A) Trial Lagrange polynomial interpolation

Definitions

A trial function for temperature φ is constructed as a fifth order Lagrange polynomial in x y and z direction. The chosen trial function is constructed in a way that  satisfies boundary conditions.

Here the fifth order Lagrange polynomials are constructed in three dimensions.

Here the Gauss points and weights are calculated for ngp×ngp×ngp Gauss numerical integration of the free energy over the domain [-.0.5m,0.5m]×[-0.5m,0.5m]×[0,1m].

Direct use of Mathematica

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G. Gradient based optimization

N. Newton method based optimization

AceGen code generation

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AceGen Solution

G. Gradient based optimization

N. Newton method based optimization

Created by Wolfram Mathematica 6.0  (13 August 2007)