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

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 Schrodinger 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.Information for our distributors: Titles in this series are co-published with the Centre de Recherches Mathematiques.

Table of Contents:
Singularity-free methods for the time-dependent Schrodinger equation for nonlinear molecules in intense laser fields--A non-perturbative approach by A. D. Bandrauk and H. Lu Feasibility and competitiveness of a reduced basis approach for rapid electronic structure calculations in quantum chemistry by E. Cances, C. Le Bris, Y. Maday, N. C. Nguyen, A. T. Patera, and G. S. H. Pau Some fundamental mathematical properties in atomic and molecular quantum mechanics by G. Chen, Z. Ding, A. Perronnet, M. O. Scully, R. Xie, and Z. Zhang Sparse tensor-product Fokker-Planck-based methods for nonlinear bead-spring chain models of dilute polymer solutions by P. Delaunay, A. Lozinski, and R. G. Owens A partial differential equation for credit derivatives pricing by M. Escobar and L. Seco A short review on computational issues arising in relativistic atomic and molecular physics by M. J. Esteban Model Hamiltonians in density functional theory by P. Gori-Giorgi, J. Toulouse, and A. Savin Simulation of quantum-classical dynamics by surface-hopping trajectories by H. Kim and R. Kapral Simulating realistic and nonadiabatic chemical dynamics: Application to photochemistry and electron transfer reactions by D. M. Koch, Q. K. Timerghazin, and G. H. Peslherbe A Maxwell-Schrodinger model for non-perturbative laser-molecule interaction and some methods of numerical computation by E. Lorin, S. Chelkowski, and A. Bandrauk Parareal in time algorithm for kinetic systems based on model reduction by Y. Maday.