Study On Some Key Technique Of 3D DGTD Method

Discontinuous Galerkin Time Domain(DGTD)method is the hotspot of computational electromagnetics in recent ten years.DGTD is made up of the concept of numerical flux and unstructured meshes that remarkably raises the efficiency while the accuracy remains unchanged.Now DGTD is in the process of vigorous development,along with DGTD in electromagnetic problems more and more widespread application(such as target characteristics,electromagnetic compatibility,microwave remote,wave propagation in complex environment,etc.).It has theoretic significance and practical value in studying DGTD based on the vector basis functions in 3D case.In this dissertation,some key problems of the DGTD method in 3D case are studied,including iterative formulas of DGTD,data exchange between adjacent elements,the implementation of UPML absorption boundary in DGTD,introduction of plane wave and near-far field extrapolation and so on.In addition,to improve accuracy while saving computational resources,the application of hierarchical vector basis functions in DGTD algorithm is studied.A DGTD scheme for dispersive media medium is presented by using the Shift-Operator method(SO-DGTD).The electromagnetic simulations of complex medium are obtained by unified SO-DGTD program for the typical dispersive model including Debye,Drude and Lorentz.Besides,our algorithm is extended to dusty plasma and magnetized cold plasma(anisotropic dispersion).At last,a parallel DGTD algorithm by using MPI(message passing interface)library is described.The main works of this dissertation is summarized as follows.1.The first part introduces the DGTD method based on vector basis functions.Starting with Maxwell equations,the weak form is developed by using Galerkin procedure.Then the leapfrog iteration formulas are derived from the weak form.DGTD is formulated on unstructured meshes,it's necessary to share the unknowns in adjacent elements by using numerical flux.To improve the efficiency of modeling when there are a huge number of elements,a fast algorithm called “Casting Box” is given to find common faces of the tetrahedrons,this algorithm uses orthogonal grids to identify adjacent tetrahedrons,which is efficient and easily realized.To handle special mediums,the boundary conditions of PEC,PMC and Silver Muller-ABC are implemented in the flux condition.2.To analysis scattering and radiation problems,the source implementation of dipole and plane wave are discussed.To extract far-field from simulation,Near-far field extrapolation technique is developed based on the equivalence principle.A good absorbing boundary is important for scattering and radiation problems,so the implementation of UPML is given in this dissertation.The optimization problem of UPML are studied based on the simulation of dipole.In order to reduce computational cost,a conformal UPML with the shape of scalene ellipsoid boundary is proposed.Compared with spheroid or sphere,scalene ellipsoid can be easily adjusted to match certain geometries and reduce computational cost.Calculations prove that this boundary has good absorption effects for outgoing waves.3.Frequency-dispersive media are materials where the permittivity or the permeability of the medium is frequency-dependent.DGTD is a time domain method,the time domain constitutive relations are needed for computing.To solve this problem,a number of methods have been proposed for time domain method,such as the recursive convolution(RC)method,the auxiliary differential equation(ADE)method and the Z-transform method,etc.A drawback of these algorithms is that different formulations are deduced from each dispersive model.Notice that the generality of Shift-Operator(SO)method,the SO-DGTD is presented for dispersive medium.This method can handle the typical dispersive models(ie.Debye,Drude,Lorentz),and it is also extended to dusty plasma and magnetized cold plasma.Time domain solutions of varying plasma problems are becoming important in the area of complex media at present.The example of time-varying plasma in a cavity is given,the wiggler magnetic field is obtained after the plasma is sudden created,the agreements between analytical value and numerical solution are excellent.4.In order to improve the accuracy and reduce the resource cost,the hierarchical vector basis functions are implemented in DGTD.Considering pure high-order elements causes the high consumption of resources,the hybrid use(mix-order)of high-order elements and low-order elements is discussed.Accuracy of high-order,low-order and mix-order is compared by numerical examples.The results show that mix-order has an advantage over others.5.Practical engineering problems are very resource hungry which made unaffordable for PC,it is necessary to parallelize DGTD algorithm in these circumstances.In this dissertation,we described a parallel DGTD algorithm by using MPI(message passing interface)library.At first,the parallel model is got by preprocessing of original model(meshes are partitioned and renumbered,the topology diagram is extracted).Then,processor 0 read the parallel model,and spreading data across each of the compute processors(only the data required by the processor).In every step,communication of data is done using MPI function,then update electronic fields and magnetic fields,and keep the cycle going.At last,outputting the result at the end of the calculation.The tests at the supercomputer demonstrate our algorithm has good parallel efficiency.The proposed parallel algorithm is capable of dealing complex problem,the plasma sheath model with complex distributed plasma is simulated by our algorithm.