Concept

Cavalieri's quadrature formula

Related publications (13)

A Combination Technique for Optimal Control Problems Constrained by Random PDEs

We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of optimal control problems (OCPs) constrained by random partial differential equ ...

2024

Comment on “Groundwater Affects the Geomorphic and Hydrologic Properties of Coevolved Landscapes” by Litwin et al.

Sara Bonetti, Shashank Kumar Anand

The objective of this comment is to correct two sets of statements in Litwin et al. (2022, https://doi.org/10.1029/2021JF006239), which consider our research work (Bonetti et al., 2018, https://doi.org/10.1098/rspa.2017.0693; Bonetti et al., 2020, https:// ...

2022

A combination technique for optimal control problems constrained by random PDEs

Fabio Nobile, Tommaso Vanzan

We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of Optimal Control Problems (OCPs) constrained by random partial differential equ ...

EPFL2022

A kernel compression scheme for fractional differential equations

Jan Sickmann Hesthaven, Daniel Henri Baffet

The nonlocal nature of the fractional integral makes the numerical treatment of fractional dierential equations expensive in terms of computational eort and memory requirements. In this paper we propose a method to reduce these costs while controlling the ...

Society for Industrial and Applied Mathematics2017

Spectral methods for tempered fractional differential equations

Jan Sickmann Hesthaven, Lijing Zhao

In this paper, we first introduce fractional integral spaces, which possess some features: (i) when 0 < α < 1, functions in these spaces are not required to be zero on the boundary; (ii)the tempered fractional operators are equivalent to the Riemann-Liouvi ...

2016

Solving Stochastic Ordinary Differential Equations by Monte Carlo and Polynomial Chaos

Gilles Brunner

In this project, we study and compare two methods to solve stochastic ordinary differential equations. The first is the Monte Carlo method and the second uses Polynomial Chaos. In the first part, we will solve a stochastic ordinary differential equation by ...

2013

Integral Equation Analysis of Plane Wave Scattering by Coplanar Graphene-Strip Gratings in the THz Range

Juan Ramon Mosig, Julien Perruisseau-Carrier, Juan Sebastian Gomez Diaz

The plane wave scattering and absorption by finite and infinite gratings of free-space standing infinitely long graphene strips are studied in the THz range. A novel numerical approach, based on graphene surface impedance, hyper-singular integral equations ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Local demodulation of holograms using the Riesz transform with application to microscopy

Michaël Unser, Christian Depeursinge, Nicolas Pavillon, Chandra Sekhar Seelamantula

We propose a Riesz transform approach to the demodulation of digital holograms. The Riesz transform is a higher-dimensional extension of the Hilbert transform and is steerable to a desired orientation. Accurate demodulation of the hologram requires a relia ...

Optical Society of America2012

A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems

Assyr Abdulle, Gilles Vilmart

The effect of numerical quadrature in finite element methods for solving quasilinear elliptic problems of nonmonotone type is studied. Under similar assumption on the quadrature formula as for linear problems, optimal error estimates in the L^2 and the H^1 ...

2012

The Cosmic Linear Anisotropy Solving System (CLASS) IV: efficient implementation of non-cold relics

Julien Lesgourgues

We present a new flexible, fast and accurate way to implement massive neutrinos, warm dark matter and any other non-cold dark matter relics in Boltzmann codes. For whatever analytical or numerical form of the phase-space distribution function, the optimal ...

2011

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