Further specifications of the model
For all points of the model, their coordinates in the initial configuration constitutes their initial condition. It is further assumed that all initial velocities and accelerations are zero. Apart from this specification of initial conditions, for a large number of nodes, additional conditions for their movements must be imposed. Since it is assumed that the model is symmetric, all points that are on the midsagittal plane are constrained to live in this plane. So their degree of freedom is only 2 while the x-coordinates of these points is fixed. Another surface area is the connection of the mandible to the model, shown in white in the figure below. All points on this surface move according to a rigid model of the mandible, which is currently only a static position, and will later be a model with two degrees of freedom (pivot of the mandible and sliding along the condile).
In this figure, the white surface represents the rigid contact with the mandible bone, and all nodes on this surface move according to the rigid body movements of the mandible. The magenta and yellow surfaces are contact areas. The tongue body underside (magenta) may or may not come in contact with the yellow surface that corresponds roughly to the surface of the floor of the mouth. Of course, this is a drastical simplification.
Another set of constraint nodes are the nodes that move according to the rigid body movements of the hyoid bone. I made a simple cludge here: The right thing to do would have been to generate the mesh of the model so that its surface follows accurately the surface of the hyoid bone, similar to how it was done with the mandible. However, this would require a much higher spatial resolution in the vicinity of the hyoid bone than is actually used. Instead, I chose to just specify fixed conditions for a few nodes that are inside or near the volume of the hyoid bone. The are shown in the figure below:
Only the lower part of the mesh here is shown without surfaces. The tip of the tongue is to the right and up. The bright region, which is completely embedded in the model, is the hyoid bone seen from the back and below. The blue nodes shown (and a few more hidden by the surfaces of the hyoidbone model) are moving according to the rigid body movements of the hyoid bone. This means that all their coordinates are defined by the translational and rotational degrees of freedom of the hyoid bone.
Node reordering.
From a mathematical point of view, the order of elements and nodes is rather irrelevant. However, for better computational behavior and other more esthetical reasons, a "nice" order of the nodes has advantages. The so-called reverse Cuthill-McKee algorithm (e.g, Cuthill, E., McKee, J: Reducing the bandwidth of sparse symmetric matrices. In Proc. ACM Nat Conf New York 1969, 157-172) was utilized to make the arbitrary order of the nodes more adhere to the neighboring relations between nodes. The one main neighborhood relation between nodes that was used is that nodes are neighbored if they belong to the same element. That's certainly simple. So, a large sparse matrix was put together that contains a one for each pair of nodes that are in the same element and is zero otherwise. Using Matlab's subroutine symrcm, a permutation of the nodes was obtained. This sheme was applied iteratively in the hope to achieve a slightly better result than with just one iteration. The result is shown in the figure below, in which the sequence of nodes is illustrated by the seuqence of the colors of the rainbow from red to blue. The matrix containing the 1's and 0's for nodes being neighbors or not is shown next to it.
The neigborhood matrix (right) shows a half-bandwidth of about 500, and it can be seen in the rainbow picture that the node numbers are lowest at the tip of the tongue and highest at near the hyoid bone. That's the way I wanted it.
Sure, with some small or bigger efford one might get even a lower bandwidth, but I must say I really don't care about this aspect until I get into building a model with a much higher spatial resolution and many more nodes. The bandwidth that can be achieved depends anyways mosty on the geometrical compactness of the model. It's easy to have small bandwidth for long skinny objects, but not for fat short ones. The tongue is probably more one of the second kind.