A Study of Possible Applications for Jacobian-Free Newton Krylov Methods in Nuclear Reactor Physics
Dion J. Koeze, Danny Lathouwers, TU Delft · 2009
A Survey of a Jacobian-free Newton Krylov method using GMRES is presented in this report. The goal of the project is to see whether JFNK has applications in nuclear reactor physics. JFNK methods are methods that solve sets of non-linear equations. The sets of non-linear equations arise from coupled physics problems, as found in nuclear reactor physics. JFNK is especially good at solving coupled sets of equations, since it does not need the Jacobian matrix to solve the problem. It uses an approximation to the Jacobian matrix, this is possible because the Jacobian matrix is only needed as a matrix vector product. In this report two test problems are used to test the JFNK method. First the heating of a one dimensional rod, while the rod cools by emiting radiation, modeled as a black body. The second test problem is a model of a molten salt reactor. Since there are many coupled problems in the area of nuclear reactor physics it can be used in many problems. All problems that were encountered in this project have been solved. The harder problems where JFNK could break down were, however, not encountered. Preconditioning is not considered in this project.