Study On Parallel Finite Difference Time-Domain Method And Hybrid Method Based On GiD

The advantages of the powerful computer are utilized by parallel Finite-difference time domain method (FDTD), which enhances the capacity forelectromagnetic analyzing for complicated and electrically large problems. Based onthe concept of aerodynamic and stealth synthesis design, a characteristic-based,Finite Volume method in Time Domain (FVTD), which stems from the techniques ofComputational Fluid Dynamics (CFD), has been applied to computational electro-magnetism (CEM). FVTD algorithm is naturally conformal and multiscale, but costsrelatively high computational cost per cell. A hybrid technique FD/FV which buildsupon modeling strengths of each algorithm will be a good choice for efficientlysimulating structures that include curved or oblique structures. The main contribute-ons of the dissertation include：1) According to the features of FDTD algorithm, the author developed aGroup Identification (GiD) problemtype by means of the Cartesian mesher belongsto GiD. GiD is a popular personal pre and postprocessor. Combining numericalcomputing modules with GiD, users can develop softwares which have the abilitiesof modeling, meshing, computing and results displaying. The software is based onparallel FDTD, and is applied for the extraction of the scattering parameters,prediction of biostatic Radar Cross Section (RCS) and calculation of the radiationpattern of antenna.2) Message Passing Interface (MPI)-based Parallel FDTD method is realizedby subdividing the whole FDTD computation space into several sub-domains andtransferring field values across the interfaces between the neighboring processes withthree field communication patterns. Hardware platform and software environmentare introduced, both of which are bases of the implementation of parallel computing.The influence of different virtual topology schemes on parallel performance ofParallel FDTD is studied in detail. The concept of “the optimum virtual topology” isput forward to obtain the highest efficiency of MPI based Parallel FDTD. Accordingto the optimum virtual topology, scattering problems of complicated and electricallylarge targets are analyzed.3) A problemtype based on GiD has been studied with Cell-Centeredunstructured FVTD method as the kernel algorithm. Left and right state variables are obtained using Van Leer’s Monotone Upstream-centered Schemes for ConservationLaws (MUSCL) scheme. Gradient is calculated from face center field values. Fluxformulation on cell interface is obtained by using Steger-Warming flux vectorsplitting and approximate Riemann solution, both of which are presentedsuccessively and demonstrated essential equal by theory and numerical results. Twosteps Runge-Kutta algorithm is used to solve the partial differential equations withrespect to time. S parameters of an air filled parallel plate waveguide and fivesections of cables with various material properties joined end to end are extracted,the fundamental mode in which both are TEM mode. A correction scheme for themagnetic field is applied that yields accurate results of the scattering parameters innon-TEM structures by performing an artificial flux separation.4) Based on GiD, a problemtype has been developed with hybrid method ofFDTD-FVTD as the kernel algorithm. The memory requirements and solution speedfor the FDTD method and FVTD method are compared. Then, a hybrid time-domainmethod combing FDTD and Cell-Centered FVTD method is presented. This methodkeeps the advantages of the FVTD method locally near the geometry of the objectsand the simplicity and the speed of Yee’s scheme for areas that are either blank orcontain structures with geometries that do not require an unstructured mesh.Generation of the surface, which surrounds the object and defined by a set ofrectangular patches, is presented in detail. The method is suitable for simulatingstructures that include curved or oblique structures.5) A new local time-step scheme for the hybrid method is introduced withoutany special requirement for meshes. Satisfactory results and high efficiency areobtained. The stability criterion for the FV scheme is generally more restrictive thanthat for the FD scheme. For FVTD method, the “worst” cell in the mesh determinesthe time step. To save the CPU time, update the field values with respective localtime-step for each cell. Thus, not all field values in every cell are computed at everystep. In case the fields are not computed, they are interpolated by the values at theprevious steps. For all the cells applied for FDTD scheme, the time step is chosen tobe the stability limit obtained from Courant-Frisdrichs-Lewy (CFL) condition. Withthe same accuracy, computing efficiency is largely enhanced because of the localtime-step scheme.6) Hybrid FDTD-FVTD method is applied to solve three dimensionalelectromagnetic problems which involve lossy media with finite conductivity. The Fractional-Step Technique (FST) for FVTD scheme is introduced to solve theseproblems. Local time-step scheme is used to enhance the efficiency of this method.One approach consists in splitting the problem of interest into two subproblems thatcan be solved independently. The first subproblem is related to the computation ofthe fields in lossless dielectrics. The second subproblem is instead an ordinarydifferential equation taking into account only the effects of conductivity of media,whose solution can be analytically found. The explicit update equations should bemodified at each temporal step. A PEC (Perfect Electric Conductor) sphere coatedwith conducting medium and a rectangular waveguide with ten oblique slots innarrow side are solved successfully.