Parallel FETI‐DP algorithm for efficient simulation of large‐scale EM problems

An efficient parallelization of the dual‐primal finite‐element tearing and interconnecting (FETI‐DP) algorithm is presented for large‐scale electromagnetic simulations. As a nonoverlapping domain decomposition method, the FETI‐DP algorithm formulates a global interface problem, whose iterative solution is accelerated with a solution of a global corner problem. To achieve a good load balance for parallel computation, the original computational domain is decomposed into subdomains with similar sizes and shapes. The subdomains are then distributed to processors based on their close proximity to minimize inter‐processor communication. The parallel generalized minimal residual method, enhanced with the iterative classical Gram‐Schmidt orthogonalization scheme to reduce global communication, is adopted to solve the global interface problem with a fast convergence rate. The global corner‐related coarse problem is solved iteratively with a parallel communication‐avoiding biconjugate gradient stabilized method to minimize global communication, and its convergence is accelerated by a diagonal preconditioner constructed from the coarse system matrix. To alleviate neighboring communication overhead, the non‐blocking communication approach is employed in both generalized minimal residual and communication‐avoiding biconjugate gradient stabilized iterative solutions. Three numerical examples are presented to demonstrate the accuracy, scalability, and capability of the proposed parallel FETI‐DP algorithm for electromagnetic modeling of general objects and antenna arrays. Copyright © 2016 John Wiley & Sons, Ltd.     

A 3D finite element analysis of large‐scale nonlinear dynamic electromagnetic problems by harmonic balancing and domain decomposition

The dual–primal finite element tearing and interconnecting (FETI‐DP) method is applied together with the harmonic balance method and the fixed‐point (FP) method to improve the efficiency of three‐dimensional finite element analysis of large‐scale nonlinear dynamic electromagnetic problems. The FETI‐DP method decomposes the original problem into smaller subdomains problems. Combined with parallel computing techniques, the total computation time can be reduced significantly. To account for nonlinear B‐H characteristics, the FP method is applied together with the polarization formulation. Because the FP method assumes a constant reluctivity, it decouples the systems of different harmonics. The FETI‐DP method can then be applied to speed up the simulation of each harmonic in each FP iteration. Two benchmark problems and a three‐phase inductor are simulated by the proposed method to validate the formulation and demonstrate its performance. Copyright © 2015 John Wiley & Sons, Ltd.     

A non‐conformal FETI‐like domain decomposition approach of FE‐BI‐MLFMA for 3‐D electromagnetic scattering/radiation problems

A non‐conformal finite element tearing and interconnecting‐like (FETI‐like) domain decomposition approach (DDA) of the hybrid finite element–boundary integral–multilevel fast multipole algorithm (FE‐BI‐MLFMA) is presented by integrating a series efficient techniques for computing electromagnetic scattering/radiation problems. The Robin transmission condition is employed to cement the non‐conformal meshes on the interconnected surfaces between the interior and exterior regions and between sub‐domains in the interior region. The FETI‐like technique is applied to reduce the FE‐BI matrix equation. Furthermore, a preconditioner is constructed to accelerate the convergent speed of this non‐conformal FETI‐like DDA. The numerical performance of the presented non‐conformal FETI‐like DDA‐FE‐BI‐MLFMA is studied for scattering/radiation problems. Copyright © 2015 John Wiley & Sons, Ltd.     

Meshfree‐enriched electromagnetic finite element formulation using nodal integration

This paper presents a meshfree‐enriched finite element formulation using nodal integration for electrostatic analysis. The meshfree‐enriched finite element method, originally proposed to solve the incompressible constraint in mechanical problem, is revisited in this paper and applied to the analysis of electrostatic problems to improve the solution accuracy of conventional finite element method. A novel nodal integration scheme based on the meshfree‐enriched finite element mesh is developed for the integration of discrete equation and is shown to pass the linear exactness in the Galerkin approximation. To demonstrate the accuracy of the proposed formulation, two numerical examples are studied and comparisons are made to several other finite element formulations. Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis of quadruple corner‐cut ridged square waveguide by hybrid mode‐matching boundary‐element method

