Solene Hegarty-Cremer is a final-year undergraduate student at Queensland University of Technology. She is studying a Bachelor of Mathematics, majoring in Applied and Computational Mathematics and minoring in Computer Science and Simulation Science. Solene is interested in the intersection between applied mathematics and the health field and hopes to pursue a Masters in this area upon completion of her undergraduate degree.
A Grid-Based Particle Method for Solving Hyperbolic Curvature Flows
The aim of this project is to adapt the so-called grid-based particle method (GBPM) to simulate the motion of biological tissue boundaries subject to a certain type of geometric control. The grid-based particle method (GBPM) is a hybrid front-tracking method able to handle complex geometries and topological changes easily. The GBPM relies on marker particles on the moving interface as well as an underlying grid. The grid is used to redistribute the marker particles after their evolution, and to search for neighbouring marker particles. This method has been used successfully to evolve PDEs on evolving surfaces using standard finite difference schemes, and is therefore well-suited to be adapted for hyperbolic curvature flows. The method will be compared with previous results in simple tissue geometries, and extended to model situations of tissue fusion and fragmentation.