Study On Stability And Accuracy Of Time Domain Boundary Element Method

The boundary element method transforms the governing equation of the actual problem into the integral equation on the boundary,and then introduces the finite element at the boundary to discretize the integral equation.It only needs to calculate the unknown quantity on the boundary,thus reducing the dimension of the problem.The introduction of the basic solution makes the boundary element method have the characteristics of analytic and numerical combination,so the precision is higher.The time domain boundary element method is a boundary element method based on the basic solution of the boundary to establish the boundary integral equation.As an efficient numerical processing tool,the time domain boundary element method has been developed rapidly in recent years.With the deepening of research,the numerical results of the instability of the problem gradually highlighted.The selection of the unit type has a great influence on the numerical results.In this paper,the linear unit are used to discrete the displacement and flux both on time and space,and the influence coefficient matrix is assembled,and the influence coefficient matrix elements are solved.The time-domain boundary element method with full linear element will have higher precision.In terms of the stability of the time domain boundary element method,the numerical examples are used to illustrate the instability,and the causes of the instability are studied,including the existing interpolation function can not meet the fluctuations in the "causal relationship" conditions,the time step is improperly chosen,accumulation of numerical integration error,where the time step is the most important factor.In view of its instability,this paper draws on the Wilson ? method in finite element which is used to improve stability,forward time prediction method,and completed the theoretical derivation and program realization.The improved time-domain boundary element method is used to calculate the classical cantilever problem,then compare the results to the results before improvement.The results show that the time domain boundary element method with full linear element discretization and improved by forward time prediction method is better in the stability of numerical results.The choice of time parameter directly determines the value of time step,and the time step is the most important factor affecting the stability of time domain boundary element method.In this paper,we study the time parameter research program,including the selection of time parameters and the calculation of errors.Then the problem of the cantilever beam and the infinite domain hole are studied according to the established research scheme.The relationship between the time parameter and the error is obtained.Finally,the reasonable range of the time parameter in the improved time domain boundary element method is given.