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The striking growth of powerful computing resources allows time-efficient solution of computationally demanding problems. In particular, advances in high-performance computing have made stochastic approaches to real-world applications more practical. The belief propagation (BP) algorithm is a probabilistic method typically used in information theory and artificial intelligence. This article exploits the probabilistic message passing attribute of BP for solving stochastic linear systems that naturally arise from finite element formulation of stochastic partial differential equations (PDEs), establishing an explicit connection between the two fields for the first time. The accuracy of the algorithm is validated by comparison to the well-known Monte Carlo method. [ABSTRACT FROM AUTHOR]

Mathematical modeling and computer simulation of heat transfer in the liver play a key role in prediction of radio frequency ablation outcome. While multi-physics modeling should be used for accurate simulation of heat transfer in a highly perfused organ like the liver, the computational cost of such a problem could have a negative impact on the simulation time. This article extends a highly parallel finite element-based method to simulate the multi-physics heat transfer problem in the liver efficiently. A message passing interface (MPI)-based strong coupling method is developed and tested on cluster nodes. The scalability of this work is assessed by performing simulations on up to 1024 cores. [ABSTRACT FROM AUTHOR]

In this article, a finite-element time-domain method is presented for the solution of the second-order vector wave equation (VWE) subject to electrically complex materials, including general combinations of linear dispersion, instantaneous nonlinearity, and dispersive nonlinearity. The presented method is novel in that it offers greater geometric flexibility than existing finite-difference methods, incorporates both instantaneous and dispersive nonlinearity, scales to arbitrary dispersive and nonlinear orders, and is simpler, faster, and requires less computational complexity than existing mixed formulations due to the use of edge elements only. [ABSTRACT FROM AUTHOR]

The purpose of this contribution is to introduce a dual-primal finite-element tearing and interconnecting (DP-FETI) method for the time-domain simulation of large electromagnetic problems. The most distinctive feature of the proposed method is that the continuity of the first-time derivative of the electric field intensity is enforced across the interfaces, unlike the existing formulations in electromagnetics. A theoretical proof is provided to demonstrate that this transmission condition guarantees unconditional stability and energy preservation of the method. Since the condition number of the global interface problem is greatly reduced compared to the standard finite-element time-domain (FETD) method, an iterative solver converges in far fewer iterations. This significantly reduces the simulation time, particularly when implemented on parallel computers. It is numerically shown that the method is scalable with respect to the number of subdomains and the time-step size. The numerical results for simulation of a cavity and bandgap devices are presented to demonstrate capability, accuracy, and efficiency of the proposed time-domain DP-FETI (TD-DP-FETI). [ABSTRACT FROM AUTHOR]

A new finite-element Gaussian belief propagation (FGaBP) algorithm for multi-physics applications is presented in this paper. The FGaBP method is first modified for solving the heat-transfer problem and then verified against an analytical solution. Combined with a Gauss–Seidel algorithm, FGaBP is used to solve the coupled electrical–thermal problem that emerges in radiofrequency ablation of hepatic tumors while the extent of the ablated zone is computed for a simplified model. The multi-physics FGaBP algorithm preserves the parallel scalability of FGaBP as in previous uni-physics works. [ABSTRACT FROM AUTHOR]

A novel implementation of a perfectly matched layer (PML) is presented for the truncation of finite-element time-domain (FETD) meshes containing electrically complex materials, exhibiting any combination of linear dispersion, instantaneous nonlinearity, and dispersive nonlinearity. Based on the complex coordinate stretching formulation of the PML, the presented technique yields an artificial absorbing layer whose matching condition is independent of material parameters. Moreover, by virtue of only modifying spatial derivatives, the incorporation of the PML into existing solvers for complex media is simple and straightforward. The resulting material-independent PML is incorporated into a nonlinear dispersive method for the vector wave equation, which leverages the $z$ transform and Newton-Raphson techniques to yield an implementation free from recursive convolutions, auxiliary differential equations, and linearizations. This permits the unprecedented truncation and attenuation of nonlinear phenomena, such as spatial and temporal solitons, within the FETD method. [ABSTRACT FROM AUTHOR]

