Adaptive Isogeometric Analysis using optimal transport and their fast solvers

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

Publikation: Beitrag in FachzeitschriftArtikelBegutachtung

2 Zitate (Scopus)

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.

OriginalspracheEnglisch
Aufsatznummer116570
FachzeitschriftComputer Methods in Applied Mechanics and Engineering
Jahrgang418
DOIs
PublikationsstatusVeröffentlicht - 5 Jan. 2024
Extern publiziertJa

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