In this paper, the square waveguide with quadruple corner‐cut ridges is analyzed using the hybrid mode‐matching boundary‐element method. Because of its symmetry, only a quarter of its cross‐section needs to be considered and it is then divided into three regions. The electromagnetic field components in two regular regions can be obtained using the mode‐matching method and the third irregular region is discretized using the boundary‐element method. The combination of two methods produces one matrix equation, from whose determinant the cutoff wavenumbers of waveguide modes can then be computed. This hybrid technique takes advantage of the mode‐matching method's high efficiency and the boundary‐element method's versatility. The convergence of this hybrid method is studied, and numerical results are compared with the conventional boundary‐element method and commercial finite‐element software package, which shows that our hybrid method can achieve the same accuracy with much less time. The influence of the cut‐corners on the cutoff wavenumbers of the dominant and higher‐order modes is then examined. A simple approximate equation is found to accurately predict the cutoff wavenumber of TE₂₀ mode. The single‐mode bandwidth of a quadruple ridged square waveguide is calculated thereafter, which shows that this corner‐cut structure can provide a broader bandwidth compared to the one without cut‐corners. Copyright © 2010 John Wiley & Sons, Ltd.     

Transient analysis of coupled non‐uniform transmission line using finite element method

This paper presents a finite element time domain model for a numerical solution of a coupled non‐uniform transmission line problem. On the basis of the finite element method, a novel numerical procedure for the solution of a system of the non‐uniform multi‐conductor transmission line equations in the time domain is presented. The results obtained by the proposed method have been compared with the solution obtained using the finite difference time domain method, and an excellent correlation has been demonstrated. Copyright © 2014 John Wiley & Sons, Ltd.     

An interface‐enriched generalized finite element analysis for electromagnetic problems with non‐conformal discretizations

An interface‐enriched generalized finite element method is presented for analyzing electromagnetic problems involving highly inhomogeneous materials. To avoid creating conformal meshes within a complex computational domain and preparing multiple meshes during optimization, enriched vector basis functions are introduced over the finite elements that intersect the material interfaces to capture the normal derivative discontinuity of the tangential field component. These enrichment functions are directly constructed from a linear combination of the vector basis functions of the sub‐elements. Several numerical examples are presented to verify the method with analytical solutions and demonstrate its h‐refinement convergence rate. The proposed interface‐enriched generalized finite element method is shown to achieve the same level of accuracy as the standard finite element method based on conformal meshes. Two examples, involving multiple microvascular channels and circular inclusions of different radii, are analyzed to illustrate the capability of the proposed approach in handling complicated inhomogeneous geometries. Copyright © 2015 John Wiley & Sons, Ltd.     

Performance Evaluation of an Axial‐Type Magnetic‐Geared Motor

This paper first proposes an axial‐type magnetic‐geared motor that uses permanent magnets only in the high‐speed rotor. The operating principle of this motor is described and the torque–speed characteristics are computed by using three‐dimensional finite element method analysis. In order to increase the torque density, a novel axial‐type magnetic‐geared motor with permanent magnets on the high‐speed rotor and stator is also proposed. The torque–speed characteristics are compared to the original model with permanent magnets only on the high‐speed rotor. Finally, the computed torque–speed characteristics are verified against measurements on a prototype.     

Fourth‐order hybrid implicit and explicit‐FDTD method

A fourth‐order hybrid implicit and explicit finite‐difference time‐domain Method has been presented in this paper. This new method investigates the use of a second‐order accurate in time and a fourth‐order accurate in space. The 2D formulation of the method is presented and the time stability condition of the method is certified. The maximum time step size in this method is only determined by one spatial discretization. The numerical dispersion is discussed. Numerical examples demonstrate that when this method is used to solve electromagnetic problems, higher computational efficiency and less dispersion error can be obtained by comparing with the traditional finite‐difference time‐domain algorithm. Copyright © 2015 John Wiley & Sons, Ltd.     

Modeling of doubly lossy and dispersive media with the time‐domain finite‐element dual‐field domain‐decomposition algorithm

A numerical scheme is presented for the time‐domain finite‐element modeling of an electrically and magnetically lossy and dispersive medium in the dual‐field domain‐decomposition method. Existing approaches for modeling doubly lossy and dispersive media are extended to the dual‐field case, yielding a general dual‐field domain‐decomposition scheme for modeling large‐scale electromagnetic problems involving such media. A quantitative analysis is performed to estimate the error induced by the modeling of medium dispersion. Copyright © 2012 John Wiley & Sons, Ltd.     

