Mathematik-Gebäude, Seminarraum M614/616

Simulating continuum reaction–diffusion processes on complex deforming surfaces requires computational methods capable of accurately tracking the geometric deformations and discretizing on them the governing equations. We present a meshless Lagrangian level-set formulation to capture the deformation of the geometry and use an embedding formulation and an adaptive particle method to discretize both the level-set equations and the corresponding reaction–diffusion. We validate the proposed method and discuss its advantages and drawbacks through simulations of reaction–diffusion equations on complex and deforming geometries. We further show extensions of the employed meshless particle method to adaptive-resolutions simulations where the particles (colocation points) self-organize. In such a discretization, neither the total number of particles, nor their spatial distribution need to be specified by the user. The user only specifies the desired error level of the solution and the particles in the simulation self-organize to a distribution that reaches this.

Dr. Ivo F. Sbalzarini

Max-Planck-Institut für Molekulare Zellbiologie und Genetik (MPI-CBG), Dresden (The MOSAIC Group: Scientific Computing for Image-based Systems Biology)