High Performance Discontinuous Galerkin Time Domain Method In Computational Electromagnetics

With the advancement of science and technology,the functionality,precision and integration of electromagnetic devices are rapidly increasing.Therefore,the modern electromagnetic environment becomes increasingly complex which demands for more accurate and efficient electromagnetic numerical modeling methods.From the perspective of computational electromagnetics,the complexity of numerical simulation of electromagnetic environment mainly lies in three aspects which are the multi-frequency scale of the excitation source,the multi-space scale of the target object,and the multi-media characteristics of the system.These complexities present challenges for high-performance,high-confidence numerical simulation of complex electromagnetic environment problems.Therefore,to solve the increasingly complex electromagnetic simulation problems,this dissertation chooses the discontinuous Galerkin time domain(DGTD)method which has received extensive attention as the starting point,studies and analyzes the advantages and disadvantages of the method,and develops several highly efficient simulation techniques based on this method.The main work and contributions of this dissertation includes the following parts:1.Aiming at high memory usage caused by numerical fluxes,a low storage scheme basedon universal matrices technique is proposed.By expressing the space basis functionusing the barycentric coordinates,the matrix in the DGTD can be decomposed into asuperposition of universal matrices and its corresponding coefficients.Therefore onlya very few of universal matrices need to be stored,so that the required memory usageis tremendously reduced.Numerical examples show that memory usage can be saved11.5 times when using a fully 2nd order basis function.2.In order to solve the problems of small and medium electrical size with multi-scalestructure more efficiently,a new time marching technique based on weighted Laguerrepolynomial is proposed.By performing the temporal and space basis function expan-sion and Galerkin process,the time variable in the whole solution system is eliminated.Therefore,the new time solving techniques are unconditionally stable.Aiming at theshortcoming that the transient electromagnetic field solved by traditional weighted La-guerre polynomials cannot meet the initial conditions,a modified temporal function isproposed.The numerical results show that by using the new temporal basis,the longtime instability of the traditional UPML can be eliminated.And it can significantlyimprove the computational performance in the multi-scale problems.In addition,theproposed new temporal basis function can reduce the error of the solution at the initialtime and improve the overall performance.3.In the framework of the new time marching technique,boundary integral is introducedto create a more accurate absorbing boundary condition.Combining the time domainboundary integral method with the DGTD method and using the new time marchingtechnique,the generated hybrid method can simultaneously achieve the accurate ab-sorbing boundary condition and unconditional stability.4.The DGTD-WE method is established,and by analyzing the numerical fluxes,cor-responding boundary conditions required in practical engineering problems are pro-posed.An empirical formula of the stability condition in both theoretical and numer-ical ways.The resultant method is compared with the DGTD-ME and FETD-WEmethod which demonstrates the excellent computational performance.5.An improved DGTD-WE(IDGTD-WE)method is proposed in which the originalDGTD-WE method is modified and built on the modified wave equation to eliminatethe late time drift phenomenon.An improved calculation method for the Maxwell-Faraday equation is proposed to ensure the accuracy of the second working variable inthe wave equation-based method.The numerical examples show that the two work-ing variables have the optimal convergence rate.And the IDGTD-WE method usingmixed 2nd order spatial basis functions is used to calculate the electric and magneticfields simultaneously,then compared with the results obtained by DGTD-WE method.It shows that 45% CPU time and 36% memory usage reduction can be achieved;Fur-ther,to take advantages of both methods,the author combines the IDGTD-WE methodwith the DGTD-ME method to obtain a hybrid method.With this hybrid approach,the author successfully solves electromagnetic problems contains dispersive medium.Numerical examples show that compared with the DGTD-WE-rFFT method,the pro-posed method can save 38% the computation time.6.In order to deal with the multi-physics problems which consist of electromagnetic fieldand circuit subsystems,a general impedance transmission boundary condition is pro-posed.In order to obtain a robust electromagnetic field-circuit hybrid method,a novelstable voltage evaluation technique is proposed for the first time.The stability and cor-rectness of the method are verified by the numerical experiments.The microwave de-vices with nonlinear components are analyzed numerically and experimentally whichdemonstrate the validity and practical value of the proposed method.Based on the DGTD method,this paper deeply researches and explores the time domain electromagnetic simulation algorithm,and develops a series of high performance time domain electromagnetic numerical simulation methods,which provides a new effective and high performance solution for complex electromagnetic multi-scale simulations.