Parallel realization of algebraic domain decomposition for the vector finite element analysis of 3D time‐harmonic EM field problems

Based on message passing interface (MPI) distributed‐memory network, we propose a parallel realization of algebraic domain decomposition method to solve the large sparse linear systems, which were derived from the vector finite element method (FEM) for three‐dimensional electromagnetic field problems. The proposed method segments the problem into several smaller sub‐problems, solves each sub‐problem in each node (i.e. computer) by the direct method, exchanges related data between nodes with MPI cluster network, and then reassembles the sub‐problem solutions together to get the global result. Multifrontal method is applied to solve intermediate equations associated with each sub‐problem and conjugate gradient methods are used to solve the reduced interface system. The simulation results demonstrate that the proposed parallel computing can save much more memory and CPU time than sequential computing. Furthermore, it can solve larger system in reasonable time and get excellent performance vs price ratio. Copyright © 2005 John Wiley & Sons, Ltd.     

Electromagnetic non‐destructive evaluation by vector finite‐element neural networks

This study proposes neural network‐based iterative inverse solutions for non‐destructive evaluation (NDE) in which vector finite elements (VFEM) represent the forward model that closely models the physical process. The iterative algorithm can eventually estimate the material parameters. Vector finite element method global matrix is stored in a compact form using its sparsity and symmetry. The stored matrix elements are employed as the neurons weights, and preconditioning techniques are used to accelerate convergence of the neural networks (NN) algorithm. Detailed algorithm describing this new method is given to facilitate implementation. Combining vector finite elements and NNs offers several advantages over each technique alone, such as reducing memory storage requirements and the easily computed fixed weights of the NN. Various examples are solved to show the performance and usefulness of the proposed method, including lossy printed circuit board and lossy inhomogeneous cylindrical problems with ferromagnetic materials. These solutions compare very well with other published data where the maximum relative error was 5%. Copyright © 2010 John Wiley & Sons, Ltd.     

Large‐scale magnetic field analysis by the hybrid finite element‐boundary element method combined with the fast multipole method

This paper describes a large‐scale magnetic field analysis by means of the hybrid finite element‐boundary element (FE‐BE) method. The hybrid FE‐BE method is well‐suited for solving open electromagnetic field problems that comprise movement, nonlinear media, and eddy current. In general, however, large memory and computational costs are required due to the dense blocks in the system matrix generated by the BE part of the hybrid formulation. In order to overcome the above difficulties, we introduce the fast multipole method (FMM) to the hybrid FE‐BE formulation developed by ourselves. Furthermore, we propose a novel preconditioning technique suitable for the hybrid FE‐BE method with the FMM. Some numerical results that demonstrate the effectiveness of the proposed approach are also presented. ©2007 Wiley Periodicals, Inc. Electr Eng Jpn, 162(1): 73–80, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20508     

Element‐free Galerkin method to the interface problems with application in electrostatic

The purpose of this paper is to develop the element‐free Galerkin method for a numerical simulation of the second‐order elliptic equation with discontinuous coefficients. Discontinuities in the solution and in its normal derivatives are prescribed on an interface inside the domain. The proposed method is one of the powerful meshless methods based on moving least squares approximation. The element‐free Galerkin method uses only a set of nodal points to discretize the governing equation. No mesh in the classical sense is needed, but a background mesh is used for integration purpose. A quadrilateral mesh unfitted with the interface is used for integration objective. The Lagrange multipliers are used to enforce both Dirichlet boundary condition and Dirichlet jump condition. The presented numerical experiments confirm the efficiency of the proposed method in comparison with some existing methods for interface problems. Copyright © 2016 John Wiley & Sons, Ltd.     

