Concept

Méthode de Simpson

Publications associées (42)

An equilibrated flux a posteriori error estimator for defeaturing problems

Annalisa Buffa, Denise Grappein, Rafael Vazquez Hernandez, Ondine Gabrielle Chanon

An a posteriori error estimator based on an equilibrated flux reconstruction is proposed for defeaturing problems in the context of finite element discretizations. Defeaturing consists in the simplification of a geometry by removing features that are consi ...

2023

Time-reversible and norm-conserving high-order integrators for the nonlinear time-dependent Schrödinger equation: Application to local control theory

Jiri Vanicek, Julien Roulet

The explicit split-operator algorithm has been extensively used for solving not only linear but also nonlinear time-dependent Schrödinger equations. When applied to the nonlinear Gross–Pitaevskii equation, the method remains time-reversible, norm-conservin ...

2021

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 ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2021

Fully-Asynchronous Fully-Implicit Variable-Order Variable-Timestep Simulation of Neural Networks

Felix Schürmann, Michael Lee Hines, Bruno Ricardo Da Cunha Magalhães

State-of-the-art simulations of detailed neurons follow the Bulk Synchronous Parallel execution model. Execution is divided in equidistant communication intervals, with parallel neurons interpolation and collective communication guiding synchronization. Su ...

2020

Support and approximation properties of Hermite splines

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann, Shayan Aziznejad

In this paper, we formally investigate two mathematical aspects of Hermite splines that are relevant to practical applications. We first demonstrate that Hermite splines are maximally localized, in the sense that the size of their support is minimal among ...

2020

Efficient geometric integrators for nonadiabatic quantum dynamics. I. The adiabatic representation

Jiri Vanicek, Seonghoon Choi

Geometric integrators of the Schrödinger equation conserve exactly many invariants of the exact solution. Among these integrators, the split-operator algorithm is explicit and easy to implement but, unfortunately, is restricted to systems whose Hamiltonian ...

2019

Efficient Greedy Coordinate Descent for Composite Problems

Martin Jaggi, Sebastian Urban Stich, Anastasiia Koloskova, Sai Praneeth Reddy Karimireddy

Coordinate descent with random coordinate selection is the current state of the art for many large scale optimization problems. However, greedy selection of the steepest coordinate on smooth problems can yield convergence rates independent of the dimension ...

2019

Efficient Greedy Coordinate Descent for Composite Problems

Martin Jaggi, Sebastian Urban Stich, Anastasiia Koloskova, Sai Praneeth Reddy Karimireddy

MICROTOME PUBLISHING2019

Greedy Non-Intrusive Reduced Order Model for Fluid Dynamics

Jan Sickmann Hesthaven

A greedy nonintrusive reduced order method (ROM) is proposed for parameterized time-dependent problems with an emphasis on problems in fluid dynamics. The nonintrusive ROM (NIROM) bases on a two-level proper orthogonal decomposition to extract temporal and ...

2018

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We analyze the accuracy of the discrete least-squares approximation of a function

u

in multivariate polynomial spaces

P_\Lambda:=span\{y\mapsto y^\nu \,: \, \nu\in \Lambda\}

with

\Lambda\subset N_0^d

over the domain

\Gamma:=[-1,1]^d

, based on the s ...

2017

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