Backward Problem

Dear Comsol Users,

I like to scale a given heatflux distribution to reach a maximum temperature in a domain.

If I know the location where I expect this max. temperature, I can do this via a global equation: f(T-Tmax) to obtain a scaling variable qscale for the heat flux distribution and an integration operator: Tmax=intop(T) specified at the point where I want to reach the temperature Tmax.

But what if I don't know the location of Tmax in the domain?

If I exchange the integration operator intop with a maximum operator maxop on the domain I get:

*******
Failed to find a solution.
Singular matrix.

There are 1 void equations (empty rows in matrix) for the variable mod1.qscale
at coordinates: (0,0), ...
Returned solution is not converged.
******

Can this issue be solved without the optimization module ?

Thank you very much for any help.

--
______
Flanell