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.

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.