Concept

Multigrid method

Publications associées (240)

MATHICSE Technical Report : Uncertainty Quantification by MLMC and Local Time-stepping For Wave Propagation

Because of their robustness, efficiency and non-intrusiveness, Monte Carlo methods are probably the most popular approach in uncertainty quantification to computing expected values of quantities of interest (QoIs). Multilevel Monte Carlo (MLMC) methods sig ...

EPFL2021

Analysis of the flexible boundary condition method

William Curtin, Ankit Gupta

The flexible boundary condition method (FBCM) is a well-established method for the efficient study of complex non-linear atomistic defects while avoiding finite-size effects. The method uses lattice Green's functions (LGFs) to effectively embed an atomisti ...

IOP PUBLISHING LTD2021

Synthesis of Kit-of-parts Structures for Reuse

Corentin Jean Dominique Fivet, Gennaro Senatore, Jan Friedrich Georg Brütting, Alex-Manuel Muresan, Ioannis Mirtsopoulos

This paper shows a computational workflow to design a kit of parts consisting of linear bars and spherical joints that can be employed to assemble, take apart, and rebuild diverse reticular structures, e.g. gridshells and space frames. Being able to reuse ...

2021

Construction of optimal spectral methods in phase retrieval

Florent Gérard Krzakala, Lenka Zdeborová

We consider the phase retrieval problem, in which the observer wishes to recover a n-dimensional real or complex signal X⋆ from the (possibly noisy) observation of |ΦX⋆|, in which Φ is a matrix of size m×n. We consider a \emph{high-dimensional} setting whe ...

2021

Adhesive wear with a coarse-grained discrete element model

Son-Jonathan Pham-Ba

All surfaces, whether they are natural or man-made, exhibit a certain amount of roughness on a range of length scales. This surface roughness evidently plays a major role in tribological processes, like friction and wear between two surfaces sliding agains ...

2021

A hybrid collocation-perturbation approach for PDEs with random domains

Fabio Nobile

Consider a linear elliptic PDE defined over a stochastic stochastic geometry a function of N random variables. In many application, quantify the uncertainty propagated to a quantity of interest (QoI) is an important problem. The random domain is split into ...

2021

A fast spectral divide-and-conquer method for banded matrices

Daniel Kressner, Ana Susnjara

Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3):A1325-A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix with small bandwidth, w ...

WILEY2021

A hierarchical preconditioner for wave problems in quasilinear complexity

Jan Sickmann Hesthaven, Boris Bonev

The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and discontinuous Galerkin formulations of elliptic problems. We exploit the property th ...

2020

Locally supported tangential vector, n-vector, and tensor fields

Christopher Brandt

We introduce a construction of subspaces of the spaces of tangential vector, n-vector, and tensor fields on surfaces. The resulting subspaces can be used as the basis of fast approximation algorithms for design and processing problems that involve tangenti ...

WILEY2020

Controlling oscillations in spectral schemes using Artificial Neural Networks

Lukas Schwander

Global Fourier spectral methods are excellent tools to solve conserva- tion laws. They enable fast convergence rates and highly accurate solutions. However, being high-order methods, they suffer from the Gibbs phenomenon, which leads to spurious numerical ...

2020

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