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General

Elmer is a multiphysics solver. Therefore you can use several main equations to solve problems. The different equations are listed here.

There are solver settings, available for all equations. These are described here. Settings only available for a particular equation are described in the pages of the corresponding equation.

Elmer offers the solving types steady-state and transient and two main solving systems, linear system and nonlinear system. The nonlinear system is used for the Flow equation and Heat equation.

Editing Settings

The solver settings can be found in the property editor after clicking on an equation in the tree view. You can edit them there directly like any other property.

Solver

Coordinate System

The default coordinate system is Cartesian 3D. For some equations, not all coordinate systems can be can be used. This is noted on the Wiki pages of the corresponding equations.

Timestepping (transient analyses)

Note: FreeCAD 0.20.x already provides the following settings but only the last time result is output. Starting with FreeCAD 0.21 you will get an output for the different times.

For transient analyses the time steps need to be defined. This is done by the following settings:

• DataBDFOrder: Order for the method BDF (Backward Differentiation Formula). It is recommended to use the default of 2.
• DataOutput Intervals: An array of intervals. A solver result file will be output every interval time step. For example, if a result file should be output every third time step, set it to 3. The array corresponds to the DataTimestep Intervals.
Note: The first result in every case will be created for the first time step. To get for example results after 25 % of the total time and if the last result should be the final time, set DataOutput Intervals to 5 and DataTimestep Intervals to 21. introduced in version 0.21
• DataTimestep Intervals: An array of time intervals. The solver will perform one time interval after another. For example, if the solver should calculate the first 10 seconds in steps of 0.1 second, then 50 seconds in steps of 1 second and then stop, you need to set the timestep intervals [100, 50] and the timestep size intervals [0.1, 1.0].
• DataTimestep Sizes: An array of timestep sizes. The time unit is second. The array corresponds to the DataTimestep Intervals.

Note: Although the terms "times" and "seconds" are used the times are actually solver progressions if the analysis is not time-dependent.

For how to visualize the results, see the Elmer visualization info.

Type

• DataSimulation type: If the simulation is Steady state, Transient or just Scanning. Transient means the development over the solver time is calculated. See section Timestepping for the necessary settings.
• DataSteady State Max Iterations: The maximum number of steady-state solver runs.
• DataSteady State Min Iterations: The minimum number of steady-state solver runs.

Equation

Base

All equations have these properties:

• DataLabel: Name of the equation in the tree view.
• DataPriority: Number determining the priority of this equation to the other equations in the analysis. The equation with the highest number in the analysis will be solved as first. If two equations have the same priority number, the one that is first in the tree view will be solved first.
• DataStabilize: If set to true, the solver will use the stabilized finite element method when solving the heat equation with a convection term. If set to false, the Residual Free Bubble (RFB) stabilization is used instead. If convection dominates, stabilization must be used to successfully solve the equation.

Linear System

This system has the following properties:

• DataBiCGstabl Degree: Polynomial degree for the iterative solver method BiCGStabl . This has only an effect if DataLinear Solver Type is Iterative and DataLinear Iterative Method is BiCGStabl. Starting with the default of 2 is recommended.
• DataIdrs Parameter: Parameter for the iterative solver method Idrs . This has only an effect if DataLinear Solver Type is Iterative and DataLinear Iterative Method is Idrs. Starting with the default of 2 is recommended. Setting the parameter to 3 might increase the solving speed a bit. For flow analyses the Idrs method is up to 30 % faster than the default BiCGStab method.
• DataLinear Direct Method: Method used for direct solving. This has only an effect if DataLinear Solver Type is Direct.
The possible methods are Banded, MUMPS and Umpfpack. Note that MUMPS usually needs to be installed before you can use it.
Note: when you use more than one CPU core for the solver (introduced in version 0.21) only MUMPS can be used. MUMPS has to be installed manually to Elmer. It is only available as a download per request via email.
• DataLinear Iterations: Maximal number of iterations for an iterative solver run. This has only an effect if DataLinear Solver Type is Iterative.
• DataLinear Iterative Method: Method used for iterative solving. This has only an effect if DataLinear Solver Type is Iterative.
• DataLinear Preconditioning: Method used for the preconditioning. For info about preconditioning, see this presentation (page 8) from Elmer.
• DataLinear Solver Type: If the solving is done Direct or Iterative.
• DataLinear System Solver Disabled: Disables the linear solver. Only use this for special cases.
It can be used to disable temporarily an equation since its solving is then not performed. There are, however cases where the solver is sent into an infinite loop instead.
• DataLinear Tolerance: The tolerance for the solver to stop. If the error is smaller than the tolerance, the solver run will be finished. Otherwise, the full number of DataLinear Iterations will be performed.
In the Elmer solver log you see how the error is minimized while the solver is running. (Look in the log at the end of every solver iteration for the value behind Relative Change). If it does not go down below a certain value but reaches a value above the current tolerance that is acceptable for you, you can increase the tolerance.

Nonlinear System

This system is iterative and has the following properties:

• DataNonlinear Iterations: Maximal number of iterations.
• DataNonlinear Newton After Iterations: The nonlinear solver starts with the robust Picard algorithm. After some iterations, the algorithm is changed to the Newton algorithm which converges faster but is less robust if the results temporarily diverge (oscillations might occur). This setting sets the number of iterations after which the switch from the Picard to the Newton algorithm is made.
Note: the switch is made whatever is reached first, DataNonlinear Newton After Iterations or DataNonlinear Newton After Tolerance.
• DataNonlinear Newton After Tolerance: The same as DataNonlinear Newton After Iterations but here a tolerance is set. The tolerance is the norm of the nonlinear residual. If this is reached, the switch from the Picard to the Newton algorithm is made.
• DataNonlinear Tolerance: The tolerance for the solver to stop. If the error is smaller than the tolerance, the solver run will be finished. Otherwise, the full number of DataNonlinear Iterations will be performed.
In the Elmer output you see how the error is minimized while the solver is running. If it does not go down below a certain value that is acceptable but above the current tolerance, you can increase the tolerance.
• DataRelaxation Factor: This is THE most important setting in case the solver does not converge:

Relaxation Factor

If the solver iteration results oscillate numerically, the solver results cannot converge to a final, stable value. To avoid that, the calculated variable ${\displaystyle T_{i}}$ of the i-th iteration/solver run is not taken as input for the next iteration, but ${\displaystyle T_{i}^{'}}$, a value that is "damped" with the result from the previous iteration. The relaxation factor ${\displaystyle \lambda }$ is thereby defined as

${\displaystyle \quad T_{i}^{'}=\lambda T_{i}+\left(1-\lambda \right)T_{i-1}}$

So for the default of 1.0, no damping is used. The smaller ${\displaystyle \lambda }$, the greater the damping and the longer the convergence time. Therefore if the solver does not converge, start changing the relaxation factor to 0.9, then to 0.8 and so on. Values below 0.3 are unusual and if you need this, you should have a closer look to the math of your analysis.
For cases, where you get a proper convergence you can set ${\displaystyle \lambda }$ above 1.0 to speed the convergence up.

• DataSteady State Tolerance: The specific steady state or coupled system convergence tolerance. All the equation solvers must meet their own tolerances for the variable ${\displaystyle \omega ^{2}}$ they calculate before the whole system is deemed converged. The tolerance criterion is:
${\displaystyle \quad \left\Vert u_{i}-u_{i-1}\right\Vert <\epsilon \left\Vert u_{i}\right\Vert }$
whereas ${\displaystyle \epsilon }$ is the steady state tolerance and ${\displaystyle u_{i}}$ is the calculated variable in the i-th iteration/solver run.