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1993 Kerkhoven, Thomas Galick, Albert Thomas 2014-12-17T20:00:38Z 2014-12-17T20:00:38Z 10000-01-01 1993 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. Made available in DSpace on 2014-12-17T20:00:38Z (GMT). No. of bitstreams: 1 9329034.pdf: 4382424 bytes, checksum: 9c10d05faf91199c7d1ea1e84698a594 (MD5) Previous issue date: 1993 Embargo set by: Seth Robbins for item 72252 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 133 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1993. http://hdl.handle.net/2142/72084 (UMI)AAI9329034 Mathematics Computer Science Efficient Solution of Large Sparse Eigenvalue Problems in Microelectronic Simulation text Computer Science Computer Science University of Illinois at Urbana-Champaign Dissertation Ph.D.