Modeling Electromagnetic Fields in Strongly Inhomogeneous Media: An Application in MRI

Modeling electromagnetic fields in MRI involves two main challenges: the solution of the scattering problem resulting from Maxwell's equations has to be accurate and it has to be obtained within short computation time. In this thesis a method that meets both requirements is searched for. The method of moments with rooftop basis functions is used to discretize different formulations of the volume integral equation corresponding to Maxwell's equations. A simple two-layer cylinder test case is used to compare each solution with a derived analytical solution for scattering on a two-layer cylinder. Two types of errors are analyzed. The good performance of a staggered grid with respect to a non-staggered grid shows that the way of treating the mixed derivative terms is of great importance. The performance of a higher order approximation scheme on a non-staggered grid is close to the performance of a second order approximation scheme on a staggered grid. A contrast study shows that these two methods are particularly beneficial for high contrasts and on low resolution. The performance of the iterative solvers IDR(s) and GMRES is tested for each discretization method. IDR(4) shows excellent performance in reducing the computation time that is obtained with GMRES. Finally, human body simulations confirm the findings from the two-layer cylinder test case.Applied MathematicsNumerical AnalysisElectrical Engineering, Mathematics and Computer Scienc