Comparative Study Of EFG Method And IEFG Method

Element Free Galerkin method(EFG)is a very important numerical method in Meshless methods.Its approximate function is constructs by the moving least squares method(MLS),the differential equation is transformed into the equivalent integral weak form by Galerkin method.The interpolation element free Galerkin method(IEFG)is also one of the Meshless methods which can apply boundary conditions directly,thus it shuns away from the use of Lagrange multiplier method or penalty function method,and now the number of unknowns in the equation sets can be reduced,so as to the computational efficiency is improved.In the second chapter,the MLS method and the interpolation moving least squares method(IMLS)is introduced,and a comparison is made between the two methods.The third chapter uses the EFG method to solve the two-dimensional steady-state heat conduction equation,when choosing the basis function as linear and quadratic,by comparing the numerical solutions and analytical solutions respectively,the influence of the order of the basis function on the precision of the EFG method is analyzed.The EFG method and the IEFG method of the potential problem are compared in the fourth chapter.The calculation program is compiled,corresponding numerical examples are given,which shows that the IEFG method has higher precision than the EFG method.