Concept

Partial differential equation

Related publications (919)

Ill-posedness of the quasilinear wave equation in the space $H^7/4 (ln H)^-Béta$ in dimension 2+1

We are interested in the well posedness of quasilinear partial differential equations of order two. Motivated by the study of the Einstein equation in relativity theory, there are a number of works dedicated to the local well-posedness issue for the quasil ...

EPFL2021

Prediction of the reaction forces of spiral-groove gas journal bearings by artificial neural network regression models

Jürg Alexander Schiffmann, Elia Iseli

This paper presents neural network regression models for predicting the nonlinear static and linearized dynamic reaction forces of spiral grooved gas journal bearings. The partial differential equations (PDEs) are sampled, based on a full factorial and ran ...

2021

A parabolic local problem with exponential decay of the resonance error for numerical homogenization

Assyr Abdulle, Doghonay Arjmand, Edoardo Paganoni

This paper aims at an accurate and efficient computation of effective quantities, e.g. the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods are based on a m ...

WORLD SCIENTIFIC PUBL CO PTE LTD2021

Substructured Two-grid and Multi-grid Domain Decomposition Methods

Tommaso Vanzan

Two-level domain decomposition methods are very powerful techniques for the efficient numerical solution of partial differential equations (PDEs). A two-level domain decomposition method requires two main components: a one-level preconditioner (or its corr ...

2021

Transverse Noise, Decoherence, and Landau Damping in High-Energy Hadron Colliders

Sondre Vik Furuseth

High-energy hadron colliders are designed to generate particle collisions within specialized detectors. A higher number of collisions is achieved with high-quality beams of low transverse emittances, meaning a small transverse cross-section, and high inten ...

EPFL2021

Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs

Assyr Abdulle, Gilles Vilmart

Explicit stabilized integrators are an efficient alternative to implicit or semi-implicit methods to avoid the severe timestep restriction faced by standard explicit integrators applied to stiff diffusion problems. In this paper, we provide a fully discret ...

EPFL2021

On the nonlinear Dirichlet-Neumann method and preconditioner for Newton's method

Tommaso Vanzan

The Dirichlet-Neumann (DN) method has been extensively studied for linear partial differential equations, while little attention has been devoted to the nonlinear case. In this paper, we analyze the DN method both as a nonlinear iterative method and as a p ...

Springer-Verlag2021

Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

Fabio Nobile, Sebastian Krumscheid, Matthieu Claude Martin

We consider the numerical approximation of an optimal control problem for an elliptic Partial Differential Equation (PDE) with random coefficients. Specifically, the control function is a deterministic, distributed forcing term that minimizes the expected ...

2021

A Continuized View on Nesterov Acceleration

Nicolas Henri Bernard Flammarion, Raphaël Jean Berthier

We introduce the "continuized" Nesterov acceleration, a close variant of Nesterov acceleration whose variables are indexed by a continuous time parameter. The two variables continuously mix following a linear ordinary differential equation and take gradien ...

2021

A dependence of the cost of fast controls for the heat equation on the support of initial datum

Hoài-Minh Nguyên

The controllability cost for the heat equation as the control time

T

goes to 0 is well-known of the order

e^{C/T}

for some positive constant

C

, depending on the controlled domain and for all initial datum. In this paper, we prove that the constant $C ...

2021

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A dependence of the cost of fast controls for the heat equation on the support of initial datum

Hoài-Minh Nguyên

The controllability cost for the heat equation as the control time

T

goes to 0 is well-known of the order

e^{C/T}

for some positive constant

C

, depending on the controlled domain and for all initial datum. In this paper, we prove that the constant $C ...

2021