A Study Of P-Adaptive Method For Finite Element Based On Hierarchical Basis Function

In the field of computational electromagnetic,finite element method has been favored by many scholars because of its advantages in dealing with inhomogeneous media and irregular geometry.With the increase of the scale and complexity of finite element method,the traditional low-order vector finite element method can no longer meet the accuracy requirements.Therefore,the higher order hierarchical vector basis function with higher interpolation accuracy is an important direction in the development of finite element.However,the introduction of higher order basis functions will bring more unknowns,which brings great challenges to computing resources of computers.In order to effectively improve the accuracy of finite element solution and reduce the demand for computing resources,this thesis studies the high-order hierarchical vector basis function and the adaptive finite element method.In the first part of this thesis,the basic theory of finite element method is introduced,including the establishment of electromagnetic field boundary value problem,solving regional discretization,finite element interpolation function selection,Galerkin method to establish the finite element variational equation,matrix assembly and solving,etc.The truncated boundary conditions for open field problems are also introduced.In the second part of this thesis,we study the basis functions of high-order hierarchical vectors,introduce the construction of high-order hierarchical vector basis functions,and introduce the coding method of the program in this paper to realize the high-order hierarchical vector basis functions and the calculation of unit integral terms.Filling,how to assemble the overall matrix,and the processing of boundaries when mixed-order units appear in the program,etc.At the end of this part,examples of dielectric balls,patch antennas and PIFA antennas are used to verify the accuracy of the program.It can be seen from the results that the high-order vector element has higher accuracy than the traditional low-order vector element.In the third part of this thesis,the finite element adaptive method is studied,and a finite element basis function order(p)adaptive method based on grid electric size is proposed..Respectively by scattering,three different types of port parameter transmission and radiation calculation based on the study of selective basis function expansion,according to the result of numerical example p-adaptive programming experience and,at last,through the waveguide width edge slot antenna with quaternary dipole array is proposed based on grid electricity right size verifies the effect of the finite element method of p-adapt,can be seen from the final results,this method has high precision,and can save memory and the solving time effect.In general,the research work in this thesis has a positive significance for improving the efficiency of finite element solution and saving computational resources,and provides a feasible option for improving the scale of finite element solution.