Comparison of Lanczos and subspace iterations for hyperspherical reaction path calculations

Conference · Fri Jan 01 04:00:00 EST 1988

DOI:https://doi.org/10.1016/0010-4655(89)90150-1· OSTI ID:6790631

Kress, J D; Parker, G A; Pack, R T; Archer, B J

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 Lab., NM (USA)
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 6790631
• Report Number(s): LA-UR-88-2484; CONF-8810119-1; ON: DE88014402
• Country of Publication: United States
• Language: English

Related Subjects

657000* -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990220 -- Computers
Computerized Models
& Computer Programs-- (1987-1989)
990230 -- Mathematics & Mathematical Models-- (1987-1989)
COMPUTER CODES
DATA
DIFFERENTIAL EQUATIONS
EIGENFUNCTIONS
ELEMENTS
EQUATIONS
FINITE ELEMENT METHOD
FLUORINE
FUNCTIONS
HALOGENS
HAMILTONIANS
HYDROGEN
INFORMATION
ITERATIVE METHODS
M CODES
MATHEMATICAL OPERATORS
MATRICES
NONMETALS
NUMERICAL DATA
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
S CODES
SCHROEDINGER EQUATION
TWO-DIMENSIONAL CALCULATIONS
WAVE EQUATIONS