Correct mesh size - a quick guide!

8 minutes read

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Mesh size is one of the most common problems in FEA. There is a fine line here: bigger elements give bad results, but smaller elements make computing so long you don&#;t get the results at all. You never really know where exactly is your mesh size on this scale. Learn how to choose the correct size of mesh and estimate at which mesh size accuracy of the solution is acceptable.

As an example, I will use a simple discretely supported shell. As an &#;outcome&#; I will use the critical load multiplier of the first eigenvalue.

It&#;s perhaps worth mentioning that the &#;outcome&#; can be anything that interests you. If you want to know the certain stress component in a certain node, or a displacement of selected DOF that is ok. Whatever you choose goes, as long as it is actually influenced by the mesh size! I took the multiplier simply as it is easy to obtain, and linear buckling computes very fast &#;

Choose a correct mesh size

You can see the model I used below. Notice how deformation shape and outcomes change with the mesh refinement. I should write that a mesh refinement check (often called mesh convergence) should be made for each problem. This is somewhat true but let&#;s face it, you won&#;t make it for each problem most likely&#; it simply takes a lot of time! I would suggest you do such a study for some of the most important projects/parts and based on that experience you can extrapolate the knowledge to similar problems.

In this example, I am using QUAD4 elements (normal 4 node quadrilateral elements, sometimes referred to as &#;S4&#;).

In order to establish suitable finite element size:

• Perform chosen analysis for several different mesh sizes.
• Notice where high deformations or high stresses occur, perhaps it is worth to refine mesh in those regions.
• Collect data from analysis of each mesh: outcome, number of nodes in the model, computing time

For our shell, I have performed some analysis for different element sizes. On the drawing above you can see the outcome for few selected meshes. Please notice, that for the biggest elements actual eigenvalue shape is different than in the case of models with more refined mesh.

What mesh size is &#;small enough&#;

Usually smaller mesh means more accurate results, but the computing time gets significant as well.

You should search for a balance between computing time and accuracy. In some instances you can increase computing time over 2 times to improve accuracy by 1% &#; for me, that seems unreasonable. Knowing your problem you will know best what makes sense and what doesn&#;t, based on what accuracy do you need.

When mesh density is being discussed in tutorials, different problems are solved with known analytical solution. You can then easily compare the FEA outcome to a known solution &#; you get an error value without trouble. This is a fantastic approach that can teach you a lot, but unfortunately in reality you don&#;t know the correct answer&#; so you can&#;t really do that can you?

Unfortunately in almost all analyses performed for commercial or scientific purposes, the solution of the problem is unknown. In those cases, the &#;typical&#; approach doesn&#;t work. Instead, you will have to &#;guess&#; the correct answer based on the models with different meshes you have done. This is done with the following chart:

Reduction of finite element size leads to more elements, which in turn leads to more nodes in the model. If we build a chart showing the outcome (in this case first eigenvalue) dependence on node count in the model, this chart will be asymptotically reaching for the correct answer (in this case 0.). Node count is only one of the parameters possible here. Since I simply decreased the element size in the entire model it made sense. You can just as easily use a number of elements on the width of your part, or the size of the &#;typical&#; element. If you refine mesh only in a small area (i.e. where the stress concentration is) you can easily use a node count in that area instead of the entire model etc.

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Whatever metric you will use, will depend on the problem you are solving. Node count is the most popular one, simply since it is the easiest one to do &#;

Make it a bit easier

The exact estimation of asymptotic value on the chart above may be problematic or time-consuming. There is a simple trick to make things easier to calculate: instead of node count on horizontal axis let us use 1 / node count. This way the correct answer will be where the horizontal axis value reaches 0. This means that if we approximate our curve with the equation (in most cases linear approximation is sufficient, Excel does this automatically) it is very easy to calculate the &#;y&#; value for x = 0.

Note that the obtained curve is almost linear which is usually the case in most models. From the equation provided by Excel, it is easy to derive the correct answer when x = 0. At this stage, since we know the correct answer, we can calculate how big errors were made in the estimation of results for each finite element size. Below is a chart showing dependence between error and computing time, and between error and finite element size:

From the above chart it is easy to notice that after a certain point, any significant increase in accuracy will &#;cost&#; enormous additional computing time. When I am asked to do a convergence check on mesh refinement those 2 charts are the real answer (you can easily change the mesh element size with node count if you like). Now you know the errors each mesh size gives and the computing time it costs &#;

Making the choice and sanity check

Now you know how accurate results you will get with a given mesh, and how much time computing will take with such an approach. Making a decision is always problematic. I usually think about how sure I am about loads or boundary conditions &#; usually, those are just &#;estimated&#; and then increased &#;just to be sure&#;. When that is a case a mistake of a few percent won&#;t do any harm.

Time is also a factor to consider here. If you have 100 similar models to calculate increasing computing time 2 times will take A LOT of time&#; just something to consider.

