Numerical study of integral formulations for scattering from biological cells
Lloyd, Thomas W. (2004) Numerical study of integral formulations for scattering from biological cells. Masters thesis, Iowa State University.
Full text available as:
Elastic light scattering spectroscopy has the potential to significantly improve medical diagnoses by providing a valuable, non-invasive means of differentiating normal from abnormal cells. The goal is to develop fast algorithms in electromagnetic simulations of light scattering from biological cells. Numerical simulations are helpful in understanding measured data and for determining the physical characteristic of cells. The findings of this project therefore may help medical researchers to more quickly and efficiently identify diseased cells. In this research, several integral formulations for electromagnetic interactions with homogeneous material bodies are studied numerically. Included are the well-known Müller and PMCHWT formulations and two previously unreported formulations. One of the two formulations introduced gives a simple form of the Neumann series for low contrast material bodies. The integral formulations are discretized to matrix equations using the method of moments. The condition numbers of the moment matrices are evaluated using several definitions of norms. Number of iterations in CG method is also presented for each formulation. In addition, a general study of a large set of the possible combined field integral equation combination constants is reported. Specifically suited to problems such as low contrast scattering, the Neumann series expansion is evaluated for its benefits in reducing the computation time when applied to both volume and surface integral formulations. Convergence data is reported for the Neumann series, the conjugate gradient method and the biconjugate gradient method.
Archive Staff Only: edit this record