Development of computer science techniques has significantly enhanced computational electromagnetic methods in recent years. The multi-core CPU computers and multiple CPU work stations are popular today for scientific research and engineering computing. How to achieve the best performance on the existing hardware platforms, however, is a major challenge. In addition to the multi-core computers and multiple CPU workstations, distributed computing has become a primary trend due to the low cost of the hardware and the high performance of network systems. In this book we introduce a general hardware acceleration technique that can significantly speed up FDTD simulations and their applications to engineering problems without requiring any additional hardware devices.
Inspec keywords: electromagnetic waves; finite difference time-domain analysis
Other keywords: frequency ranges; GPU; undergraduate education; acceleration techniques; optical analysis; VALU; electromagnetic phenomena; acoustic analysis; AVX; parallel FDTD methods; closely-related techniques
Subjects: Artificial electromagnetic wave materials and structures; Other numerical methods
The finite-difference time domain (FDTD) method is a numerical technique based on the finite difference concept. It is employed to solve Maxwell's equations for the electric and magnetic field distributions in both the time and spatial domains. The FDTD method utilizes the central difference approximation to discretize two of Maxwell's curl equations, namely, Faraday's and Ampere's laws, in both the time and spatial domains, and then solve the resulting equations numerically to derive the electric and magnetic field distributions at each time step and spatial point using the explicit leap-frog scheme. The FDTD solution, thus derived, is second-order accurate, although the difference formulation is first order, and is stable if the time step size is chosen to satisfy the special criterion.
Popular central processing units (CPUs) for high-performance workstations and servers are made by either AMD (www.amd.com) or Intel (www.intel.com). Both are useful for general purposes. It is difficult to compare the performance of AMD and Intel CPUs because there are no absolute rules to judge CPU performance in a given system.
Perfectly matched layers (PMLs) play an important role in the FDTD method for simulation of the open space problems. PML is a special anisotropic absorbing material located outside the computational domain.
In this chapter, we will introduce parallel processing techniques including OpenMP, MPI (message processing interface), and their combination with SSE. Today, most computers are designed based on single instruction multiple data (SIMD).
This paper introduce the basic concept, implementation, and engineering applications of graphics processor unit (GPU) acceleration of parallel FDTD method based on compute unified device architecture (CUDA). Several typical examples are employed to demonstrate the performance of GPU and VALU acceleration techniques.
In this chapter, we apply the FDTD method advanced by the parallel processing and SSE acceleration techniques [1-9] in solutions to a variety of practical engineering problems and demonstrate its advantages over other electromagnetic simulation techniques. We first introduce the hardware platform configuration and then apply the parallel FDTD code enhanced by the SSE technique to solve the problems. The performance of VALU acceleration is associated not only with the hardware configuration and code structure but also with the problem model, excitation type, and output options. The parallel FDTD code used in this chapter has been optimized for the best performance in terms of the VALU acceleration, mesh generation, model handling, excitation, and output processing. The examples include a helix antenna array, dielectric lens, electromagnetic analysis of an automobile and a helicopter, finite-sized frequency selective surface (FSS), curved FSS, microwave filter, reverberation chamber, airplane wireless fidelity (WIFI) analysis, low-pass filter, microwave divider, and waveguide slot antenna array.
Cloud computing describes a new supplement, consumption, and delivery model for the software and hardware services based on the Internet protocols, and it typically involves provisioning of dynamically scalable and often virtualized resources. It is a byproduct and consequence of the ease-of-access to remote computing sites provided by the Internet. This may take the form of web-based tools or applications that the end users can access and use through a web browser as if the programs were installed locally on their own computers. Therefore, the end users may not need to install any application software on their local computers. All the computations and data processing happen in the remote resource.
In this appendix, we present a 3-D parallel FDTD demonstration code enhanced by the VALU acceleration, which can be used for general electromagnetic problems. The source code includes the electric and magnetic field updates, CPML update, 3-D parallel processing, VALU acceleration, OpenMp, and MPI. The code is programmed in the C language. The readers can modify it for different applications by adding different subroutines and functions.