24 lines
1.0 KiB
HTML
24 lines
1.0 KiB
HTML
<a href="ex9.c.html"><h2>Example 9</h2></a>
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<p>
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This code solves a system corresponding to a discretization
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of the biharmonic problem treated as a system of equations
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on the unit square. Specifically, instead of solving
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Delta^2(u) = f with zero boundary conditions for u and
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Delta(u), we solve the system A x = b, where
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<p>
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<center> A = [ Delta -I ; 0 Delta], x = [ u ; v] and b = [ 0 ; f]
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</center>
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<p>
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The corresponding boundary conditions are u = 0 and v = 0.
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<p>
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The domain is split into an N x N processor grid. Thus, the
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given number of processors should be a perfect square.
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Each processor's piece of the grid has n x n cells with n x n
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nodes. We use cell-centered variables, and, therefore, the
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nodes are not shared. Note that we have two variables, u and
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v, and need only one part to describe the domain. We use the
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standard 5-point stencil to discretize the Laplace operators.
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The boundary conditions are incorporated as in Example 3.
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<p>
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We recommend viewing Examples 3, 6 and 7 before this example.
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