![]() In addition, curve fitting of continuous solution data can be a convenient way to estimate the higher-order spatial derivatives of the solution. (Note that there is no one-size-fits-all strategy for data compaction several other approaches, such as using probe tables and selections, are described in this Knowledge Base entry on reducing the amount of solution data stored in a model). ![]() If we can find a linear combination of functions that gives good agreement with the full solution, then we can communicate much of the information from that full solution just by sharing the values of a few function coefficients. What about curve fitting to the solution data from a previous study in the COMSOL Multiphysics model? One immediate benefit is data compaction. Raw experimental data (black dots) fit to a cubic polynomial (red curve). Furthermore, fitting the discrete data to a smooth function provides access to higher-order derivatives of that function, whereas trying to numerically differentiate the raw data can be very noisy and error prone. For example, if we try to use the raw experimental data to define a material property directly, then the statistical fluctuations in the data can make it more difficult for the solver to converge. In a previous blog post about fitting discrete experimental data, we explained how curve fitting can be useful for the ensuing simulation work. We will then introduce the concept of orthogonality and explain how fitting the solution data to a set of orthogonal functions reduces to a simple and convenient postprocessing operation. In a previous blog post, we explained how to fit discrete empirical data to a curve, but here, we will instead consider the fitting of continuous solution data. ![]() After solving a model in the COMSOL Multiphysics® software, we may want to fit the solution data to a set of functions defined in the simulation domain. ![]()
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