disc12

# disc12 - For the special case of a square domain and...

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Department of Chemical Engineering University of California, Santa Barbara ChE 230A Fall 2006 Instructor: Glenn Fredrickson Discussion Topic #12 For Discussion Section: Friday, December 1, 2006 Consider the solution of Poisson’s equation 2 u ( x, y ) = ρ ( x, y ) for an unknown function u ( x, y ), where the function ρ ( x, y ) is a prescribed function (e.g. a charge density) for some domain of x and y , and subject to appropriate boundary conditions.
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Unformatted text preview: For the special case of a square domain and periodic boundary conditions in both x and y , devise a spectral method using two-dimensional FFTs to solve the equation. Provide a numerical example using one or more arbitrary choices for ρ . Note that ρ ( x,y ) must have the property that R dx R dy ρ ( x,y ) = 0, where the domain of integration is over the square. Can you explain why?...
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