This paper proposes a procedure for the modeling of linear passive devices with distributed parameters as Hamiltonian systems with a finite number of ports, in the view of their coupling with external systems with lumped parameters (circuits). To obtain this particular Dirac structure, appropriate boundary conditions (BC) are used for the PDEs of several physical fields. Originally, they are Electric Circuit Element BC, here generalized for multidisciplinary fields such as elastic solids, acoustic and thermal devices Their internal field is discretized by the Finite Element Method, thus obtaining the stiffness, damping and mass matrices of a second order ODEs system, transformed then into a first order pH canonical form, having as interaction variables the flow and effort of each terminal.

Dual full-wave (FW) frequency-domain E and H formulations, with scalar potentials on the boundary, and with electric circuit element boundary conditions are discussed and details about their implementation in the finite element method are given. For some magneto-quasi-static devices this duality frames the exact solution thus allowing the accuracy control. In such cases the geometric mean of the dual solutions exhibits a better accuracy and higher convergence rate than the individual numerical solutions. For FW devices the dual formulations allow a compromise between model accuracy and computational effort, especially if the models are not 3D. Implementation is available for free in onelab. Validation for test cases with analytic solution are provided: a conducting cylinder and a coaxial cable.

Electric Circuit Element (ECE) are special boundary conditions that enable a natural coupling between electromagnetic devices and circuits. ECE can be generalized to allow for parts on the domain boundary where absorbing boundary conditions can be set, to model the unbounded space. This paper illustrates the implementation of radiant ECE in the 2D and 3D-finite element method, for a full-wave time-harmonic field in dual frequency-domain E and H formulations. The weak formulations are implemented in the free environment Open Numerical Engineering LABoratory (onelab). The formulations are proven to be well-posed (existence, uniqueness and stability of the weak solution are proven) and validated for a monopole antenna.

This paper is a commented review of our contributions related to the modelling and simulation of interconnects, presented throughout the years in scientific communities that belong mainly to electrical engineering and mathematics. The emphasis is on important topics that we feel that are not yet much used by the electronics packaging community, such as the electric circuit element boundary conditions in the electromagnetic field formulation as well as complexity reduction techniques throughout the modelling flow.

The information is transmitted in neurons through axons, many of whom have myelin-covered sections, whose main purpose is to increase the speed of electrical signal transmission. Modeling the myelinated axons in a realistic way, by maintaining the physical meaning of components may lead to complex systems, described by high-dimensional systems of PDEs, whose solution is computationally demanding. Analysis of larger neuronal circuits including multiple myelinated axons therefore requires the generation of equivalent low-order models to control complexity. Such models must preserve the physical interpretation and properties of the original system including its passivity and stability. The axons' port-based structure makes them suitable to be modeled as port-Hamiltonian systems. This paper uses a structure-preserving reduction method for port-Hamiltonian systems to reduce the description of a myelinated compartment into a model with comparable accuracy with the previously used vector fitting technique. The reduced system is synthesized into an equivalent passive circuit with no controlled sources and only positive elements, amenable for inclusion in standard neuronal simulators.

A natural coupling of a circuit with an electromagnetic device is possible if special boundary conditions, called Electric Circuit Element (ECE), are used for the electromagnetic field formulation. This contribution shows how these ECE boundary conditions can be implemented into the 3D-finite element method for solving coupled full-wave electromagnetic (EM) field-circuit problems in the frequency domain. The frequency response allows the extraction of a reduced order model of the analyzed device, accounting for all the EM field effects. The implementation is based on a weak formulation that uses the electric field strength E strictly inside the domain and a scalar potential V defined solely at the boundary. Edge elements for E are used inside the three-dimensional domain and nodal elements for V are used on its two-dimensional boundary. The weak formulation is described and implemented in the free environment Open Numerical Engineering LABoratory (onelab). The validation is carried out on 3D examples.

Purpose The purpose of this paper is to propose a physics-aware algorithm to obtain radio frequency (RF)-reduced models of micro-electromechanical systems (MEMS) switches and show how, together with multiphysics macromodels, they can be realized as circuits that include both lumped and distributed parameters. Design/methodology/approach The macromodels are extracted with a robust procedure from the solution of Maxwell’s equations with electromagnetic circuit element (ECE) boundary conditions. The reduced model is extracted from the simulations of three electromagnetic field problems, in full-wave regime, that correspond to three configurations: signal lines alone, switch in the up and down positions. Findings The technique is exemplified for shunt switches, but it can be extended for lateral switches. Moreover, the algorithm is able take frequency dependence into account both for the signal lines and for the switch model. For the later, the order of the model is increased until a specified accuracy is achieved. Originality/value The use of ECE as boundary conditions for the RF simulation of MEMS switches has the advantage that the definition of ports is unambiguous and robust as the ports are clearly defined. The extraction approach has the advantage that the simplified model keeps the basic phenomena, i.e. the propagation of the signal along the lines. As the macromodel is realized with a netlist that uses transmission lines models, the lines’ extension is natural. The frequency dependence can be included in the model, if needed.

