Solver Settings

Analysis > Options > Solution Settings > Solver Settings

The Solver Settings allow the user to set the Flux solvers options which will be taken by Flux (in batch) to solve the current solution.

Soft non linear B(H) approximation

In AC Magnetic solutions, the quantities as the magnetic field H and magnetic flux density B are sinusoidal time dependent.

But in reality, when soft non linear materials are considered, H and B cannot have both sinusoidal time dependency simultaneously.

To take this consideration into account, an approximation can be done by using one of the following models:


Model	Hypothesis	Equivalent B(H) curve
Curve not modified	-	Real B(H)
Sine wave flux density	B sinusoid	This model is based on the following energetic equivalence: This model is more adapted for the simulation of devices with a voltage supply.
Sine wave magnetic field	H sinusoid	This model is based on the following energetic equivalence: This model is more adapted for the simulation of devices with a current supply.
Mixed	-	This model is the linear combination of the two preceding ones: where α is a weighting coefficient chosen empirically in the interval [0,1]
Average value of Nu over a cycle	B sinusoid	This model relies on an equivalent reluctivity ν_eq calculated by getting the average of reluctivity over a period of time: It is much less precise than the others for high values of magnetic flux density, as it does not observe the asymptote of µ₀ slope.

The most commonly used models are:

Sine wave flux density
Sine wave magnetic field
Curve not modified

The Automatic mode which is enabled by default works as following:

If a voltage source component exists, Sine wave flux density model is used
If a current source component exists, Sine wave magnetic field model is used
If there is no source or if both sources type exist, Curve not modified is used

Coefficient for circuit connected coils

A coil is defined by two objects:

an electrical component of stranded coil conductor type defined in the circuit
a coil geometrically defined entity to define the shape of coils

A coil is described in a finite element domain that can be bounded by symmetries and/or periodicities.

from an electric point of view, there is only one electrical component
from a geometric point of view, there is an "original" coil (the one described in the FE domain) and its "duplicates" by symmetry and/or periodicity

In this situation, the electrical component is a component that comprises several geometric coils.

To compute the magnetic flux through this component (i.e. through the "original" coil and its "duplicates"), Flux evaluates:

the coefficient C_M, which takes into account the number and types of symmetries and/or periodicities
the field Conductors in series or in parallel, which takes into account the configuration type of associated conductors (all in series, all in parallel).

In the Automatic mode which is suitable for most cases, the coefficient C_M takes into account the number and types of symmetries and/or periodicities.

But it is possible to define manually the coefficient C_M defined either as an integer or a fraction.

An example which needs a manual C_M definition is a speed sensor defined with symmetry/periodicity, but the coils must not be duplicated. Then C_M is defined by the value 1.

The 3 possible choices are explained in the table below:


Option	Description
Automatic coefficient (symmetry and periodicity taken into account)	C_M is automatically computed with taking active symmetries and active rotation periodicities of the problem into account.
Imposed coefficient (integer)	C_M is an integer: C_M = N N is the number of repetitive patterns described in the finite elements domain (The finite elements domain corresponds to 1/N fraction of the real device)
Imposed coefficient (fraction)	C_M is a quotient of 2 integers: C_M = N1/N2 The finite elements domain corresponds to 1/N1 fraction of the real device. N1 is the number of repetitive patterns described in the finite elements domain N2 is the number of repetitive patterns supplied by the electric circuit

Initialization

Variables initialization at the start of a step

This option concerns the initialization of the state variables at the start of a step.

It is used for the following solutions:

Transient solutions
Static and AC solutions with Motion load and constraint

By default, the state variables are initialized with the previous step solution, except if there is any hysteretic material, the state variable will be initialized with a predicted solution. A solving option allows the user to modify the initialization to one of the following options:

With zero solution
Robust for non-linear convergence
With the previous step solution (by default)
Faster, but can impact the non-linear convergence
With a predicted solution
Recommended for hysteretic materials.

Linear Solver Options

A linear system of n equations and n unknowns can be written under the following matrix form:

AX=B

where:

A is a square matrix of n x n size (with n lines and n columns)
X is a column vector of size n, representing the system unknowns
B is a column vector of size n, with known components

To find the solution, i.e. the vector X, a linear solver must be employed. Two types of solvers can be distinguished: the Direct and Iterative solvers.

The Direct solvers follow a process that leads to a very accurate solution but at the cost of several time and memory-expensive operations for large problems.

The Iterative solvers follow an iterative process that approximates a solution at each iteration. Usually, the process tends to provide a solution closer to the real solution of the linear system from iteration to the next. The process comes with a stopping criterion, depending on the accuracy threshold set for the approximated solution and the maximal number of iterations. Thus, the Iterative solver can lead to faster solutions and lower memory consumption for large problems but can be less accurate.

The linear solver is used in all EM solutions.

The automatic solver bases its decision to use the Direct or Iterative solver on the solution type and the number of unknowns, as summarized in the following Table:


Dimension	2D	3D
Solution	Any	Others		Magnetostatic Integral method	Steady-state AC
Number of nodes	Any	< 500,000	> 500,000	Any	Any
Solver	Direct	Direct	Iterative	Iterative	Direct

When a user wants to manually select the solver considering its computational resources, we can advise with the following guidelines:

For HPC (High Performance Computing) hardware or computers with a great amount of RAM, the Direct solver will be the most suitable choice thanks to its scalability and parallel potential.
For computers with a low amount of RAM, it would be more advisable to use the Iterative solver for its low memory consumption.
For 2D problems, the number of unknowns is relatively low, thus Direct solver should deliver better results in terms of solving time.

This section targets advanced users and wants to help understand what solver parameters do. Here are the solver options for Direct and Iterative solvers:

The Direct solver option available consists in using the disk for the solving in addition to the RAM. This option is very useful since it allows extending the amount of usable memory. However, using the disk implies slower operations since disks are significantly slower to compute i/o operations. If the disk memory usage is checked and no directory is selected, the default scratch directory is taken.

On the right-hand side figure, two options are displayed for the Iterative solver: the precision level (or threshold) and the maximal number of iterations. The automatic accuracy level is based on the problem type. It is possible to select a High accuracy level to ensure the result quality but it will lead to slower computation. The maximal number of iterations field allows to set a limitation on the solving time. Increasing the value can lead to more accurate results but with slower computation. Reducing the value can lead to faster computation but with reduced accuracy.