Softcover ISBN:  9780821838532 
Product Code:  CRMP/41 
194 pp 
List Price:  $92.00 
MAA Member Price:  $82.80 
AMS Member Price:  $73.60 
Electronic ISBN:  9781470439552 
Product Code:  CRMP/41.E 
194 pp 
List Price:  $86.00 
MAA Member Price:  $77.40 
AMS Member Price:  $68.80 

Book DetailsCRM Proceedings & Lecture NotesVolume: 41; 2007MSC: Primary 65; 35; Secondary 76;
Highdimensional spatiotemporal 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 highdimensional partial differential equations in various fields of science and engineering with special emphasis on chemistry and physics.ReadershipGraduate students and research mathematicians interested in numerical solutions of highdimensional PDE's.

Table of Contents

Chapters

Singularityfree methods for the timedependent Schrödinger equation for nonlinear molecules in intense laser fields—A nonperturbative 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 tensorproduct Fokker–Planckbased methods for nonlinear beadspring 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 quantumclassical dynamics by surfacehopping trajectories

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

A MaxwellSchrödinger model for nonperturbative lasermolecule interaction and some methods of numerical computation

Parareal in time algorithm for kinetic systems based on model reduction


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Highdimensional spatiotemporal 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 highdimensional 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 highdimensional PDE's.

Chapters

Singularityfree methods for the timedependent Schrödinger equation for nonlinear molecules in intense laser fields—A nonperturbative 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 tensorproduct Fokker–Planckbased methods for nonlinear beadspring 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 quantumclassical dynamics by surfacehopping trajectories

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

A MaxwellSchrödinger model for nonperturbative lasermolecule interaction and some methods of numerical computation

Parareal in time algorithm for kinetic systems based on model reduction