[Getdp] Newton Raphson method with a time dependent problem

Olivier Castany castany at quatramaran.ens.fr
Fri Jul 30 13:48:15 CEST 2010


Hello,

> Galerkin { [ lambda[{T}] * Dof{d T} , {d T} ];  In Vol_The; 
>            Integration I1; Jacobian Jac;  }      
> // The set up of JacNL for this line is clear.

could you show it, please ? I would like to know if we agree on this point.

> Galerkin { DtDof [ rho[] * c[{T}] * Dof{T} , {T} ]; In Vol_The; 
>            Integration I1; Jacobian Jac;  }  
> // But how to set up the JacNL for this part??

First, I would have used Dt instead of DtDof. I think the time derivative
must be applied to rho*c(T)*T, do you agree ?

For this term, I think the JacNL should be :
JacNL [ rho[] * dcdT[{T}] * Dof{T} * {T} , {T} ]
where dcdT[] is a function providing the first derivative of c with T.

Best regards,

O.C.