High-Dimensional Partial Differential Equations in Science and Engineering ( CRM Proceedings & Lecture Notes )

Publication series :CRM Proceedings & Lecture Notes

Author: André Bandrauk;Michel C. Delfour;Claude Le Bris  

Publisher: American Mathematical Society‎

Publication year: 2017

E-ISBN: 9781470439552

P-ISBN(Paperback): 9780821838532

Subject: O1 Mathematics

Keyword: 暂无分类

Language: ENG

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High-Dimensional Partial Differential Equations in Science and Engineering

Description

High-dimensional spatio-temporal partial differential equations are a major challenge to scientific computing of the future. Up to now deemed prohibitive, they have recently become manageable by combining recent developments in numerical techniques, appropriate computer implementations, and the use of computers with parallel and even massively parallel architectures. This opens new perspectives in many fields of applications. Kinetic plasma physics equations, the many body Schrödinger equation, Dirac and Maxwell equations for molecular electronic structures and nuclear dynamic computations, options pricing equations in mathematical finance, as well as Fokker–Planck and fluid dynamics equations for complex fluids, are examples of equations that can now be handled. The objective of this volume is to bring together contributions by experts of international stature in that broad spectrum of areas to confront their approaches and possibly bring out common problem formulations and research directions in the numerical solutions of high-dimensional partial differential equations in various fields of science and engineering with special emphasis on chemistry and physics.

Chapter

Title page

Contents

Preface

List of participants

List of speakers

Singularity-free methods for the time-dependent Schrödinger equation for nonlinear molecules in intense laser fields—A non-perturbative approach

Feasibility and competitiveness of a reduced basis approach for rapid electronic structure calculations in quantum chemistry

Some fundamental mathematical properties in atomic and molecular quantum mechanics

Sparse tensor-product Fokker–Planck-based methods for nonlinear bead-spring chain models of dilute polymer solutions

A partial differential equation for credit derivatives pricing

A short review on computational issues arising in relativistic atomic and molecular physics

Model Hamiltonians in density functional theory

Simulation of quantum-classical dynamics by surface-hopping trajectories

Simulating realistic and nonadiabatic chemical dynamics: Application to photochemistry and electron transfer reactions

A Maxwell-Schrödinger model for non-perturbative laser-molecule interaction and some methods of numerical computation

Parareal in time algorithm for kinetic systems based on model reduction

Back Cover

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