Improving SIR : A Semi-Implicit Root Solver with Particular Applications to Global Solution of PDEs

• Main Author: Håkansson, Cristian
• Format: Others
• Language: English
• Published: Uppsala universitet, Institutionen för informationsteknologi 2009
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-103030

The computational core of the Generalized Weighted Residual Method (GWRM) is the Semi-implicit Root Solver (SIR), originally written in Maple. In this paper, we improve the performance of the SIR algorithm. This improvedversion is then implemented in MATLAB. We incorporate this MATLAB version into GWRM and compare it to a similarly improved pure Maple implementation.Furthermore, Newton's method with line search (NL) is also implemented inMATLAB and compared to SIR. In order to perform this comparison we introduce convergence maps as a new,compact, way to visualize convergence properties as we vary the initial guess. These are employed in order to compare SIR and NL in terms of stability of convergence. The tests are carried out on a predefined set of standard problems. We conclude that the MATLAB implementation of SIR is a substantial improvement over the Maple implementation when used in GWRM. Furthermore, compared to NL, SIR is shown to have a greatly reduced sensitivity to variations in the initial guess. Conversely, NL is shown to perform slightly better when using only the initial guesses defined along with the standard problems. This paper ends with a few suggestions on how the algorithm can be furtherimproved.