Subdivision Surface Technique In Solving The Boundary Integral Equation

Subdivision surface is a new technology that has been developing for about twenty years in Computer Graphics.it can depict complicated models with the controlling graphic grids using the Computer Graphic disposal method and fractionize the grids according to the precision requirements. The model can be depicted to C~n continuum with subdivision surface. So far. the traditional boundary element method can not depict the complicated model accurately or coarctate the meshes automatically; moreover, the CAD model cannot be used directly for numerical simulation. In this paper, a new paradigm for boundary element method is developed based on the use of subdivision surface to: i) accurately describe the boundary geometry to reduce the error from the disfigurement on depicting models when using the traditional boundary element method with which only the boundary curves or surfaces are discrete, ii) realize growing the mesh density automatically and iii) offer an approach to use the CAD models directly in CAE.The main research work and conclusions are listed as follow:(1) The arithmetic theory of subdivision surface is introduced as well as the subdivision surface method applied in this thesis; the disposal method of boundary and the convergence of subdivision surface are also presented.(2) How to apply the subdivision surface to boundary element method, including the interpolating method in single element, the changing of shape functions and the integral coordination, is depicted in detail.(3) Both of the constructing course based on the wavelet and the expressions of coefficients of the boundary spectral method are introduced; the combination of the boundary spectral method and subdivision surface is discussed too.(4) The elasticity torsion problem, problems with more than one surface of Laplace's equation, Posson's equation problem and the problem of two- dimension acoustic radiation and scattering are discussed with the method introduced in this paper; and finally, the results obtained with the method introduced in this paper are compared with those obtained with the traditional boundary element method.