We summarize and compare our recent methods for reducing the complexity of computational problems, in particular dimensional reduction methods based on the Mori-Zwanzig formalism of statistical physics, block Monte-Carlo methods, and an averaging method for deriving an effective equation for a nonlinear wave propagation problem. We show that their common thread is scale change and renormalization.
Bibliographical noteFunding Information:
We are grateful to Prof. G.I. Barenblatt and to Dr. P. Stinis for many enlightening discussions, suggestions, and comments. This work was supported in part by the National Science Foundation under Grant DMS 97-32710, and in part by the Office of Science, Office of Advanced Scientific Computing Research, Mathematical, Information, and Computational Sciences Division, Applied Mathematical Sciences Subprogram, of the U.S. Department of Energy, under Contract No. DE-AC03-76SF00098.
- Problem reduction