduce a mesh density function that is used to define a criterion to decide, where a simplicial mesh should be fine (dense) and where it should be coarse. Further, we propose a new bisection algorithm that chooses for bisection an edge in a given mesh associated with the maximum value of the criterion function. Dividing this edge at its midpoint, we correspondingly bisect all simplices sharing this edge. Repeating this process, we construct a sequence of conforming nested simplicial meshes whose shape is determined by the mesh density function. We prove that the corresponding mesh size of the sequence tends to zero for d∈=∈2, 3 as the bisection algorithm proceeds. It is also demonstrated numerically that the algorithm seems to produce only a finite number of similarity-distinct triangles.

Original languageEnglish
Title of host publicationLarge-Scale Scientific Computing - 7th International Conference, LSSC 2009, Revised Papers
Pages571-579
Number of pages9
Volume5910 LNCS
DOIs
Publication statusPublished - 2010
MoE publication typeA4 Article in a conference publication
EventInternational Conference on Large-Scale Scientific Computations - Sozopol, Bulgaria
Duration: 4 Jun 20098 Jun 2009
Conference number: 7

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5910 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Conference

ConferenceInternational Conference on Large-Scale Scientific Computations
Abbreviated titleLSSC
CountryBulgaria
CitySozopol
Period04/06/200908/06/2009

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