Modified Z‐transform‐based FDTD algorithm for the anisotropic perfectly matched layer

A modified Z‐transform‐based algorithm for implementing the D‐H anisotropic perfectly matched layer (APML) is presented for truncating the finite‐difference time‐domain (FDTD) lattices. The main advantage is that, as compared with the previous Z‐transform‐based implementation for the D‐H APML, the proposed algorithm requires less auxiliary variables in the PML regions, and thus the memory requirement and the computational time are saved. These formulations are simple and independent of the material properties of the FDTD computational domain. Two numerical tests have been carried out to validate these formulations. Copyright © 2007 John Wiley & Sons, Ltd.     

On the development of efficient FDTD‐PML formulations for general dispersive media

A novel implementation of the perfectly matched layer (PML) absorbing boundary condition (ABC) to terminate the finite‐difference time‐domain (FDTD) algorithm for general dispersive and negative index materials is presented. The proposed formulation also adopts the complex frequency‐shifted (CFS) approach, involves simple FDTD expressions and avoids complex arithmetic. Several FDTD‐PML simulations with different parameters are conducted for the termination of various dispersive media validating the stability, accuracy and effectiveness of the schemes and indicating the advantage of the CFS‐PML. Copyright © 2008 John Wiley & Sons, Ltd.     

Extending the enlarged cell and uniformly stable conformal techniques to modeling curved conductors in two‐dimensional high‐order finite‐difference time‐domain algorithms

The critical tool of modeling irregularly shaped perfect conductors is developed for the extended‐stencil high‐order two‐dimensional M24 variant of the finite‐difference time‐domain (FDTD) method. Two standard FDTD conformal approaches are analyzed and successfully extended to work accurately with M24. They both afford higher order convergence with respect to mesh density than a previously developed technique, which better matches M24's characteristics. Both approaches rely on borrowing weighted electromotive forces from nearby extended‐stencil cells to ensure accuracy and numerical stability while the overall algorithm is efficiently operated at the maximum allowable time steps by FDTD and M24 theories. Validation examples demonstrate that M24's amplitude and phase accuracies using coarse numerical meshes were not compromised. Copyright © 2012 John Wiley & Sons, Ltd.     

Absorbing boundary conditions for the FD‐TLM method : the perfectly matched layer and the one‐way equation technique

This paper investigates the absorbing boundary conditions for the frequency domain transmission line matrix method. Two approaches are presented, namely the perfectly matched layer (PML) technique and the one‐way wave equation. Concerning the PML technique, two‐dimensional and three‐dimensional transmission line matrix (TLM) nodes, already used in time domain, are exploited in frequency domain where a rigorous formulation of these PML–TLM nodes is presented. In addition, two types of one‐way wave operators are also transposed from time to frequency domain TLM approach: Taylor expansion and Higdon's boundary conditions. The simulation of a wideband matched load WR‐28 rectangular waveguide is presented for validation. Excellent results are obtained with a very thin PML layer. Results concerning one‐way operator techniques also show very good return loss performances. For instance, Higdon's boundary condition was extended beyond third‐order approximation, and a return loss better than 160 dB was obtained. Copyright © 2013 John Wiley & Sons, Ltd.     

High‐order absorbing boundary conditions for the meshless radial point interpolation method in the frequency domain

The meshless radial point interpolation method (RPIM) in frequency domain for electromagnetic scattering problems is presented. This method promises high accuracy in a simple collocation approach using radial basis functions. The treatment of high‐order non‐reflecting boundary conditions for open waveguides is discussed and implemented up to fourth‐order. RPIM allows the direct calculation of high‐order spatial derivatives without the introduction of auxiliary variables. High‐order absorbing boundary conditions offer a choice of absorbing angles for each degree of spatial derivatives. For general applications, a set of these absorbing angles is calculated using global optimization. Numerical experiments show that at the same computational cost, the numerical reflections of the absorbing boundary conditions are much lower than conventional perfectly matched layers, especially at high angles of incidence. Copyright © 2013 John Wiley & Sons, Ltd.     