Notice that this chart is asymptomatically reaching 0%&#; if you have made all the steps, described here, and your chart does not go toward 0 chances are you used too big elements. Just know that if you are not sure it is wise to make one model with &#;extremely&#; small elements &#; you know&#; just in case.

How to speed things up?

When you first do mesh convergence you will realize, that to have a great accuracy computing time will be significant. That is true, but you are not defenseless. Look at the similar shell below. Coarse mesh gives bad results for sure, but the very fine mesh takes a lot of time to compute. Knowing that the stability failure occurs at the bottom I have made a third model (on the right) that has a very fine mesh where it is important, and a coarse mesh where &#;nothing happens&#;.

This way I go the accurate outcome without incredible long computing time. Of course, there are limits, since you cannot be sure where failure will occur, etc. in some problems. Regardless it is always a good idea to make a coarse mesh, check when things will go south, and then refine the mesh in those &#;hot regions&#; rather than on the entire model. This does not work in all cases, but it works in some &#;

To sum this up

• The too coarse mesh can lead to results with very big errors
• Mesh density analysis helps in the decision how refined mesh should be used in the analysis in order to obtain results with satisfactory accuracy
• Reducing element sizes in places where big deformations/stresses/instabilities take place, allow for greatly increased accuracy without great expense in computing time

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Post by trystan » 07 Feb , 20:13

I am trying to simulate heating through radiation in 3D and, working on the VM, with rather coarse grids I got satisfying results(I attached a picture).
The next step now was to make the grid finer, in order to hopefully design a new heater in the future.
I made the models with FreeCad and then meshes them with gmsh, now however with a element size factor of 0.1 instead of 1, like before.
Elmer shows the model as expected, and i can apply all equation, boundary-conditions etc. like before. If I start the solver now however I can following errors:
If i use a heating ring, the solver log looks like this:

