Direct and Inverse Computational Methods for Electromagnetic Scattering in Biological Diagnostics

Scattering theory has had a major roll in twentieth century mathematical physics. Mathematical modeling and algorithms of direct,- and inverse electromagnetic scattering formulation due to biological tissues are investigated. The algorithms are used for a model based illustration technique within the microwave range. A number of methods is given to solve the inverse electromagnetic scattering problem in which the nonlinear and ill-posed nature of the problem are acknowledged.Comment: 61 pages, 5 figure

Combined electric, electromagnetic, and thermal modeling based on a PEEC approach

The thermal design of printed circuit boards (PCB:s) has become a critical process in the early development stages of electronic packages. This increasingly important design has been brought about by rapid advancements in chip technology and packaging techniques. This master's thesis combines the partial element equivalent circuits (PEEC) formulation to give mathematical models for development of heat and temperature in electric circuits and networks. The numerical stability of solving integral and differential equations for PEEC currents and the electrothermal solution, respectively, has also been discussed in this work. Computer implementation and simulation of the electrothermal modeling of a lightning protection system (LPS) show that the finite difference methods are applicable to con-figurate the integral equation-based method of PEEC with the differential equation-based method for solving the conduction of heat in such electrical networks. In this model combination, however, there will be restrictions on numerical solution of the thermal modeling in which carefulness in choosing the number of time step-sizes is of absolute importance.Validerat; 20101217 (root

Mathematical modeling of electromagnetic disturbances in railway system

By introduction of modern electronics into railway system, new challenges in understanding the electric and electromagnetic behavior of these systems arise. In this thesis, electromagnetic modeling of electric networks above dielectric and perfect electrically conducting surfaces are studied. The approach is based on the Partial Element Equivalent Circuit (PEEC) method for solving Maxwell's equations. The most challenging problem within electromagnetic modeling of large systems is computational speed and for railway systems, modeling of the ground becomes the major bottleneck. The purpose of the thesis is to develop maintenance program for the railway system in the northern Sweden to deal with the failures created by electromagnetic disturbances using mathematical modeling of the electromagnetic phenomena. First, a grid PEEC approach is used to improve the computation time of the original program. This approach utilizes an algorithm to distribute the calculations on computers in a local area network. It is shown that the computation time for large systems can be improved in some stages of the computation process. The second approach to improve the computational efficiency of the PEEC method utilizes the theory of complex images. This results in an appropriate mathematical tool to study and describe the generated electric fields above the earth, as a dielectric- or perfectly electric conducting surface. Different mathematical models are applied to analyze and plot the current distribution on structures and the electric field generated by several structures above a perfect electrical conducting surface. The tests are verified by analytical methods and the traditional PEEC computation method. In the traditional PEEC method, the numerical solution of mathematical modeling of the ground constitutes the major effort due to the large number of unknown variables in the corresponding linear equation system. By using of the complex image methods, where the effect of the ground is approximated, the computational time will clearly be improved in the case studies. This combination of the PEEC method and the method of complex images results into an ultimate linear equation system by a smaller number of unknown variables and therefore a considerable improvement of the computational time. By use of electromagnetic modeling, it will be possible to study the disturbances due to transients and discharges, and also to expand the data bases for artificial intelligence. Defining the problem and determining what can be obtained by using of computational electromagnetic modeling, will be a step towards developing a more appropriate maintenance program for the railway system in the northern Sweden.Godkänd; 2006; 20061115 (ysko)</p

Mathematical Tools Applied in Computational Electromagnetics for a Biomedical Application and Antenna Analysis

To ensure a high level of safety and reliability of electronic/electric systems EMC (electromagnetic compatibility) tests together with computational techniques are used. In this thesis, mathematical modeling and computational electromagnetics are applied to mainly two case studies. In the first case study, electromagnetic modeling of electric networks and antenna structures above, and buried in, the ground are studied. The ground has been modelled either as a perfectly conducting or as a dielectric surface.  The second case study is focused on mathematical modeling and algorithms to solve the direct and inverse electromagnetic scattering problem for providing a model-based illustration technique. This electromagnetic scattering formulation is applied to describe a microwave imaging system called Breast Phantom. The final goal is to simulate and detect cancerous tissues in the human female breast by this microwave technique.   The common issue in both case studies has been the long computational time required for solving large systems of equations numerically. This problem has been dealt with using approximation methods, numerical analysis, and also parallel processing of numerical data. For the first case study in this thesis, Maxwell’s equations are solved for antenna structures and electronic networks by approximation methods and parallelized algorithms implemented in a LAN (Local Area Network). In addition, PMM (Point-Matching Method) has been used for the cases where the ground is assumed to act like a dielectric surface. For the second case study, FDTD (Finite-Difference Time Domain) method is applied for solving the electromagnetic scattering problem in two dimensions. The parallelized numerical FDTD-algorithm is implemented in both Central Processing Units (CPUs) and Graphics Processing Units (GPUs).För att säkerställa människors säkerhet och tillförlitligheten hos elektriska/elektroniska system används EMC (elektromagnetisk kompatibilitet)-tester i kombination med matematisk modellering. För att undersöka biologiska vävnaders egenskaper används så kallade elektromagnetiska spridningsmetoder vid sidan om elektromagnetisk modellering. I denna avhandling har matematisk modellering och beräkningsmetoder använts för huvudsakligen två fallstudier. Den första fallstudien handlar om att analysera antennstrukturer och elektriska nät ovanför, och nergrävda i marken. Marken har modellerats antingen som en elektriskt ledande yta eller en dielektrisk yta. Den andra fallstudien fokuserar på matematisk modellering och algoritmer för att lösa ett elektromagnetiskt spridningsproblem för att beskriva en modellbaserad illustrationsteknik. Spridningsformuleringen tillämpas för att modellera ett avbildningssystem som använder mikrovågor, kallat Bröstfantomen. Det slutliga målet är att upptäcka cancervävnader i kvinnobröst genom denna mikrovågsteknik. Flaskhalsen i de båda fallstudierna har visat sig vara de långa beräkningstider som krävs för att lösa stora numeriska system. För att lösa problemet har approximationsmetoder, numerisk analys och även parallella beräkningar genomförts i detta arbete. För den första fallstudien har Maxwells ekvationer lösts genom CEM (Complex Image Methods) och med parallellisering i ett LAN (Local Area Network). I de fall där marken betraktas som en dielektrisk yta, har PMM (Point-Matching Method) tillämpats. I samband med den andra fallstudien har FDTD (Finite-Difference Time Domain) metoder tillämpats för att lösa ett elektromagnetiskt spridningsproblem i två dimensioner. En parallelliserad FDTD-algoritm har implementerats i både CPU:s (Central Processing Units) och GPU:s (Graphics Processing Units).RALF