How to choose numerical settings to optimize calculation time of 3D induction heating simulation?

How to choose numerical settings
to optimize calculation time of
3D induction heating simulation?
Short guide and practical tips

Contents
1. Simplify geometry………………………………………………………………………….…3
2. Calculate skin depth…………………………………………………………………….…..4
3. Create optimal mesh…………………………………………………………………….….5
4.1. Calculation settings - 2D cases………………………………………………….....6
4.2. Calculation settings - 3D cases………………………………………………..……7
4.3. Calculation settings - light 3D case…………………………………………...….9
4.4. Calculation settings - normal 3D case…………………………………………10
4.5. How to estimate applicable magnetic permeability?………………….11
4.6. Fast vs. Accurate results…………………………………………………………..….12
4.7. Calculation settings - heavy 3D case……………………………………..……13
4.8. Calculation settings - extreme 3D case……………………………….………14
5. About…………………………………………………………………………………….…………16

1. Simplify geometry
A. Get rid of assembly parts which do not affect induction or do not affect the induction significantly.
B. Simplify peripheral shapes of inductor and workpiece which are outside the zone of induction. If possible, simplify
the geometry in the zone of induction as well, as far as it does not significantly affect induction (e.g. remove drills,
fillets, etc).
C. If there is a chance to use axial symmetric estimation, simplify geometry to 2D axial symmetric instead of 3D. You
can run a couple of 2D calculations within an hour, while 3D cases may require even overnight calculation.
D. If the geometry is in 3D, check carefully - if it's possible to use any other type of symmetry to cut half, quarter,
sector or slice of the geometry. There are two types of symmetry boundary conditions in majority of simulation
software – Flux parallel and Flux normal (read more here). By using those, you can save calculation time by half,
sometimes even tenfold.
(Read some practical tips how to simplify geometry here)
3

2. Calculate skin depth
where 𝜎 - electric conductivity of workpiece material;
𝑓 - power frequency;
𝜇0 - magnetic permeability of free space;
𝜇 𝑟 - relative (dimensionless) permeability of workpiece material.
B. If the frequency is so high that δ is less than 0,5% of the linear size of a workpiece in the direction of heating (e.g.,
thickness, diameter, etc), you can use Surface Impedance method to get accurate results. It may be applicable for high
frequencies from several hundreds of kHz or MHz.
This method is available in some simulation software (ANSYS, Flux 2D/3D, CENOS).
By using Surface Impedance method, you can reduce calculation time from several hours to few minutes. Check this
blog post for the details.
C. If the skin depth is not small enough to apply the surface impedance method, no worries, you’ll get the result by
following classical FEM method as further described.
4
A. Calculate electromagnetic skin depth
according to the following formula:
(metric system)

3. Create optimal mesh
A. Create skin-layers on the surfaces of induction heating. You should put 3-
10 layers within the skin depth (5 is recommended). Refinement of the skin layer in the
workpiece is super essential to get accurate results. It is handy to use mesh layers at
the surface like in CFD (so-called viscous layers), check CENOS tutorials.
NB! In case you can use the Surface Impedance method (see previous slide), you can
skip skin layer refinement and just create rough mesh to thermal calculation, thus
saving significantly on calculation time.
B. If you’d like to get energy economics (apparent power, inductivity of the
system, etc.) – some software programs like ANSYS or CENOS will provide it, you have
to refine the skin-layer in the inductor as well. Otherwise, if you are looking for heating
results only, refinement of the skin layer in the inductor is not necessary.
5
C. Create the rest of the mesh - workpiece, inductor, air domain and other objects. Be sure that in the areas
of heating you've made the mesh fine enough and more rough in the periphery. Just be sure your mesh has at least few
elements (minimum 3) in thin places like splines, gear teeth, plain geometry elements, air gaps, etc.

4.1. Calculation settings - 2D cases
If you have a 2D case up to few tens of thousands of mesh elements, you can freely use full non-linear properties:
• Temperature dependence of all parameters, including magnetic permeability
• B-H curve for ferromagnetic materials
It should not cause significant delay in the calculation.
You can also use adaptive time step for your convenience (majority of simulation software do have such option).
Adaptive time step will ensure accurate simulation with small time steps in the beginning when heating is rapid and
adapt time steps later on when heating pace is already slower. Calculation time for 2D cases usually should be within
acceptable range.
In case you know your estimated heating time (till Curie point or your target temperature below it), you can get the
result even in shorter time using fixed time step (manually defined). For accurate results, use time step which is at least
1/5 of estimated heating time or smaller.
6

For 3D cases, first check if your processor has enough RAM to simulate the mesh that you created.
Electromagnetic task is efficiently solved by direct solver (directly solves the matrix). The solution requires sufficient
RAM, which is proportional to the size of matrix represented by degrees of freedom (DoF). However, to make it more
simple, we can check the number of nodes of the mesh, which approximately correlates with DoF.
7
Number of nodes in the mesh
(don’t mix up with elements!)
RAM requirements*
75k 8Gb
125k 16Gb
220k 32Gb
590k 128Gb
* estimated by observing peak memory usage of CENOS program. The results are approximate. RAM
requirements differ from case to case, as number of nodes is not precise representation of the matrix size.