In this paper, a mixed finite-element time-domain (FETD) method is presented for the simulation of electrically complex materials, including general combinations of linear dispersion, instantaneous nonlinearity, and dispersive nonlinearity. Using both edge and face elements, the presented method offers greater geometric flexibility than existing finite-difference time-domain (FDTD) implementations, and in contrast to existing nonlinear FETD methods, also incorporates both linear and nonlinear material dispersions. Dielectric nonlinearity is incorporated into the Crank–Nicolson mixed FETD formulation via a straightforward Newton–Raphson approach, for which the associated Jacobian is derived. Moreover, the dispersion is modeled via the Möbius $z$ transform method, yielding a simpler more general algorithm. The method’s accuracy and convergence are verified, and its capability demonstrated via the simulation of several nonlinear phenomena, including temporal and spatial solitons in two spatial dimensions. [ABSTRACT FROM AUTHOR]

An efficient method based on the recursive fast Fourier transform (FFT) to incorporate both the intra-band and inter-band conductivity terms of graphene into the finite-difference time-domain (FDTD) method is proposed. As it only requires numerical values of the conductivity, it not only does not enforce any restrictions on the conductivity models, but also can directly take into account material properties obtained from measurement. It reduces the total computational cost from O(N²) to O(N log² N) where N is the length of the unknown. The FDTD method is also modified and proven to retain the stability condition of the standard FDTD method. [ABSTRACT FROM AUTHOR]

In this paper, a novel graphics-processing unit (GPU) implementation of the recently proposed correction function method (CFM) is presented, for the finite-difference solution of Poisson problems with surface-charge distributions. The CFM is a robust and versatile method most notable for its immersed treatment of interface problems of any geometry, to an arbitrary order of accuracy. Given the well-known interface jump conditions associated with the electric scalar potential, the CFM is here shown to be immediately applicable to the computation of electrostatic fields, in the presence of curved surface-charge distributions. Moreover, an in-depth analysis of the CFM algorithm is presented, in which performance bottlenecks are investigated and significant potential for parallelizability is identified. The resulting parallel CFM algorithm is then implemented using NVIDIA’s compute unified device architecture GPU language, yielding a significant increase in performance. [ABSTRACT FROM AUTHOR]

In this paper, a new finite element Gaussian belief propagation (FGaBP) method is presented for time-domain applications. The unconditionally stable Newmark time-stepping scheme is combined with FGaBP for this purpose. As shown empirically, the method converges for increasing time step sizes without losing stability. The combined FGaBP-time stepping is able to retain the parallel scalability from FGaBP as in previous work. In addition, this paper also shows that lossy material properties can be easily supported by the method with minimal changes to its formulation. [ABSTRACT FROM AUTHOR]

A novel use of graphics processing units (GPUs) is presented in the execution of the dispersive finite-element time-domain (FETD) method, based upon the Möbius (bilinear) z -transform technique. By utilizing the immense computational power of modern GPUs via NVIDIA’s compute unified device architecture (CUDA) language, a narrowing of the performance gap, which currently exists between dispersive FETD methods and their non-dispersive counterparts, can be achieved, thus facilitating the study of a wider range of physical phenomena. An analysis of the z -transform dispersive FETD algorithm is presented in order to both identify dispersive overhead bottlenecks and determine its suitability to parallelization. Numerical studies are then undertaken to measure the performance increase as a function of simulation parameters, such as number of variables, the amount of dispersive material present, and floating point precision. [ABSTRACT FROM AUTHOR]

