The Research Of Visualization Technology For Numerical Manifold Method

Numerical manifold method (NMM) is a new numerical method that is widely used in many fields of engineering computations and is the research hotspot in CAD/CAM. The theory and method of NMM's visualization is investigated based on its basic principle and property. We first set up the hiberarchy of the NMM's visualization and focus on the study of PEM's visual process. Then the coupling equation of PEM is deduced and a rapid algorithm for solutions of bordered tridiagonal linear equations is put forward. In the last of the thesis, elementary system of deformation geometry unified for manifold's structure is studied primarily via the idea of unified modeling and some theoretic results for analytical visualization are given out under the system of Frenet frame of arbitrary parameters.Concretely, the keynotes of the thesis are as follows:1. The hiberarchy of NMM and key technology of the PEM's visualization are pur forward by basic principle and propertyes of NMM.2. The governing equation of patch element is built up for Robin condition based on the theory of FEM-BEM coupling.3. Aiming at the property of large-scale matrix produced in the numerical computation, a fast algorithm of Bordered Tridiagonal Linear Equations is given out. The experimentation indicates that the algorithm is effective and possesses the prorperty of parallel computation based on the isomerous computers.4. The elementary theory of deformation geometry is dicussed in term of the idea of unified modeling, and complex relationship in the procedure of deformation of geometry object is expressed analytically. It makes that the traditionally numerical demonstrating method of visualization gives way to analytical one based on the continual theory, so that exact visualization is realized.