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High-Dimensional Partial Differential Equations in Science and Engineering

Edited by: André Bandrauk Université de Sherbrooke, Sherbrooke, QC, Canada
Michel C. Delfour Université de Montréal, Montréal, QC, Canada
Claude Le Bris École Nationale des Ponts et Chaussés, Marne La Vallée, France and INRIA Rocquencourt, Le Chesnay, France
A co-publication of the AMS and Centre de Recherches Mathématiques
Available Formats:
Softcover ISBN: 978-0-8218-3853-2
Product Code: CRMP/41
List Price: $92.00 MAA Member Price:$82.80
AMS Member Price: $73.60 Electronic ISBN: 978-1-4704-3955-2 Product Code: CRMP/41.E List Price:$86.00
MAA Member Price: $77.40 AMS Member Price:$68.80
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $138.00 MAA Member Price:$124.20
AMS Member Price: $110.40 Click above image for expanded view High-Dimensional Partial Differential Equations in Science and Engineering Edited by: André Bandrauk Université de Sherbrooke, Sherbrooke, QC, Canada Michel C. Delfour Université de Montréal, Montréal, QC, Canada Claude Le Bris École Nationale des Ponts et Chaussés, Marne La Vallée, France and INRIA Rocquencourt, Le Chesnay, France A co-publication of the AMS and Centre de Recherches Mathématiques Available Formats:  Softcover ISBN: 978-0-8218-3853-2 Product Code: CRMP/41  List Price:$92.00 MAA Member Price: $82.80 AMS Member Price:$73.60
 Electronic ISBN: 978-1-4704-3955-2 Product Code: CRMP/41.E
 List Price: $86.00 MAA Member Price:$77.40 AMS Member Price: $68.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$138.00 MAA Member Price: $124.20 AMS Member Price:$110.40
• Book Details

CRM Proceedings & Lecture Notes
Volume: 412007; 194 pp
MSC: Primary 65; 35; Secondary 76;

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.

Graduate students and research mathematicians interested in numerical solutions of high-dimensional PDE's.

• Chapters
• 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

• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 412007; 194 pp
MSC: Primary 65; 35; Secondary 76;

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.

Graduate students and research mathematicians interested in numerical solutions of high-dimensional PDE's.

• Chapters
• 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
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
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