Attention was  focussed on a ternary diffusion model having unknown non-linear interdiffusion coefficients. A least-squares approach was applied; using the adjoint equation to drive the optimization process. In order to speed up computations further, free-form determination of the unknown coefficients, Dij(u,v), was used in 2 dimensions; combined with a mapping process to space coordinates. This resulted in a reduced adjoint equation of the same form as the direct equation.

Multicomponent Diffusion Coefficient Determination in Metallurgy by a Reduced Adjoint System. B.Malengier: Journal of Physics - Conference Series, 2008, 135[1], 012070