The Segregated Solver
Segregated in the COMSOL Multiphysics Programming Reference Manual
Termination Criterion for a Segregated Solver
For the Solution termination criterion: The Segregated solver terminates after iteration k if, for all the groups j, the error estimate is smaller than the specified tolerance,
The number tol is the Relative tolerance specified in the parent Stationary Solver or Time-Dependent Solver multiplied by the Tolerance factor specified in the Segregated solver. The error estimate in segregated iteration k considers both updates done in the individual segregated groups and the total solution change relative to iteration k − 1,
If within each group the field variables are numbered 1 ≤ p ≤ Mj and 1 ≤ i ≤ Nj,p is the index of degrees of freedom belonging to the field p, then the largest damped Newton error is estimated by
Here l is taken for all iterations in all substeps solving for the group j, αl,j is the damping factor, ΔU l, j, k,p is the full Newton increment vector, and Nj,p is the number of DOFs in the field p. The weight factor is described below.
for segregated steps set to Constant (Newton) with Damping factor equal to 1, and so does not contribute to the error estimate.
Moreover,
is the relative increment over one complete iteration k. In this expression, Uj,k,p is the segregated solution vector for the group j.
The scale factor used in the error estimates is
where Sp is a scale factor that the solver determines from the settings in the Scaling section of the Field or State node corresponding to p under the Dependent Variables node. There, the following choices are available in the Method list:
•
For Automatic, Sp is the factor 0.1 times the average of |Um| for all DOFs m in field p.
•
For Manual, Sp is the factor 0.1 times the value given in the Manual scaling field for field p or its parent Dependent Variables feature.
•
For Initial value based, Sp is the factor 0.1 times the average of |U0m| for all DOFs m in field p, where U0 is the solution vector corresponding to the initial value.
•
For None, . In this case the error is the mean absolute change in the solution, rather than a relative error.
Sp is a constant for each field variable p.
For the Residual termination criterion, the segregated solver terminates after iteration k when the following convergence criterion is satisfied: For all the groups j, the error estimate is smaller than the specified tolerance, errj,k < tol, where
where F is the current residual, and are the weights determined as explained under Termination Criterion for the Fully Coupled and Segregated Attribute Nodes. The iterations can also terminate if the relative solution-based error is in the range of a hundred machine epsilon.
Pseudo Time Stepping
Pseudo time stepping is available in a stationary segregated approach as well; see Pseudo Time Stepping for a description of the CFL control. For the segregated solver, the error estimate en in Equation 20-1 is the arithmetic average of the errors in the different segregated groups.