34. TDME_JOULE_SOLVER Namelist

This namelist specifies the parameters that pertain to the time-domain Joule heat solver, which integrates the periodically-forced Maxwell equations in time until a periodic steady state solution is attained, and then computes the time-averaged Joule heat over one cycle of the forcing. This solver is used by the induction heating physics model; see the INDUCTION_HEATING namelist.

34.1. Namelist Variables

steps_per_cycle

The number of time steps per cycle of the periodic forcing used to integrate the EM field equations.

Type:

integer

Default:

20

Valid Values:

> 0

Notes:

Increasing the number of time steps per cycle increases the accuracy and stability of the Joule heat computation, while generally increasing the execution time. A reasonable range of values is [10,40]; anything less than 10 is severely discouraged.

steady_state_tol

Convergence to the periodic steady state is measured by comparing the computed Joule heat field averaged over the last source field cycle, \(q_\text{last}\), with the result from the previous cycle, \(q_\text{prev}\). The Joule heat computation is considered converged when \(\lVert{q_\text{last}-q_\text{prev}}\rVert_\infty < \delta\, \lVert{q_\text{last}}\rVert_\infty\) where \(\delta\) is the value of this parameter.

Type:

real

Default:

\(10^{-2}\)

Valid Values:

> 0

Notes:

Depending on the accuracy of the other physics, \(10^{-2}\) or \(10^{-3}\) are adequate values. The measured error is more properly the error in \(q_\text{prev}\); the actual error in \(q_\text{last}\) will be significantly less.

max_source_cycles

Specifies the time limit, measured in cycles of the periodic forcing, allowed for convergence to the periodic steady state. If convergence is not attained within this limit, the last result is returned and a warning issued, but execution continues.

Type:

integer

Default:

5

Valid Values:

> 0

Notes:

To avoid ringing, the amplitude of the external source field is phased in and is not at full strength until after approximately two cycles have passed. Consequently this input variable should normally be at least 3. Convergence to a periodic steady state is commonly attained within 5 cycles; see steady_state_tol.

rel_tol

The convergence tolerance \(\eta\) for the conjugate gradient (CG) solution of the linear time step system. The CG iteration is considered converged when the residual \(r\) satisfies \(\lVert{r}\rVert<\eta\lVert{r_0}\rVert\).

Type:

real

Default:

\(10^{-8}\)

Valid Values:

\((0, 0.1)\)

Notes:

The numerical characteristics of the EM system require that the linear systems be solved to significantly greater accuracy than might otherwise be required. Too loose a tolerance will manifest itself in a significant build-up of noise in the solution of the electric field over the course of the simulation.

max_iter

The maximum number of conjugate gradient (CG) iterations allowed. It is a fatal error if convergence is not attained within this number of iterations.

Type:

integer

Default:

500

Valid Values:

> 0

c_ratio

In the quasi-magnetostatic regime, Maxwell’s equations can become become very ill-conditioned and difficult to solve in regions with zero electrical conductivity, such as free space. Artificially reducing the speed of light in those regions helps ameliorate that difficulty, and this numerical parameter is that reduction factor \(r\). A value of 1 means no reduction and is the default.

Type:

real

Default:

1

Valid Values:

\(\in(0,1]\)

Notes:

This is implemented by altering the permittivity, \(\epsilon\to\epsilon/r^2\), which only modifies the displacement current term \(\partial\epsilon\vec{E}/\partial t\). In the magnetostatic regime, this term functions as a very small perturbation in Maxwell’s equations.

For common induction heating applications, this parameter can be taken fairly small, \(10^{-3}\) or \(10^{-4}\), without any signficant effect on the computed Joule heat.

More generally, \(\omega\epsilon\ll\sigma\) in the magnetostatic regime, where \(\omega\) is the frequency of the external driving field, and one wants to ensure that this separation of scales is maintained when choosing the reduction factor, \(\omega\epsilon/r^2\ll\sigma\).

graphics_output

A flag that enables output of the EM solution for graphics visualization.

Type:

logical

Default:

.false.

Notes:

When enabled, the solver generates its own graphics data file in VTKHDF format, which is compatible with the ParaView visualization software. The solver produces a separate sequentially-numbered file for each use, identifiable by the .vtkhdf suffix. This setting does not affect the standard graphics output generated by Truchas, which is configured elsewhere. Since these files are simply HDF5 files structured to the VTKHDF specification, they can also be used with generic HDF5 tools.

relax_type (experimental)

Specifies the type of relaxation used within the linear system preconditioner.

Type:

integer

Default:

0

Valid values:

0, Gauss-Seidel; 1, Hypre Boomer AMG

Notes:

Boomer is significantly more expensive without any obvious benefit.