ParCommInit: Initialize #PEs: 1
MAIN:
MAIN: =============================================================
MAIN: ElmerSolver finite element software, Welcome!
MAIN: This program is free software licensed under (L)GPL
MAIN: Copyright 1st April - , CSC - IT Center for Science Ltd.
MAIN: Webpage
MAIN: Version: 9.0 (Rev: 5d27ebd8, Compiled: -11-26)
MAIN: Running one task without MPI parallelization.
MAIN: Running with just one thread per task.
MAIN: HYPRE library linked in.
MAIN: MUMPS library linked in.
MAIN: Lua interpreted linked in.
MAIN: Zoltan library linked in.
MAIN: =============================================================
LoadInputFile: Reading only "Run Control" section
MAIN:
MAIN:
MAIN: -------------------------------------
MAIN: Reading Model: case.sif
LoadInputFile: Scanning input file: case.sif
LoadInputFile: Scanning only size info
LoadInputFile: First time visiting
LoadInputFile: Reading base load of sif file
LoadInputFile: Loading input file: case.sif
LoadInputFile: Reading base load of sif file
LoadInputFile: Number of BCs: 2
LoadInputFile: Number of Body Forces: 0
LoadInputFile: Number of Initial Conditions: 1
LoadInputFile: Number of Materials: 2
LoadInputFile: Number of Equations: 1
LoadInputFile: Number of Solvers: 1
LoadInputFile: Number of Bodies: 2
ElmerAsciiMesh: Base mesh name: ./.
LoadMesh: Elapsed REAL time: 0. (s)
MAIN: -------------------------------------
AddVtuOutputSolverHack: Adding ResultOutputSolver to write VTU output in file: case
RadiationFactors: ----------------------------------------------------
RadiationFactors: Computing radiation factors for heat transfer
RadiationFactors: ----------------------------------------------------
RadiationFactors: Total number of Radiation Surfaces out of
ViewFactors:
ViewFactors: ==================================================
ViewFactors: E L M E R V I E W F A C T O R S, W E L C O M E
ViewFactors: ==================================================
ViewFactors:
ViewFactors:
ViewFactors: Reading Model...
LoadInputFile: Scanning input file: case.sif
LoadInputFile: Scanning only size info
LoadInputFile: First time visiting
LoadInputFile: Reading base load of sif file
LoadInputFile: Loading input file: case.sif
LoadInputFile: Reading base load of sif file
LoadInputFile: Number of BCs: 2
LoadInputFile: Number of Body Forces: 0
LoadInputFile: Number of Initial Conditions: 1
LoadInputFile: Number of Materials: 2
LoadInputFile: Number of Equations: 1
LoadInputFile: Number of Solvers: 1
LoadInputFile: Number of Bodies: 2
ElmerAsciiMesh: Base mesh name: ./.
LoadMesh: Elapsed REAL time: 0. (s)
ViewFactors: Computing view factors for radiation body 1
ViewFactors: Number of surfaces participating in radiation:
ViewFactors: Computing viewfactors...
surfs: , min(407)=0.00, max()=0.70, avg=0.04
ViewFactors: View factors computed in time (s): 57.16 58.09
ViewFactors:
ViewFactors: Viewfactors before manipulation:
ViewFactors: Minimum row sum: 0.000E+00
ViewFactors: Maximum row sum: 6.985E-01
ViewFactors: Symmetrizing Factors...
ViewFactors: View factors manipulated in time (s): 4.42
ViewFactors:
ViewFactors: Viewfactors after manipulation:
ViewFactors: Minimum row sum: 0.000E+00
ViewFactors: Maximum row sum: 6.985E-01
WARNING:: ViewFactors: Rowsum of view factors should not be smaller than one!
Killed
ERROR:: systemc: Command exit status was 137
RadiationFactors: Message
RadiationFactors: All done time (s) 8.E-02
RadiationFactors: ----------------------------------------------------
OptimizeBandwidth: ---------------------------------------------------------
OptimizeBandwidth: Computing matrix structure for: heat equation...done.
OptimizeBandwidth: Half bandwidth without optimization:
OptimizeBandwidth:
OptimizeBandwidth: Bandwidth Optimization ...done.
OptimizeBandwidth: Half bandwidth after optimization: 162
OptimizeBandwidth: ---------------------------------------------------------
ElmerSolver: Number of timesteps to be saved: 1
MAIN:
MAIN: -------------------------------------
MAIN: Steady state iteration: 1
MAIN: -------------------------------------
MAIN:
HeatSolver: Solving the energy equation for temperature
HeatSolve:
HeatSolve:
HeatSolve: -------------------------------------
HeatSolve: TEMPERATURE ITERATION 1
HeatSolve: -------------------------------------
HeatSolve:
HeatSolve: Starting Assembly...
