Speeding up the simulation of deformable objects through mesh improvement

Abstract

We propose a novel mesh optimization approach that is useful for speeding up a simulation of finite elements-based deformable objects. The approach is based on a quality metric derived from the critical simulation time step of explicit time integration schemes (i.e., the stability limit for the integration of dynamic equations). Our mesh smoothing approach consists of a set of small and independent spring systems. These are made up of a reference mesh node connected to a set of fixed endpoints, which represent the positions that maximize the time step of the elements adjacent to that node. The reference node is displaced to an equilibrium position through a few local iterations. Each spring's stiffness is weighted depending on the quality of its corresponding element. All spring systems can be computed in parallel. Global iterations update the mesh and spring systems. In addition, we combine our smoothing algorithm with topological transformations. With this approach, the simulation performance could be increased by more than 30% depending on the mesh. This approach is suitable for the generation of finite element method meshes, particularly those requiring interactive applications and haptic rendering.

A Smoothed Finite Element‐Based Elasticity Model for Soft Bodies

“…The traditional and most promising way to improve mesh quality is the adaptive remeshing. However, remeshing methods are daunting because they involve tedious mesh topology and geometry operations and projections of field variables from the previous mesh [3,4]. Even excellent field variable projection schemes might lead to significant errors in displacements and velocities [5].…”