The following are approximate relations between the number of nodes and the number of elements in 2D and 3D for Lagrange elements of different order. Additional background information on the degrees of freedom in a model can be found in the blog post that discusses how much memory is needed to solve large models, under the section of text explaining what degrees of freedom are. ![]() For thin geometries, where a large proportion of the elements lie on the boundary, the number of nodes per element is a bit higher. The relation is only approximate, since it depends on the ratio of the elements that lie on the boundary of the geometry. The relation between the number of nodes and the number of elements depends on the order of the elements and differs between 2D and 3D. This means that the number of degrees of freedom is given by the number of nodes multiplied by the number of dependent variables. It is often desirable to be able to estimate the number of degrees of freedom based on the number of elements in the model.įor most physics interfaces, each dependent variable is present in all nodes in the mesh. The solution time and memory requirements to compute a model are strongly related to the number of degrees of freedom in the model. What Does Degrees of Freedom Mean in COMSOL Multiphysics ®? ![]() In this article, we explain the importance of the degrees of freedom for a model and how to estimate the number of degrees of freedom. In the COMSOL Multiphysics ® software, the number of degrees of freedom (DOFs) in a model have a significant correlation to, and effect on, the computation of a model. How to Estimate the Number of Degrees of Freedom in a Model
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