Development, Analysis and Application of Numerical Methods for Nonlinear Partial Differential Equations

点击翻译按钮获取中文摘要

9706827 Stanley Osher This research is concerned with the accurate and efficient computation of "irregular" solutions of partial differential equations (PDEs). This includes solutions with discontinuities, singularities, fine scale structure, or persistent oscillations. The main topics include (1) kinetic formulations of nonlinear PDE's and applications; (2) interface capturing through the level set method; (3) discontinuity capturing based on ideas developed for the numerical solution of conservation laws; and (4) numerical and analytical study of oscillations and critical threshold phenomena. The proposed research will impact numerous areas of science and technology. With the advent of modern computers, formerly intractable problems can be solved accurately. This, of course, requires accurate and convergent algorithms for these difficult nonlinear and computationally intense problems. The algorithms formerly developed by this group are already in wide use throughout the country in national laboratories and industry. The proposed methods to be developed here will be useful in a host of applications including combustion, oil recovery, crystal growth, electromagnetic and acoustic scattering, thin film semiconductor growth, aircraft design, to name just a few.