The Use of Intrinsic Properties of Physical System for Derivation of High-Performance Computational Algorithms

  • Alexander V. Bogdanov
  • Elena N. Stankova
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2110)


We discuss some new approach for derivation of computational algorithms for certain types of evolution equations. The main idea of the algorithm is to make functional transformation of variables on the base of symmetry properties of pertinent physical system to make it quasi-diagonal. The approach is illustrated with the help of two important examples - the scattering in molecular system with elementary chemical reactions and the system of chemical kinetics for the many components system. The use of proposed approach show substantial speed-up over the standard algorithms and seems to be more effective with the increase of the size of the problem.


High Performance Computing Elementary Chemical Reaction Nozzle Flow Asymptotical Boundary Condition Functional Transformation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ebeling W., Freund J., Schweitzer F.: Komplexe Strukturen: Entropic und Information. B.G. Teubner, Stuttgart, Leipzig (1998)Google Scholar
  2. 2.
    Zakharov, V.E., Kuznetzov, E.A.: Hamiltonian formalism for nonlinear waves. In: Russian Uspekhi Fizicheskhich Nauk, Vol. 167. Nauka, Moscow (1997) 1137–1167Google Scholar
  3. 3.
    Itkin A.L., Kolesnichenko E.G.: Microscopic Theory of Condensation in Gases and Plasma. World Scientific, Singapore New Jersey London Hong Kong (1998)Google Scholar
  4. 4.
    Bogdanov A.V., Gorbachev Yu.E., Strelchenya V.M.: Relaxation and condensation processes influence on flow dynamics. in Proccedings of XV Intern. Symp. Rarefied Gas Dyn. Grado (Italy) (1986) 407–408Google Scholar
  5. 5.
    Topaler M., Makri N.: Multidimensional path integral calculations with quasidiabatic propagators: Quantum dynamics of vibrational relaxation in linear hydrocarbon chains. J.Chem.Phys. Vol. 97,12, (1992) 9001–9015CrossRefGoogle Scholar
  6. 6.
    Greenberg W.R., Klein A., Zlatev I.: From Heisenberg matrix mechanics to semiclassical quantization: Theory and first applications. Phys. Rev. A Vol.54,3, (1996) 1820–1836.CrossRefMathSciNetGoogle Scholar
  7. 7.
    Dubrovskiy G.V., Bogdanov A.V. Chem.Phys.Lett., Vol. 62,1 (1979) 89–94.CrossRefGoogle Scholar
  8. 8.
    Bogdanov A.V.: Computation of the inelastic quantum scattering amplitude via the solution of classical dynamical problem. In:Russian Journal of Technical Physics, 7 (1986) 1409–1411.Google Scholar
  9. 9.
    A.V. Bogdanov, A.S. Gevorkyan, A.G. Grigoryan, Stankova E.N.: Use of the Internet for Distributed Computing of Quantum Evolution. in Proccedings of 8th Int. Conference on High Performance Computing and Networking Europe (HPCN Europe’ 2000), Amsterdam, The Netherlands (2000)Google Scholar
  10. 10.
    Bogdanov A.V., Dubrovskiy G.V., Gorbachev Yu.E., Strelchenya V.M.: Theory of vibration and rotational excitation of polyatomic molecules. Physics Reposrts, Vol.181,3, (1989) 123–206.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Alexander V. Bogdanov
  • Elena N. Stankova
    • 1
  1. 1.Institute for High Performance Computing and Data BasesSt-PetersburghRussia

Personalised recommendations