In ElmerSolver there is a possibility to scan over the parameter space. Unfortunately this uses time stepping in a special way so it is not applicable for transient cases. However, for steady state and harmonic problems it may be very useful.
To perform scanning in the Simulation section set
Simulation Type = Transient Timestep Intervals = 100 Output Intervals = 10
The time will automatically go as 1,2,3,… and you can have all variables be dependent on this pseudotime.
For example, you could scan over Youngs modulus in Material section
Material 1 Name = "structure" Youngs modules = Variable time Real MATC "1.23*tx" ...
or inlet velocity as Boundary condition
Boundary Condition 1 Target Boundaries(1) = 1 Name = "inlet" Velocity 1 = Variable Coordinate 2, time Real MATC "tx(0)*(1-tx(0))*tx(1)" ...
Often you like to save some lumped results after each scanned parameter values. For that you may want to study the SaveScalars solver that allows saving a such quantities to a text file to be analyzed.