HeatSolve: Assembly:
ERROR:: ElementMetric: Degenerate 3D element:
ElementMetric: Body Id: 1 DetG: 0.000E+00
ElementMetric: Node: 1 Coord: -3.071E+01 -1.194E+01 3.750E-01
ElementMetric: Node: 2 Coord: -2.985E+01 -1.275E+01 0.000E+00
ElementMetric: Node: 3 Coord: -3.071E+01 -1.194E+01 0.000E+00
ElementMetric: Node: 4 Coord: -2.985E+01 -1.275E+01 3.750E-01
ElementMetric: Node: 2 dCoord: 8.634E-01 -8.031E-01 -3.750E-01
ElementMetric: Node: 3 dCoord: 0.000E+00 0.000E+00 -3.750E-01
ElementMetric: Node: 4 dCoord: 8.634E-01 -8.031E-01 0.000E+00
ERROR:: ElementMetric: Degenerate 3D element:
ElementMetric: Body Id: 1 DetG: 0.000E+00
ElementMetric: Node: 1 Coord: -3.071E+01 -1.194E+01 3.750E-01
ElementMetric: Node: 2 Coord: -2.985E+01 -1.275E+01 0.000E+00
ElementMetric: Node: 3 Coord: -3.071E+01 -1.194E+01 0.000E+00
ElementMetric: Node: 4 Coord: -2.985E+01 -1.275E+01 3.750E-01
ElementMetric: Node: 2 dCoord: 8.634E-01 -8.031E-01 -3.750E-01
ElementMetric: Node: 3 dCoord: 0.000E+00 0.000E+00 -3.750E-01
ElementMetric: Node: 4 dCoord: 8.634E-01 -8.031E-01 0.000E+00
ERROR:: ElementMetric: Degenerate 3D element:
ElementMetric: Body Id: 1 DetG: 0.000E+00
ElementMetric: Node: 1 Coord: -3.071E+01 -1.194E+01 3.750E-01
ElementMetric: Node: 2 Coord: -2.985E+01 -1.275E+01 0.000E+00
ElementMetric: Node: 3 Coord: -3.071E+01 -1.194E+01 0.000E+00
ElementMetric: Node: 4 Coord: -2.985E+01 -1.275E+01 3.750E-01
ElementMetric: Node: 2 dCoord: 8.634E-01 -8.031E-01 -3.750E-01
ElementMetric: Node: 3 dCoord: 0.000E+00 0.000E+00 -3.750E-01
ElementMetric: Node: 4 dCoord: 8.634E-01 -8.031E-01 0.000E+00
ERROR:: ElementMetric: Degenerate 3D element:
ElementMetric: Body Id: 1 DetG: 0.000E+00
ElementMetric: Node: 1 Coord: -3.071E+01 -1.194E+01 3.750E-01
ElementMetric: Node: 2 Coord: -2.985E+01 -1.275E+01 0.000E+00
ElementMetric: Node: 3 Coord: -3.071E+01 -1.194E+01 0.000E+00
ElementMetric: Node: 4 Coord: -2.985E+01 -1.275E+01 3.750E-01
ElementMetric: Node: 2 dCoord: 8.634E-01 -8.031E-01 -3.750E-01
ElementMetric: Node: 3 dCoord: 0.000E+00 0.000E+00 -3.750E-01
ElementMetric: Node: 4 dCoord: 8.634E-01 -8.031E-01 0.000E+00
ERROR:: ElementMetric: Degenerate 3D element:
ElementMetric: Body Id: 1 DetG: 0.000E+00
ElementMetric: Node: 1 Coord: -2.392E+01 2.219E+01 0.000E+00
ElementMetric: Node: 2 Coord: -2.279E+01 2.254E+01 0.000E+00
ElementMetric: Node: 3 Coord: -2.279E+01 2.254E+01 3.750E-01
ElementMetric: Node: 4 Coord: -2.392E+01 2.219E+01 3.750E-01
ElementMetric: Node: 2 dCoord: 1.127E+00 3.461E-01 0.000E+00
ElementMetric: Node: 3 dCoord: 1.127E+00 3.461E-01 3.750E-01
ElementMetric: Node: 4 dCoord: 0.000E+00 0.000E+00 3.750E-01
ERROR:: ElementMetric: Degenerate 3D element:
ElementMetric: Body Id: 1 DetG: 0.000E+00
ElementMetric: Node: 1 Coord: -2.392E+01 2.219E+01 0.000E+00
ElementMetric: Node: 2 Coord: -2.279E+01 2.254E+01 0.000E+00
ElementMetric: Node: 3 Coord: -2.279E+01 2.254E+01 3.750E-01
ElementMetric: Node: 4 Coord: -2.392E+01 2.219E+01 3.750E-01
ElementMetric: Node: 2 dCoord: 1.127E+00 3.461E-01 0.000E+00
ElementMetric: Node: 3 dCoord: 1.127E+00 3.461E-01 3.750E-01
ElementMetric: Node: 4 dCoord: 0.000E+00 0.000E+00 3.750E-01
ERROR:: ElementMetric: Degenerate 3D element:
ElementMetric: Body Id: 1 DetG: 0.000E+00
ElementMetric: Node: 1 Coord: -2.392E+01 2.219E+01 0.000E+00
ElementMetric: Node: 2 Coord: -2.279E+01 2.254E+01 0.000E+00
ElementMetric: Node: 3 Coord: -2.279E+01 2.254E+01 3.750E-01
ElementMetric: Node: 4 Coord: -2.392E+01 2.219E+01 3.750E-01
ElementMetric: Node: 2 dCoord: 1.127E+00 3.461E-01 0.000E+00
ElementMetric: Node: 3 dCoord: 1.127E+00 3.461E-01 3.750E-01
ElementMetric: Node: 4 dCoord: 0.000E+00 0.000E+00 3.750E-01
ERROR:: ElementMetric: Degenerate 3D element:
ElementMetric: Body Id: 1 DetG: 0.000E+00
ElementMetric: Node: 1 Coord: -2.392E+01 2.219E+01 0.000E+00
ElementMetric: Node: 2 Coord: -2.279E+01 2.254E+01 0.000E+00
ElementMetric: Node: 3 Coord: -2.279E+01 2.254E+01 3.750E-01
ElementMetric: Node: 4 Coord: -2.392E+01 2.219E+01 3.750E-01
ElementMetric: Node: 2 dCoord: 1.127E+00 3.461E-01 0.000E+00
ElementMetric: Node: 3 dCoord: 1.127E+00 3.461E-01 3.750E-01
ElementMetric: Node: 4 dCoord: 0.000E+00 0.000E+00 3.750E-01
ERROR:: ComputeRadiationLoad: Gebhardt factors not calculated for boundary!
Note: The following floating-point exceptions are signalling: IEEE_UNDERFLOW_FLAG IEEE_DENORMAL
STOP 1

