Modern methods in scientific computing and applications : proceedings of the NATO Advanced Study Institute and Séminaire de mathématiques supérieures on Modern Methods in Scientific Computing and Applications, Montréal, Québec, Canada, 9-20 July 2001

When we first heard in the spring of 2000 that the Seminaire de matMmatiques superieures (SMS) was interested in devoting its session of the summer of 200l-its 40th-to scientific computing the idea of taking on the organizational work seemed to us somewhat remote. More immediate things were on our minds: one of us was about to go on leave to the Courant Institute, the other preparing for a research summer in Paris. But the more we learned about the possibilities of such a seminar, the support for the organization and also the great history of the SMS, the more we grew attached to the project. The topics we planned to cover were intended to span a wide range of theoretical and practical tools for solving problems in image processing, thin films, mathematical finance, electrical engineering, moving interfaces, and combustion. These applications alone show how wide the influence of scientific computing has become over the last two decades: almost any area of science and engineering is greatly influenced by simulations, and the SMS workshop in this field came very timely. We decided to organize the workshop in pairs of speakers for each of the eight topics we had chosen, and we invited the leading experts worldwide in these fields. We were very fortunate that every speaker we invited accepted to come, so the program could be realized as planned. Front Matter....Pages i-xxii Computation of large-scale quadratic forms and transfer functions using the theory of moments, quadrature and Padé approximation....Pages 1-30 Thin film dynamics: theory and applications....Pages 31-79 Numerical turbulent combustion: an asymptotic view via an idealized test-case....Pages 81-102 Multigrid methods: from geometrical to algebraic versions....Pages 103-153 One-way operators, absorbing boundary conditions and domain decomposition for wave propagation....Pages 155-209 Deterministic and random dynamical systems: theory and numerics....Pages 211-254 Optimal investment problems and volatility homogenization approximations....Pages 255-281 Image processing with partial differential equations....Pages 283-321 Interface connections in domain decomposition methods....Pages 323-364 A review of level set and fast marching methods for image processing....Pages 365-396 Recent developments in the theory of front propagation and its applications....Pages 397-449 Computing finite-time singularities in interfacial flows....Pages 451-487 Back Matter....Pages 489-492

The influence of scientific computing has become very wide over the last few decades: almost every area of science and engineering is greatly influenced by simulations - image processing, thin films, mathematical finance, electrical engineering, moving interfaces and combustion, to name but a few.

One half of this book focuses on the techniques of scientific computing: domain decomposition, the absorption of boundary conditions and one-way operators, convergence analysis of multi-grid methods and other multi-grid techniques, dynamical systems, and matrix analysis.

The remainder of the book is concerned with combining techniques with concrete applications: shastic differential equations, image processing, thin films, and asymptotic analysis for combustion problems.

The influence of scientific computing has become very wide over the last few decades: almost every area of science and engineering is greatly influenced by simulations - image processing, thin films, mathematical finance, electrical engineering, moving interfaces and combustion, to name but a few. One half of this book focuses on the techniques of scientific computing: domain decomposition, the absorption of boundary conditions and one-way operators, convergence analysis of multi-grid methods and other multi-grid techniques, dynamical systems, and matrix analysis. The remainder of the book is concerned with combining techniques with concrete applications: stochastic differential equations, image processing, thin films, and asymptotic analysis for combustion problems. Proceedings of the NATO Advanced Study Institute and Séminaire de Mathématiques Supérieures on Modern Methods in Scientific Computing and Applications, Montréal, Québec, Canada, 9-20 July 2001 Proceedings of the NATO Advanced Study Institute and Seminaire de Mathematiques Superieures on Modern Methods in Scientific Computing and Applications, Montreal, Quebec, Canada, 9-20 July 2001 In the 1973 paper entitled "Some Modified Eigenvalue Problems" by Golub [34], numerical calculation of several matrix computation problems are considered.