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.     

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.     

Finite element power diode model optimized through experiment‐based parameter extraction

This paper presents a finite element physics‐based power diode model with parameters established through an extraction procedure validated experimentally. The model core is a numerical module that solves the ambipolar diffusion equation through a variational formulation followed by an approximate solution with the finite element method. Other zones of the device are modeled with classical methods in an analytical module. This hybrid approach enables accurate modeling and simulation of power bipolar semiconductor devices, using standard SPICE circuit simulators, with low execution times. As physics‐based models need a significant number of parameters, an automatic parameter extraction method has been developed. The procedure, based on an optimization algorithm (simulated annealing), enables an efficient extraction of parameters using some simple device waveform measurements. Implementation details of power diode model, in IsSpice simulator, are presented. Experimental validation is performed. Results prove the usefulness of the proposed methodology for efficient design of power circuits through simulation. Copyright © 2008 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.     

The surface charging effects in three‐dimensional simulation of the profiles of plasma‐etched nanostructures

Particles and fields represent two major modeling paradigms in pure and applied science at all. Particles typically exist in a spatial domain and they may interact with other particles or with field quantities defined on that domain. A field, on the other hand, defines a set of values on a region of space. In this paper, a methodology and some of the results for three‐dimensional (3D) simulations that includes both field and particle abstractions are presented. In our studies, charging damage to a semiconductor structure during plasma etching is simulated by using 3D level set profile evolution simulator. The surface potential profiles and electric field for the entire feature were generated by solving the Laplace equation using finite elements method. Calculations were performed in the case of simplified model of Ar⁺/CF₄ non‐equilibrium plasma etching of SiO₂. 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.     

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.     

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.     

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.     

Frequency‐dependent modeling of transmission lines using bergeron cells

This paper proposes using Bergeron's equivalent circuit with traveling time equal to the simulation time step as an element for frequency‐dependent modeling of transmission lines for electromagnetic transient (EMT) simulations of power systems. According to the simulation time step used, a transmission line is divided into aforementioned Bergeron's equivalents, each of which is called a ‘Bergeron cell’ in this paper. In this way, the traveling‐wave nature of a line is represented by the cascaded Bergeron cells. Then, the frequency‐dependent loss nature of the line is represented by a matrix partial fraction expansion, and this is inserted at each connection point of the Bergeron cells in the form of a multiphase Norton equivalent. Since the frequency‐dependent loss is modeled in the dimension of impedance, the change of the line length is easily taken into account by a simple multiplication. This methodology thus allows variable‐length modeling and completely avoids modal decomposition in both model identification and EMT simulation stages. The proposed methodology is applied to the frequency‐dependent modeling of overhead and submarine‐cable transmission lines, and its accuracy is assessed.     

Accelerated convergence in numerical simulations of surface supersaturation for crystal growth in solution under steady‐state conditions

This is an investigative paper which reports the results of comparisons of two numerical techniques for the solution of the Burton Cabrera and Frank (BCF) equation for the growth on crystal surfaces under steady state conditions. A successive over‐relaxation (SOR) scheme for the equivalent finite difference equation gives rapid convergence to the static solution. It is known that a suitable choice of scattering parameters in a transmission line matrix (TLM) network analogue of the Laplace equation yields ultra‐fast convergence. The results of numerical experiments which are reported here suggests that a similar situation also applies to the solution of the Poisson equation with shunt losses (the BCF equation), although the choice of optimum conditions appears to be different for different spatial positions within the solution space. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

Krylov model order reduction of finite element approximations of electromagnetic devices with frequency‐dependent material properties

A methodology is presented for the Krylov subspace‐based model order reduction of finite element models of electromagnetic structures with material properties and impedance boundary conditions exhibiting arbitrary frequency dependence. The proposed methodology is a generalization of an equation‐preserving Krylov model order reduction scheme for methodology for second‐order, linear dynamical systems. The emphasis of this paper is on the application of this method to the broadband model order reduction of planar circuits including lossy strips of arbitrary thickness and lossy reference planes. In particular, it is shown that the proposed model order reduction methodology provides for the accurately modelling of the impact of the frequency dependence of the internal impedance per unit length of the thick lossy strip on the electromagnetic response of the stripline structure over a very broad, multi‐GHz frequency band, extending all the way down to frequencies in the DC neighbourhood. In addition, the application of the proposed methodology to the broadband modelling of electromagnetic coupling between strips on either side of a lossy ground plane is demonstrated. Copyright © 2007 John Wiley & Sons, Ltd.     

