Adaptive Isogeometric Analysis using optimal transport and their fast solvers

M. Bahari; A. Habbal; A. Ratnani; E. Sonnendrücker

doi:10.1016/j.cma.2023.116570

Adaptive Isogeometric Analysis using optimal transport and their fast solvers

M. Bahari, A. Habbal, A. Ratnani, E. Sonnendrücker

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this work, we devise fast solvers and adaptive mesh generation procedures based on the Monge–Ampère Equation using B-Splines Finite Elements, within the Isogeometric Analysis framework. Our approach ensures that the constructed mapping is a bijection, which is a major challenge in Isogeometric Analysis. First, we use standard B-Splines Finite Elements to solve the Monge–Ampère Equation. An analysis of this approach shows serious limitations when dealing with high variations near the boundary. In order to solve this problem, a new formulation is derived using compatible B-Splines discretization based on a discrete DeRham sequence. A new fast solver is devised in this case using the Fast Diagonalization method. Different tests are provided and show the performance of our new approach.

Original language	English
Article number	116570
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	418
DOIs	https://doi.org/10.1016/j.cma.2023.116570
State	Published - 5 Jan 2024
Externally published	Yes

Keywords

B-spline discretization
Isogeometric Analysis
Mesh generation
Multi level
Optimal transport
r-refinement

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10.1016/j.cma.2023.116570

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title = "Adaptive Isogeometric Analysis using optimal transport and their fast solvers",

abstract = "In this work, we devise fast solvers and adaptive mesh generation procedures based on the Monge–Amp{\`e}re Equation using B-Splines Finite Elements, within the Isogeometric Analysis framework. Our approach ensures that the constructed mapping is a bijection, which is a major challenge in Isogeometric Analysis. First, we use standard B-Splines Finite Elements to solve the Monge–Amp{\`e}re Equation. An analysis of this approach shows serious limitations when dealing with high variations near the boundary. In order to solve this problem, a new formulation is derived using compatible B-Splines discretization based on a discrete DeRham sequence. A new fast solver is devised in this case using the Fast Diagonalization method. Different tests are provided and show the performance of our new approach.",

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T1 - Adaptive Isogeometric Analysis using optimal transport and their fast solvers

AU - Bahari, M.

AU - Habbal, A.

AU - Ratnani, A.

AU - Sonnendrücker, E.

PY - 2024/1/5

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N2 - In this work, we devise fast solvers and adaptive mesh generation procedures based on the Monge–Ampère Equation using B-Splines Finite Elements, within the Isogeometric Analysis framework. Our approach ensures that the constructed mapping is a bijection, which is a major challenge in Isogeometric Analysis. First, we use standard B-Splines Finite Elements to solve the Monge–Ampère Equation. An analysis of this approach shows serious limitations when dealing with high variations near the boundary. In order to solve this problem, a new formulation is derived using compatible B-Splines discretization based on a discrete DeRham sequence. A new fast solver is devised in this case using the Fast Diagonalization method. Different tests are provided and show the performance of our new approach.

AB - In this work, we devise fast solvers and adaptive mesh generation procedures based on the Monge–Ampère Equation using B-Splines Finite Elements, within the Isogeometric Analysis framework. Our approach ensures that the constructed mapping is a bijection, which is a major challenge in Isogeometric Analysis. First, we use standard B-Splines Finite Elements to solve the Monge–Ampère Equation. An analysis of this approach shows serious limitations when dealing with high variations near the boundary. In order to solve this problem, a new formulation is derived using compatible B-Splines discretization based on a discrete DeRham sequence. A new fast solver is devised in this case using the Fast Diagonalization method. Different tests are provided and show the performance of our new approach.

KW - B-spline discretization

KW - Isogeometric Analysis

KW - Mesh generation

KW - Multi level

KW - Optimal transport

KW - r-refinement

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JO - Computer Methods in Applied Mechanics and Engineering

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Adaptive Isogeometric Analysis using optimal transport and their fast solvers

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Keywords

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