Concept

Gaussian quadrature

Related publications (54)

Factorized structure of the long-range two-electron integrals tensor and its application in quantum chemistry

We introduce two new approximation methods for the numerical evaluation of the long-range component of the range-separated Coulomb potential and the approximation of the resulting high dimensional Two-Electron Integrals tensor (TEI) with long-range interac ...

San Diego2023

Quadrature-free immersed isogeometric analysis

Pablo Antolin Sanchez, Thibaut Hirschler

This paper presents a novel method for solving partial differential equations on three-dimensional CAD geometries by means of immersed isogeometric discretizations that do not require quadrature schemes. It relies on a newly developed technique for the eva ...

SPRINGER2022

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

Theory of the Drift-Wave Instability at Arbitrary Collisionality

Paolo Ricci, Rogério Manuel Cabete De Jesus Jorge

Drift-waves (DW) are low-frequency modes that arise in a magnetized plasma when a finite pressure gradient is present. In order to become unstable, DW require some form of dissipation, such as finite resistivity, electron inertia or wave-particle resonance ...

2019

PDE-constrained optimal control problems with uncertain parameters using SAGA

Fabio Nobile, Matthieu Claude Martin

We consider an optimal control problem for an elliptic partial differential equation (PDE) with random coefficients. The control function is a deterministic, distributed forcing term that minimizes an expected quadratic regularized loss functional. We cons ...

2018

Theory of the Drift-Wave Instability at Arbitrary Collisionality

Paolo Ricci, Rogério Manuel Cabete De Jesus Jorge

A numerically efficient framework that takes into account the effect of the Coulomb collision operator at arbitrary collisionalities is introduced. Such a model is based on the expansion of the distribution function on a Hermite-Laguerre polynomial basis t ...

2018

Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction

Jan Sickmann Hesthaven, Boris Bonev

We present a novel high-order discontinuous Galerkin discretization for the spherical shallow water equations, able to handle wetting/drying and non-conforming, curved meshes in a well-balanced manner. This requires a well-balanced discretization, that can ...

2018

A three-scale offline–online numerical method for fluid flow in porous media

Assyr Abdulle, Ondrej Budác

A new multiscale method combined with model order reduction is proposed for flow problems in three-scale porous media. We derive an effective three-scale model that couples a macroscopic Darcy equation, a mesoscopic Stokes-Brinkman equation, and a microsco ...

2017

Finite strain FFT-based non-linear solvers made simple

Thomas Willem Jan de Geus

Computational micromechanics and homogenization require the solution of the mechanical equilibrium of a periodic cell that comprises a (generally complex) microstructure. Techniques that apply the Fast Fourier Transform have attracted much attention as the ...

Elsevier2017

MATHICSE Technical Report : Multiscale methods and model order reduction for flow problems in three-scale porous media

Assyr Abdulle, Ondrej Budác

MATHICSE2016

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