Vertex-Ball Spring Smoothing: An efficient method for unstructured dynamic hybrid meshes

Spring analogy approach is one of the most popular dynamic mesh deformation methods. In the ball-vertex method, perpendicular linear springs are introduced to deal with the element collapse problem. However, it is not very efficient as a large system of linear equations has to be resolved. In order to overcome this difficulty, the Vertex-Ball Spring Smoothing algorithm (VerBSS) is proposed in this paper. Following the mesh smoothing concept, a sub-spring system derived from the “ball-vertex” model is built and solved on a node by node basis using an LDLT solver. Interior nodes are smoothed layer by layer in an iterative manner to achieve the best result. Parallel scheme is also introduced in the smoothing process for further improvement of the efficiency. Numerical examples in two and three dimensions show that VerBSS is much more efficient than the ball-vertex method, and is capable of dealing with practical engineering objects with complex geometries subject to large deformations. VerBSS can be applied to complicated mesh topologies as well, not only to 2D/3D dynamic mesh, but also to the hybrid dynamic mesh.