Post-processing Technology Research On Discontinuous Galerkin Method For Maxwell Equations

Classical electromagnetism based on Maxwell equations is widely used in real life.Most electromagnetic phenomena are simulated by Maxwell equations.Classical electromagnetism also has a wide range of applications in various fields and practical daily life,such as magnetic levitation technology,optical fiber,antenna radar,medical imaging and so on.At the same time,electromagnetism is also widely used in various engineering fields,with great practical operability.However,Maxwell equations and their solution areas and material composition are complicated to some extent,and in general,accurate analytical solutions cannot be obtained.Therefore,accurate and efficient numerical methods are needed to simulate accurate solutions to achieve the purpose of solving Maxwell equations.In the process of development,there are many kinds of numerical methods.Whether the numerical method selected is feasible and effective requires theoretical analysis to illustrate the operability of this algorithm.Discontinuous Galerkin time-domain(DGTD)method has hp adaptive and can perform numerical solutions for complex computational regions.The advantages of this numerical method make it widely used in electromagnetic calculation.Therefore,the DG method is used in thesis to solve the Maxwell equations,and the error estimation and precision convergence of the numerical solution and the exact solution after post-processing are carried out.At the same time,the negative-order norm estimation of the post-treated solution is carried out,and the error accuracy is proved by theoretical analysis.Comprehensive research content of thesis includes following three aspects:1.First need to use in the process of theoretical analysis and computation of symbol is explained,and then using the discontinuous Galerkin method to Maxwell equations under the differential form of time domain numerical calculation,the numerical solution of the Maxwell equations is obtained by DG scheme in space and time discretization,then use specific numerical example to verify the numerical calculation process is feasible and accurate.2.Explain the post-processing technology Smoothness-Increasing Accuracy-Conserving(SIAC)filter,and theoretically analyze the post-processing of the numerical solution of linear hyperbolic equation solved by DGTD method.Numerical examples are given to illustrate the effectiveness of this post-processing technique.3.Negative-order norm estimation and convergence analysis were carried out for the DG solution of Maxwell equations in time domain,and the convolution post-processing was carried out for the DG solution,and the convergence order estimation and error analysis were carried out for the obtained post-processing solution.Numerical experiments were conducted to verify that post-processing can make the numerical solution achieve higher accuracy and the feasibility of post-processing.