Automatic Differentiation (AD) for PDE's
All,
what is Automatic Differentiation (AD) research field about. can anyone explain to me the field and how can I find more about it with its applications Many thanks, 
Re: Automatic Differentiation (AD) for PDE's
I have not used AD, so I can only tell you a few things that I have read here and there. You might have used symbolic differentiation in Mathematica or Maple. THis is ok if the function to be differentiated is not very complicated. AD also helps you to differentiate but it is not symbolic differentiation. With AD you input a C or Fortran source code (which calculates the function of your interest) and the AD tool outputs a new source code for calculating the derivatives of the function with respect to any independent variables that you have specified. Note that the source code can be REALLY huge, e.g., an entire package like Fluent. Since derivatives are essential in numerical optimization AD is popular in the optimization community. One of the pioneers is Andreas Griewank, so you can search on google. See the AD page http://wwwunix.mcs.anl.gov/autodiff

Re: Automatic Differentiation (AD) for PDE's
Can I ask you why it is popular in the optimization community. Still I couldn't see the relation between PDE's, derivatives, numerics, optimization and numerical optimization AD.

Re: Automatic Differentiation (AD) for PDE's
It is popular in the optimization community because the derivative is the most crutial information for optimization. While calculating all the derivative by hardcoding is too tedious, AD is thus becoming promising.

Re: Automatic Differentiation (AD) for PDE's
remember in calculus when you learned to optimize a function by setting it's derivative to zero? Same idea except "numericalized". If you're trying to optimize a design whos performance is governed by a PDE that you model in a computer program it is useful if you automatically create source code that can calculate the derivative of the performance variable (eg drag) with respect to the design variables that you're looking at (eg chord or wingspan). These derivatives are then used by your optimization software (that needs to know what the gradient is) to optimise your design.

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