Multiple GPUs Based FDTD Parallel Algorithm And Its Applications In Electromagnetic Simulation

Combination of theory, experiment and computation has become the basic pattern of scientific research. In the electromagnetics science and engineering field, finite-difference time-domain (FDTD) has been an important method for electromagnetics analysis. FDTD is a time domain method solving for Maxwell equations. Electromagnetic fields are discretized with Yee cells. Maxwell equations are changed to difference equations by using central difference both in space and time domain. Then electric fields and magnetic fields can be updated alternatively in time domain. This method is simple both in implementation and comprehending. Most dielectric and complex objects can be constructed easily with this method. And it can be used to solve radiation, transmission and scattering problems because all the propagation phenomena are implicitly taken into account throughout its formulation. It has been developing and widely applied in the electromagnetics simulations in any band of the whole spectrum since 1966 proposed by Yee.As a difference method, FDTD is restricted by numerical dispersion and stability, and therefore the space and time step must be small enough to guarantee the accuracy of FDTD method. The space steps should be less than 1/10 of the wavelength generally. If the geometric model is more complex, samples in one wavelength should be increased to simulate the object as closely as possible. The time step must be satisfies Courant stability condition, which has relationship with the space step. So it will be take long time to simulate electrically large or fine structures using FDTD method.As FDTD is an inherently data parallel algorithm, parallel computing is an efficient way to reduce computation time and accelerate the progress of simulations. Most parallel FDTD computing algorithms are based on computer network, including supercomputer systems and personal computer clusters. However, this method is not cost-effective because of the expensive equipments of supercomputers or the network speed of clusters. Using programmable devices is another way, but the hardware program language is too complex to do FDTD computing and the developing of devices is slower than the personal computer. So this method has not been widely used.In recent years, graphics processing unit (GPU) has been developing faster more than Moore's Law as the developing of game demand. The floating-point processing performance of GPU is much higher than contemporary CPU. The implementation of GPU in general scientific computation is an increasing concern. And more and more general algorithms in many scientific fields are applied on GPU with the developing of general purpose computation on GPU (GPGPU) technology. The programming on GPU becomes rapid and efficient as the appearance of compute unified device architecture (CUDA) model. It has been popular with scientific researchers and applied in many fields rapidly.The content of this dissertation is a part of a National Basic Research Program of China, which is named effect of localization coupling in metal/dielectric nano heterogeneity structure and its'applications in photoelectric conversion devices. Its purpose is researching parallel computation system for simulation of light emitting diode (LED) by using general computation on graphics processing unit technology. In this dissertation, parallel FDTD algorithm is studied. Hybrid parallel FDTD computing is implemented on multi-GPU platforms, which greatly improves computational speed of simulation with FDTD method. The parallel computational system researched by this dissertation is used for LED simulation, such as enhancement light emission power by using top photonic crystal. This dissertation is divided into the following sections:Firstly, background and related knowledge is presented, including electromagnetic computing and basic information of parallel computing technology. The significance of the study and the content are introduced. Then parallel computing technology is studied. Various computing methods are demonstrated and contrasted. The development and application of GPU and GPGPU technology are discussed. Software and hardware environment of CUDA are investigated. And CUDA model is chosen to be used as parallel FDTD computing implement.Secondly, Basic FDTD algorithm and relative knowledge are introduced, such as numerical dispersion, boundary conditions and sources. The situation of parallel FDTD computing development is discussed, which induces the content of this dissertation.Two-dimensional (2D) and three-dimensional (3D) parallel FDTD algorithm implematations are proposed based on CUD A model.2D FDTD with uniaxial perfect matched layer (UPML), three dimensional FDTD with UPML and convolutional PML (CPML) are implemented on GPU. Line electronic current source in 2D, dipole and plane wave sources in 3D are implemented. One-dimensional FDTD with Mur absorbing boundary condition is implemented in 3D plane wave sources application.2D thread assigned to control electromagnetic field updating for solving 2D problems. Several memory access optimization schemes are proposed in order to accelerate computing speed, such as two ways for shared memory access and using texture memory. Two thread arrangement schemes are proposed and implemented to solve 3D problems. Optimization is proposed and speed of two schemes is contrasted, which is shown that above 10 times speedup are obtained in almost every case. PML parameters expanding and discrete computing are used to process UPML and CPML respectively. And corresponding optimization approaches are implemented for each PML. The speed of PML-FDTD computation is accelerated above 20 times commonly ensuring the computational accuracy.The parallel FDTD algorithm is extended to multiple GPUs (multi-GPU). Domain decomposition and appropriate boundary data exchanging are used in multi-GPU system, and synchronous memory copy scheme is used for data exchanging between GPU and CPU memory. In order to hide the memory transmission time, asynchronous memory copy scheme is used, which is proved to be efficient for multi-GPU parallel computing. Parallel computing on single GPU, parallel computing on multi-GPU, parallel tasks of computing and data exchanging is implemented for the first time. The performance of these schemes is evaluated on multi-GPU system, which contains 8 GTX295 graphics cards. Speed of above 4000Mcell/s is obtained in 3D FDTD application with 10 layers CPML.The effect on absorption of parameters in CPML is tested on GPU platform. Microstrip antenna and filter are simulated by 3D parallel FDTD computing. Method of calculating radiation power of dipole with FDTD is proposed and verified on multi-GPU system. A light emitting diode (LED) model is computed and its radiation power is calculated with our method. Photonics crystal is used for emitting enhancement.