Publication

Remarks on Poincare and interpolation estimates for Truncated Hierarchical B-splines

Publications associées (30)

An a posteriori error estimator for isogeometric analysis on trimmed geometries

Ondine Gabrielle Chanon, Annalisa Buffa, Rafael Vazquez Hernandez

Trimming consists of cutting away parts of a geometric domain, without reconstructing a global parametrization (meshing). It is a widely used operation in computer-aided design, which generates meshes that are unfitted with the described physical object. T ...

2022

Investigation and Validation of Unstructured Mesh Methodologies for Modeling Experimental Reactors

Andreas Pautz, Mathieu Hursin, Carlo Fiorina, Tom Mager

This paper summarizes a methodology developed at Ecole Polytechnique Federale de Lausanne for the neutronic modeling of the CROCUS experimental reactor and proposes solutions to the challenges one may face while modeling a research reactor with a complex g ...

MDPI2022

Adaptive analysis-aware defeaturing

Ondine Gabrielle Chanon, Annalisa Buffa, Rafael Vazquez Hernandez

Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. But depen ...

2022

Quadratic serendipity element shape functions on general planar polygons

Juan Cao, Xiaodong Wei

This paper proposes a method for the construction of quadratic serendipity element (QSE) shape functions on planar convex and concave polygons. Existing approaches for constructing QSE shape functions are linear combinations of the pair-wise products of ge ...

ELSEVIER SCIENCE SA2022

Synthesis and Analysis of 3D shapes with Geometric Deep Learning in Computer-Aided Engineering

Edoardo Remelli

In this thesis, we advocate that Computer-Aided Engineering could benefit from a Geometric Deep Learning revolution, similarly to the way that Deep Learning revolutionized Computer Vision. To do so, we consider a variety of Computer-Aided Engineering pr ...

EPFL2022

On Linear Interpolation in the Latent Space of Deep Generative Models

Quentin Christian Becker, Mike Yan Michelis

The underlying geometrical structure of the latent space in deep generative models is in most cases not Euclidean, which may lead to biases when comparing interpolation capabilities of two models. Smoothness and plausibility of linear interpolations in lat ...

2021

How to teach neural networks to mesh: Application on 2-D simplicial contours

François Avellan, Pascal Clausen, Alexis Papagiannopoulos

A machine learning meshing scheme for the generation of 2-D simplicial meshes is proposed based on the predictions of neural networks. The data extracted from meshed contours are utilized to train neural networks which are used to approximate the number of ...

2021

Tessellation and lmprovement of Simplicial Meshes using Neural Networks

Alexis Papagiannopoulos

Modern mesh generation addresses the development of robust algorithms that construct a discrete representation of the geometry into polytopal elements conforming to divergent properties: (i) fidelity to complex geometrical features, (ii) support for high s ...

EPFL2021

Last iterate convergence of SGD for Least-Squares in the Interpolation regime

Aditya Vardhan Varre, Nicolas Henri Bernard Flammarion, Loucas Pillaud-Vivien

Motivated by the recent successes of neural networks that have the ability to fit the data perfectly \emph{and} generalize well, we study the noiseless model in the fundamental least-squares setup. We assume that an optimum predictor fits perfectly inputs ...

Advances in Neural Information Processing Systems 20212021

An arbitrary-order Cell Method with block-diagonal mass-matrices for the time-dependent 2D Maxwell equations

Bernard Kapidani

We introduce a new numerical method for the time-dependent Maxwell equations on unstructured meshes in two space dimensions. This relies on the introduction of a new mesh, which is the barycentric-dual cellular complex of the starting simplicial mesh, and ...

2021