| The problems encountered in physics, mechanics and engineering, which belong to initial value and boundary value problems, generally it need utilize the numeric approximation method to be solved except for some simple ones.Boundary element method is a kind of boundary numeric method, which is based on the boundary integral equation, and adopts element discretization technique. The virtual boundary element method is a relatively new numerical method, which belongs to indirect BEM, with highly computational accuracy and less prepared data, symmetrical coefficient matrix and it could avoid singularity integral in the direct boundary element method.The multi-domain composite problem with the virtual boundary is used to solve the frame-shearwall structure; it not only approves the practicability and reliability of the method, but also let us could know the higher efficiency than other methods. The idea of this paper can be applied to solve the problems about multi-domain thin plate with the same thickness, composite body with different material property, composite material laminated plate, contact problem, and coupling technology of virtual boundary element method and finite element method, etc.Fast Multipole Method (FMM) is a new numerical method; it brings a revolutionary change to Boundary Element Method. In the paper we use the Taylor expanding formula on planar complex number and the self-adapting tree structure, and deduce the multipole expanding and transfer format which adapt to two dimensional elastostatics, and form Fast Multipole Virtual Boundary Element Method with O(N) order of magnitude. This method won't form the coefficient matrix in explicit formulation. It can save EMS memory and improve precision of answers under the GMRES to solve equations. This method is fit for solving the elasticity mechanics with large degree of freedoms, accelerate the solving of equations, so it extend the adapt area of Virtual Boundary Element Method.
|
PDF Full Text Request