Szabolcs Gyimothy

Transient eddy current analysis of pulsed eddy current testing by finite element method

Transient eddy current analysis of pulsed eddy current testing was performed by time-stepping method and Fourier transform method. The characteristics of two methods were evaluated by using a simple model. The accuracy was examined by the comparison of calculated and measured data. The calculated results of the two methods provided good agreement with measured data. However, it was clear that the Fourier transform method provided higher accuracy of amplitude than the time-stepping method. As a three-dimensional problem of pulsed eddy current testing, the TEAM Workshop Problem 27 was analyzed by an edge-element finite element method.

Parallel Realization of the Element-by-Element FEM Technique by CUDA

The utilization of Graphical Processing Units (GPUs) for the element-by-element (EbE) finite element method (FEM) is demonstrated. EbE FEM is a long known technique, by which a conjugate gradient (CG) type iterative solution scheme can be entirely decomposed into computations on the element level, i.e., without assembling the global system matrix. In our implementation NVIDIAs parallel computing solution, the Compute Unified Device Architecture (CUDA) is used to perform the required element-wise computations in parallel. Since element matrices need not be stored, the memory requirement can be kept extremely low. It is shown that this low-storage but computation-intensive technique is better suited for GPUs than those requiring the massive manipulation of large data sets.

Characterization of a 3D defect using the expected improvement algorithm

Purpose – The purpose of this paper is to provide a new methodology for the characterization of a defect by eddy‐current testing (ECT). The defect is embedded in a conductive non‐magnetic plate and the measured data are the impedance variation of an air‐cored probe coil scanning above the top of the plate.Design/methodology/approach – The inverse problem of defect characterization is solved by an iterative global optimization process. The strategy of the iterations is the kriging‐based expected improvement (EI) global optimization algorithm. The forward problem is solved numerically, using a volume integral approach.Findings – The proposed method seems to be efficient in the light of the presented numerical results. Further investigation and comparison to other methods are still needed.Originality/value – This is believed to be the first time when the EI algorithm has been used to solve an inverse problem related to the ECT.

Calculation of losses in laminated ferromagnetic materials

A numerical method for calculation of the power losses of nonlinear laminated ferromagnetic cores is presented. The calculation is made in two subsequent steps. In the first step, the approximate magnetic field distribution in the material is determined assuming a nonlaminated bulk nonlinear ferromagnetic material with anisotropic conductivity. In the second step, the nonlinear ferromagnetic material of the laminated core is replaced to linear material with spatially inhomogeneous permeability. The actual permeability distributions of the lamination are determined based on the magnetic field obtained from the first calculation and the nonlinear B-H curve of the material. In this paper, the outlined method is verified through calculations and measurements made on simple benchmark arrangements. Different methods for assigning the inhomogeneous permeability are also investigated.

Solution of Inverse Problems in Nondestructive Testing by a Kriging-Based Surrogate Model

The inverse problems of electromagnetic nondestructive testing are often solved via the solution of several forward problems. For the latter, precise numerical simulators are available in most of the cases, but the associated computational cost is usually high. Surrogate models (or metamodels)-which are getting more and more widespread in electromagnetics-might be promising alternatives to heavy simulations. Traditionally, such surrogates are used to replace the forward model. However, in this paper the direct use of surrogate models for the solution of inverse problems is studied and illustrated via eddy-current testing examples.

Modeling of Resonant Wireless Power Transfer With Integral Formulations in Heterogeneous Media

A full-wave integral formulation has recently been proposed for the simulation of magnetically coupled resonant wireless power transfer (WPT) arrangements in homogeneous medium. In this paper, the formulation is extended to the case where two different types of dielectrics are separated by a planar interface. This configuration has extensive practical interest nowadays, especially for modeling biomedical WPT applications. The new formulation is based on a stationary approximation, which is valid at the typical operating frequencies. The proposed scheme requires much less computational resources compared with standard finite-element simulations. The results are validated against alternative simulations and measured data as well.

