Isogeometric collocation methods for Cosserat rods and rod structures

O Weeger, SK Yeung, ML Dunn - Computer Methods in Applied Mechanics …, 2017 - Elsevier
We present a novel method for the mechanical simulation of slender, elastic, spatial rods
and rod structures subject to large deformation and rotation. We develop an isogeometric …

Planar multi-patch domain parameterization via patch adjacency graphs

F Buchegger, B Jüttler - Computer-Aided Design, 2017 - Elsevier
As a remarkable difference to the existing CAD technology, where shapes are represented
by their boundaries, FEM-based isogeometric analysis typically needs a parameterization of …

Simultaneous boundary and interior parameterization of planar domains via deep learning

Z Zhan, W Wang, F Chen - Computer-Aided Design, 2024 - Elsevier
In isogeometric analysis (IGA), domain parameterization plays a crucial role as it
significantly impacts the results of subsequent numerical analyses. Previous literature has …

Locally refined quad meshing for linear elasticity problems based on convolutional neural networks

CL Chan, F Scholz, T Takacs - Engineering with Computers, 2022 - Springer
In this paper we propose a method to generate suitably refined finite element meshes using
neural networks. As a model problem we consider a linear elasticity problem on a planar …

Volumetric boundary correspondence for isogeometric analysis based on unbalanced optimal transport

Y Zheng, F Chen - Computer-Aided Design, 2021 - Elsevier
Abstract Domain parameterization, ie, constructing a map from a parameter domain to a
computational domain, is a key step in isogeometric analysis. Before parameterizing the …

Splines parameterization of planar domains by physics-informed neural networks

A Falini, GA D'Inverno, ML Sampoli, F Mazzia - Mathematics, 2023 - mdpi.com
The generation of structured grids on bounded domains is a crucial issue in the
development of numerical models for solving differential problems. In particular, the …

Boundary Correspondence for Iso-Geometric Analysis Based on Deep Learning

Z Zhan, Y Zheng, W Wang, F Chen - Communications in Mathematics and …, 2023 - Springer
One of the key problems in isogeometric analysis (IGA) is domain parameterization, ie,
constructing a map between a parametric domain and a computational domain. As a …

Discontinuous Galerkin isogeometric analysis of elliptic diffusion problems on segmentations with gaps

C Hofer, U Langer, I Toulopoulos - SIAM Journal on Scientific Computing, 2016 - SIAM
We propose a new discontinuous Galerkin (dG) isogeometric analysis (IgA) technique for
the numerical solution of elliptic diffusion problems in computational domains decomposed …

Analysis of discontinuous Galerkin dual-primal isogeometric tearing and interconnecting methods

C Hofer - Mathematical Models and Methods in Applied …, 2018 - World Scientific
In this paper, we present the analysis of the discontinuous Galerkin dual-primal isogeometric
tearing and interconnecting method (dG-IETI-DP) for a multipatch discretization in two-space …

[HTML][HTML] Discontinuous Galerkin isogeometric analysis of elliptic problems on segmentations with non-matching interfaces

C Hofer, I Toulopoulos - Computers & Mathematics with Applications, 2016 - Elsevier
In this paper, we develop a discontinuous Galerkin Isogeometric Analysis method for solving
elliptic problems on decompositions of the computational domain into volumetric patches …