ELMER SOLVER (v 9.0) STARTED AT: /02/07 19:04:37ParCommInit: Initialize #PEs: 1MAIN:MAIN: =============================================================MAIN: ElmerSolver finite element software, Welcome!MAIN: This program is free software licensed under (L)GPLMAIN: Copyright 1st April - , CSC - IT Center for Science Ltd.MAIN: Webpage http://www.csc.fi/elmer , MAIN: Version: 9.0 (Rev: 5d27ebd8, Compiled: -11-26)MAIN: Running one task without MPI parallelization.MAIN: Running with just one thread per task.MAIN: HYPRE library linked in.MAIN: MUMPS library linked in.MAIN: Lua interpreted linked in.MAIN: Zoltan library linked in.MAIN: =============================================================LoadInputFile: Reading only "Run Control" sectionMAIN:MAIN:MAIN: -------------------------------------MAIN: Reading Model: case.sifLoadInputFile: Scanning input file: case.sifLoadInputFile: Scanning only size infoLoadInputFile: First time visitingLoadInputFile: Reading base load of sif fileLoadInputFile: Loading input file: case.sifLoadInputFile: Reading base load of sif fileLoadInputFile: Number of BCs: 2LoadInputFile: Number of Body Forces: 0LoadInputFile: Number of Initial Conditions: 1LoadInputFile: Number of Materials: 2LoadInputFile: Number of Equations: 1LoadInputFile: Number of Solvers: 1LoadInputFile: Number of Bodies: 2ElmerAsciiMesh: Base mesh name: ./.LoadMesh: Elapsed REAL time: 0. (s)MAIN: -------------------------------------AddVtuOutputSolverHack: Adding ResultOutputSolver to write VTU output in file: caseRadiationFactors: ----------------------------------------------------RadiationFactors: Computing radiation factors for heat transferRadiationFactors: ----------------------------------------------------RadiationFactors: Total number of Radiation Surfaces out of ViewFactors:ViewFactors: ==================================================ViewFactors: E L M E R V I E W F A C T O R S, W E L C O M EViewFactors: ==================================================ViewFactors:ViewFactors:ViewFactors: Reading Model...LoadInputFile: Scanning input file: case.sifLoadInputFile: Scanning only size infoLoadInputFile: First time visitingLoadInputFile: Reading base load of sif fileLoadInputFile: Loading input file: case.sifLoadInputFile: Reading base load of sif fileLoadInputFile: Number of BCs: 2LoadInputFile: Number of Body Forces: 0LoadInputFile: Number of Initial Conditions: 1LoadInputFile: Number of Materials: 2LoadInputFile: Number of Equations: 1LoadInputFile: Number of Solvers: 1LoadInputFile: Number of Bodies: 2ElmerAsciiMesh: Base mesh name: ./.LoadMesh: Elapsed REAL time: 0. (s)ViewFactors: Computing view factors for radiation body 1ViewFactors: Number of surfaces participating in radiation: ViewFactors: Computing viewfactors...surfs: , min(407)=0.00, max()=0.70, avg=0.04ViewFactors: View factors computed in time (s): 57.16 58.09ViewFactors:ViewFactors: Viewfactors before manipulation:ViewFactors: Minimum row sum: 0.000E+00ViewFactors: Maximum row sum: 6.985E-01ViewFactors: Symmetrizing Factors...ViewFactors: View factors manipulated in time (s): 4.42ViewFactors:ViewFactors: Viewfactors after manipulation:ViewFactors: Minimum row sum: 0.000E+00ViewFactors: Maximum row sum: 6.985E-01WARNING:: ViewFactors: Rowsum of view factors should not be smaller than one!KilledERROR:: systemc: Command exit status was 137RadiationFactors: MessageRadiationFactors: All done time (s) 8.E-02RadiationFactors: ----------------------------------------------------OptimizeBandwidth: ---------------------------------------------------------OptimizeBandwidth: Computing matrix structure for: heat equation...done.OptimizeBandwidth: Half bandwidth without optimization: OptimizeBandwidth:OptimizeBandwidth: Bandwidth Optimization ...done.OptimizeBandwidth: Half bandwidth after optimization: 162OptimizeBandwidth: ---------------------------------------------------------ElmerSolver: Number of timesteps to be saved: 1MAIN:MAIN: -------------------------------------MAIN: Steady state iteration: 1MAIN: -------------------------------------MAIN:HeatSolver: Solving the energy equation for temperatureHeatSolve:HeatSolve:HeatSolve: -------------------------------------HeatSolve: TEMPERATURE ITERATION 1HeatSolve: -------------------------------------HeatSolve:HeatSolve: