Adaptive Semi-Structured Mesh Refinement Techniques for the Finite Element Method
The adaptive mesh techniques applied to the Finite Element Method have continuously been an active research line. However, these techniques are usually applied to tetrahedra. Here, we use the triangular prismatic element as the discretization shape for a Finite Element Method code with adaptivity. T...
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doaj-175d1eac0fed46219ba63c23cc9e53c92021-04-19T23:04:25ZengMDPI AGApplied Sciences2076-34172021-04-01113683368310.3390/app11083683Adaptive Semi-Structured Mesh Refinement Techniques for the Finite Element MethodAdrian Amor-Martin0Luis E. Garcia-Castillo1Signal Theory and Communications Department, University Carlos III of Madrid, 28911 Leganes, SpainSignal Theory and Communications Department, University Carlos III of Madrid, 28911 Leganes, SpainThe adaptive mesh techniques applied to the Finite Element Method have continuously been an active research line. However, these techniques are usually applied to tetrahedra. Here, we use the triangular prismatic element as the discretization shape for a Finite Element Method code with adaptivity. The adaptive process consists of three steps: error estimation, marking, and refinement. We adapt techniques already applied for other shapes to the triangular prisms, showing the differences here in detail. We use five different marking strategies, comparing the results obtained with different parameters. We adapt these strategies to a conformation process necessary to avoid hanging nodes in the resulting mesh. We have also applied two special rules to ensure the quality of the refined mesh. We show the effect of these rules with the Method of Manufactured Solutions and numerical results to validate the implementation introduced.https://www.mdpi.com/2076-3417/11/8/3683finite element methodadaptivityperiodic boundary conditionscomputational electromagnetics |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Adrian Amor-Martin Luis E. Garcia-Castillo |
spellingShingle |
Adrian Amor-Martin Luis E. Garcia-Castillo Adaptive Semi-Structured Mesh Refinement Techniques for the Finite Element Method Applied Sciences finite element method adaptivity periodic boundary conditions computational electromagnetics |
author_facet |
Adrian Amor-Martin Luis E. Garcia-Castillo |
author_sort |
Adrian Amor-Martin |
title |
Adaptive Semi-Structured Mesh Refinement Techniques for the Finite Element Method |
title_short |
Adaptive Semi-Structured Mesh Refinement Techniques for the Finite Element Method |
title_full |
Adaptive Semi-Structured Mesh Refinement Techniques for the Finite Element Method |
title_fullStr |
Adaptive Semi-Structured Mesh Refinement Techniques for the Finite Element Method |
title_full_unstemmed |
Adaptive Semi-Structured Mesh Refinement Techniques for the Finite Element Method |
title_sort |
adaptive semi-structured mesh refinement techniques for the finite element method |
publisher |
MDPI AG |
series |
Applied Sciences |
issn |
2076-3417 |
publishDate |
2021-04-01 |
description |
The adaptive mesh techniques applied to the Finite Element Method have continuously been an active research line. However, these techniques are usually applied to tetrahedra. Here, we use the triangular prismatic element as the discretization shape for a Finite Element Method code with adaptivity. The adaptive process consists of three steps: error estimation, marking, and refinement. We adapt techniques already applied for other shapes to the triangular prisms, showing the differences here in detail. We use five different marking strategies, comparing the results obtained with different parameters. We adapt these strategies to a conformation process necessary to avoid hanging nodes in the resulting mesh. We have also applied two special rules to ensure the quality of the refined mesh. We show the effect of these rules with the Method of Manufactured Solutions and numerical results to validate the implementation introduced. |
topic |
finite element method adaptivity periodic boundary conditions computational electromagnetics |
url |
https://www.mdpi.com/2076-3417/11/8/3683 |
work_keys_str_mv |
AT adrianamormartin adaptivesemistructuredmeshrefinementtechniquesforthefiniteelementmethod AT luisegarciacastillo adaptivesemistructuredmeshrefinementtechniquesforthefiniteelementmethod |
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1721518808365006848 |