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Math Help - Algorithm-numerical techniques-help required

  1. #1
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    Algorithm-numerical techniques-help required

    My problem is like this:
    I have a 2 dimensional domain
    Now, that domain is made up of eleemnts- these elemnts are triangular
    or quadrilateral in shape. Each triangualr and quadrilateral element has 3 and 4 vertices (a triangular element has 3 vertices and quadrilateral has 4 vertices).
    We have fixed function values at these vertices- the function is (Say) F
    In that 2-D domain we define a strip (a strip is just a part of the area of that domain), A strip may have several sections - (those) lines as in attached figure (summary-figure.jpg)- the vertical lines are sections.
    What I need is::
    I need to integrate the resultant (function) along the length of each design strip section and
    hence across the width of the design strip.
    I could think to proceed in the following steps::
    The inputs are:
    A) All the triangle/quadrilateral vertices
    B) Function values at all the vertices
    C) The line over which you want to integrate
    D)geometry of the strip
    The broad algorithm would be like this:
    1. Find which quadrilaterals/triangles this line intersects
    2. Find the function values at the points of intersection of the line with the sides of these quadrilatrals/triangles
    3. Use numerical integration to integrate the function from these values
    Can anyone help me with a better algorithm?
    Also, how would I proceed with 3 above?What would be the best for numerical integration?
    Someone suggested about Chebyshev polynomials- but I do not have any idea of it!
    Please please can anyone help?
    Attached Thumbnails Attached Thumbnails Algorithm-numerical techniques-help required-summary-figure.jpg  
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by shalinisingh View Post

    3. Use numerical integration to integrate the function from these values
    Can anyone help me with a better algorithm?
    Also, how would I proceed with 3 above?What would be the best for numerical integration?
    Someone suggested about Chebyshev polynomials- but I do not have any idea of it!
    Please please can anyone help?
    The simplest way to integrate over an elementary quadrilateral or triangle is to average the function value at the vertices then multiply by the area.

    More complicated methods can probably be found in Abramowitz and Stegun.

    CB
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  3. #3
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    Thank you-Integration over the section

    Thanks for the reply.But, I would like to integrate over the section (the section is the line in green colour in my jpg).A section may intersect some elemennts and I need to integrate over the whole section using the results per element- I will also have the result at the centroid of each element and I can make use of this result to integrate over the whole section
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by shalinisingh View Post
    Thanks for the reply.But, I would like to integrate over the section (the section is the line in green colour in my jpg).A section may intersect some elemennts and I need to integrate over the whole section using the results per element- I will also have the result at the centroid of each element and I can make use of this result to integrate over the whole section
    What you have posted is rather difficult to follow but:-

    You sum the integrals over the elements in the strip

    CB
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  5. #5
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    Thanks again and sorry-I'll try and make it clear

    Sorry, if I wasn’t clear in the above post.

    What I intend doing is a line integral- that is: integrate the function values along a line (or section as marked in my figure).

    But, reading your post I find that you seem to be taking the integration over an area, that is: integrating the function over each of the triangles/quadrilaterals in the path.

    Can you give some clue to solve this now- thanks a million for your help till now!
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  6. #6
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    Awaiting your reply

    Looking forward to your reply-Please help!!
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