Using Parallel Processing on GPUs to Accelerate Finite-Difference Time-Domain Algorithms for Electromagnetic and Seismic Applications

Each SIMD engine contains 80 stream PEs organized into 16 thread processors. Each thread processor consists of 5 PEs, a branch unit and general purpose registers. The 5 PEs include 4 32-bit general purpose floating point multiply and add units and 1 special purpose unit to support floating point multiply, add, and transcendental functions.

Performance: Using the GPGPU Computational Performance benchmark from SiSoftware Sandra 2010, the ATI Radeon HD 5870 GPU scores 1820 Mpixels/s.^[a] SiSoftware Sandra calculates the Mandelbrot set using OpenCL.    Benchmarking with ComputeMark, the ATI Radeon HD 5870 GPU scores 2212.^[b] ComputeMark is a DirectX® 11 Shader Compute benchmark and is well suited to measure GPGPU performance, as it is capable of utilizing 99% of GPGPU resources.

OpenCL: The Open Computing Language, or OpenCL, is the open standard for parallel programming of GPGPUs and multi-core CPUs. OpenCL provides for a portable and a high-performance framework for the development of cross platform and vendor independent applications. An OpenCL application is partitioned into two primary components comprised of one or more computational kernels that are executed on the compute devices, and a host program that coordinates the asynchronous execution of the kernels and manages the movement of data to distributed memory resources.

GPGPU Implementation of Finite-Difference Time-Domain Solvers

Finite-Difference Time-Domain Methods: Finite-Difference Time-Domain (FDTD) methods are used to iteratively solve time-dependent partial differential equations by discretizing the equations and representing the solution on a spatial grid. The solution is evolved in time using an iterative time-stepping algorithm. An important feature of FDTD algorithms is the use of a local stencil so that the solution at any point in the grid is dependent upon the values of neighboring grid points. FDTD methods are used in many fields of scientific modeling and simulation and form the basic computational kernel upon which many software packages are built.

Electromagnetics: The FDTD method is used in computational electromagnetics where the time-dependent relationship between electric and magnetic field components is governed by Maxwell’s equations,

Using the FDTD method ^[1], the electric (E) and magnetic (H) field vectors are represented on staggered-grids and the solution is generated by updating E and H using a leap-frog algorithm that approximates the time-dependent solution through small discrete time-steps. The result is a time-varying solution that describes the propagation of electromagnetic waves. The FDTD method for electromagnetics is used for modeling and simulation in military and commercial applications ranging from radar to radio communications.

Seismic: The FDTD method is also used to model seismic wave propagation governed by the elastic wave equation,

The time-dependent solution describes the propagation of acoustic waves in an elastic medium. The solution for the particle velocity vector (ν) and stress tensor (σ) is represented on staggered-grids similar to those used in computational electro-magnetics. The Velocity-Stress FDTD (VS-FDTD) method ^[2] is an important algorithm used in seismic forward modeling with applications to oil and gas exploration and also military applications for detecting buried structures.