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Numerical evaluation is Mathematica bottleneck?!

• To: mathgroup at smc.vnet.net
• Subject: [mg69024] Numerical evaluation is Mathematica bottleneck?!
• From: gregorc <gregor.cernivec at fe.uni-lj.si>
• Date: Sun, 27 Aug 2006 01:23:44 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Dear mathgroup members,

I am solving a non-linear semiconductor PDE problem with finite 
difference discretization. The Compiled algebraic equation and its 
Jacobian  take as input central point and two adjacent neighbors and 
they are Threaded over the whole mesh. A LinearSolve and some damping 
schemes are used to obtain next step towards the solution. Typical mesh 
is about 300 points and the solution is usually found in 7 iterations, 
which takes about 7 seconds of computational time.This is already too 
slow, but since I plan to solve the problem in 2D this is much too 
slow!!! The bottleneck is the numerical evaluation of the compiled 
equation and its Jacobian. I am thinking of using MathLink and write the 
numerical evaluation routine in C++, which would take a list of data and 
return evaluated function and the Jacobian.
 
Is this the right way? Could the link itself be a timing bottleneck? Any 
other suggestions?

Regards,

Gregor