Comparison of Lanczos and subspace iterations for hyperspherical reaction path calculations
In an accurate treatment of 3-dimensional reactive scattering using Adiabatically-adjusting, Principal axes Hyperspherical (APH) coordinates, we obtain a 2-dimensional Schr/umlt o/dinger equation defined on the surface of a hypersphere. The surface Hamiltonian, which depends parametrically on the sector hyperradius /rho//sub h/, must be diagonalized for many (100/endash/200) values of /rho//sub h/. The surface (eigen)functions are expanded in a finite element basis, where a non-uniform finite element mesh is allowed to adjust for each /rho//sub h/. Projection of the finite element basis onto the surface Hamiltonian yields a generalized eigenvalue problem. Typically of the lowest 50/endash/100 eigenvalues and eigenfunctions are required at each /rho//sub h/. Since the calculation of the surface functions is currently the expensive step for our reactive scattering procedure, it is necessary to calculate these functions as efficiently as possible. In this paper, we use both the subspace iteration and block Lanczos (with selective orthogonalization) methods to calculate the surface functions. Using both solution methods, we diagonalize the finite element matrices (of order = 1729 and of half bandwidth = 109) constructed for the LiH + F in equilibrium Li + HF system. CPU timings for both methods are examined as a function of the number of converged eigenvalues. Since we can generate a good initial subspace form the eigenvectors calculated at the previous value of /rho//sub h/, we find that the subspace iteration is competitive with the block Lanczos method when many (90) eigenvalues are calculated. 20 refs., 6 figs., 1 tab.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 6790631
- Report Number(s):
- LA-UR-88-2484; CONF-8810119-1; ON: DE88014402
- Resource Relation:
- Journal Volume: 53; Journal Issue: 1-3; Conference: Workshop on practical iterative methods for large scale computations, Minneapolis, MN, USA, 23 Oct 1988; Other Information: Portions of this document are illegible in microfiche products
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
SCHROEDINGER EQUATION
TWO-DIMENSIONAL CALCULATIONS
EIGENFUNCTIONS
FINITE ELEMENT METHOD
FLUORINE
HAMILTONIANS
HYDROGEN
ITERATIVE METHODS
M CODES
MATRICES
NUMERICAL DATA
S CODES
COMPUTER CODES
DATA
DIFFERENTIAL EQUATIONS
ELEMENTS
EQUATIONS
FUNCTIONS
HALOGENS
INFORMATION
MATHEMATICAL OPERATORS
NONMETALS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
WAVE EQUATIONS
657000* - Theoretical & Mathematical Physics
990220 - Computers
Computerized Models
& Computer Programs- (1987-1989)
990230 - Mathematics & Mathematical Models- (1987-1989)