Finite-element Eigenmode Analysis Of Any Resonant Cavities Based On High-order Hierarchical-basis Functions

For the requirements of general projects, better numerical method is always the keyof the electromagnetic theory calculation research. The vector finitte-element method iswidely researched and applied in the area of electromagnetic calculation, because it hasthe ability to solve complex geometry and nonuniform medium. For now, the vectorfinite-element method researches are focusing on creating primary function andimproving the convergence rate of the numerical simulation process. The vectorfinite-element method with the concentration of high-order hierarchical-basis function isresearched in this thesis. In this process, a new universal matric method is brought in.Firstly, first order vector finite-element method is applied to eigen analysis therectangle resonant cavities of microwave pipes. Secondly, vector finite-elementmethods based on second order and third order basis functions are applied in thecalculation of rectangle resonant cavities, then we’ve discussed the pros and cons ofsecond order and third order basis functions. Thirdly, a new vector finite-elementmethod based on universal matrix is applied in the calculation of rectangle resonantcavities, and the merits are discussed. Finally, we’ve discussed the theory of vectorfinite-element method based on curvilinear element.The primary work and innovations are listed below:1. Electromagnetic field vector finite-element method has been researched andvector finite-element method theories and derivation has been mastered. Resonantcavities vector finite-element method has been discussed with the eletromagnetictheories, function equation is derivated from boundary-value problem. Matrix equationsthat can be numerically solved have been achieved by the dispersed function equationswith the vector interpolation function;2. Based on the researches of vector finite-element method with conventional firstorder primary function, the vector finite-element method with second order and thirdorder hierarchical-basis functions have been discussed and applied in numerialsimulation process;3. Univeral matrix complaint with second order and third order hierarch primary functions has been derivated, calculation cost of vector finite-element method can bedecreased by using universal matrix. This is one of the innovations of this thesis;4. The vector finite-element method based on curvilinear element has beendiscussed, this is also one of the innovations of this thesis;5. Testing programs are written with C++on the platform of Windows, validity ofuniversal matrix and accuracy of calculation program have been verified by comparingthe actual calculation results and the analytic value.