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Title: | Efficient Solution of Large Sparse Eigenvalue Problems in Microelectronic Simulation |
Author(s): | Galick, Albert Thomas |
Doctoral Committee Chair(s): | Kerkhoven, Thomas |
Department / Program: | Computer Science |
Discipline: | Computer Science |
Degree Granting Institution: | University of Illinois at Urbana-Champaign |
Degree: | Ph.D. |
Genre: | Dissertation |
Subject(s): | Mathematics
Computer Science |
Abstract: | We present a new Chebyshev-Arnoldi algorithm for finding the lowest energy eigen-functions of an elliptic operator. The algorithm, which is essentially the same for symmetric, nonsymmetric, and complex nonhermitian matrices, is adapted to a specific problem by two subroutines which encapsulate the problem-specific definition of energy, plus the discretization and matrix-vector multiply routines. We adapt the algorithm to two important problems, the self-consistent Schrodinger-Poisson model of quantum-effect devices, and the vector Helmholtz equation for a dielectric waveguide, addressing other important physical, numerical and computational issues as they arise. An asymptotic convergence estimate is derived which shows the Chebyshev-Arnoldi algorithm to be superior to Chebyshev-preconditioned subspace iteration. We also examine Newton methods for general large sparse eigenvalue problems satisfying the overdamping condition and show how to use sparse iterative solvers more effectively in them. |
Issue Date: | 1993 |
Type: | Text |
Description: | 133 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1993. |
URI: | http://hdl.handle.net/2142/72084 |
Other Identifier(s): | (UMI)AAI9329034 |
Date Available in IDEALS: | 2014-12-17 |
Date Deposited: | 1993 |
This item appears in the following Collection(s)
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Dissertations and Theses - Computer Science
Dissertations and Theses from the Dept. of Computer Science -
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois