Domain Decomposition Approach for Efficient Time-Domain Finite-Element Computation of Winding Losses in Electrical Machines

Finite element analysis of winding losses in electrical machines can be computationally uneconomical. Computationally lightermethods often place restrictions on the winding configuration or have been used for time-harmonic problems only. This paperproposes a domain decomposition type approach for solving this problem. The slots of the machine are modelled by their impulseresponse functions and coupled together with the rest of the problem. The method places no restrictions on the winding and naturallyincludes all resistive AC loss components. The method is then evaluated on a 500 kW induction motor. According to the simulations,the method yields precise results 70–100 faster compared to the established finite element approach.Peer reviewe

Numerical treatment of floating conductors based on the traditional finite element formulation

A method to model a conductor with undefined potential (commonly known as floating conductor), is sometimes required in the electric field analysis. This paper presentsand compares the main methods to deal with such issue, based on the traditional finite element formulation. The purpose is to guide the reader in the selection of a method under the following criteria: Accuracy, implementation and simplicity. The accuracy of each method was evaluated against the analytic solution of the capacitance matrix for a system of parallel cylindrical conductors. Based on the results of the simulations, the characteristics of the methods and this paper’s criteria, a qualification of each method performance is done. Additionally, particular cases in which a specific method could be the most suitable option to deal with floating conductors, are analyzed. In general, the Virtual Permittivity method exhibits the best performance. However, it is shown that the method’s accuracy is influenced by the rounding errors. This paper proposes an additional consideration on the method formulation in order to verify the accuracy of the results

Multiscale models of colloidal dispersion of particles in nematic liquid crystals

We use homogenization theory to develop a multiscale model of colloidal dispersion of particles in nematic liquid crystals under weak-anchoring conditions. We validate the model by comparing it with simulations by using the Landau–de Gennes free energy and show that the agreement is excellent. We then use the multiscale model to study the effect that particle anisotropy has on the liquid crystal: spherically symmetric particles always reduce the effective elastic constant. Asymmetric particles introduce an effective alignment field that can increase the Fredericks threshold and decrease the switch-off time

Capacitive sensor array for nondestructive evaluation applications

Electromagnetic sensors come in different versions: capacitive, inductive, microwave, optics, etc. Eddy current probes (inductive sensors) have been used for decades in nondestructive evaluation (NDE) applications to detect flaws in conducting objects. Inductive probes are discussed by Rosegreen and Cooley (Bahr, and Rosegreen, 1987; Bahr, 1982; Bahr, and Cooley, 1983; Bahr, 1985). Capacitive sensors have been widely used for many decades also, but these applications have been based on extremely simple physical concepts; there has been no attempt to exploit the sophisticated sensing capabilities of generalized electric field probes. In NDE, there is a requirement to know not only how a probe behaves analytically under different probe geometry transformations, but also how a probe interacts with objects of different shapes and material properties

Admittance Method for Estimating Local Field Potentials Generated in a Multi-Scale Neuron Model of the Hippocampus

Significant progress has been made toward model-based prediction of neral tissue activation in response to extracellular electrical stimulation, but challenges remain in the accurate and efficient estimation of distributed local field potentials (LFP). Analytical methods of estimating electric fields are a first-order approximation that may be suitable for model validation, but they are computationally expensive and cannot accurately capture boundary conditions in heterogeneous tissue. While there are many appropriate numerical methods of solving electric fields in neural tissue models, there isn\u27t an established standard for mesh geometry nor a well-known rule for handling any mismatch in spatial resolution. Moreover, the challenge of misalignment between current sources and mesh nodes in a finite-element or resistor-network method volume conduction model needs to be further investigated. Therefore, using a previously published and validated multi-scale model of the hippocampus, the authors have formulated an algorithm for LFP estimation, and by extension, bidirectional communication between discretized and numerically solved volume conduction models and biologically detailed neural circuit models constructed in NEURON. Development of this algorithm required that we assess meshes of (i) unstructured tetrahedral and grid-based hexahedral geometries as well as (ii) differing approaches for managing the spatial misalignment of current sources and mesh nodes. The resulting algorithm is validated through the comparison of Admittance Method predicted evoked potentials with analytically estimated LFPs. Establishing this method is a critical step toward closed-loop integration of volume conductor and NEURON models that could lead to substantial improvement of the predictive power of multi-scale stimulation models of cortical tissue. These models may be used to deepen our understanding of hippocampal pathologies and the identification of efficacious electroceutical treatments

