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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
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