Visualization and Filters

In elasticity problems one often wants to see the material stress, which is obtained by a formula that combines the derivatives of the two displacement components. Hermes implements postprocessing through Filters. Filter is a special class which takes up to three Solutions, performs some computation and in the end acts as another Solution (which can be visualized, passed into another Filter, passed into a weak form, etc.). More advanced usage of Filters will be discussed later. In elasticity examples we typically use the predefined VonMisesFilter:

VonMisesFilter stress(Tuple<MeshFunction*>(u_sln, v_sln), lambda, mu);
view.show_mesh(false);
view.show(&stress, HERMES_EPS_HIGH);

Flags HERMES_EPS_LOW, HERMES_EPS_NORMAL, and HERMES_EPS_HIGH

The second line tells Hermes not to display mesh edges. The second parameter of show() is the visualization accuracy. It can have the values HERMES_EPS_LOW, HERMES_EPS_NORMAL (default) and HERMES_EPS_HIGH. This parameter influences the number of linear triangles that Hermes uses to approximate higher-order polynomial solutions within finite elements. Using linear triangles is required by OpenGL, so Hermes at least performs automatic adaptivity to reduce their number to a minimum. The above parameters are used to set the accuracy of this piecewise-linear approximation.

The method show() has an optional third parameter to indicate whether function values or partial derivatives should be displayed. For example, HERMES_FN_VAL_0 stands for the function value of solution component 0 (first solution component which in this case is the VonMises stress). HERMES_FN_VAL_1 would mean the function value of the second solution component (relevant for vector-valued Hcurl or Hdiv elements only), HERMES_FN_DX_0 means the x-derivative of the first solution component, etc.

Visualizing deformed computational domain (in elasticity)

Finally, in elasticity problems it may be desirable to deform the computational domain according to the calculated displacements. The method View::show() has additional three optional parameters for this:

VonMisesFilter stress(Tuple<MeshFunction*>(&u_sln, &v_sln), lambda, mu);
view.show(&stress, HERMES_EPS_HIGH, HERMES_FN_VAL_0, &u_sln, &v_sln, 1.5e5);

Here the fourth and fifth parameters are the displacement components used to distort the domain geometry, and the sixth parameter is a scaling factor to multiply the displacements. Of course, the color map still shows the Von Mises stress as before.