Study On The Mesh Generation Based On Geometry Decomposition

The numerical methods play an increasingly important role in various scientific calculations and engineering designs.The mesh generation has become one of the key steps when using the numerical methods.Different applications have different requirements for type,shape and quality of mesh.Although the mesh generation technology has become quite mature,but the existing mesh generation methods and softwre cannot generate required mesh for some numerical analysis applications.Therefore,it is necessary to improve the existing mesh generation methods and develop appropriative program based on the characteristics ofthe applications.In this thesis,the research of mesh generation and program development are carried out based on the special requirements of mesh in some specific applications.A mesh generation based on geometric decomposition is proposed,which has meet the special requirements of mesh in these applications.Electromagnetic analysis is an important part of the design of radio frequency integrated circuits.The common used numerical method for electromagnetic analysis is the method of moment(MoM).Different with traditional numerical methods,the most suitable mesh type for the MoM are rectangles or mixed triangle-rectangles and the more rectangles,the better.Although the grid-based method can generate mixed triangular-rectangular meshes,but when using it generate mesh for integrated circuits directly,the proportion of rectangles are too small to result in low efficiency and accuracy of the numerical analysis.According to the characteristic of local regular shape of integrated circuit,a mesh generation method based on geometry decomposition is proposed.The geometry of integrated circuits is decomposed into a series of rectangular sub-regions,and then the rectangular sub-regions can be meshed into rectangles and the remaining non-rectangular sub-regions meshed into triangle-rectargles by using the grid-based method.Decomposing the geometry of integrated circuits into as many rectangular sub-regions as possible is the key to this method.A geometry decomposition method based on constrained Delaunay triangle(CDT)mesh is proposed to simplify the decomposition.The CDT mesh is generated on the region and the geometric vertex make perpendicular to the opposite edge according to the topology of the CDT mesh,and then regenerating the CDT mesh.The edges of triangle mesh are selected based on certain criteria to decompose the region into a serious of rectangular regions and remaining regions.The number of rectangles of integrated circuit can be greatly improved by using the mesh generation method based on geometry decomposition.When calculating section properties and carrying out finite element analysis for thin-walled steel box girder,quadrilateral meshes needed to be generated on its section.Because the thin-walled steel box girder section has large span,thin wall and many U-shaped ribs,it is always generate irregular shape or poor quality of mesh when using the existing finite element software.In this thesis,according to the characteristics of thin-walled steel box girder section,a method similar with the mesh generation method of integrated circuits is proposed.The geometry ofthin-walled steel box girders section is decomposed into a series of quadrilateral regions,and then regular quadrilateral mesh can be generated on each quadrilateral sub-region.The mesh generation method for thin-walled steel box girder section can generate the regular quadrilateral mesh on the whole region and the quality of mesh generated by this method are better than the mesh generated by the existing software.An automatic quadrilateral surface mesh generation for 3D is proposed by applying the geometry decomposition to the 3D surface.The 3D surface model is decomposed into a series of sub-regions and then each sub-region is flatten to 2D to generate quadrilateral mesh and finally,the 2D quadrilateral mesh be mapped back to 3D to obtain the quadrilateral surface mesh.To improve the poor quality mesh on the boundaries of 3D sub-regions,an effective boundary optimization method is proposed.The quadrilateral surface mesh generation method based on decomposition reduces the complexity and enhances the efficiency of mesh generation.Based on the method proposed in this thesis,the mesh generation program for integrated circuit,thin-walled steel box girder section and 3D surface are developed by using C++ language.Several examples for mesh generation are given to demonstrate the reliability of the method and verifies that the mesh can meet the requirement of practical engineering analysis.