Starting Assembly...HeatSolve: Assembly:ERROR:: ElementMetric: Degenerate 3D element: ElementMetric: Body Id: 1 DetG: 0.000E+00ElementMetric: Node: 1 Coord: -3.071E+01 -1.194E+01 3.750E-01ElementMetric: Node: 2 Coord: -2.985E+01 -1.275E+01 0.000E+00ElementMetric: Node: 3 Coord: -3.071E+01 -1.194E+01 0.000E+00ElementMetric: Node: 4 Coord: -2.985E+01 -1.275E+01 3.750E-01ElementMetric: Node: 2 dCoord: 8.634E-01 -8.031E-01 -3.750E-01ElementMetric: Node: 3 dCoord: 0.000E+00 0.000E+00 -3.750E-01ElementMetric: Node: 4 dCoord: 8.634E-01 -8.031E-01 0.000E+00ERROR:: ElementMetric: Degenerate 3D element: ElementMetric: Body Id: 1 DetG: 0.000E+00ElementMetric: Node: 1 Coord: -3.071E+01 -1.194E+01 3.750E-01ElementMetric: Node: 2 Coord: -2.985E+01 -1.275E+01 0.000E+00ElementMetric: Node: 3 Coord: -3.071E+01 -1.194E+01 0.000E+00ElementMetric: Node: 4 Coord: -2.985E+01 -1.275E+01 3.750E-01ElementMetric: Node: 2 dCoord: 8.634E-01 -8.031E-01 -3.750E-01ElementMetric: Node: 3 dCoord: 0.000E+00 0.000E+00 -3.750E-01ElementMetric: Node: 4 dCoord: 8.634E-01 -8.031E-01 0.000E+00ERROR:: ElementMetric: Degenerate 3D element: ElementMetric: Body Id: 1 DetG: 0.000E+00ElementMetric: Node: 1 Coord: -3.071E+01 -1.194E+01 3.750E-01ElementMetric: Node: 2 Coord: -2.985E+01 -1.275E+01 0.000E+00ElementMetric: Node: 3 Coord: -3.071E+01 -1.194E+01 0.000E+00ElementMetric: Node: 4 Coord: -2.985E+01 -1.275E+01 3.750E-01ElementMetric: Node: 2 dCoord: 8.634E-01 -8.031E-01 -3.750E-01ElementMetric: Node: 3 dCoord: 0.000E+00 0.000E+00 -3.750E-01ElementMetric: Node: 4 dCoord: 8.634E-01 -8.031E-01 0.000E+00ERROR:: ElementMetric: Degenerate 3D element: ElementMetric: Body Id: 1 DetG: 0.000E+00ElementMetric: Node: 1 Coord: -3.071E+01 -1.194E+01 3.750E-01ElementMetric: Node: 2 Coord: -2.985E+01 -1.275E+01 0.000E+00ElementMetric: Node: 3 Coord: -3.071E+01 -1.194E+01 0.000E+00ElementMetric: Node: 4 Coord: -2.985E+01 -1.275E+01 3.750E-01ElementMetric: Node: 2 dCoord: 8.634E-01 -8.031E-01 -3.750E-01ElementMetric: Node: 3 dCoord: 0.000E+00 0.000E+00 -3.750E-01ElementMetric: Node: 4 dCoord: 8.634E-01 -8.031E-01 0.000E+00ERROR:: ElementMetric: Degenerate 3D element: ElementMetric: Body Id: 1 DetG: 0.000E+00ElementMetric: Node: 1 Coord: -2.392E+01 2.219E+01 0.000E+00ElementMetric: Node: 2 Coord: -2.279E+01 2.254E+01 0.000E+00ElementMetric: Node: 3 Coord: -2.279E+01 2.254E+01 3.750E-01ElementMetric: Node: 4 Coord: -2.392E+01 2.219E+01 3.750E-01ElementMetric: Node: 2 dCoord: 1.127E+00 3.461E-01 0.000E+00ElementMetric: Node: 3 dCoord: 1.127E+00 3.461E-01 3.750E-01ElementMetric: Node: 4 dCoord: 0.000E+00 0.000E+00 3.750E-01ERROR:: ElementMetric: Degenerate 3D element: ElementMetric: Body Id: 1 DetG: 0.000E+00ElementMetric: Node: 1 Coord: -2.392E+01 2.219E+01 0.000E+00ElementMetric: Node: 2 Coord: -2.279E+01 2.254E+01 0.000E+00ElementMetric: Node: 3 Coord: -2.279E+01 2.254E+01 3.750E-01ElementMetric: Node: 4 Coord: -2.392E+01 2.219E+01 3.750E-01ElementMetric: Node: 2 dCoord: 1.127E+00 3.461E-01 0.000E+00ElementMetric: Node: 3 dCoord: 1.127E+00 3.461E-01 3.750E-01ElementMetric: Node: 4 dCoord: 0.000E+00 0.000E+00 3.750E-01ERROR:: ElementMetric: Degenerate 3D element: ElementMetric: Body Id: 1 DetG: 0.000E+00ElementMetric: Node: 1 Coord: -2.392E+01 2.219E+01 0.000E+00ElementMetric: Node: 2 Coord: -2.279E+01 2.254E+01 0.000E+00ElementMetric: Node: 3 Coord: -2.279E+01 2.254E+01 3.750E-01ElementMetric: Node: 4 Coord: -2.392E+01 2.219E+01 3.750E-01ElementMetric: Node: 2 dCoord: 1.127E+00 3.461E-01 0.000E+00ElementMetric: Node: 3 dCoord: 1.127E+00 3.461E-01 3.750E-01ElementMetric: Node: 4 dCoord: 0.000E+00 0.000E+00 3.750E-01ERROR:: ElementMetric: Degenerate 3D element: ElementMetric: Body Id: 1 DetG: 0.000E+00ElementMetric: Node: 1 Coord: -2.392E+01 2.219E+01 0.000E+00ElementMetric: Node: 2 Coord: -2.279E+01 2.254E+01 0.000E+00ElementMetric: Node: 3 Coord: -2.279E+01 2.254E+01 3.750E-01ElementMetric: Node: 4 Coord: -2.392E+01 2.219E+01 3.750E-01ElementMetric: Node: 2 dCoord: 1.127E+00 3.461E-01 0.000E+00ElementMetric: Node: 3 dCoord: 1.127E+00 3.461E-01 3.750E-01ElementMetric: Node: 4 dCoord: 0.000E+00 0.000E+00 3.750E-01ERROR:: ComputeRadiationLoad: Gebhardt factors not calculated for boundary!Note: The following floating-point exceptions are signalling: IEEE_UNDERFLOW_FLAG IEEE_DENORMALSTOP 1