A new parallelization strategy for solving time‐dependent 3D Maxwell equations using a high‐order accurate compact implicit scheme

With progress in computer technology there has been renewed interest in a time‐dependent approach to solving Maxwell equations. The commonly used Yee algorithm (an explicit central difference scheme for approximation of spatial derivatives coupled with the Leapfrog scheme for approximation of temporal derivatives) yields only a second‐order of accuracy. On the other hand, an increasing number of industrial applications, especially in optic and microwave technology, demands high‐order accurate numerical modelling. The standard way to increase accuracy of the finite difference scheme without increasing the differential stencil is to replace a 2nd‐order accurate explicit scheme for approximation of spatial derivatives with the 4th‐order accurate compact implicit scheme. In general, such a replacement requires additional memory resources and slows the computations. However, the curl‐based form of Maxwell equations allows us to construct an effective parallel algorithm with the alternating domain decomposition (ADD) minimizing the communication time. We present a new parallel approach to the solution of three‐dimensional time‐dependent Maxwell equations and provide a theoretical and experimental analysis of its performance. Copyright © 2006 John Wiley & Sons, Ltd.     

Implementation of the stretched co‐ordinate‐based PML for waveguide structures in TLM

A novel implementation of the stretched co‐ordinate‐based perfectly matched layer (SCB PML) is presented to terminate waveguide structures in transmission‐line modelling (TLM). A generalized SCB PML, the complex frequency shifted PML (CFS PML) is also implemented to investigate its performance for evanescent waves. State variables in the Z‐domain are employed to obtain update equations for incident voltage pulses. Numerical results for a rectangular waveguide filled with a lossy medium as well as free space, and for a parallel plate waveguide are presented. Copyright © 2004 John Wiley & Sons, Ltd.     

Time‐domain sensitivity analysis of planar structures using first‐order one‐way wave‐equation boundaries

An efficient adjoint variable method technique is developed for time‐domain sensitivity analysis of planar structures with transmission‐line modeling complemented by a first‐order one‐way wave‐equation absorbing boundaries. A backward‐running adjoint simulation is derived and solved. The validity of the technique is illustrated through three microstrip circuits. The examples demonstrate the efficiency and accuracy of the technique in comparison with the classical finite‐difference approaches to the estimation of the response sensitivities. Copyright © 2007 John Wiley & Sons, Ltd.     

Exact stability conditions in upwinding‐scheme FDTD for the Boltzman transport equation

An in‐depth stability analysis of the FDTD method under the upwinding scheme for the Boltzmann transport equation (BTE) under the relaxation time approximation is provided. Both time forward and time backward difference equations are considered. In the time forward differencing case, a sufficient stability condition is derived for the BTE with variable coefficients, and a necessary and sufficient condition is derived for the BTE with constant coefficients. In the time backward differencing case, it is shown that the differencing equations are unconditionally stable. It is shown numerically that the previously reported stability conditions in the literature are not accurate. Copyright © 2013 John Wiley & Sons, Ltd.     

A high‐order discontinuous Galerkin method with time‐accurate local time stepping for the Maxwell equations

We present an explicit numerical method to solve the time‐dependent Maxwell equations with arbitrary high order of accuracy in space and time on three‐dimensional unstructured tetrahedral meshes. The method is based on the discontinuous Galerkin finite element approach, which allows for discontinuities at grid cell interfaces. The computation of the flux between the grid cells is based on the solution of generalized Riemann problems, which provides simultaneously a high‐order accurate approximation in space and time. Within our approach, we expand the solution in a Taylor series in time, where subsequently the Cauchy–Kovalevskaya procedure is used to replace the time derivatives in this series by space derivatives. The numerical solution can thus be advanced in time in one single step with high order and does not need any intermediate stages, as needed, e.g. in classical Runge–Kutta‐type schemes. This locality in space and time allows the introduction of time‐accurate local time stepping (LTS) for unsteady wave propagation. Each grid cell is updated with its individual and optimal time step, as given by the local Courant stability criterion. On the basis of a numerical convergence study we show that the proposed LTS scheme provides high order of accuracy in space and time on unstructured tetrahedral meshes. The application to a well‐acknowledged test case and comparisons with analytical reference solutions confirm the performance of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

