Spectral element eigensolver for inhomogeneous media

Details Spectral element eigensolver for inhomogeneous media Spectral element eigensolver for inhomogeneous media

2005-06-21

2009-11-10

Shah, Kamini S. (Department: 2128)

Data processing: structural design, modeling, simulation, and em

Modeling by mathematical expression

C703S001000, C703S006000

Reexamination Certificate

active

07617081

ABSTRACT:
Methods are provided to generate eigenvalues and eigenfunctions for structures that include inhomogeneous media. In embodiments, eigenvalues and eigenfunctions generated as solutions to differential equations provide parameters for analyzing and constructing structures modeled by the differential equations.

REFERENCES:
patent: 7398162 (2008-07-01), Downs et al.
Alonso-Mallo et al., “Weak ill-posedness of spatial discretizations of absorbing boundary conditions for Schrodinger-type equations”, SIAM Journal on Numerical Analysis, vol. 40, No. 1, 2003, pp. 134-158.
Anwar, A, et al., “Density of states for double-barrier quantum-well structures under the influence of external fields and phase-breaking scattering”,Physical Review B(Condensed Matter), 50(15), (Oct. 15, 1994), 10864-7.
Braun, M, et al., “An efficient Chebyshev-Lanczos method for obtaining eigensolutions of the Schrodinger equation on a grid”,Journal of Computational Physics, 126(2), (Jul. 1996), 315-27.
Cizek, M., et al., “On shooting methods for calculation of potential resonances”,Journal of Physics A(Mathematical and General), 29(19), (Oct. 7, 1996), 6325-42.
Coutsais, E. A, et al., “Integration preconditioners for differential operators in spectral methods”,Proc. Of International Conference on Spectral and High Order Methods, ICOSAHOM'95, Houston, USA, (1995), 21-38.
Coutsias, E. A, et al., “An efficient spectral method for ordinary differential equations with rational function coefficients”,Mathematics of Computation, 65(214), (Apr. 1996), 611-35.
De La Madrid, R, et al., “A pedestrian introduction to Gamow vectors”,Journal of Physics, 70(6), (Jun. 2002), 626-38.
Gottlieb, D, et al., “On the Gibbs phenomenon and its resolution”,SIAM Review, 39(4), (Dec. 1997), 644-68.
Guo, B-Y., et al., “Chebyshev rational spectral and pseudospectral methods on a semi-infinite interval”,International Journal for Numerical Methods in Engineering, 53(1), (Jan. 10, 2002), 65-84.
Hagstrom, T, “New results on absorbing layers and radiation boundary conditions”,Topics in Computational Wave Propagation, M. Ainsworth, P. Davies, D. Duncan, P. Martin, and B. Rynne, eds., Springer-Verlag, (2003), 1-42.
Hernandez, E, et al., “Jordan blocks and Gamow-Jordan eigenfunctions associated with a degeneracy of unbound states”,Physical Review A—Atomic, Molecular, and Optical Physics, 67(2), (Feb. 2003), 022721/1-022721/15.
Leonhardt, U, et al., “State reconstruction in one-dimensional quantum mechanics: the continuous spectrum”,Physical Review A. Atomic, Molecular, and Optical Physics, 56(4), (Oct. 1997), 2549-2556.
Levy, M. F, “Perfectly matched layer truncation for parabolic wave equation models”,Proceedings of the Royal Society of London, Series A(Mathematical, Physical and Engineering Sciences), 457(2015), (Nov. 8, 2001), 2609-24.
McIntosh, H. V, “Quantization as an Eigenvalue Problem”,Theory and its Applications, (EM Loebl, ed), Academic Press, New York, (1975), 333-368.
Midy, P, et al., “Complex eigenenergy spectrum of the Schrodinger equation using Lanczos' tau method”,Journal of Physics B(Atomic, Molecular and Optical Physics), 26(5), (Mar. 14, 1993), 835-53.
Peres, A, “Transfer matrices for one-dimensional potentials”,Journal of Mathematical Physics, 24(5), (May 1983), 1110-19.
Rheinhard, W. P, “Complex coordinates in the theory of atomic and molecular structure and dynamics”,Annual Review of Physical Chemistry, 33, (1983), 223-255.
Shen, J., “Stable and efficient spectral methods in unbounded domains using Laguerre functions”,SIAM Journal on Numerical Analysis, 38(4), (2000), 1113-1133.
Shibata, T, “Absorbing boundary conditions for the finite-difference time-domain calculation of the one dimensional Schrodinger equation”,Physical Review B, 43(8), (1991), 6760-6763.
Siyyam, H. I, “Laguerre Tau methods for solving higher-order ordinary differential equations”,Journal of Computational Analysis and Applications, 3(2), (Apr. 2001), 173-182.
Tisseur, F., et al., “The quadratic eigenvalue problem”,SIAM Review, 43(2), (Jun. 2001), 235-286.

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