13 Notes on modeling errors
"... Under no circumstances does a competent microwave designer assume that the results of an EM analysis (or of a measurement) are correct. They do not even assume that the results might be wrong. The competent designer assumes the results are in fact wrong, and takes on the job of estimating by just how much the results are wrong..."
James C. Rautio
Microwave De-embedding, 2014
In every computer simulation of physical phenomena, we construct the mathematical model of that phenomena that aims to be as close to the reality as possible. It is still only an approximation. One needs to remember that the outcome of a computer simulation is strongly dependent on the model that was used, its properties and the solution techniques. Therefore, the user should always verify the simulation results and try to estimate how far from reality they might be.
There are several types of errors that influence the outcome of the simulation that a competent user should be aware of [5], two of them are:
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• Limitations of mathematical models. While the Maxwell equations are a proper description of electromagnetic wave interaction with matter (at least when quantum effects are not included), the models are derived from those equations with some assumptions than you should be aware of. For example, radiation boundary conditions, or lossy conductor boundary conditions, are just approximations of real-life phenomena and have to be used with care. The recommended solution is to validate the mathematical model with prototype measurements.
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• Discretization. When solving the electromagnetic problem with FEM, the fields inside the domain are approximated using base functions. The number of base functions used (or mesh density) strongly influences the results of simulation and it is model dependent. In theory, when the mesh is refined, the results should converge to a "real" solution. In reality, it is hard to determine if the current mesh is dense enough. Therefore, even the application of adaptive mesh refinement does not guarantee the convergence of the solution.
However, errors of the simulation are not the only problem that can be encountered. Even if the simulation is exact, there is still a risk of encountering manufacturing tolerance errors when manufacturing the device. The resulting prototype would then be slightly different from the computer model. Therefore, you should always look for the compromise between simulation accuracy and manufacturing accuracy during the design phase.