Kriging for Eddy-Current Testing Problems

Accurate numerical simulation of Eddy-Current Testing (ECT) experiments usually requires large computational efforts. So, a natural idea is to build a cheap approximation of the expensive-to-run simulator. This paper presents an approximation method based on functional kriging. Kriging is widely used in other domains, but is still unused in the ECT community. Its main idea is to build a random process model of the simulator. The extension of kriging to the case of functional output data (which is the typical case in ECT) is a recent development of mathematics. The paper introduces functional kriging and illustrates its performance via numerical examples using an ECT simulator based on a surface integral method. A comparison with other classical data interpolation methods is also carried out.

Finite-Element-Integral Equation Full-Wave Multisolver for Efficient Modeling of Resonant Wireless Power Transfer

With resonant wireless power transfer systems in operation, objects and/or humans having divers material properties come into the vicinity of the resonant coils. To model such systems efficiently, a novel full-wave multisolver is developed where the tangentially continuous vector finite element (FE) method is coupled with a method of moments (MoM) technique. The MoM technique is based on an electric field integral equation specifically designed to model the singular behavior of the thin coil wires, while the FE method is used to model the scattered field due to material inhomogeneities. A simplified sequential solver similar to the scattered field formulation is derived from the linear system of the multisolver in order to be applied as an efficient preconditioner, thereby speeding up the solution time significantly. The impedance change due to the material inhomogeneities can be calculated directly by applying the reaction concept. This ensures that the accuracy of the impedance change does not depend on the relative magnitude of the impedance change compared with the total impedance. The performance of the multisolver is illustrated by solving a test problem with a helical coil and a dielectric sphere with moderate conductivity, and comparing the multisolver results with the full FE solutions.

Fast analysis of metallic antennas by parallel moment method implemented on CUDA

In this paper a modeling technique enabling the fast analysis of antenna arrangements built-up from metallic parts is presented in detail. A calculation method which accelerates the solution of integral equations discretized by the Method of Moments have been implemented in a massively parallel computing environment, a general purpose video card (GPU). Rao-Wilton-Glisson edge basis functions are used to expand surface currents, while radiated field is computed using the dipole model. Since the entire computation takes place on the GPU exclusively, the overall computational time could be significantly reduced. To obtain such an acceleration, a novel computational technique is proposed for the filling of the impedance matrix, which takes full advantage of the given platform. Analysis of antenna structures can be made very efficiently using the frequency domain (FD) integral equationformulation, discretizedby the Methodof Moments (MoM) (1). The FD-MoM implementation employing surface patch modeling (2) of the (infinitesimally thin) metal surfaces lacks the incorporation of the surrounding air. This is a major advantage over Finite Element Method (FEM), where the surrounding air is part of the model and therefore must be discretized as well. As the computational complexity (demand) is proportional to the number of discrete geometrical elements constituting the model, in the latter case the Degrees of Freedom (DoF) of the resulting linear equation system to be finally solved is significantly higher than in the preceding one. Furthermore, as the correct behavior for the radiation condition is automatically incorporated in the moment method, there is no need for special termination -by e.g., a Perfectly Matched Layer (PML) or Absorbing Boundary Condition (ABC)- of the problem domain, as in FEM. Unfortunately, the advantagesof MoM are spoiled by its well-known high demands for computational resources in terms of memory capacity and CPU time. Although spectacular reduction techniques like the so-called multi-level fast multiple Method (MLFMM) exist, these can not be applied to all practical problems, hence often the tedious standard MoM formulation is to be utilized. In this paper the acceleration of the standard MoM method is carried out using a massively parallel computing environment, the GPU. Although several similar works have already been published (3,4),

High locality and increased intra-node parallelism for solving finite element models on GPUs by novel element-by-element implementation

The utilization of Graphical Processing Units (GPUs) for the element-by-element (EbE) finite element method (FEM) is demonstrated. EbE FEM is a long known technique, by which a conjugate gradient (CG) type iterative solution scheme can be entirely decomposed into computations on the element level, i.e., without assembling the global system matrix. In our implementation, NVIDIAs parallel computing solution, the Compute Unified Device Architecture (CUDA), is used to perform the required element-wise computations in parallel. Since element matrices need not be stored, the memory requirement can be kept extremely low. It is shown that this low-storage but computation-intensive technique is better suited for GPUs than those requiring the massive manipulation of large data sets. This study of the proposed parallel model illustrates a highly improved locality and minimization of data movement, which could also significantly reduce energy consumption in other heterogeneous HPC architectures.