lec26 (1)

lec26 (1) - 2-D Integration (from 3-D problems) Reminder...

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SMA-HPC ©2002 MIT 2-D Integration (from 3-D problems) Reminder Calculating Matrix Elements Panel j i c x Collocation point ( , , i c ij panel j Gx x A dS = ( , , i c entroi i d j Area G x x A One point quadrature Approximation x y z ( int 4 , 1 * 4 i o c j p Ar A ea x = Four point quadrature Approximation ) ) j c ) , j
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SMA-HPC ©2002 MIT Symmetrically Normalized 2-D Problem Quadrature Scheme General n-point formula , i xy n points, n weights 2n parameters -1 1 1 -1 y x ( ( 1 11 , , n i i i wf x fx y yd x = −− ∫∫ . i ) ) i
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SMA-HPC ©2002 MIT Symmetrically Normalized 2-D Problem Quadrature Scheme 2-D Gaussian Quadrature ( ( 11 1 1 1 , , n il i i i l w y px x y p x = −− = ∫∫ l-th order 2-D poly definition Exactness for l-th order polys ( ( , , i l j ij l p xy x y α +≤ = ( ( ) 1 Number of terms = 2 l + ) ) d ) ) j i ) 2 l +
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SMA-HPC ©2002 MIT Symmetrically Normalized 2-D Problem Quadrature Scheme Product Method 1) Get a 1-d formula () ( 1 1 1 1 m d i i wf x fx dx = .
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lec26 (1) - 2-D Integration (from 3-D problems) Reminder...

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