A uniformly stable conformal FDTD‐method in Cartesian grids

A conformal finite‐difference time‐domain algorithm for the solution of electrodynamic problems in general perfectly conducting 3D geometries is presented. Unlike previous conformal approaches it has the second‐order convergence without the need to reduce the maximal stable time step of conventional staircase approach. A novel proof for the local error rate for general geometries is given, and the method is verified and compared to other approaches by means of several numerical 2D examples. Copyright © 2003 John Wiley & Sons, Ltd.     

有限元法结合渐近边界条件技术求解无界平面静电场问题

根据二维拉普拉斯方程的通解级数,推导出圆形人工边界上的零阶、一阶和二阶渐近边界条件,并将它们与有限元法结合,使得在求解区域不大情况下的二维静电场计算结果仍保持足够高的精度。同时,这种技术仍然保持了有限元刚度矩阵对称、正定和稀疏的性质。将这种方法应用于一个具有解析解的例子,说明了这种方法的正确性和有效性,也说明了在同一人工边界上,高阶的渐近边界条件较之于低阶的渐近边界条件具有更高的精度。最后,采用二阶渐近边界条件计算了一个实例。     

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.     

A dual‐primal finite‐element tearing and interconnecting method combined with tree‐cotree splitting for modeling electromechanical devices

The dual‐primal finite‐element tearing and interconnecting (FETI‐DP) method is combined with the tree‐cotree splitting (TCS) method to expand the capability and improve the efficiency of the finite‐element analysis of electromechanical devices. With the FETI‐DP method, an original large‐scale problem is decomposed into smaller subdomain problems and parallel computing schemes are then employed to reduce the computation time significantly. The TCS method is adopted to deal with the low‐frequency breakdown problem, which often accompanies the finite‐element analysis of electromechanical problems. On the basis of the computed magnetic field values, the force is computed with the use of the Maxwell stress tensor method. The proposed technique is applied to solve both high‐contrast magnetostatic problems and eddy‐current problems. Results are compared with both measurement data and brute‐force finite‐element calculations without domain decomposition. Comprehensive tests are conducted to investigate the parallel efficiency and numerical scalability. The results show that the proposed method can achieve a good parallel efficiency and an excellent numerical scalability with respect to the number of subdomains and the size of the problem. Copyright © 2012 John Wiley & Sons, Ltd.     

A Laplace domain finite element method (LDFEM) applied to diffusion and propagation problems in electrical engineering

This paper presents a new finite element formulation in the Laplace domain for both diffusion and wave equations with applications in the field of electrical engineering. With the aid of congruence transformation of matrices, the finite element equations in the Laplace domain are solved and time-domain results can be obtained through the inverse Laplace transform. In a test problem, good agreement between the numerical results derived with the present method and the analytical solutions has been found. For applications in which only Dirichlet and Neumann boundary conditions are involved, this new finite element approach can be applied and provide both frequency-domain and time-domain results in one run without any timestepping scheme. The limitations of using the congruence transformation in solving propagation problems are also addressed in this paper.     

Non‐minimum phase switched systems: HOSM‐based fault detection and fault identification via Volterra integral equation

In this paper, the problem of continuous and discrete state estimation for a class of linear switched systems with additive faults is studied. The class of systems under study can contain non‐minimum phase zeroes in some of their ‘operating modes’. The conditions for exact reconstruction of the discrete state are given using structural properties of the switched system. The state space is decomposed into the strongly observable part, the non‐strongly observable part, and the unobservable part, to analyze the effect of the unknown inputs. State observers based on high‐order sliding mode to exactly estimate the strongly observable part and Luenberger‐like observers to estimate the remaining parts are proposed. For the case when the exact estimation of the state cannot be achieved, the ultimate bounds on the estimation errors are provided. The proposed strategy includes a high‐order sliding‐mode‐based fault detection and a fault identification scheme via the solution of a Volterra integral equation. The feasibility of the proposed method is illustrated by simulations. Copyright © 2013 John Wiley & Sons, Ltd.