Figure 3: Example of triangular mesh relaxation
Figure 3 shows an example of 2D mesh relaxation. Initial node position is randomly chosen and triangulation is not optimal. After 20 iterations this example converged to stable state with minimal mesh energy. Ratio between minimal and initial energy can be used as mesh improvement indicator.
When generating required connection lengths from node spacing function, element type should be considered to provide consistent lengths and angles. If this is not the case, resulting node positions will always be between initial and desired. Nodes at boundaries are also movable and under constrain of the node spacing function. Angles at boundary corners should be considered in neighbouring nodes.
In our tests, node placement began with placing nodes at boundaries followed by interior node placement. Mixed types of elements has been selected when testing efficiency. Convergence condition (4) can sometimes be lowered resulting faster convergence.