Mohammed F. Hadi

A modified FDTD (2, 4) scheme for modeling electrically large structures with high-phase accuracy

A new fourth-order finite-difference time-domain (FDTD) scheme has been developed that exhibits extremely low-phase errors at low-grid resolutions compared to the conventional FDTD scheme. Moreover, this new scheme is capable of combining with the standard Yee (1966) scheme to produce a stable hybrid algorithm. The problem of wave propagation through a building is simulated using this new hybrid algorithm to demonstrate the large savings in computing resources it could afford. With this new development, the FDTD method can now be used to successfully model structures that are thousands of wavelengths large, using the present day computer technology.

Optimizing the Compact-FDTD Algorithm for Electrically Large Waveguiding Structures

This work investigates the unique numerical dispersion behavior of the Compact-FDTD method for waveguide analysis, especially when the waveguide dimensions are much larger than the operating wavelength as in high-frequency EMC analysis or radio-wave propagation in tunnels. The divergence of this dispersion behavior from the standard FDTD algorithm is quantified and a major source of dispersion error is isolated and effectively eliminated. Optimized modeling parameters in terms of appropriate spatial and temporal resolutions are generated for computationally efficient and error-free numerical simulations of electrically large waveguiding structures.

A Finite Volumes-Based 3-D Low Dispersion FDTD Algorithm

An algorithm extension to three dimensions is developed and presented for the highly phase-coherent modified second-order in time, fourth-order in space (or M24) finite-difference time-domain (FDTD) algorithm. A finite-volumes approach in conjunction with Yees standard FDTD lattice is used for algorithm development. The corresponding dispersion relation is also developed, analyzed and compared to both the standard second-order and fourth-order FDTD algorithms as well as to two closely related high-order phase-coherent algorithms. Wideband algorithm attributes are also presented as well as sets of ready to use optimized algorithm coefficients.

A High-Order Compact-FDTD Algorithm for Electrically Large Waveguide Analysis

To model electrically large waveguiding structures, the compact-finite-difference time-domain (FDTD) algorithm needs to use severely scaled down time steps to properly contain the rapidly growing numerical dispersion errors with increased operating frequency. In this work, a high-order compact-FDTD algorithm based on fourth-order spatial central finite differencing and fourth-order temporal backward finite differencing is developed. The accuracy and efficiency of this proposed algorithm are verified through its dispersion relation analysis and validated by modeling high-frequency wave propagation through an earth tunnel. The obtained computational efficiency allows this high-order algorithm to model wireless propagation through longitudinally-invariant road and railway tunnels using several hundred compact-FDTD cells as opposed to the several million FDTD cells required by three-dimensional FDTD algorithms.

PHASE-MATCHING THE HYBRID FV24/S22 FDTD ALGORITHM

This work demonstrates an efficient and simple approach for applying high-order extended-stencil FDTD algorithms near planar perfect electric conductors (PEC) boundaries while minimizing spurious reflections off the interface between the high-order grid and the mandated special compact cells around PEC boundaries. This proposed approach eliminates the need for cumbersome subgridding implementations and provides a superior alternative in minimizing spurious reflections without any added modeling complexity or computing costs. The high-order algorithm used in this work is the recently proposed three-dimensional FV24 algorithm and the proposed approach can be easily extended to the standard Fang high-order FDTD algorithm which represents a special case of the highly phasecoherent FV24 algorithm.

INTEGRAL PML ABSORBING BOUNDARY CONDITIONS FOR THE HIGH-ORDER M24 FDTD ALGORITHM

This work demonstrates an efficient and simple PML absorbing boundary conditions (ABCs) implementation for the highorder extended-stencil M24 FDTD algorithm. To accomplish this objective, the integral forms of the PML split-field formulations were derived and discretized using the same M24 weighted multiple-loop approach, resulting in ABC performances that match the standard FDTD-based PML formulations. This proposed approach eliminates the impedance mismatches caused by switching from M24 to regular FDTD update equations within the PML regions and the necessary cumbersome subgridding implementations needed to minimize the effects of these mismatches. It also eliminates the need to use large separations between the scatterers and the PML regions as a simpler though more costly alternative. This achievement coupled with the recent effective resolution of the PEC modeling issue finally eliminates the last hurdles hindering the wide adoption of the M24 algorithm and its three-dimensional counterpart, the FV24 algorithm, as a viable option for accurate and computationally efficient modeling of electrically large structures.

A Versatile Split-Field 1-D Propagator for Perfect FDTD Plane Wave Injection

A new staggered field design and formulation for the one-dimensional propagator of the total-field/scattered-field source implementation in finite-difference time domain (FDTD) scattering simulations are presented. The new equations are based on split-field Maxwells equations and the resulting technique extends the functionality of the multipoint auxiliary propagator to sourcing FDTD lattices hosting extended-stencil high-order algorithms. This technique virtually eliminates numerical dispersion, field location and polarization mismatches between propagator and main grid. The resulting machine accuracy-level leakage error from implementing this technique is confirmed for the standard low and high-order FDTD schemes as well as the M24 high-order algorithm. Normalized field leakage for all three algorithm implementations outside the total-field region was measured at below - 295 dB.

Near-Field PML Optimization for Low and High Order FDTD Algorithms Using Closed-Form Predictive Equations

The convolutional perfectly-matched-layer (CPML) absorbing boundary condition is fully capable of handling near-field wave absorption that usually combines near-grazing wave incidence with wave evanescence. The appropriate choice of the various CPML parameters to realize this potential for any given simulation problem is a challenging task that is typically achieved through exhaustive and time-consuming searches that involve large numbers of full-scale simulations. The presented work here uses a previously developed predictive system of equations that accurately determines numerical reflections off the PML interface and embeds it into a global optimization routine that reliably computes the required optimum CPML parameters. This predictive system of equations has also been extended and validated for the M24 and FV24 integral-based high-order FDTD algorithms. With this approach, the task of selecting optimum CPML parameters that would usually take several days of intense computations can now be accomplished within a few minutes on an average personal computer.

The Case for Higher Computational Density in the Memory-Bound FDTD Method within Multicore Environments

It is argued here that more accurate though more compute-intensive alternate algorithms to certain computational methods which are deemed too inefficient and wasteful when implemented within serial codes can be more efficient and cost-effective when implemented in parallel codes designed to run on todays multicore and many-core environments. This argument is most germane to methods that involve large data sets with relatively limited computational density—in other words, algorithms with small ratios of floating point operations to memory accesses. The examples chosen here to support this argument represent a variety of high-order finite-difference time-domain algorithms. It will be demonstrated that a three- to eightfold increase in floating-point operations due to higher-order finite-differences will translate to only two- to threefold increases in actual run times using either graphical or central processing units of today. It is hoped that this argument will convince researchers to revisit certain numerical techniques that have long been shelved and reevaluate them for multicore usability.

Simplified Graphical Processor Acceleration of the Standard and High-Order Finite-Difference Time-Domain Algorithms

Abstract A computationally efficient and streamlined approach for coding a high-order finite-difference time-domain algorithm on both central and graphical processing units is presented. This objective was achieved through extending the update equations of the convolutional perfectly-matched layer absorbing boundary conditions throughout the numerical domain with appropriate parameter selections. It is demonstrated that the resulting appreciable increase in the floating-point operations count would result in only a negligible loss of overall computational efficiency using either central processing units or graphical processing units. This achievement translates into sizable reductions in code complexity and development costs. Comparative analyses were also presented for the standard finite-difference time-domain method, resulting in an efficient accelerated algorithm that does not degrade with model size reduction.