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.



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 CM, 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 CM takes into account the number and types of symmetries and/or periodicities.

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

An example which needs a manual CM definition is a speed sensor defined with symmetry/periodicity, but the coils must not be duplicated. Then CM 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) CM is automatically computed with taking active symmetries and active rotation periodicities of the problem into account.
Imposed coefficient (integer)

CM is an integer:

CM = 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)

CM is a quotient of 2 integers:

CM = 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.

  • Transient initialization at the 1st step

    The transient solution can be initialized either:
    • with zero
    • with static computation
    • with a Finite Element solution. This initialization type is not defined in the Solver Settings dialog box. For more details, please refer to Initialization by a FE Solution.
    The initialization with zero can lead to a numeric transient which distorts the solving process:
    • Increase of calculation time
    • False results over the first time steps
    • Convergence issues, especially in 3D
    That happens especially in the following situations:
    • There are magnets or non-null sources of current at the initial time step t=0s
    • There are solid conductors and/or coil conductors coupled with electric circuit

    The sources quantities gap at t=0s leads to very high derivative values at this time step which generates the numeric transient.

    The initialization by static calculation is characterized by particular calculation conditions for the first time step: conditions, which permit to annul all the terms in d/dt at the step t = 0s.

    These conditions are summed up in the table below.

    Element of the device Hypotheses / conditions of calculation at t = 0 s
    in the finite elements domain in the electric circuit
    Solid conductor Active (circuit coupling) Skin effects, proximity effects are not taken into consideration (= non magnetic conducting regions) DC resistance (electric conduction resistance)
    Passive (no circuit coupling) Induced currents are not taken into consideration (= non conducting magnetic region) -
    Coil conductor Current in coil (=circuit current) Resistance (of coil conductor)
    Element of the device in the electric circuit
    Resistor Resistance (values of the Resistor component)
    Inductor Inductance replaced by a resistor with small resistance
    Capacitor with initial voltage Uc Capacitor replaced by a voltage source * (U = Uc)
    without initial voltage Capacitor replaced by an open circuit

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.

Nonlinear Solver Options

A nonlinear system (n equations and n unknowns) can be written under the form:

[A(X)].[X] = [B]

where the system matrix A depends on the vector solution X.

The solution of a nonlinear system is obtained by using an iterative procedure, i.e. by solving a set of linear systems, the solutions of which are convergent towards the solution of the nonlinear system.

There are different techniques of solving nonlinear systems, but the convergence of the solving process is never guaranteed. The method used in Flux is the Newton-Raphson (NR) one. This method is applied to equations of the form f(x) = 0 for which the derivative f'(x) of the function f can be computed.

The option Continue transient solving when non linear convergence is not reached, available in transient EM solutions, allows the transient simulation to continue even if nonlinear convergence is not fully reached on one of the transient steps.