Numerical methods for nonlinear elliptic eigenvalue problems
This project deals with the problem of solving nonlinear eigenvalue problems, namely, nonlinear systems with parameter dependence, primarily through the use of continuation methods. One of the major issues that we are interested in is in solving large and sparse problems. In particular, we put special emphasis on nonlinear elliptic eigenvalue problems, partly because these constitute an important class of applications, and partly because this class brings out some of the fundamental computational aspects of algorithms for solving general nonlinear eigenvalue problems. Specifically, we are interested in the nonlinear and linear algebraic techniques involved, which usually constitute the most time consuming part of these algorithms. Another major objective is the accurate computation of singular points, which are often of great physical interest. A primary goal of our project is to develop a well-documented piece of mathematical software that incorporates results from our algorithmic studies (and others) and that can be used to trace solution curves of rather general, large and sparse nonlinear eigenvalue problems.
- Research Organization:
- Yale Univ., New Haven, CT (USA). Dept. of Computer Science
- DOE Contract Number:
- AC02-81ER10996
- OSTI ID:
- 5001906
- Report Number(s):
- DOE/ER/10996-T2; ON: DE84010408
- Country of Publication:
- United States
- Language:
- English
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