A novel low‐spur DDFS utilizing the twice second‐order high‐pass error feedback architecture

In this paper, the twice second‐order high‐pass error feedback (EF) (twice second‐order high‐pass EF (HPEF)) utilizing re‐feedback process and phase‐bit splitting technique in the second‐order HPEF to design a simplified low‐spur direct digital frequency synthesizer is proposed. The proposed method performs phase‐bit splitting technique and re‐feedback process in order to make the phase change tremendously and scramble the periodicity of the phase sequences violently in the original feedback path. In addition, the noise spectrum power is spread more uniformly in order to effectively suppress the spurs due to phase‐truncated error effect. Thus, the twice second‐order HPEF is implemented on a field programmable gate array development board, the Altera Stratix II EP2S60. The simulation and experimental results show that the proposed method can effectively achieve better spectrum performance, such as spurious‐free dynamic range, as compared to basic phase truncation, first‐order HPEF and second‐order HPEF architectures. Copyright © 2012 John Wiley & Sons, Ltd.     

A high‐speed RSD‐based flexible ECC processor for arbitrary curves over general prime field

This workpresents a novel high‐speed redundant‐signed‐digit (RSD)‐based elliptic curve cryptographic (ECC) processor for arbitrary curves over a general prime field. The proposed ECC processor works for any value of the prime number and curve parameters. It is based on a new high speed Montgomery multiplier architecture which uses different parallel computation techniques at both circuit level and architectural level. At the circuit level, RSD and carry save techniques are adopted while pre‐computation logic is incorporated at the architectural level. As a result of these optimization strategies, the proposed Montgomery multiplier offers a significant reduction in computation time over the state‐of‐the‐art. At the system level, to further enhance the overall performance of the proposed ECC processor, Montgomery ladder algorithm with (X,Y)‐only common Z coordinate (co‐Z) arithmetic is adopted. The proposed ECC processor is synthesized and implemented on different Xilinx Virtex (V) FPGA families for field sizes of 256 to 521 bits. On V‐6 platform, it computes a single 256 to 521 bits scalar point multiplication operation in 0.65 to 2.6 ms which is up to 9 times speed‐up over the state‐of‐the‐art.     

Use of WKB approximation for analytical boundary conditions in numerical solution of Schrödinger equation: application to semiconductor–high‐k dielectric interfaces

Numerical methods used to solve 1D Schrödinger's equation in quantum structures, such as Numerov's integration of wavefunction or the shooting method iterative solution of energy levels, require knowledge of two‐point boundary conditions at interfaces. This is especially true when the interfaces are not symmetrical or where exponential decay of wavefunction at asymptotically large distances does not hold. A closed‐form expression for boundary conditions, which is not sensitive to intermediate solutions at interfaces, can minimize possible divergence during iterations and relax simulation grid size and simulation time. In this work, the Wentzel‐Kramers‐Brillouin (WKB) approximation within potential barriers is proposed to analytically calculate the boundary conditions for abrupt interfaces, such as dielectric–semiconductor interface. An analytical expression for the slope at the interface is derived, and the errors are estimated with respect to numerical methods. An application is shown for self‐consistent solution of coupled Poisson–Schrödinger's equations at multi‐layer HfO₂‐SiO₂ dielectric gate stack corresponding to International Technology Roadmap for Semiconductors‐projected 10 nm bulk single‐gate Complementary Metal‐Oxide‐Semiconductor (CMOS) technology node, where wavefunction penetration into the dielectric is of critical importance. Application to dual gate structures with 5 nm fin width and high‐k dielectric with 0.5 nm equivalent oxide thickness is also shown. A quantum mechanical simulator ‘hksim’ based on this principle is posted for public domain usage. Copyright © 2015 John Wiley & Sons, Ltd.