In using the 3D Amaze programs, the ever-present question is how to choose element sizes. The choice depends on the nature of the application, so there is no simple formula. Building a good mesh is an art, requiring experience and insight. I am acutely aware of the problem when I receive tech-help requests with user-prepared input files. Invariably, the meshes contain too many elements. The examples may take hours to run, so I have to adjust the dimensions to have any hope of detecting the trouble. I suspect there are two reasons for the large meshes:
- The user isn't sure how to pick a size and uses small elements for safety.
- Having bought an expensive computer and high-powered 3D software, the user feels compelled to create BIG solutions.
In this post, I will offer some guidelines for setting mesh resolution. As the prime directive, I suggest the old-fashioned goal of computational elegance. Virtue lies in achieving the required accuracy with the minimum number of elements and the shortest run time. A 4-hour run should not be a source of pride.
Here are some suggestions for improving calculations:
- When you approach a new problem, use a relatively coarse mesh for a fast turn-around. This way, you can quickly detect errors and non-optimal parameter choices. Furthermore, the initial solution provides a basis of comparison for production runs with smaller elements.
- Remember that the purpose of a conformal mesh is to achieve accuracy with fewer elements.
- Use symmetry boundaries whenever possible.
- Don't waste time making accurate models of parts that are far from critical regions of interest. Don't include parts if they have little affect on the solution.
The underlying issue is how do you know if the solution is accurate enough with a given choice of element size? Here are some ways to improve your modeling judgment:
- Inspect the mesh choices we have made in the example libraries. All examples have been carefully constructed to provide good accuracy and to run quickly.
- If you throw a large number of elements at every problem, you won't learn anything. Set aside some time to model a system where you know the answer from theory (i.e., concentric spherical electrodes, long solenoid,...). Experiment with conformal and non-conformal meshes and with different element sizes. Get a sense of how the mesh affects the field calculation.
- If you have a solution and you are worried that the elements are too large, make a comparison solution with smaller elements to see if there is a significant change.
In summary, we should break the mindset of feverishly piling on elements like sandbags before a swelling river. Try to view a field solution as a puzzle, where the winner arrives at the goal in the minimum number of steps.
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