A three dimensional (3-D) capacitance extraction algorithm based on a kernel independent hierarchical method and geometric moments is described. Several techniques are incorporated, which leads to a better overall performance for arbitrary interconnect systems. First, the new algorithm hierarchically partitions the bounding box of all interconnect panels to build the partition tree. Then it uses simple shapes to match the low order moments of the geometry of each box in the partition tree. Finally, with the help of a fast matrix-vector product, GMRES is used to solve the linear system. Experimental results show that our algorithm reduces the linear system's size greatly and at the same time maintains a satisfying accuracy. Compared with FastCap, the running time of the new algorithm can be reduced more than a magnitude and the memory usage can be reduced more than thirty times.

Thesis (Ph. D.)--Auburn University, 2008. / Abstract. Includes bibliographical references (p. 121-127).

Thesis (Ph. D.)--University of Canterbury, 2009. / Typescript (photocopy). "May 2009." Includes bibliographical references (p. 10/1-10/9). Also available via the World Wide Web.

Not available / text

This thesis presents a detailed study of the numerical errors and the associated accuracy-efficiency tradeoffs encountered in the solution of frequency- and time-domain integral equations. For frequency-domain integral equations, the potential integrals contain singular Green’s function kernels and the resulting singular and near-singular integrals must be carefully evaluated, using singularity extraction or cancellation techniques, to ensure the accuracy of the method-of-moments impedance matrix elements. This thesis presents a practical approach based on the progressive Gauss-Patterson quadrature rules for implementing the radial-angular-transform singularity-cancellation method such that all singular and near-singular integrals are evaluated to an arbitrary pre-specified accuracy. Numerical results for various scattering problems in the high- and low-frequency regimes are presented to quantify the efficiency of the method and contrast it to the singularity extraction method. For time-domain integral equations, the singular Green’s function kernels are functions of space and time and sub-domain temporal basis functions rather than entire-domain sinusoidal/Fourier basis functions are used to represent the time variation of currents/fields. This thesis also investigates the accuracy-efficiency tradeoff encountered when choosing sub-domain temporal basis functions by contrasting two prototypical ones: The causal piecewise polynomial interpolatory functions, sometimes called shifted Lagrange interpolants, and the band-limited interpolatory functions based on approximate prolate spheroidal wave functions. It is observed that the former is more efficient for low to moderate accuracy levels and the latter achieves higher, but extrapolation-limited, accuracy levels. / text

Not available / text

Zernike moments are sets of mathematical quantities that uniquely characterize an image. It is known that they are invariant under rotation and reflection and robust to noise. In this thesis several other algorithms have been used to calculate these moments. The intent of this thesis is: 1. to use the classical method and the algorithms to reconstruct an image using Zernike moments and study their accuracy and 2. to examine if the invariance and noise insensitivity property of the calculated Zernike moments are upheld by these procedures. It is found that the constructed images using these algorithms do not resemble the original image. This prevents us from carrying out further study of these algorithms. The classical method has been successfully used to reconstruct an image when the height and width are equal. The classical method is also shown to be invariant under rotation and reflection and robust to Poisson noise. xxxvii

Zernike moments are sets of mathematical quantities that uniquely characterize an image. It is known that they are invariant under rotation and reflection and robust to noise. In this thesis several other algorithms have been used to calculate these moments. The intent of this thesis is: 1. to use the classical method and the algorithms to reconstruct an image using Zernike moments and study their accuracy and 2. to examine if the invariance and noise insensitivity property of the calculated Zernike moments are upheld by these procedures. It is found that the constructed images using these algorithms do not resemble the original image. This prevents us from carrying out further study of these algorithms. The classical method has been successfully used to reconstruct an image when the height and width are equal. The classical method is also shown to be invariant under rotation and reflection and robust to Poisson noise. xxxvii

No description available.

Thesis (Ph D.)--University of Nevada, Reno, 2007. / "May 2007." Includes bibliographical references (leaves 61-63). Online version available on the World Wide Web.