Title: A smooth subdivision multigrid method and its application in life sciences
Abstract: We introduce a smooth subdivision theory-based geometric multigrid method. While theory and efficiency of geometric multigrid methods rely on grid regularity, this requirement is often not directly fulfilled in applications where partial differential equations are defined on complex geometries. Instead of generating multigrid hierarchies with classical linear refinement, we propose the use of smooth subdivision theory for automatic grid hierarchy regularization within a geometric multigrid solver. This subdivision multigrid method is compared to the classical geometric multigrid method for two benchmark problems. Numerical tests show significant improvement factors for iteration numbers and solve times when comparing subdivision to classical multigrid. A second study focusses on the regularizing effects of surface subdivision refinement, using the Poisson-Nernst-Planck equations as a model problem. Various applications to problems in life-sciences are presented.