A hierarchical Markov chain based solver for very-large-scale capacitance extraction

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 79-80).This thesis presents two hierarchical algorithms, FastMarkov and FD-MTM, for computing the capacitance of very-large-scale layout with non-uniform media. Fast- Markov is Boundary Element Method based and FD-MTM is Finite Difference based. In our algorithms, the layout is first partitioned into small blocks and the capacitance matrix of each block is solved using standard deterministic methods, BEM for Fast- Markov and FDM for FD-MTM. We connect the blocks by enforcing the boundary condition on the interfaces, forming a Markov Chain containing the capacitive characteristic of the layout. Capacitance of the full layout is then extracted with the random walk method. By employing the "divide and conquer" strategy, our algorithm does not need to assemble or solve a linear system of equations at the level of the full layout and thus eliminates the memory problem. We also propose a modification to the FastMarkov algorithm (FastMarkov with boundary fix) to address the block interface issue when using the finite difference method. We implemented FastMarkov with boundary fix in C++ and parallelized the solver with Message Passing Interface. Compared with standard FD capacitance solver, our solver is able to achieve a speedup almost linear to the number of blocks the layout is partitioned into. On top of it, FastMarkov is easily parallelizable because the computation of the capacitance matrix of one block is independent of other blocks and one path of random walk is independent of other paths. Results and comparisons are presented for parallel plates example and for a large Intel example.by Yan Zhao.S.M

Parallel algorithms for three dimensional electrical impedance tomography

This thesis is concerned with Electrical Impedance Tomography (EIT), an imaging technique in which pictures of the electrical impedance within a volume are formed from current and voltage measurements made on the surface of the volume. The focus of the thesis is the mathematical and numerical aspects of reconstructing the impedance image from the measured data (the reconstruction problem). The reconstruction problem is mathematically difficult and most reconstruction algorithms are computationally intensive. Many of the potential applications of EIT in medical diagnosis and industrial process control depend upon rapid reconstruction of images. The aim of this investigation is to find algorithms and numerical techniques that lead to fast reconstruction while respecting the real mathematical difficulties involved. A general framework for Newton based reconstruction algorithms is developed which describes a large number of the reconstruction algorithms used by other investigators. Optimal experiments are defined in terms of current drive and voltage measurement patterns and it is shown that adaptive current reconstruction algorithms are a special case of their use. This leads to a new reconstruction algorithm using optimal experiments which is considerably faster than other methods of the Newton type. A tomograph is tested to measure the magnitude of the major sources of error in the data used for image reconstruction. An investigation into the numerical stability of reconstruction algorithms identifies the resulting uncertainty in the impedance image. A new data collection strategy and a numerical forward model are developed which minimise the effects of, previously, major sources of error. A reconstruction program is written for a range of Multiple Instruction Multiple Data, (MIMD), distributed memory, parallel computers. These machines promise high computational power for low cost and so look promising as components in medical tomographs. The performance of several reconstruction algorithms on these computers is analysed in detail

Interconnect capacitance extraction under geometric uncertainties

Interconnects are an important constituent of any large scale integrated circuit, and accurate interconnect analysis is essential not only for post-layout verification but also for synthesis. For instance, extraction of interconnect capacitance is needed for the prediction of interconnect-induced delay, crosstalk, and other signal distortion related effects that are used to guide IC routing and floor planning. The continuous progress of semiconductor technology is leading ICs to the era of 45 nm technology and beyond. However, this progress has been associated with increasing variability during the manufacturing processes. This variability leads to stochastic variations in geometric and material parameters and has a significant impact on interconnect capacitance. It is therefore important to be able to quantify the effect of such process induced variations on interconnect capacitance. In this thesis, we have worked on a methodology towards modeling of interconnect capacitance in the presence of geometric uncertainties. More specifically, a methodology is proposed for the finite element solution of Laplace's equation for the calculation of the per-unit-length capacitance matrix of a multi-conductor interconnect structure embedded in a multi-layered insulating substrate and in the presence of statistical variation in conductor and substrate geometry. The proposed method is founded on the idea of defining a single, mean geometry, which is subsequently used with a single finite element discretization, to extract the statistics of the interconnect capacitance in an expedient fashion. We demonstrate the accuracy and efficiency of our method through its application to the extraction of capacitances in some representative geometries for IC interconnects