Adaptive Mesh Refinement in 2D – An Efficient Implementation in Matlab

This paper deals with the efficient implementation of various adaptive mesh refinements in two dimensions in Matlab. We give insights into different adaptive mesh refinement strategies allowing triangular and quadrilateral grids with and without hanging nodes. Throughout, the focus is on an efficien...

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Published in:Journal of computational methods in applied mathematics Vol. 20; no. 3; pp. 459 - 479
Main Authors: Funken, Stefan A., Schmidt, Anja
Format: Journal Article
Language:English
Published: Minsk De Gruyter 01.07.2020
Walter de Gruyter GmbH
Subjects:
65N30
65N50
68N15
Adaptive Mesh Refinement
Adaptivity
Data structures
Finite Element Method
Grid refinement (mathematics)
Matlab
Matlab Program
Quadrilaterals
ISSN:1609-4840, 1609-9389
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Abstract This paper deals with the efficient implementation of various adaptive mesh refinements in two dimensions in Matlab. We give insights into different adaptive mesh refinement strategies allowing triangular and quadrilateral grids with and without hanging nodes. Throughout, the focus is on an efficient implementation by utilization of reasonable data structure, use of Matlab built-in functions and vectorization. This paper shows the transition from theory to implementation in a clear way and thus is meant to serve educational purposes of how to implement a method while keeping the code as short as possible – an implementation of an efficient adaptive mesh refinement is possible within 71 lines of Matlab. Numerical experiments underline the efficiency of the code and show the flexible deployment in different contexts where adaptive mesh refinement is in use. Our implementation is accessible and easy-to-understand and thus considered to be a valuable tool in research and education.
AbstractList This paper deals with the efficient implementation of various adaptive mesh refinements in two dimensions in Matlab. We give insights into different adaptive mesh refinement strategies allowing triangular and quadrilateral grids with and without hanging nodes. Throughout, the focus is on an efficient implementation by utilization of reasonable data structure, use of Matlab built-in functions and vectorization. This paper shows the transition from theory to implementation in a clear way and thus is meant to serve educational purposes of how to implement a method while keeping the code as short as possible – an implementation of an efficient adaptive mesh refinement is possible within 71 lines of Matlab. Numerical experiments underline the efficiency of the code and show the flexible deployment in different contexts where adaptive mesh refinement is in use. Our implementation is accessible and easy-to-understand and thus considered to be a valuable tool in research and education.
This paper deals with the efficient implementation of various adaptive mesh refinements in two dimensions in Matlab.We give insights into different adaptive mesh refinement strategies allowing triangular and quadrilateral grids with and without hanging nodes.Throughout, the focus is on an efficient implementation by utilization of reasonable data structure, use of Matlab built-infunctions and vectorization.This paper shows the transition from theory to implementation in a clear way and thus is meant to serve educational purposes of how to implement a method while keeping the code as short as possible – an implementation of an efficient adaptive mesh refinement is possible within 71 lines of Matlab.Numerical experiments underline the efficiency of the code and show the flexible deployment in different contexts where adaptive mesh refinement is in use.Our implementation is accessible and easy-to-understand and thus considered to be a valuable tool in research and education.
Author Schmidt, Anja
Funken, Stefan A.
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  givenname: Anja
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  fullname: Schmidt, Anja
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  organization: Institut für Numerische Mathematik, Universität Ulm, Helmholtzstraße 20, 89081 Ulm, Germany
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Snippet This paper deals with the efficient implementation of various adaptive mesh refinements in two dimensions in Matlab. We give insights into different adaptive...
This paper deals with the efficient implementation of various adaptive mesh refinements in two dimensions in Matlab.We give insights into different adaptive...
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SubjectTerms 65N30
65N50
68N15
Adaptive Mesh Refinement
Adaptivity
Data structures
Finite Element Method
Grid refinement (mathematics)
Matlab
Matlab Program
Quadrilaterals
Title Adaptive Mesh Refinement in 2D – An Efficient Implementation in Matlab
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Volume 20
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