A matrix‐exponential decomposition‐based time‐domain method for band structure calculation of one‐dimensional periodic structures

A time‐domain method for calculating the band structure of one‐dimensional periodic structures is proposed. During the time‐stepping of the method, the column vector containing the spatially sampled field data is updated by multiplying with an iteration matrix. The iteration matrix is first obtained by using the matrix‐exponential decomposition technique. Then, the small nonzero elements of the matrix are pruned to improve its sparse structure, so that the efficiency of the matrix–vector multiplication involved in each time‐step is enhanced. The numerical results show that the method is conditionally stable but is much more stable than the conventional finite‐difference time‐domain (FDTD) method. The time‐step with which the method runs stably can be much larger than the Courant–Friedrichs–Lewy (CFL) limit. And moreover, the method is found to be particularly efficient for the band structure calculation of large‐scale structures containing a defect with a very high wave speed, where the conventional FDTD method may generally lose its efficiency severely. For this kind of structures, not only the stability requirement can be significantly relaxed, but also the matrix‐pruning operation can be very effectively performed. In the numerical experiments for large‐scale quasi‐periodic phononic crystal structures containing a defect layer, significantly higher efficiency than the conventional FDTD method can be achieved by the proposed method without an evident accuracy deterioration if the wave speed of the defect layer is relatively high. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive finite‐time control for high‐order nonlinear systems with mismatched disturbances

In this paper, adaptive finite‐time control is addressed for a class of high‐order nonlinear systems with mismatched disturbances. An adaptive finite‐time controller is designed in which variable gains are adjusted to ensure finite‐time stabilization for the closed‐loop system. Chattering is reduced by a designed adaptive sliding mode observer which is also used to deal with the mismatched disturbances in finite time. The proposed adaptive finite‐time control method avoids calculating derivative repeatedly of traditional backstepping methods and reduces computational burden effectively. Three numerical examples are given to illustrate the effectiveness of the proposed method.     

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.     

Higher‐order CN‐FETD method for analysis of microwave circuit structures

In this paper, the hierarchical high‐order basis functions on tetrahedrons are introduced to the Crank–Nicolson (CN) finite‐element time‐domain (FETD) with the 3D Maxwell equations for analysis of the microwave circuit structures. Whitney 1‐form high‐order hierarchical basis functions are used to expand the electric field and Whitney 2‐form high‐order hierarchical basis functions for the magnetic field. The CN scheme is employed in the FETD method to lead to an unconditionally stable algorithm. Numerical results were presented to demonstrate the accuracy and efficiency of the proposed high‐order CN‐FETD method. Copyright © 2012 John Wiley & Sons, Ltd.     

Delay‐dependent filtering for discrete‐time state‐delayed systems with small gain conditions in finite frequency ranges

This paper is concerned with the delay‐dependent filtering problem for linear discrete‐time multi‐delay systems with small gain conditions in finite frequency ranges. A new multiplier method is developed to convert the resulting nonconvex filtering synthesis conditions to the ones based on linear matrix inequalities (LMIs). Thus, sufficient conditions for the existence of feasible filters are given in terms of solutions to a set of LMIs. For the entire frequency case, it is shown that the proposed result is less conservative than the relative existing results. Finally, the procedures and the advantages of the proposed approach in comparison with the existing ones in the entire frequency range are illustrated via numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

Algebraic multigrid Laplace solver for the extraction of capacitances of conductors in multi‐layer dielectrics

This paper describes the development of a robust multigrid, finite element‐based, Laplace solver for accurate capacitance extraction of conductors embedded in multi‐layer dielectric domains. An algebraic multigrid based on element interpolation is adopted and streamlined for the development of the proposed solver. In particular, a new, node‐based agglomeration scheme is proposed to speed up the process of agglomeration. Several attributes of this new method are investigated through the application of the Laplace solver to the calculation of the per‐unit‐length capacitance of configurations of parallel, uniform conductors embedded in multi‐layer dielectric substrates. These two‐dimensional configurations are commonly encountered as high‐speed interconnect structures for integrated electronic circuits. The proposed method is shown to be particularly robust and accurate for structures with very thin dielectric layers characterized by large variation in their electric permittivities. More specifically, it is demonstrated that for such geometries the proposed node‐based agglomeration systematically reduces the problem size and speeds up the iterative solution of the finite element matrix. Copyright © 2007 John Wiley & Sons, Ltd.