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periodic and cyclic boundary conditions

hello, Could anyone tell me what is the difference between cyclic and periodic boundary conditions? Thanks in advance Regards Hadi

 Praveen. C June 29, 2007 05:46

Re: periodic and cyclic boundary conditions

Think of an O-grid in 2-D. There is one set of grid-lines which are closed; the first and last point on these lines are the same. You need cyclic conditions; its not really a boundary. For example if the grid index that goes around is i, and it ranges from 1 to imax, then u(1,j) = u(imax,j) for all j. Also in a finite difference scheme, if you need u(i-1,j) for i=1, then it will be u(imax-1,j). You get the idea.

A function is periodic if

u(x+L) = u(x)

Note that it is defined in all of R, the real number set. But it is enough to compute it in say [0,L]. When you apply some finite difference or your favourite scheme, you may need values outside [0,L]. Then you make use of the periodic condition to get these values.