Application Of The Interlaced Sweep Method For The Solution Of Problems In Field Theory

Aloizs Ratnieks, Marina Uhanova

Abstract


For solution of problems in field theory the method of sweep is very popular. The authors suggest a very effective method of interlaced sweep. The essence of the interlaced sweep method lies in the fact that matrix of the linear algebraic equations system is broken into parts and the solution of separate blocks is sought by direct methods. Usually for each line of the grid a separate block is created. The system of block equations has a tridiagonal matrix where only elements of the main diagonal and two neighboring diagonals are different from zero. The system of equations with such a matrix is easily solved by the method of elimination of unknowns.

By solving the problems by the finite element method, the nodes of touching of neighboring elements can be placed on curved lines, and the sweep on these lines can be performed observing the principle of interlaced sweep. By following this method, the neighboring lines should not belong to the same half-step.


Keywords


sweep method; differential equation; system of equations

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References


O. Zienkiewicz, R. L Taylor and D. D. Fox, The Finite Element Method for Solid and Structural Mechanics. ELSEVIER, 2011.

William F. Ames, Numerical Methods For Partial Differential Equations. Academic Press Inc, 1992.

В. Вазов, Дж. Форсайт. Разностные методы решения дифференциальных уравнений в частных производных. ИЛ, М., 1963.




DOI: http://dx.doi.org/10.17770/etr2015vol3.190

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