Building a Software Package for Solving Large Sparse Nonlinear Systems of Equations
Abstract
We developed a preliminary version of general purpose code on a nonlinear version of GMRES, a method for solving nonsymmetric linear systems. Using the Jacobian-free approach, we were able to solve relativity hard problems in a short period of time and with a minimum of programming effort, thus demonstrating the viability of the proposed code. Among the strongest points of the projected package are its ease of use and the variety of proposed techniques. Although there has recently been progress in research on nonlinear problems, there is no commercially available software package for dealing with them. The objective of Phase I in this project was to write and test a preliminary code to show the feasibility of a general purpose nonlinear solver. In doing so, we concentrated on: 1) Considering appropriate simple techniques for handling nonlinearities; 2) Choosing the most appropriate linear system packages to incorporate in the package; and 3) Improving and incorporating more sophisticated algorithms for handling nonlinearities. We emphasized the first and third objectives. For the second objective we have also done some tests with PCGPAK, the Preconditioned Conjugate Gradient Package of subroutines for the iterative solution of large, sparse, nonsymmetric systems of linear equations, a package implemented by Scientific Computing Associates.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 24, 1986
- Accession Number
- ADA211758