Tangente (géométrie)

Reach For the Arcs: Reconstructing Surfaces from SDFs via Tangent Points

We introduce an algorithm to reconstruct a mesh from discrete samples of a shape's Signed Distance Function (SDF). A simple geometric reinterpretation of the SDF lets us formulate the problem through a point cloud, from which a surface can be extracted wit ...

Association for Computing Machinery2024

Transportation-based functional ANOVA and PCA for covariance operators

Victor Panaretos, Yoav Zemel, Valentina Masarotto

We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Vari ...

Inst Mathematical Statistics-Ims2024

Avoidance of Concave Obstacles Through Rotation of Nonlinear Dynamics

Aude Billard, Lukas Huber

Controlling complex tasks in robotic systems, such as circular motion for cleaning or following curvy lines, can be dealt with using nonlinear vector fields. This article introduces a novel approach called the rotational obstacle avoidance method (ROAM) fo ...

Ieee-Inst Electrical Electronics Engineers Inc2024

Grassmannian diffusion maps based surrogate modeling via geometric harmonics

Ketson Roberto Maximiano Dos Santos

A novel surrogate model based on the Grassmannian diffusion maps (GDMaps) and utilizing geometric harmonics (GH) is developed for predicting the response of complex physical phenomena. The method utilizes GDMaps to obtain a low-dimensional representation o ...

Wiley2022

Rank-adaptive structure-preserving model order reduction of Hamiltonian systems

Jan Sickmann Hesthaven, Nicolò Ripamonti, Cecilia Pagliantini

This work proposes an adaptive structure-preserving model order reduction method for finite-dimensional parametrized Hamiltonian systems modeling non-dissipative phenomena. To overcome the slowly decaying Kolmogorov width typical of transport problems, the ...

EDP SCIENCES S A2022

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Nicolas Boumal, Christopher Arnold Criscitiello

We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...

SPRINGER2022

Symplectic dynamical low rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash, Eva Vidlicková

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of 2S dynamical ...

2020

Coordinate parameterisation and spectral method optimisation for Beltrami field solver in stellarator geometry

David Pfefferlé, Aravind Kumar Chandiran, Antoine Baillod, Ajay Kumar

The numerical solution of the stepped pressure equilibrium (Hudson et al 2012 Phys. Plasmas 19 112502) requires a fast and robust solver to obtain the Beltrami field in three-dimensional geometry such as stellarators. The spectral method implemented in the ...

2020

A Study of Several Artificial Viscosity Models within the Discontinuous Galerkin Framework

Jan Sickmann Hesthaven

Dealing with strong shocks while retaining low numerical dissipation traditionally has been one of the major challenges for high order methods like discontinuous Galerkin (DG). In the literature, shock capturing models have been designed for DG based on va ...

GLOBAL SCIENCE PRESS2020

Tangente (géométrie)

Reach For the Arcs: Reconstructing Surfaces from SDFs via Tangent Points

Transportation-based functional ANOVA and PCA for covariance operators

Avoidance of Concave Obstacles Through Rotation of Nonlinear Dynamics

Grassmannian diffusion maps based surrogate modeling via geometric harmonics

Rank-adaptive structure-preserving model order reduction of Hamiltonian systems

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Structure-preserving approaches and data-driven closure modeling for model order reduction

Symplectic dynamical low rank approximation of wave equations with random parameters

Coordinate parameterisation and spectral method optimisation for Beltrami field solver in stellarator geometry

A Study of Several Artificial Viscosity Models within the Discontinuous Galerkin Framework

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Reach For the Arcs: Reconstructing Surfaces from SDFs via Tangent Points

Transportation-based functional ANOVA and PCA for covariance operators

Avoidance of Concave Obstacles Through Rotation of Nonlinear Dynamics

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Symplectic dynamical low rank approximation of wave equations with random parameters

Grassmannian diffusion maps based surrogate modeling via geometric harmonics

A Study of Several Artificial Viscosity Models within the Discontinuous Galerkin Framework

Coordinate parameterisation and spectral method optimisation for Beltrami field solver in stellarator geometry

Rank-adaptive structure-preserving model order reduction of Hamiltonian systems

Structure-preserving approaches and data-driven closure modeling for model order reduction