Parallel FDTD Algorithm Based On Network And Applications In Electromagnetic Problems

As a powerful numerical technique, The FDTD (Finite Difference Time Domain)method has been widely applied to various electromagnetic problems, such as thesimulation of photonic crystals, the calculation of bioelectromagnetic dosimetry, and soon. However, in order to meet the requirement of precision and Courant stabilitycondition, the FDTD method have to generate enormous grids when simulating theelectrically-large-size or complex objects. Hence two problems have to be confronted:huge memory consumption and long execution time.With the rapid development of the personal computer and the network technique,the FDTD method combined with the parallel technique divides the wholecomputational space into some subspaces and assigns every subspace to one node in aparallel system. Thus, the requirements of the huge memory and CPU time can besharply decreased, which provides a feasible approach for simulating theelectrically-large-size or complex objects. The research for the parallel FDTDcomputing based on network has become a hotspot in numerical applications forelectromagnetic field now, nevertheless, for the existing parallel FDTD algorithm, theperformance indexes, such as parallel efficiency and computation stability, will dropobviously with the quantity of computers increasing. This constrains heavily thepractical application of the parallel FDTD algorithm.As compared to the traditional cluster, the modern LAN (local area network)possesses a series of new hardware and software features, which are as follows:1) The CPUs with hyper-threading or multi-core technology have becomewidespread, which can give directly support to multiple tasks from the hardware.2) The programmable GPU (Graphics Processing Unit) is widely adopted.3) The interoperability protocol for the LAN operating system is more perfect.To improve the parallel performance, and reduce the complexity of implementationfor parallel FDTD algorithm, this dissertation studies how to apply the new softwareand hardware characteristic in FDTD algorithm, and improve the design andimplementation for parallel FDTD algorithm, so as to promote the application of the parallel technique in the electromagnetic computation.The major achievements of this dissertation are as follows:(1) The concept of "two level parallelization on PC cluster" is presented. Byusing two-level parallelization of the data and tasks, a high performance MPI-OpenMPhybrid FDTD algorithm is developed on PC cluster for the first time. The numericalresults show the strategy of two level parallelization can improve substantially thescalability and efficiency of parallel FDTD algorithm, which is well suited for the finegrained parallel FDTD computing on PC cluster, and moreover, it can also lessen theinfluence of the subspaces virtual topology on the parallel FDTD performance.(2) A universal and efficient interpolation technique based on the superabsorbingboundary principle is studied, which can improve the interpolation accuracybetween subdomains and ensure the stability of the parallel FDTD iterative procedure.Thus, the computational space is divided mostly according to the features of the originalproblem, and the meshes are created in local coordinates. During the iteration process ofparallel FDTD, the data are exchanged between adjacent subdomains with theinterpolation technique, which can largely enhance the convenience and flexibility ofthe parallel FDTD for building the model.(3) The concepts of time and space fault-tolerance are presented, and by usingthe principle of the memory-mapped file, the simplifying and extending technique basedon the LAN characteristic is studied for the parallel FDTD system. Besides, severalstructures of the photonic crystal waveguides are investigated in virtue of this approach.For the electromagnetic coupling effect of photonic crystal waveguide, the relationshipbetween the different radius ratio of dielectric cylinders and the coupling length of thewaveguide is discussed. For the photonic crystal 90°waveguide bend, the characteristicof transmission efficiency is calculated. The numerical experiments confirm the fact thatthe approach proposed can reduce availably the complexity of the algorithm design forparallel FDTD system, and enhance the capacity of cooperating well with the commoncomputing software, which further improves the efficiency of the FDTD computing.(4) For the first time, the collaborative computation of the GPU and CPU isachieved for the Alternative Direction Implicit Finite Difference Time Domain(ADI-FDTD) algorithm. An implementation frame for the general purpose computationon GPU is given, and a detail analysis for solving linear equations system on GPU is presented. The performance test results show that the collaborative algorithm is moreefficient as compared to the general CPU-ADI-FDTD algorithm under the sameconditions.(5) Using the interpolation technique, the human models in the different postureare built for the parallel FDTD computation. The SAR (Specific Absorption Rate)values in the head are calculated, and the effect of human-body posture on the SAR isanalyzed for two different postures: the standard standing and arms stretching up, whenthe human body is exposed to the electromagnetic radiation from a mobile phone. Theresults show that the SAR values in the brain, as a critical organ in the head, aresensitive to the change of the body posture, and increase obviously in arms up postureas compared with those in standard standing posture.