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some confusion about the inner product

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Old   January 10, 2006, 10:18
Default some confusion about the inner product
  #1
ztdep
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hi:

i don not know how to caculate the (ui,uj) (,) means a inner product, but what exactly is the meanning of the inner product.

where u is a matrix which record a two dimensional velocity field (only u velocity).

regards

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Old   January 10, 2006, 10:40
Default Re: some confusion about the inner product
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Jonas Holdeman
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Your matrix is a data structure. You could have used a linear array, or a linked list as well. So don't confuse the the vector inner product with the way you store your data.

The inner product at the point represented by the matrix indices (i,j) is (u(i,j)_x*u(i,j)_x + u(i,j)_y*u(i,j)_y). That is, inner products of the the velocities in the array are the array of inner products.
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Old   January 10, 2006, 23:37
Default Re: some confusion about the inner product
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ztdep
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hi Jonas Holdeman:

thank you for your feedback!

but i have saw some people describe it in a definite integral format:

integral( u u ) while some pelple says the integral format is only use for the case that u is a function of coordinate x, y. when we perform numerical simulation, we can only get the u in a discreate format, then how should i do !

any feedback is welcome!
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Old   January 11, 2006, 00:30
Default Re: some confusion about the inner product
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Kasyap
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hi....

wat i feel on ur problem is to go for any numerical integration method like simson's rule...m not sure about this...pls correct me if m giving a wrong idea...

thanks in advance

Kasyap
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Old   January 11, 2006, 03:23
Default Re: some confusion about the inner product
  #5
ztdep
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but what is the meaning of :

discretised version of inner product ?

i think i can use the simpson's rule in a one-dimensional region, but how to use it in a two-dimensional region..

i have confused between the matrix and a grid system in a lid-driven problem? regards
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Old   January 11, 2006, 06:30
Default Re: some confusion about the inner product
  #6
TITAN Algorithms, Staff
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Ztdep

the inner product of a matrix (tensor) can be thought of as the analogy of a dot product of a vector. Example, the turbulence production rate:

G = SQRT(Vi,j + Vj,i) * Vi,j))

is a scalar that is defined at each node or control volume in your simulation. It is the inner product of two tensors:

Vi,j + Vj,i = GRAD(V.i).j + GRAD(V.j).i

and

Vj,i = GRAD(V.j).i

where i and j indicate row and column format for a 3x3 matrix.

The inner product takes each element of the matrix (tensor) and multiplies it by the adjoining element in the other matrix and sums it together to create the scalar.

Kind Regards

DSS

www.TITANAlgorithms.com
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