FE Magnetic Vector Potential Solver Reference

Magnetic Vector Potential Solver Properties

Under-Relaxation Factor

During computation, the solver under-relaxes the change in the solution $A$ as:

$$A^{n+1}=A^n+\omega A^{\prime }$$

(349)

where $\omega$ is the under-relaxation factor. At each iteration, the under-relaxation factor governs the extent to which the new solution replaces the previous one.

The default value is 1.0. If residuals show solution divergence and do not decrease, reduce the under-relaxation factor.

Solver Method

Allows you to choose the finite element solution method between Direct and Iterative (see Finite Element Solvers Reference). Depending on the method, Simcenter STAR-CCM+ adds the following controls under the Magnetic Vector Potential solver node:

Method	Activated Controls
Direct	Direct > Sparse Direct Solver For more information on the direct solver properties, see FE Sparse Direct Solver Reference. Matrix Update Strategy At each solver iteration i, Simcenter STAR-CCM+ solves Eqn. (4839) for the magnetic vector potential. The solver assembles the tangent matrix $T$ during the first iteration. In subsequent iterations, the solver reassembles or reuses the tangent matrix based on the selected Update Strategy. The available options are: Full Newton—the solver factorizes the tangent matrix at each iteration. This option is appropriate for nonlinear applications, which require frequent updates of the tangent matrix in order to reach a converged solution. Modified Newton—the solver factorizes the tangent matrix at a specified iteration frequency. This option is appropriate for linear or moderately nonlinear applications, which do not require frequent updates of the tangent matrix in order to reach a converged solution. You define the update frequency using the properties of the Modified Newton Update > Start Iteration node: Start Reusing—specifies the number of iterations n that the solver runs before it starts reusing the tangent matrix. The solver factorizes the matrix at each iteration for the first n iterations. In subsequent iterations, the solver reuses the tangent matrix until the next matrix update (as defined by the Update Frequency property). Update Frequency—specifies the tangent matrix update frequency, M. For M=0, Simcenter STAR-CCM+ stops updating the matrix when the Start Reusing criterion is met. For M>0, Simcenter STAR-CCM+ continues updating the tangent matrix every M iterations, after the Start Reusing criterion is met. Note When running a simulation with second order time discretization, run the first time-step using the Full Newton method. After the first time-step, you can change the Update Strategy to Modified Newton. Note Simcenter STAR-CCM+ does not retain the tangent matrix when you save and close a simulation. In restart scenarios, the solver always computes the tangent matrix during the first iteration, then reuses it based on the specified reuse settings. Integration Method Specifies the time integration method. The available options depend on the temporal discretization scheme for the Implicit Unsteady solver. For more information on the available options, see Integration Method. Line Search Method See Magnetic Vector Potential Solver Controls.
Iterative	Iterative For more information on the iterative solver properties, see FE Iterative Solver Reference. Integration Method Specifies the time integration method. The available options depend on the temporal discretization scheme for the Implicit Unsteady solver. For more information on the available options, see Integration Method. Line Search Method See Magnetic Vector Potential Solver Controls.

When you use the Finite Element Magnetic Vector Potential model with the Excitation Coil Lumped Parameter model, the solver method that you select for the Magnetic Vector Potential solver also dictates the solver method for the Excitation Coil Lumped Parameter solver. See Excitation Coil Lumped Parameter Solver Reference.

Temporary Storage Retained

When activated, Simcenter STAR-CCM+ retains the residual vector that is computed at each iteration and stores it in the vector field function Magnetic Vector Potential Residual.

For other properties, see Finite Element Solvers Reference.

Magnetic Vector Potential Solver Controls

In addition to the controls that depend on the specific solver settings (see Magnetic Vector Potential Solver Properties), the following controls are always available:

Line Search Method

Allows you to select the method for determining the factor that under-relaxes the solution increment (see Eqn. (349)). You can specify the under-relaxation factor manually or instruct Simcenter STAR-CCM+ to calculate an optimal under-relaxation factor using the Line Search method. This method speeds up the convergence of nonlinear problems.

Note

When the magnetic permeability $\mu$ of the material is specified with a field function, you must specify the Under-Relaxation Factor manually. The Line Search method is not compatible with such a material model specification and cannot be used. In such a scenario, an error message is displayed and you are instructed to deselect the Line Search Method option.

The available options are:

Line Search Method	Activated Controls
None You specify the under-relaxation factor manually using the Under-Relaxation Factor property for the Magnetic Vector Potential Solver. See Magnetic Vector Potential Solver Properties.	None
Energy Reduction Activates the line search method, which determines the under-relaxation factor $\omega$ (see Eqn. (349)) that reduces the energy potential. Recommended for nonlinear simulations.	Energy Reduction Allows you to set the following properties: Verbosity: when activated, the Output window displays additional information about convergence and energy values. Cutoff Residual: specifies a cutoff energy value. When the energy norm reaches the specified value, no line search is performed and the full update is applied (that is, $\omega =1$ ). Cutoff Iteration: when the inner iteration (unsteady) or iteration (steady) number exceeds the specified value, the line search stops and returns the current under-relaxation factor. Maximum Iterations: when the line search iteration exceeds the specified value, the line search stops and returns the current under-relaxation factor.