If i use cyllinders with less radius than before, the solver log looks like this.

ParCommInit: Initialize #PEs: 1
MAIN:
MAIN: =============================================================
MAIN: ElmerSolver finite element software, Welcome!
MAIN: This program is free software licensed under (L)GPL
MAIN: Copyright 1st April - , CSC - IT Center for Science Ltd.
MAIN: Webpage
MAIN: Version: 9.0 (Rev: 5d27ebd8, Compiled: -11-26)
MAIN: Running one task without MPI parallelization.
MAIN: Running with just one thread per task.
MAIN: HYPRE library linked in.
MAIN: MUMPS library linked in.
MAIN: Lua interpreted linked in.
MAIN: Zoltan library linked in.
MAIN: =============================================================
LoadInputFile: Reading only "Run Control" section
MAIN:
MAIN:
MAIN: -------------------------------------
MAIN: Reading Model: case.sif
LoadInputFile: Scanning input file: case.sif
LoadInputFile: Scanning only size info
LoadInputFile: First time visiting
LoadInputFile: Reading base load of sif file
LoadInputFile: Loading input file: case.sif
LoadInputFile: Reading base load of sif file
LoadInputFile: Number of BCs: 2
LoadInputFile: Number of Body Forces: 0
LoadInputFile: Number of Initial Conditions: 1
LoadInputFile: Number of Materials: 2
LoadInputFile: Number of Equations: 1
LoadInputFile: Number of Solvers: 1
LoadInputFile: Number of Bodies: 6
ElmerAsciiMesh: Base mesh name: ./.
LoadMesh: Elapsed REAL time: 0. (s)
MAIN: -------------------------------------
AddVtuOutputSolverHack: Adding ResultOutputSolver to write VTU output in file: case
RadiationFactors: ----------------------------------------------------
RadiationFactors: Computing radiation factors for heat transfer
RadiationFactors: ----------------------------------------------------
RadiationFactors: Total number of Radiation Surfaces out of
ViewFactors:
ViewFactors: ==================================================
ViewFactors: E L M E R V I E W F A C T O R S, W E L C O M E
ViewFactors: ==================================================
ViewFactors:
ViewFactors:
ViewFactors: Reading Model...
LoadInputFile: Scanning input file: case.sif
LoadInputFile: Scanning only size info
LoadInputFile: First time visiting
LoadInputFile: Reading base load of sif file
LoadInputFile: Loading input file: case.sif
LoadInputFile: Reading base load of sif file
LoadInputFile: Number of BCs: 2
LoadInputFile: Number of Body Forces: 0
LoadInputFile: Number of Initial Conditions: 1
LoadInputFile: Number of Materials: 2
LoadInputFile: Number of Equations: 1
LoadInputFile: Number of Solvers: 1
LoadInputFile: Number of Bodies: 6
ElmerAsciiMesh: Base mesh name: ./.
LoadMesh: Elapsed REAL time: 0. (s)
ViewFactors: Computing view factors for radiation body 1
ViewFactors: Number of surfaces participating in radiation:
ViewFactors: Computing viewfactors...
Killed
ERROR:: systemc: Command exit status was 137
RadiationFactors: Message
RadiationFactors: All done time (s) 6.E-02
RadiationFactors: ----------------------------------------------------
OptimizeBandwidth: ---------------------------------------------------------
OptimizeBandwidth: Computing matrix structure for: heat equation...done.
OptimizeBandwidth: Half bandwidth without optimization:
OptimizeBandwidth:
OptimizeBandwidth: Bandwidth Optimization ...done.
OptimizeBandwidth: Half bandwidth after optimization: 188
OptimizeBandwidth: ---------------------------------------------------------
ElmerSolver: Number of timesteps to be saved: 1
MAIN:
MAIN: -------------------------------------
MAIN: Steady state iteration: 1
MAIN: -------------------------------------
MAIN:
HeatSolver: Solving the energy equation for temperature
HeatSolve:
HeatSolve:
HeatSolve: -------------------------------------
HeatSolve: TEMPERATURE ITERATION 1
HeatSolve: -------------------------------------
HeatSolve:
HeatSolve: Starting Assembly...
HeatSolve: Assembly:
ERROR:: ComputeRadiationLoad: Gebhardt factors not calculated for boundary!
STOP 1

