Electromagnetic model subdivision and iterative solvers for surface and volume double higher order numerical methods and applications

2019 Fall.Includes bibliographical references.Higher order methods have been established in the numerical analysis of electromagnetic structures decreasing the number of unknowns compared to the low order discretization. In order to decrease memory requirements even further, model subdivision in the computational analysis of electrically large structures has been used. The technique is based on clustering elements and solving/approximating subsystems separately, and it is often implemented in conjunction with iterative solvers. This thesis addresses unique theoretical and implementation details specific to model subdivision of the structures discretized by the Double Higher Order (DHO) elements analyzed by i) Finite Element Method - Mode Matching (FEM-MM) technique for closed-region (waveguide) structures and ii) Surface Integral Equation Method of Moments (SIE-MoM) in combination with (Multi-Level) Fast Multipole Method for open-region bodies. Besides standard application in decreasing the model size, DHO FEM-MM is applied to modeling communication system in tunnels by means of Standard Impedance Boundary Condition (SIBC), and excellent agreement is achieved with measurements performed in Massif Central tunnel. To increase accuracy of the SIE-MoM computation, novel method for numerical evaluation of the 2-D surface integrals in MoM matrix entries has been improved to achieve better accuracy than traditional method. To demonstrate its efficiency and practicality, SIE-MoM technique is applied to analysis of the rain event containing significant percentage of the oscillating drops recorded by 2D video disdrometer. An excellent agreement with previously-obtained radar measurements has been established providing the benefits of accurately modeling precipitation particles

Orientation and anisotropy of multi-component shapes from boundary information

We define a method for computing the orientation of compound shapes based on boundary information. The orientation of a given compound shape S is taken as the direction α that maximises the integral of the squared length of projections, of all the straight line segments whose end points belong to particular boundaries of components of S to a line that has the slope α. Just as the concept of orientation can be extended from single component shapes to multiple components, elongation can also be applied to multiple components, and we will see that it effectively produces a measure of anisotropy since it is maximised when all components are aligned in the same direction. The presented method enables a closed formula for an easy computation of both orientation and anisotropy

Automatic creation of boundary-representation models from single line drawings

This thesis presents methods for the automatic creation of boundary-representation models of polyhedral objects from single line drawings depicting the objects. This topic is important in that automated interpretation of freehand sketches would remove a bottleneck in current engineering design methods. The thesis does not consider conversion of freehand sketches to line drawings or methods which require manual intervention or multiple drawings. The thesis contains a number of novel contributions to the art of machine interpretation of line drawings. Line labelling has been extended by cataloguing the possible tetrahedral junctions and by development of heuristics aimed at selecting a preferred labelling from many possible. The ”bundling” method of grouping probably-parallel lines, and the use of feature detection to detect and classify hole loops, are both believed to be original. The junction-line-pair formalisation which translates the problem of depth estimation into a system of linear equations is new. Treating topological reconstruction as a tree-search is not only a new approach but tackles a problem which has not been fully investigated in previous work