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Unformatted text preview: Department of Mathematics University of Houston Numerical Analysis I Dr. Ronald H.W. Hoppe Numerical Analysis I (2nd Practical Homework Assignment) Practical Exdercise 2 ( cg method ) The deflection u = u ( x ) , x = ( x 1 ,x 2 ) T := (0 , 1) 2 of a clamped membrane due to an exterior force of force density f = f ( x ) , x can be described by the boundary value problem u ( x ) = ( x 2 1 u ( x ) + x 2 2 u ( x )) = f ( x ) , x u ( x ) = 0 , x := . The approximation of the 2D Laplacian := x 2 1 + x 2 2 by finite differences x 2 1 u ( x ) u ( x 1 h,x 2 ) 2 u ( x 1 ,x 2 ) + u ( x 1 + h,x 2 ) h 2 , x 2 2 u ( x ) u ( x 1 ,x 2 h ) 2 u ( x 1 ,x 2 ) + u ( x 1 ,x 2 + h ) h 2 with respect to a uniform grid of mesh size h > 0 results in a linear algebraic system with the coefficient matrix A = ( a ij ) n 1 i,j =0 lR n n ,n = k 2 , k lN, which is given by a ij =...
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 Spring '12
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