The Research Of Adaptive Numerical Manifold Method

With the progress of modern computer technology, numerical simulation method has been got the rapid development, many developing numerical simulation methods have been widely applied to the specific practical engineering problems. However, most of the numerical simulation methods are only for the continuity of actual problems, Numerical manifold method (NMM) as a representative simulation methods of researching non-continuous problems received more and more attention of researchers. Currently, the research on manifold units formed by two cover systems is also unusual in the research field of numerical manifold method. This article researched adaptive manifold units of NMM based on the improvement of the accuracy of the numerical solution.The first chapter consists of three parts, firstly, the current existence of the numerical simulation methods were simple outlined; Secondly, the research status of numerical manifold method were outlined; The last, the contents of this paper were proposed based on the existing problems of NMM.The second chapter introduced the basic principles of NMM and the handling methods of fixed boundaries constraints, by learning the formation mechanism of manifold units and each matrix that solves manifold units, I have a comprehensive understanding of NMM.The third chapter focused on the basic theory of adaptive numerical manifold method, the specific content includes:a. Adaptive numerical manifold method was put forward; b. Two adaptive analytical methods; c. The adaptive manifold unit types. Adaptive numerical manifold methods are:adaptive analysis of interpolation function and adaptive analysis of manifold units; The adaptive analysis of manifold units were focus of analyzed, the formation process of adaptive manifold units and adaptive strategies of NMM were discussed, and a numerical example were conducted.The fourth chapter divided the optimization of adaptive manifold units, the optimization includes two types of encryption and thinning. The optimization of triangle manifold units and quadrilateral manifold unit manifold units were researched, the encryption of triangle manifold units were validated as a numerical examples, the results show that the quality of triangle manifold units and calculation accuracy have improved, so this program was feasible. In sofa scheme, the Delaunay triangle manifold units as the initial manifold units were researched.