The saltatory conduction is the way the action potential is transmitted along a myelinated axon. The potential diffuses along the myelinated compartments and is regenerated in the Ranvier nodes due to the ionic channels that allow the flow of ions across the membrane. For an efficient simulation of large-scale neuronal networks, it is important to develop low order models especially for myelinated compartments where the potential satisfies PDEs and have control over the accuracy of the reduced models and access to the inner parameters. The paper proposes two coupled macro models for the simulation of the saltatory conduction in myelinated axons, one as circuits, implemented in a circuit simulator (Spice), and the second as systems, implemented in Simulink. In both formulations, the global model is obtained by concatenating reduced order models of 1D myelinated compartments with nonlinear OD models of the Ranvier nodes.

Purpose This paper proposes an algorithm for the extraction of reduced order models of MEMS switches, based on using a physics aware simplification technique. Design/methodology/approach The reduced model is built progressively by increasing the complexity of the physical model. The approach starts with static analyses and continues with dynamic ones. Physical phenomena are introduced sequentially in the reduced model whose order is increased until accuracy, computed by assessing forces that are kept in the reduced model, is acceptable. Findings The technique is exemplified for RF-MEMS switches, but it can be extended for any device where physical phenomena can be included one by one, in a hierarchy of models. The extraction technique is based on analogies that are carried out for both the multiphysics and the full-wave electromagnetic phenomena and their couplings. In the final model, the multiphysics electromechanical phenomena is reduced to a system with lumped components with nonlinear elastic and damping forces, coupled with a system with distributed and lumped components which represents the reduced model of the RF electromagnetic phenomena. Originality/value Contrary to the order reduction by projection methods, this approach has the advantage that the simplified model can be easily understood, the equations and variables have significance for the user and the algorithm starts with a model of minimal order, which is increased until the approximation error is acceptable. The novelty of the proposed method is that, being tailored to a specific application, it is able to keep physical interpretation inside the reduced model. This is the reason why, the obtained model has an extremely low order, much lower than the one achievable with general state-of-the-art procedures.

The paper presents a hierarchical series of computational models for myelinated axonal compartments. Three classes of models are considered, either with distributed parameters (2.5D EQS–ElectroQuasi Static, 1D TL-Transmission Lines) or with lumped parameters (0D). They are systematically analyzed with both analytical and numerical approaches, the main goal being to identify the best procedure for order reduction of each case. An appropriate error estimator is proposed in order to assess the accuracy of the models. This is the foundation of a procedure able to find the simplest reduced model having an imposed precision. The most computationally efficient model from the three geometries proved to be the analytical 1D one, which is able to have accuracy less than 0.1%. By order reduction with vector fitting, a finite model is generated with a relative difference of 10− 4 for order 5. The dynamical models thus extracted allow an efficient simulation of neurons and, consequently, of neuronal circuits. In such situations, the linear models of the myelinated compartments coupled with the dynamical, non-linear models of the Ranvier nodes, neuronal body (soma) and dendritic tree give global reduced models. In order to ease the simulation of large-scale neuronal systems, the sub-models at each level, including those of myelinated compartments should have the lowest possible order. The presented procedure is a first step in achieving simulations of neural systems with accuracy control.

The main objective of this paper is to develop a parallel algorithm aiming to reduce the computational time required to solve coupled multiphysics problems that arise in the RF -MEMS switches elasto-static analysis so that their consequent model order reduction can be carried out more efficiently.

The present paper studies two different high performance computing (HPC) approaches to speed up a non-destructive electromagnetic testing (NDET) forward problem, namely general purpose computing for graphics processing units (GPGPU) and multiprocessor programming. The two methods are studied and compared for a set of cracks, non-conductive or partial conductive with uniform conductivity. Both HPC techniques use professional libraries such as MAGMA or Intel MKL.