8
Secondly, for 3D cases, choose simulation settings carefully to keep calculation time reasonable.
Check the number of mesh elements (carefully, don’t mix up with nodes!):
Number of mesh elements~100k* ~250k* ~500k*
Light case Normal case Heavy case Extreme case
NB! Calculation time increases like exponentially depending on the number of mesh elements
* NB! The number of mesh elements which indicates the boundaries strongly depends on computer parameters (RAM, processor speed).
Approximate numbers provided here are the most optimal according to our practice using CENOS simulation software with Intel i7
processor and 16GB of RAM. However, these numbers still can be used as indicative boundaries only.

4.3. Calculation settings - light 3D case
9
< ~100k mesh elements*
Light 3D cases can be treated the same way as 2D cases:
• You can use full non-linear properties (temperature dependence, B-H curve)
• Adaptive time step is also OK.
See more at slide #5 (2D cases)

4.4. Calculation settings - normal 3D case
10
< 100k - 250k mesh elements*
Unless you can prepare a light 3D case, we really recommend to do your best to optimize the mesh to get into this category.
In order to keep calculation time in a reasonable range, we strongly recommend to follow these restrictions:
• You CAN use temperature dependent parameters, incl. magnetic permeability;
• Do NOT use B-H curve, use fixed (approximate) magnetic permeability – see the next slide for ideas how to estimate it;
• Do NOT use adaptive time step, it will unnecessary increase the calculation time. Be sure to define time step, which is
at least 1/5 of estimated heating time (till Curie point) or smaller.
• Unless super high accuracy of results is required, we recommend using weak coupling of EM – thermal parts of
algorithms (in CENOS – Fast algorithm, see slide #12)
By following these recommendations, you can still run few calculations within a day to perform an optimization task.

4.5. How to estimate applicable magnetic permeability?
11
If you have no idea about approximate value of magnetic permeability in your case, the
estimation of it is not an easy task. Nevertheless, we recommend the following procedure.
1) Do your best to prepare 2D case, which is as similar to your 3D case as possible
2) Run full non-linear (B-H) 2D simulation with the same frequency and current/voltage
– use the result as a benchmark
3) Run several 2D simulations with your best estimate for fixed magnetic permeability
4) Compare them to your benchmark results and choose the best estimate of fixed
magnetic permeability – use it for the 3D case
NB! If you change geometry, current or frequency, the estimated fixed magnetic
permeability will not be valid anymore (unless your parameter change is insignificant). This
is because it is the effective (integral) value of magnetic permeability you define, due to
harmonic changes of magnetic permeability in time and field decay in the skin depth.

4.6. Fast vs. Accurate results
12
There are two approaches for simulation of non-linear induction heating cases (both available in CENOS):
Fast algorithm means weak coupling between EM and thermal algorithm blocks. It’s good for estimation and it's
fast, but yields less precise calculations. In case of steep change of properties, it may require smaller time step.
Accurate algorithm means strong coupling between EM and thermal algorithm blocks with an iterative
recalculation. The algorithm can cause significantly longer calculation time, but leads to super accurate results
(sure, if relevant parameters are defined). Relatively large time step can be used.
See more details here

4.7. Calculation settings - heavy 3D case
13
~250k – ~500k mesh elements*
Such case will require several hours or calculation. Therefore, the best option would be to run such case
overnight.
Similarly with optimal 3D cases, we strongly recommend to follow these recommendations to avoid
even longer calculation time:
• Do NOT use B-H curve, use fixed (approximate) magnetic permeability – see slide #11 for ideas
how to estimate it;
• Do NOT use adaptive time step, it will unnecessary increase calculation time. Be sure to define time
step, which is at least 1/5 of estimated heating time (till Curie point) or smaller.
• We recommend using Fast algorithm, see slide #12
And still, if there is any chance to optimize a mesh, so it fits into the Optimal range, it is definitely worth
doing that. Due to a long calculation time, optimization of induction task is very limited for heavy 3D
cases.

4.8. Calculation settings - extreme 3D case
14
> 500k mesh elements*
Such cases can take a day or even few days.
Evaluate processing of such cases very carefully. If there is any chance to optimize the mesh, consider
doing that. Remember that simulation time grows like exponentially with the number of mesh elements.
However, if there is no way to optimize the mesh to fit in a lower category, just be aware of longer
calculation time and enjoy your time by doing something more useful meanwhile :)

Optimize calculation time and
maximize the value of simulation

5. About
CENOS was developed by a team of experienced PhDs, engineers and software developers with a simple vision
of bringing sharing economy to the engineering world, saving engineers time and accelerating innovations.
Visit our site to learn more: www.cenos-platform.com
16
Dr. phys. Mihails Scepanskis
CEO and co-founder of CENOS LLC
10+ years of scientific and
engineering career, former
researcher at Argonne National
Laboratory and University of
Latvia, 19 peer-reviewed
publications
Dr. phys. Vadims Geza
Chief Scientist at CENOS LLC
10+ years in induction heating,
former researcher at Leibnitz
University of Hanover, simulation
expert in numerous industrial
projects

How to choose numerical settings to optimize calculation time of 3D induction heating simulation?

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