Vertebrate limb bud development - Computational advances and challenges in simulating organogenesis.
Tuesday, 3.5.11, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Limb bud development is regarded as an ideal model system to gain\ninsight into vertebrate organogenesis. Due to its simplicity, the limb\nbud has attracted theoretical modellers already decades ago and now all the\nmore in the advent of systems biology. Numerous genetic studies provide the\nbasic logic of signaling interactions as well as the domains of gene\nexpression [1, 2]. This has enabled us to build and experimentally test a\nreaction-diffusion PDE model of the molecular regulatory network that\ncontrols the initiation, propagation, and termination of signaling as well\nas the patterning during digit formation [3]. We are solving our models on\ngrowing domains of realistic shape using finite element methods. Given the\nsharp domain boundaries, travelling wave character of some solutions, and\nthe stiffness of the reactions we are facing numerous numerical challenges\nthat we will discuss.\n\n\n\n1. Rolf Zeller et al., Vertebrate Limb bud development: moving towards\nintegrative analysis of organogenesis. Nature Reviews Genetics 10, 845\n(2009).\n\n\n2. Jean-Denis Benazet et al., A self-regulatory system of interlinked\nsignaling feedback loops controls mouse limb patterning. Science 323, 1050\n(2009).\n\n\n3. Probst et al. Development, in press.\n
Scalable adaptive mesh refinement and large-scale applications in computational geosciences.
Tuesday, 17.5.11, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Many geophysical systems can be modeled by partial differential equations\n(PDEs) derived from fluid or solid mechanics. These systems give rise to\ncomplex multiscale behavior, which motivates to use of adaptive mesh refinement\nand coarsening (AMR) techniques. AMR refers to the ability to adapt the mesh\nresolution to local characteristics of the physical system, investing a dense\nmesh only in areas where high resolution is required, which can reduce the\nproblem size by several orders of magnitude. AMR is thus an attractive option\nfor the adequate discretization of localized multiscale phenomena, and even\nmore so if it supports dynamically changing the mesh to track moving features\nof the solution.\n\n\n\nThe challenge, however, lies in the fact that each processor in a parallel\nsimulation can only store a small part of the adaptive mesh, and that the\ntopological relations between mesh elements are irregular both within one and\nbetween neighboring processors. These facts entail complex storage and\ncommunication patterns, which have traditionally incurred a large computational\noverhead and severely limited the successful use of parallel dynamic AMR. I\nhave addressed these challenges by developing a collection of new parallel\ntechniques for forest-of-octree AMR, and I will describe the central ideas and\nessential concepts in this talk. I will conclude with a presentation of\nselected applications in mantle dynamics and seismic wave propagation.\n