[PDF] Improved Moore-Penrose continuation algorithm for the computation of problems with critical points-论文阅读讨论-ReadPaper

摘要

Using typical solution strategies to compute the solution curve ofchallenging problems often leads to the break down of the algorithm. To improvethe solution process, numerical continuation methods have proved to be a veryefficient tool. However, these methods can still lead to undesired results. Inparticular, near severe limit points and cusps, the solution process frequentlyencounters one of the following situations : divergence of the algorithm, achange in direction which makes the algorithm backtrack on a part of thesolution curve that has already been obtained and omitting important regions ofthe solution curve by converging to a point that is much farther than the oneanticipated. Detecting these situations is not an easy task when solvingpractical problems since the shape of the solution curve is not known inadvance. This paper will therefore present a modified Moore-Penrosecontinuation method that will include two key aspects to solve challengingproblems : detection of problematic regions during the solution process andadditional steps to deal with them. The proposed approach can either be used asa basic continuation method or simply activated when difficulties occur.Numerical examples will be presented to show the efficiency of the newapproach.

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