A new finite-difference time-domain (FDTD) formulation for modeling graphene is proposed, in which the graphene is modeled as a resistive sheet with a frequency-dependent conductivity. The formulation is first developed in the context of the vector wave finite-element time-domain and then reduced to the FDTD based on the equivalence between these two techniques. The obtained formulation is easy to implement and does not alter the original FDTD update equations. It can be applied to an existing FDTD code by simply adding a correction term to appropriate variables. One of the main contributions of this paper is analyzing the stability of the proposed formulation, which has not been done previously. [ABSTRACT FROM AUTHOR]

The finite-element Gaussian belief propagation (FGaBP) method, introduced recently, provides a powerful alternative to the conventional finite-element method solvers to efficiently utilize high-performance computing platforms. In this paper, we accelerate the FGaBP convergence by combining it with two methods based on residual minimization techniques, namely, the flexible generalized minimum residual and the iterant recombination method. The numerical results show considerable reductions in the total number of operations compared with the stand-alone FGaBP method, while maintaining the scalability features of FGaBP. [ABSTRACT FROM AUTHOR]

Two hybrid formulations combining the finite-element time-domain and the finite-difference time-domain methods are proposed for modeling dispersive materials. The methods are coupled to each other in a non-overlapping fashion using a new finite-element tearing and interconnecting algorithm. In addition, one of them is a fully unconditionally stable hybrid method, in which the time step is not restricted by a stability criterion. The effect of medium dispersion is considered using the Möbius transformation technique. The proposed methods are validated through numerical studies. [ABSTRACT FROM PUBLISHER]

The finite-element time-domain (FETD) solution of the vector wave equation (VWE) is directly extended to doubly dispersive media using the bilinear transform approach. The proposed formulation is quite general and flexible in the sense of material dispersion model in contrast to limitations of existing convolutional-based approaches. In addition, it can be implemented in a very straightforward and efficient manner. A stability analysis is performed that demonstrates the unconditional stability of the original formulation is preserved in the dispersive case. However, in order to avoid the well-known late-time instabilities that arise in this formulation, an alternative formulation is considered and extended to the dispersive case with the same approach. Several numerical examples are simulated to verify the validity and accuracy of the proposed formulations. The late-time stability of the alternative formulation is tested through a numerical example with 20 million time steps. The solution is completely free from late-time growth. [ABSTRACT FROM PUBLISHER]

A general framework to combine the finite-difference time-domain (FDTD) and the finite-element time-domain (FETD) formulations, both based on the vector wave equation, is proposed. In contrast to the existing stable hybrid FETD-FDTD, there is no transition layer between two subdomains. In addition, the stability of the proposed approach is analytically proved. This framework allows combining different FDTD and FETD formulations together. Particularly, a fully unconditionally stable hybrid method is proposed, which is proved to be energy conservative too. The key ingredient is a finite-element tearing and interconnecting method for electromagnetic problems with a new interface condition that preserves the stability of the numerical method in each region. Several numerical examples are considered in order to validate the proposed methods. The numerical results match with the reference solutions very well in all cases. [ABSTRACT FROM PUBLISHER]

Accelerating numerical algorithms for solving sparse linear systems on parallel architectures has attracted the attention of many researchers due to their applicability to many engineering and scientific problems. The solution of sparse systems often dominates the overall execution time of such problems and is mainly solved by iterative methods. Preconditioners are used to accelerate the convergence rate of these solvers and reduce the total execution time. Sparse approximate inverse (SAI) preconditioners are a popular class of preconditioners designed to improve the condition number of large sparse matrices. We propose a GPU accelerated SAI preconditioning technique called GSAI, which parallelizes the computation of this preconditioner on NVIDIA graphic cards. The preconditioner is then used to enhance the convergence rate of the BiConjugate Gradient Stabilized (BiCGStab) iterative solver on the GPU. The SAI preconditioner is generated on average 28 and 23 times faster on the NVIDIA GTX480 and TESLA M2070 graphic cards, respectively, compared to ParaSails (a popular implementation of SAI preconditioners on CPU) single processor/core results. The proposed GSAI technique computes the SAI preconditioner in approximately the same time as ParaSails generates the same preconditioner on 16 AMD Opteron 252 processors. [ABSTRACT FROM AUTHOR]