ELMER SOLVER (v 9.0) STARTED AT: /02/07 19:10:01ParCommInit: Initialize #PEs: 1MAIN:MAIN: =============================================================MAIN: ElmerSolver finite element software, Welcome!MAIN: This program is free software licensed under (L)GPLMAIN: Copyright 1st April - , CSC - IT Center for Science Ltd.MAIN: Webpage http://www.csc.fi/elmer , MAIN: Version: 9.0 (Rev: 5d27ebd8, Compiled: -11-26)MAIN: Running one task without MPI parallelization.MAIN: Running with just one thread per task.MAIN: HYPRE library linked in.MAIN: MUMPS library linked in.MAIN: Lua interpreted linked in.MAIN: Zoltan library linked in.MAIN: =============================================================LoadInputFile: Reading only "Run Control" sectionMAIN:MAIN:MAIN: -------------------------------------MAIN: Reading Model: case.sifLoadInputFile: Scanning input file: case.sifLoadInputFile: Scanning only size infoLoadInputFile: First time visitingLoadInputFile: Reading base load of sif fileLoadInputFile: Loading input file: case.sifLoadInputFile: Reading base load of sif fileLoadInputFile: Number of BCs: 2LoadInputFile: Number of Body Forces: 0LoadInputFile: Number of Initial Conditions: 1LoadInputFile: Number of Materials: 2LoadInputFile: Number of Equations: 1LoadInputFile: Number of Solvers: 1LoadInputFile: Number of Bodies: 6ElmerAsciiMesh: Base mesh name: ./.LoadMesh: Elapsed REAL time: 0. (s)MAIN: -------------------------------------AddVtuOutputSolverHack: Adding ResultOutputSolver to write VTU output in file: caseRadiationFactors: ----------------------------------------------------RadiationFactors: Computing radiation factors for heat transferRadiationFactors: ----------------------------------------------------RadiationFactors: Total number of Radiation Surfaces out of ViewFactors:ViewFactors: ==================================================ViewFactors: E L M E R V I E W F A C T O R S, W E L C O M EViewFactors: ==================================================ViewFactors:ViewFactors:ViewFactors: Reading Model...LoadInputFile: Scanning input file: case.sifLoadInputFile: Scanning only size infoLoadInputFile: First time visitingLoadInputFile: Reading base load of sif fileLoadInputFile: Loading input file: case.sifLoadInputFile: Reading base load of sif fileLoadInputFile: Number of BCs: 2LoadInputFile: Number of Body Forces: 0LoadInputFile: Number of Initial Conditions: 1LoadInputFile: Number of Materials: 2LoadInputFile: Number of Equations: 1LoadInputFile: Number of Solvers: 1LoadInputFile: Number of Bodies: 6ElmerAsciiMesh: Base mesh name: ./.LoadMesh: Elapsed REAL time: 0. (s)ViewFactors: Computing view factors for radiation body 1ViewFactors: Number of surfaces participating in radiation: ViewFactors: Computing viewfactors...KilledERROR:: systemc: Command exit status was 137RadiationFactors: MessageRadiationFactors: All done time (s) 6.E-02RadiationFactors: ----------------------------------------------------OptimizeBandwidth: ---------------------------------------------------------OptimizeBandwidth: Computing matrix structure for: heat equation...done.OptimizeBandwidth: Half bandwidth without optimization: OptimizeBandwidth:OptimizeBandwidth: Bandwidth Optimization ...done.OptimizeBandwidth: Half bandwidth after optimization: 188OptimizeBandwidth: ---------------------------------------------------------ElmerSolver: Number of timesteps to be saved: 1MAIN:MAIN: -------------------------------------MAIN: Steady state iteration: 1MAIN: -------------------------------------MAIN:HeatSolver: Solving the energy equation for temperatureHeatSolve:HeatSolve:HeatSolve: -------------------------------------HeatSolve: TEMPERATURE ITERATION 1HeatSolve: -------------------------------------HeatSolve:HeatSolve: Starting Assembly...HeatSolve: Assembly:ERROR:: ComputeRadiationLoad: Gebhardt factors not calculated for boundary!STOP 1

Are there options I have to adjust in order to be able to handle finer meshes? Or do you see where else I went wrong?

Hello everybody,I am trying to simulate heating through radiation in 3D and, working on the VM, with rather coarse grids I got satisfying results(I attached a picture).The next step now was to make the grid finer, in order to hopefully design a new heater in the future.I made the models with FreeCad and then meshes them with gmsh, now however with a element size factor of 0.1 instead of 1, like before.Elmer shows the model as expected, and i can apply all equation, boundary-conditions etc. like before. If I start the solver now however I can following errors:If i use a heating ring, the solver log looks like this:If i use cyllinders with less radius than before, the solver log looks like this.Are there options I have to adjust in order to be able to handle finer meshes? Or do you see where else I went wrong?

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