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Two different ‘a posteriori’ error estimation techniques are proposed in this paper. The effectiveness of the error estimates in adaptive mesh refinement for 2D and 3D electrostatic problems are also analyzed with numerical test results. The post‐processing method employs an improved solution to estimate the error, whereas the gradient of field method utilizes the gradient of the field solution for estimating the ‘a posterior’ error. The gradient of field method is computationally inexpensive, since it solves a local problem on a patch of elements. The error estimates are tested by solving a set of self‐adjoint boundary value problems in 2D and 3D using a hierarchical minimal tree based mesh refinement algorithm. The numerical test results and the performance evaluation establish the effectiveness of the proposed error estimates for adaptive mesh refinement.

Several second order edge elements have been applied to solving magnetostatic problems. The performances of these elements are compared through an example of magnetic circuit. In order to ensure the compatibility of the system equations and hence the convergence, the current density is represented by the curl of a source field. This avoids an explicit gauge condition which is cumbersome in the case of high order elements.

Ground Penetrating Radar is a multidisciplinary Nondestructive Evaluation technique that requires knowledge of electromagnetic wave propagation, material properties and antenna theory. Under some circumstances this tool may require auxiliary algorithms to improve the interpretation of the collected data. Detection, location and definition of target’s geometrical and physical properties with a low false alarm rate are the objectives of these signal post-processing methods. Basic approaches are focused in the first two objectives while more robust and complex techniques deal with all objectives at once. This work reviews the use of Artificial Neural Networks and Machine Learning for data interpretation of Ground Penetrating Radar surveys. We show that these computational techniques have progressed GPR forward from locating and testing to imaging and diagnosis approaches.

Problem 2 of the International Workshop for Eddy Current Code Comparison is a hollow cylinder with its axis perpendicular to a uniform sinuosoidal field. A total of 10 solutions, employing 9 different computer codes, are described and compared with analytic results. Most codes were 2‐D finite element and were found to give satisfactory solutions.

This work discusses the use of exponentially and reciprocally decaying infinite elements and assesses their respective value for magnetostatic and eddy current problems. In particular, the need for different decaying parameters for different materials is shown to be detrimental to their application in many practical situations. A simple method, whereby a 2‐D solution is used to find the approximate boundary conditions for a closely truncated 3‐D mesh is presented and shown to give good results without the complications of infinite elements. This method is applied to a large eddy current problem.

The purpose of this paper is the derivation and efficient implementation of surface impedance boundary conditions (SIBCs) for nonlinear magnetic conductors.

An approach based on perturbation theory is proposed, which expands to nonlinear problems the methods already developed by the authors for linear problems. Differently from the linear case, for which the analytical solution of the diffusion equation in the semi-infinite space for the magnetic field is available, in the nonlinear case the corresponding nonlinear diffusion equation must be solved numerically. To this aim, a suitable smooth map is defined to reduce the semi-infinite computational domain to a finite one; then the diffusion equation is solved by a Galerkin method relying on basis functions constructed via the push-forward of a Lagrangian polynomial basis whose degrees of freedom are collocated at Gauss–Lobatto nodes. The use of such basis in connection with a suitable under-integration naturally leads to mass-lumping without impacting the order of the method. The solution of the diffusion equation is coupled with a boundary element method formulation for the case of parallel magnetic conductors in terms of E and B fields.

The results are validated by comparison with full nonlinear finite element method simulations showing very good accordance at a much lower computational cost.

Limitations of the method are those arising from perturbation theory: the introduced small parameter must be much less than one. This implies that the penetration depth of the magnetic field into the magnetic and conductive media must be much smaller than the characteristic size of the conductor.

The efficient implementation of a nonlinear SIBC based on a perturbation approach is proposed for an electric and magnetic field formulation of the two-dimensional problem of current driven parallel solid conductors.

The purpose of this paper is to develop a generalized observer and controller for brushless direct current (BLDC) motor to make the system more robust for parameter variations, load torque and speed tracking.

A robust interconnection and damping assignment passivity-based control (IDA-PBC) technique for BLDC motor is introduced in this paper. The IDA-PBC is used to obtain the reference voltages for pulse width modulation (PWM) control. The immersion and invariance (I&I) observer is used to estimate the load torque and speed of the BLDC motor. At the time of starting, the motor rotates in arbitrary direction, and sometimes, because of the cogging action, it may take a huge current. Therefore, a new start-up method is proposed for the BLDC motor, which maintains the alignment of the rotor.

From the simulation and experimental results, it can be seen that the proposed controller and observer satisfactorily work for parameter variations, load torque and speed tracking.

The authenticity of the proposed technique is tested experimentally on two different BLDC motors using low-cost 32-bit STM32F407VG microcontroller. The response of the proposed technique is evaluated by changing motor parameters such as stator resistance, inductance, flux linkage constant and torque constant.

A summary of results for Problem 9 of the TEAM workshop is presented in the form of a documentation of the available results. Due to unforseen complications in the problem no comparisons have been made and the problem, with modification, will be retained for future workshops.

Presents a review on implementing finite element methods on supercomputers, workstations and PCs and gives main trends in hardware and software developments. An appendix included at the end of the paper presents a bibliography on the subjects retrospectively to 1985 and approximately 1,100 references are listed.

To provide a time domain formulation for reconstruction of transient currents flowing in massive parallel conductors from magnetic data collected in the dielectric space surrounding the conductors.

A boundary integral equation (BIE) formulation involving Mitzner's and Rytov's high order surface impedance boundary conditions (SIBCs) is used. Input data of the inverse problem are the magnetic fields at given locations near the conductors. In order to validate the inversion algorithm, the magnetic field data are computed solving the direct problem with FEM for given current waveforms.

The improvement in reconstruction accuracy of the new time domain BIE formulation employing high order SIBCs has been demonstrated numerically in a simple test case. The range of validity of the technique has been extended to current pulses of longer duration and the computational burden has shown to increase only by a factor of 4.

The proposed formulation can be compared with other possible formulations, both in the time and in the frequency domain.

Based on this formulation a new current sensing technique is proposed for realization of low cost current sensors based on magnetic sensor arrays.

The inverse problem addressed in the paper has been solved for the first time.