Final technical report.

[摘要] In the last two dcades or so, many multiscale algorthms have been proposed to enable large scale computations which were thought as nearly intractable. For example, the fast multipole algorithm and other similar ideas have allowed to considerably speed up fundamental computations in electromagnetism, and many other fields. The thesis underlying this proposal is that traditional multiscale methods have been well-developed and it is clear that we now need new ideas in areas where traditional spatial multiscaling is ill-suited. In this context, the proposal argues that clever phase-space computations is bound to plan a crucial role in advancing algorithms and high-performance scientific computing. Our research past accomplishments have shown the existence of ideas beyond the traditional scale-space viewpoint such as new multiscale geometric representations of phase-space. We have shown that these clever representations lead to enhanced sparsity. We have shown that enhanced sparsity has significant important implications both for analysis, and for numerical applications, where sparsity allows for faster algorithms. We have implemented these ideas and built computational tools to be used as new building blocks of a new generation of wave propagation solvers. Finally, we have deployed these ideas into novel algorithms. In this last year, we assembled all these techniques and made significant progress in solving a variety of computational problems, which we then applied in selected areas of considerable scientific interest.

[发布日期] 2007-11-06

[学科分类] 社会科学、人文和艺术（综合）

[关键词] ALGORITHMS;ELECTROMAGNETISM;MULTIPOLES;PHASE SPACE;VELOCITY;WAVE PROPAGATION Curvelets;Sparsity;Wave Equations;High-Frequency Wave Propagation;Fast Multiscale Geometri