The Optimesh method locates nodes of an element in such a way as to minimize the energy of deformation of the mesh. This energy of deformation is a function of the angular distortion of the elements, and of the elongation of "springs" located along the segments and diagonals of the mesh (see Figure 16.7: How the Optimesh Remeshing Works). One non-dimensional parameter controls the relative weight of the angular and diagonal springs. When , only angular springs exist, so the relative size of the elements is uncontrolled. A reasonable mesh regularity is usually obtained for , which is the condition used by Ansys Polydata (and cannot be modified). also leads to optimal convergence of the remeshing method.

Figure 16.7: How the Optimesh Remeshing Works

Angular springs are nonlinear, in order to produce an infinite deformation energy when elements become degenerate. This guarantees that the mesh is regular upon convergence of the remeshing method. This also makes the remeshing problem itself nonlinear.