Research On Equation Of Evolution Using Element-Free Precision Integration Method

The equation of evolution studied in this paper is limited to partial differential equation, such as heat conduction equation and oscillatory differential equation. It is hardly to get and express the solution of the equation of evolution by the analysis, so it used to solve the equation by numerical method. The method puted forward in this paper is a new numerical method which combined the meshless method and time precision integration method togethert to solve the equation of evolution.Element free Galerkin method (EFGM), similar to FEM, is a new numerical method developed recently. In EFGM, in order to get a numerical solution for a partial differential equation, shape function is constructed by moving least square method, control equation is produced from the weak form of variational equation and Lagrange multipliers are used to satisfy essential boundary conditions. EFGM methods require only nodal data, no element connectivity is need. This method not only has high accuracy but also has lower difficulty. In this paper the EFGM is used to discretized the equation of evolution in time domain. The physics meaning of the Lagrange multipliers which is derived by modified variation principle is used to satisfy the essential boundary conditions, it reduced the total number of indeterminate and increased computing efficiency .Time precision integration method is a mature numerical algorithm to solve the ordinary differential equation.it has the merits of large time step, higher accuracy , unconditional stability, etc. It is used to solve the discretized equation which is derived by EFGM. So the final result of the equation of evolution is gotten. The chief work is:1. Modified variational principles of the heat conduction problems are derived, element free galerkin-precision integration method in the one and two dimensional heat conduction problems is gotten.2. The element free galerkin-precision integration method in convection problem is studyed.3. Modified variational principles of the 2-0 dynamics problems are derived, element free galerkin-precision integration method in 2-D dynamics problems is gotten.4. The program of above algorithm is complied, and the valid of this algorithm is verified by analytic solution and ANSYS simulate.