Whenever possible, start with a simplified model (back to the top)
The simplified model can give some useful insights into both physical and computational aspects of the model. Once the simplified model is working, it can be easier to create the full model. Here are some examples:
Take care of geometry details (back to the top)
Include only the details that are necessary to create an accurate model. Small features and sharp corners require the most attention.
Small features can lead to very fine meshes, thus increasing computation times and memory requirements. If these fine features are not critical to the problem at hand then they should be omitted.
Sharp corners lead to (a) field singularities and (b) very fine meshes if automatic mesh refinement is used. Field singularities manifest themselves in large field values at the corners. These values are not physical because real corners are never infinitely sharp, so the model results must interpreted carefully with the understanding of field behavior at sharp corners. Of course, field singularity problems can be mitigated by rounding the sharp corners; however, rounding the corners leads to the fine-mesh issues associated with small features.
Sharp corners can be retained in a model, and they can be meshed coarsely if they do not influence the field solutions in the region of interest; otherwise, it is better to round the corners in order to create more realistic models.
Take care of proper geometrical extent of unbounded models (back to the top)
Unbounded problems are handled differently by different numerical methods. MoM easily deals with unbounded regions, and the fields can be calculated anywhere in space during post-processing of the results. FDTD and FEM methods require space-truncation techniques like perfectly-matched layers (PMLs) or conformal transformations. The extent of the modeling space will influence the accuracy of the results, so it is advisable to conduct a study that determines the best trade-off between accuracy and mesh size.
Ensure proper mesh resolution (back to the top)
Proper mesh resolution is required in order to achieve desired accuracy. For wave propagation models there is a minimum resolution requirement of about 8 elements or nodes per wavelength. For lossy conductors skin depth must be adequately resolved. These requirements can impose practical limitations on mesh size for volume-based numerical methods.
The other major consideration for adequate mesh resolution is accuracy. The model should be meshed in such a way as to find a balance between mesh size and model accuracy. Such balance is found through a convergence study of accuracy vs. mesh size.
Understand model's critical parts and ensure proper meshing (back to the top)
Identify regions that have the greatest influence on the accuracy of the model. Sometimes such regions are quite apparent, other times they are discovered during the process of model creation. Always make sure that the critical regions have sufficiently fine mesh to ensure desired accuracy. Regions with skin effects or evanescent waves can lead to considerable numerical challenges because they may require meshing that is much finer than is needed for the rest of the model.
Partition geometry for better meshing control (back to the top)
Automatic meshing features greatly simplify the meshing of the models. However, sometimes resulting meshes are of poor quality due to complicated geometries. Of course, it is possible to mesh the model manually, but the process can be lengthy, especially if the model has to be remeshed several times due to geometry changes or due to other requirements. In the alternative, it is possible to subdivide the geometry into partitions that may not be necessary from the geometry standpoint, but are very beneficial from the automatic meshing standpoint.
Avoid geometries that lead to poor mesh quality (back to the top)
Certain geometric features can lead to poor-quality meshes and should be avoided. For example, a sphere resting on a flat surface can lead to meshing problems because the angle at the point of contact approaches zero. As a rule, elements with greatly disproportionate side-length ratios and with very small internal angles are poor quality elements. The resulting systems of linear equations can be ill-conditioned, and the solutions may not converge. When creating your geometry try to avoid creating long and narrow regions or regions with very sharp internal angles.
Define required accuracy and understand convergence (back to the top)
Model accuracy is an often-ignored issue, but it is, of course, very important. Model accuracy is frequently limited by the practical limitations of computer hardware, so if a model reaches the limits of the hardware, it is no longer possible to improve its accuracy. However, it is useful to estimate how close is any given model to a converged solution. Performing convergence studies is an important aspect of numerical simulations and should be performed for every model in order to estimate its accuracy.
Appropriately choose finesse and brute force approaches (back to the top)
The brute-force approach of automesh-and-run is a quick way to get results. It provides an immediate insight into the nature of the solutions without having to spend a lot of time on finessing the mesh. In fact, if the solution is valid and accurate, the brute-force approach is the only required approach. However, further mesh refinement may be necessary to improve the accuracy of the results or to reduce execution time.
It is important to find a balance between the time needed to finesse the mesh to an optimum and the time needed to execute a model that has been meshed finer than necessary. For example, 2D or 2D-axisymmetric models typically have fast execution times, so it may not be necessary to spend a lot of time on creating a mesh that minimizes execution time while maintaining required accuracy. A very fine mesh that leads to greater-than-required accuracy is acceptable. On the other hand, 3D models can quickly overwhelm even the most powerful hardware systems. Consequently, for fixed hardware resources, it often pays of to spend significant amount of time on finessing and refining the mesh in order to obtain accurate results.
Images made using COMSOL Multiphysics® and are provided courtesy of COMSOL®
Electromagnetics and Multiphysics
Modeling and Simulation
Creating an accurate electromagnetics model requires understanding of
both electromagnetic principles and numerical methods. Scroll down to find some tips that can help.
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