Programs in Physics & Physical Chemistry
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|Manuscript Title: FESSDE 2.2: A new version of a program for the finite-element solution of the coupled-channel Schrodinger equation using high-order accuracy approximations.|
|Authors: A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin|
|Program title: FESSDE 2.2|
|Catalogue identifier: ACVU_v2_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 115(1998)90|
|Programming language: Fortran.|
|Computer: DEC 3000 ALPHA AXP 800.|
|Operating system: UNIX4.0, AIX3.2.5, SunOs4.1.2, HP/UX9.01, Irix4.05.|
|RAM: 4.4M words|
|Word size: 64|
|Keywords: Finite element method, Sturm-liouville problem, High-order accuracy, Approximations, Schrodinger equation, Eigensolutions, Ordinary, Differential equations, Atomic, Molecular, Chemical physics, General purpose.|
Nature of problem:
Coupled second-order differential equations of the form
d dY(x) - --[P(x)-----] + [U(x) - lambdaR(x)]Y(x) = 0, x in [a,b], dx dxwith boundary conditions
dY(x)| Y(a) = 0 or -----| = 0, dx |x=a dY(x)| Y(b) = 0 or -----| = 0, dx |x=bare solved. Here lambda is an eigenvalue, Y(x) is an eigenvector, P(x), U(x), and R(x) are symmetrical matrices, P(x) is a diagonal matrix, elements of which are the differentiable functions on a given interval [a,b], and R(x) is a positive matrix throughout the interior of interval [a,b]. Such systems of coupled differential equations usually arise in atomic, molecular and chemical physics calculations after separating the scattering (radial) coordinate from the rest of variables in the multidimensional Schrodinger equation. The purpose of this paper is to present the finite element method procedure based on the use of high-order accuracy approximations for high-precision calculation of the approximate eigensolutions for systems of coupled ordinary differential equations.
The coupled differential equations are solved by the finite element method using high-order accuracy approximations . The generalized algebraic eigenvalue problem A Y = lambda B Y arising from the replacement of the differential problem by the finite-element approximation of high order of accuracy is solved by the subspace iteration method .
Summary of revisions:
The computer memory requirements depend on: (a) the number of equations to be solved; (b) the order of shape functions and the number of finite elements chosen; and (c) the number of eigensolutions required. Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see Long Write-Up and listing of  for details). The user must also supply subroutines which evaluate the differential equation coefficient matrices P(x), U(x) and R(x) at a given x.
The running time depends critically upon: (a) the number of coupled differential equations; (b) the number of required eigensolutions;, (c) the order and number of finite elements on interval [a,b]. The test run which accompanies the program took 3.22 min of the DECstation 3000 Model 800.
|||NAG Fortran Library Manual, Mark 15 (The Numerical Algorithms Group Limited, Oxford, 1991).|
|||A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin, Comput. Phys. Commun. 85 (1995) 40.|
|||K.J. Bathe, Finite Element Procedures in Engineering Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1982).|
|||A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin, Comput. Phys. Commun. 85 (1995) 65.|
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