Library for Simulation of Hyper Elastic Materials under Large Deformations using GPU

Master thesis defense by Kasper Steenstrup


With the goal of producing a fast library for simulation of large deformations in hyper elastic material, the raw structure of the material’s mesh is examined and optimized for large scale parallelism, where a strict code setup is used for integration in larger frameworks.

The simulations are derived as a non-linear semi-implicit finite element method using the Cauchy momentum equation, giving the possibility for large time steps, where the stiffness of the material is calculated for each time step. The calculation in the simulation was examined and two different matrix representations were used of the equation, both using the compressed sparse row block matrix method for better cache allocation. For graphics card acceleration, the CUDA, Thrust and CUSP library were studied, and the CUSP library was altered for using the block representation as well. Here, preliminary testing yielded a approximately 3 faster calculation on the host side, but 0.75 slower calculation on the device side. The simulation was examined for parallelism using graphic cards, thus giving three additional versions of the simulation, one for each optimization step. A time comparison of the five versions of the simulation yielded an approximately 200 times faster simulation compared to the first version, giving the possibility of simulating large deformations of material meshes of minimum 47640 tetrahedra in real time. Validation of the simulations showed that the five simulations were identical in their calculation.


Thomas Jakobsen, Havok Copenhagen


Kenny Erleben, DIKU