Several finite-element time-domain (FETD) formulations to model inhomogeneous and electrically/magnetically/doubly dispersive materials based on the second-order vector wave equation discretized by the Newmark-\beta scheme are developed. In contrast to the existing formulations, which employ recursive convolution (RC) approaches, we use a Möbius transformation method to derive our new formulations. Hence, the obtained equations are not only simpler in form and easier to derive and implement, but also do not suffer from the intrinsic limitations of the RC methods in modeling arbitrary high-order media. To obtain the formulations, we first demonstrate that the update equation for the electric field strength \e\ in the mixed Crank-Nicolson (CN) FETD formulation, which is based on expanding the electric and magnetic field in terms of the edge and face elements in space and discretizing the resultant first-order differential equations using Crank-Nicolson scheme in time, is equivalent to the unconditionally stable (US) second-order vector wave equation for the same variable (\e\) discretized by the Newmark-\beta method with \beta =1/4. In addition, we show that the update equation for the magnetic flux density \b\ in CN-FETD is the same as the second-order vector wave equation for \b\ on the dual grid discretized again by a similar Newmark-\beta method. [ABSTRACT FROM PUBLISHER]

Scalability and low power consumption are major issues in designing custom hardware platforms for accelerating computation intensive electromagnetic applications. Clustered architectures decreases wire delays, power consumption and enhance scalability. We introduce a new steering algorithm that increases the performance of electromagnetic applications on such architectures, making clustering an even more attractive design alternative. The effectiveness of the new method is illustrated for two representative electromagnetic benchmarks. [ABSTRACT FROM AUTHOR]

The design and implementation of parallel finite element methods (FEMs) is a complex and error-prone task that can benefit significantly by simulating models of them first. However, such simulations are useful only if they accurately predict the performance of the parallel system being modeled. The purpose of this contribution is to present a new, practical methodology for validation of a promising modeling and simulation approach for parallel 3-D FEMs. To meet this goal, a parallel 3-D unstructured mesh refinement model is developed and implemented based on a detailed software prototype and parallel system architecture parameters in order to simulate the functionality and runtime behavior of the algorithm. Estimates for key performance measures are derived from these simulations and are validated with benchmark problem computations obtained using the actual parallel system. The results illustrate the potential benefits of the new methodology for designing high performance parallel FEM algorithms. [ABSTRACT FROM AUTHOR]

A new, efficient pipelined communication strategy that significantly reduces latency for parallel 3-D finite element mesh refinement with tetrahedra is proposed. A Petri Nets-based model is developed in order to simulate the interprocessor communication costs for both the target mesh refinement algorithm and parallel architecture. Benchmark results show that the new pipelined design yields improved communication performance and overall parallel speedup for a range of refinement problem sizes, using different numbers of processors. [ABSTRACT FROM AUTHOR]

The majority of evolutionary algorithm applications in electromagnetic design have focused on optimization of device dimensions. This approach preconceives the final device shape. To facilitate the evolution of complex and creative designs through genetic algorithms, a novel genome and genetic operators are introduced. They are then used to evolve a patch antenna for dual-frequency operation. The final design that emerges has a fitness roughly triple that of the standard approach. [ABSTRACT FROM AUTHOR]

Exploring the vast search space of possible wire antenna designs is a task well suited for genetic algorithms. Many of the current implementations use a direct mapping between genome and antenna feature, or evolve drawing instructions. We explore the evolution of antennas using a growth process. The design of wire antennas for communication applications demonstrates the feasibility of this approach. [ABSTRACT FROM AUTHOR]

Communication strategies in parallel finite element methods can greatly affect system performance. The communication cost for a proposed parallel 3-D mesh refinement method with tetrahedra is analyzed. A Petri Nets-based model is developed for a target mesh refinement algorithm and parallel computing system architecture, which simulates the inter-processor communication. Subsequently, estimates for performance measures are derived from discrete event simulations. The potential benefits of this approach for developing high performance parallel mesh refinement algorithms are demonstrated by optimizing the system communication costs for varying problem size and numbers of processors. [ABSTRACT FROM AUTHOR]

