We develop negative-norm least-squares methods to solve the three-dimensional Maxwell equations for static and time-harmonic electromagnetic fields in the case of axial symmetry. The methods compute solutions in a two-dimensional cross section of the domain, thereby reducing the dimension of the problem from three to two. To achieve this dimension reduction, we work with weighted spaces in cylindrical coordinates. In this setting, approximation spaces consisting of low order finite element functions and bubble functions are analyzed. In contrast to other methods for axisymmetric Maxwell equations, our leastsquares methods allow for discontinuous coefficients with large jumps and non-convex, irregular polygonal domains discretized by unstructured meshes. The resulting linear systems are of modest size, are symmetric positive definite, and can be solved very efficiently. Computations demonstrate the robustness of the methods with respect to the coefficients and domain shape.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1975. / Vita. Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

No description available.

Controlling and understanding the propagation of optical pulses through dispersive media forms the basis for optical communication, medical imaging, and other modern technological advances. Integral to this control and understanding is the ability to describe the transients which occur immediately after the onset of a signal. This thesis examines the transients of such a system when a unit step function is applied. The electromagnetic field is described by an integral resulting from Maxwell’s Equations. It was previously believed that optical precursors, a specific transient effect, existed only for only a few optical cycles and contributed only small magnitudes to the field. The main results of this thesis show that the transients arising from this integral are entirely precursors and that they may exist on longer time scales and contribute larger magnitudes to the field. The experimental detection of precursors has previously been recognized only through success comparison to the transient field resulting from an application of the method of steepest descent to that field integral. For any parameter regime where steepest descents may be applied, this work gives iterative methods to determine saddle points which are both more accurate than the accepted results and to extend into regimes where the current theory has failed. Furthermore, asymptotic formulae have been derived for regions where previous attempts at steepest descent have failed. Theory is also presented which evaluates the applicability of steepest descents in the represention of precursor behavior for any set of parameters. Lastly, the existence of other theoretical models for precursor behavior who may operate beyond the reach of steepest descent is validated through successful comparisons of the transient prediction of those methods to the steepest descent based results of this work. / Dissertation

Texte remanié de: Diss.--Göttingen, 1999. / Bibliogr. p. 392-402. Index.

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (leaves 102-112).

Thesis (MScIng)--University of Stellenbosch, 2007. / Bibliography.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1939. / Vita. Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references and abstract.

Thesis (Ph. D.)--University of Birmingham, 1985. / Includes bibliographical references (leaves 423-427).

Thesis (Ph. D.)--Columbia University, 1941. / Published also without thesis note. Vita. Bibliography: p. [535]-563.