Cohomology in electromagnetic modeling

Electromagnetic modeling provides an interesting context to present a link between physical phenomena and homology and cohomology theories. Over the past twenty-five years, a considerable effort has been invested by the computational electromagnetics community to develop fast and general techniques for potential design. When magneto-quasi-static discrete formulations based on magnetic scalar potential are employed in problems which involve conductive regions with holes, \textit{cuts} are needed to make the boundary value problem well defined. While an intimate connection with homology theory has been quickly recognized, heuristic definitions of cuts are surprisingly still dominant in the literature. The aim of this paper is first to survey several definitions of cuts together with their shortcomings. Then, cuts are defined as generators of the first cohomology group over integers of a finite CW-complex. This provably general definition has also the virtue of providing an automatic, general and efficient algorithm for the computation of cuts. Some counter-examples show that heuristic definitions of cuts should be abandoned. The use of cohomology theory is not an option but the invaluable tool expressly needed to solve this problem

Lean cohomology computation for electromagnetic modeling

Solving eddy current problems formulated by using a magnetic scalar potential in the insulator requires a topological pre-processing to find the so-called first cohomology basis of the insulating region, which may be very time-consuming for challenging industrially driven problems. The physics-inspired D\u142otko-Specogna (DS) algorithm was shown to be superior to alternatives in performing such a topological pre-processing. Yet, the DS algorithm is particularly fast when it produces as output not a regular cohomology basis but a so-called lazy one, which contains the regular one but it keeps also some additional redundant elements. Having a regular basis may be advantageous over the lazy basis if a technique to produce it would take about the same time as the computation of a lazy basis. In the literature, such a technique is missing. This paper covers this gap by introducing modifications to the DS algorithm to compute a regular basis of the first cohomology group in practically the same time as the generation of a lazy cohomology basis. The speedup of this modified DS algorithm with respect to the best alternative reaches more than two orders of magnitudes on challenging benchmark problems. This demonstrates the potential impact of the proposed contribution in the low-frequency computational electromagnetics community and beyond. \ua9 2017 IEEE

Sensor coil optimization

In some embodiments, a coil design system is provided. In particular, a method of providing an optimized position locating sensor coil design in presented. The method includes receiving a coil design; simulating position determination with the coil design to form a simulated performance; comparing the simulated response with the specification to provide a comparison; and modifying the coil design based on a comparison between the simulated performance and a performance specification to arrive at an updated coil design

Ex vivo Time Evolution of Thrombus Growth through Optical and Electrical Impedance data fusion

We designed a novel sensor specifically aimed at ex vivo measurements of white thrombus volume growth; a white thrombus is induced within an artificial micro-channel where hemostasis takes place starting from whole blood under flow conditions. The advantage of the proposed methodology is to identify the time evolution of the thrombus volume by means of an original data fusion methodology based on 2D optical and electrical impedance data simultaneously processed. On the contrary, the present state of the art optical imaging methodologies allow the thrombus volume estimation only at the end of the hemostatic process