We develop a simulation-based approach for the computational analysis and design of dynamic load balancing algorithms in parallel three-dimensional unstructured mesh refinement with tetrahedra. A Petri Nets model is implemented based on a random polling algorithm and the target multiprocessor architecture, which simulates the behavior of the parallel mesh refinement. Subsequently, estimates for performance measures are derived from discrete event simulations. The benefits of this new approach for developing high-performance parallel mesh refinement algorithms are demonstrated with results for an example geometric mesh refinement model. [ABSTRACT FROM AUTHOR]

Developing models from computational data is a major focus in electromagnetic design. This paper introduces ways of creating customized neural models based on a fuzzy clustering of responses. Fuzzy-clustered neural network (FCNN) models are explored, leading to increases in accuracy. The information contained within FCNN models can also be applied to space mapping electromagnetic optimization. This optimization approach strives to combine the accuracy of fine models (such as finite elements) with the low cost of coarse models. These FCNN enhancements are demonstrated through a patch antenna test case. [ABSTRACT FROM AUTHOR]

An electromagnetic system can be described in a variety of ways. Coarse models provide fast evaluations but lack the required accuracy in the final stages of design. Fine models are highly accurate, but prohibitively expensive. Finding a compromise between these extremes may assist in overcoming bottlenecks in design automation and optimization. One approach is to carry out optimization in the coarse model space and use fine model simulations to fine-tune the result via space mapping. A new response surface space mapping (RSSM) strategy is presented and applied to an E-shaped patch antenna test case. The solutions that emerge are comparable to full fine model optimization at a fraction of the cost. [ABSTRACT FROM AUTHOR]

The potential benefits of employing optimal discretization-based (ODB) refinement criteria for vector tetrahedra to achieve load balancing in three-dimensional parallel adaptive finite-element electromagnetic analysis are considered. Specifically, the ability of this class of adaption refinement criteria to resolve effective domain decompositions based on initial discretizations with only relatively few tetrahedra is examined for generalized vector Helmholtz systems. The effectiveness of the new load balancing method is demonstrated with adaptively refined finite-element meshes for benchmark systems. [ABSTRACT FROM AUTHOR]

Undergraduate electromagnetic field courses entail significant teaching and learning challenges. The use of simulation technologies in these courses can be an effective teaching strategy if designed properly. An assessment-based approach for identifying difficult concepts to incorporate into simulation-oriented learning is investigated. The potential benefits of the approach are illustrated with a case study. [ABSTRACT FROM AUTHOR]

Finite-element (FE) accuracy can be directly affected by mesh quality. The potential benefits and related costs of a family of new mesh quality improvement systems are investigated using a suite of electromagnetic benchmarks and mesh quality measures theoretically linked to FE accuracy. Experimental findings suggest error reductions on the order of 10% for half-second runtimes. [ABSTRACT FROM AUTHOR]

In this letter, we describe an easy approach to implement the first-order Bayliss-Turkel-like absorbing boundary condition (ABC) in two mixed finite-element time-domain (FETD) formulations, namely the Crank–Nicolson FETD (CN-FETD) and the leap-frog FETD (LF-FETD). The idea is to introduce a current source distribution on the outer boundary of the domain such that it cancels outgoing waves. The current distribution is obtained based on the ABC relation. In addition, we show that the CN-FETD and the LF-FETD are equivalent to the FETD based on the vector wave equation discretized by the Newmark-\beta method in time with \beta=1/4 and 0, respectively. Having utilized these equivalences, we demonstrate that our approach to implement the ABC in the mixed formulations lead to the same result as the vector wave FETD truncated with the same ABC. A numerical example is provided to validate our formulations. [ABSTRACT FROM PUBLISHER]