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Asynchronous algorithms for poisson's equation with nonlinear boundary conditions

Asynchrone Algorithmen für die Poisson-Gleichung mit nichtlinearen Randbedingungen

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Abstract

Poisson's equation with nonlinear boundary conditions is discretized with the method of lines to obtain a system of second order differential equations with multi-point boundary conditions. This differential system is converted, using invariant imbedding for each one-dimensional problem, into a fixed point problem and then the asynchronous algorithms are applied.

Zusammenfassung

Die Poisson-Gleichung mit nichtlinearen Randbedingungen wird mittels der Linienmethode diskretisiert und ergibt ein System von gewöhnlichen Differentialgleichungen zweiter Ordnung mit Randbedingungen. Durch invariante Einbettung für jedes eindimensionale Problem wird dieses System in ein Fixpunktproblem verwandelt, auf das dann die asynchronen Algorithmen angewandt werden.

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Anwar, M.N., El Tarazi, M.N. Asynchronous algorithms for poisson's equation with nonlinear boundary conditions. Computing 34, 155–168 (1985). https://doi.org/10.1007/BF02259842

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AMS Subject Classifications

  • 65 H 10
  • 65 M 20
  • CR: 5.15
  • 5.17