The paper studies the efficiency of a QPSO (Quantum-behaved Particle Swarm Optimization) algorithm enhanced with neighborhood strategies to solve a NDET (Non-Destructive Electromagnetic Testing) inverse problem, formulated as an optimization problem. Two different neighborhood strategies are analyzed and compared with the classic QPSO, one based on disjoint subswarms, and the other based on informants. Among the neighborhood strategies, some problem specific local search techniques are applied to speed up the inversion process. The NDT inverse problem consists in the reconstruction of 3D partially conductive cracks with uniform conductivity, conductivity smaller than the conductivity of the tested specimen.

This paper proposes simple models of high computational efficiency for Transcranial Magnetic Stimulation (TMS). Since the magnetic field is produced by currents of low frequency, the physical model is based on a unidirectional coupling between a Magneto-“Steady-state” (MG) formulation and an Electric Conduction (EC) formulation. The coupling is ensured by the Faraday's law of induction and it is unidirectional because the magnetic effect of the resultant eddy currents is neglected. The models we propose consider simplified geometries. However, the source coil in which an imposed current flows is described by a parametric curve, which can be of any shape. The human head is modeled by a conductive homogeneous sphere. The paper describes all the modeling steps: geometrical, physical, mathematical, analytical, numerical and computational models. Numerical results are compared with analytical ones and, aiming to quantify the uncertainties (UQ), the expression of the modeling error was determined. The result is a hierarchical series of approximate surrogate models, which have different levels of accuracy and complexity. The performed UQ may be used to control the modeling error, keeping the complexity at a minimal level. Three test cases are studied, for different shapes of the source coil: 1-circular, 2-circular planar 8-shaped, 3-circular arranged in the 3D space.

This contribution proposes a method to extract parametric reduced models that describe the coupled structural-electric behavior of RF MEMS switches. The equivalent capacitance coefficients and the effective elastic coefficients are extracted from coupled structural-electrostatic analysis. Parametric models are built based on the sensitivities of the extracted equivalent coefficients. The method is validated on two benchmarks: one for which experimental values are available, and the other one from the literature. The results show that, for the tested configurations, even a model of order 1 or 2 can catch accurately enough (e.g. relative error of less than 5 %) the pull-in voltage of the full order model, for a variation of the investigated parameter of less than 20 %. Such a reduced parametric model is useful in early stages of the design.

Starting from the Electro-Quasi-Static field equations a new 1D-RC transmission line model of axons is extracted. Based on this bio-physical model mathematical and numerical models are proposed and used to compute the main transmission parameters such as: neural signal attenuation, maximal transmission length (the admissible distance between Ranvier nodes = length of Schwann cells) and the nerve conduction velocity. It is predicted the dependence of this velocity versus the axon diameter, in both myelinated and unmyelinated cases, matching the results of measurements presented in literature.

Several neighborhood strategies for QPSO algorithms are proposed and analyzed in order to improve the performances of the original methods. The proposed strategies are applied to some of the most well known QPSO algorithms such as the QPSO with random mean, the QPSO with Gaussian attractor and of course the basic QPSO. To prevent the premature convergence and to avoid being trapped in local minima the neighborhoods are dynamically changed during the optimization process. For testing the efficiency of the neighborhood techniques two benchmark optimization problems from the electromagnetic field computation have been chosen, Loney's solenoid and TEAM22.

Two parallelization techniques, GPGPU and Pthreads for multiprocessor architectures, are used to implement a SPSO algorithm in order to solve electromagnetic optimization problems. Several configurations for the GPGPU implementation are tested and a new full parallel minimum branching implementation is proposed. The best GPGPU approaches are then compared with a Pthreads implementation in terms of speed up and solution quality. To test the efficiency of the parallelization techniques two electromagnetic optimization problems were chosen, namely the TEAM22 benchmark and Loney’s solenoid. In the end the paper provides suggestions regarding what parallelization technique should be used considering the implementation features of the optimization function.

A method to extract macromodels for RF MEMS switches is proposed. The macromodels include both the coupled structural-electric behavior of the switch as well as its RF behavior. The device with distributed parameters is subject to several analyses from which the parameters of the macromodel are extracted, by model reduction. From the coupled structural-electrostatic analysis the parametric capacitance and the effective stiffness coefficients of the switch are extracted. From the RF characteristics in the up stable state, the transmission line parameters are extracted. Finally, all parameters are combined in a Spice circuit model, which is controlled by the MEMS actuation voltage and is excited with the RF signal. The procedure is applied to a capacitive switch. Relative modeling errors with respect to the non-reduced model, considered as reference, of less than 3 % for the RF characteristics and less than 1 % for the mechanical characteristics are obtained.