Investigations with the Finite Element Method. The collinear H + H2, F + H2 and Ne + H+2 reactions

  • Ralph Jaquet
Part of the NATO ASI Series book series (ASIC, volume 277)

Abstract

We are investigating systematic the application of the finite element method (FEM) for solving the Schrödinger equation. The subsequent work is devoted to the calculation of vibrational transition probabilities for the collinear reactive system A + BC (i.e. H + H 2 and their isotopes, F + H 2 and Ne + H + 2). We have performed an extensive analysis of FEM on the vector-computer Cyber 205 and have developed a vector code for the efficient use in two mathematical dimensions. The implementation of a three dimensional program is now in progress. The details of our FEM calculations are the following: The integration area is discretized into triangles where quadratic polynomials for the local wavefunctions are defined. With this simple ansatz convergent results can be reached for most reactions with ≈ 10000 grid points. In case of 3D calculations a much larger number of grid points is necessary. Different 1D–3D eigenvalue problems with higher degree polynomials are investigated to reduce the number of grid points and to optimize the geometry of the finite elements. Applying this experience to reactive problems, much less grid points will be needed for comparable accuracy. The main computing time results from solving linear equations and generalized eigenvalue equations for very large, but sparse matrices. Direct methods (e.g. Cholesky or Jacobi ) are needed for starting, and if good starting vectors are available, iterative methods (e.g. conjugated gradients or coordinate overrelaxation ) can be used.

Keywords

Finite Element Method Grid Point Integration Area Stationary Wavefunction Finite Element Method Calculation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Ralph Jaquet
    • 1
  1. 1.Theoretische ChemieUniversität SiegenSiegenWest-Germany

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