Efficient Solution of Large Sparse Eigenvalue Problems in Microelectronic Simulation
Galick, Albert Thomas
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https://hdl.handle.net/2142/72084
Description
Title
Efficient Solution of Large Sparse Eigenvalue Problems in Microelectronic Simulation
Author(s)
Galick, Albert Thomas
Issue Date
1993
Doctoral Committee Chair(s)
Kerkhoven, Thomas
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(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.
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