Historically, there have been two approaches to tracking evolving interfaces: Lagrangian and Eulerian. While it is difficult to track an interface that changes topology using a Lagrangian approach, the Eulerian approach handles such cases with ease. Unless expensive high-order finite differencing schemes are used however, the Eulerian approach exhibits what is observed as a loss of mass. These orthogonal strengths and weaknesses of the Lagrangian and Eulerian approaches have lead to an interest in a third, hybrid approach.

A number of hybrid methods have been proposed in recent literature that augment the level-set method, which take an Eulerian approach, with Lagrangian-style particles. In this thesis, a comparison is made between a number of these proposals. The Self-Adaptive Oriented Particles Level-Set (SA-OPLS) method was found to provide excellent results with respect to mass-preservation, while additionally containing a robust self-adaptive mechanism.

The advent of programmable graphics processing units (GPUs) has provided access to a highly parallel computing platform. Both the Lagrangian and Eulerian approach, and therefore naturally also a hybrid approach, have been recognized to exhibit a large amount of parallelism, allowing them to benefit from such highly parallel architectures. One example is the GPU-accelerated Sorted Tile List (GPU-STL) method, which provides a highly efficient implementation of the level-set method.

In this thesis, a hybrid level-set implementation on the GPU is proposed, based on the combination of GPU-STL and SA-OPLS. The final results of this implementation are promising, comparing favourably against similar work presented in recent related literature.