Fast Algorithms for Generating Static and Dynamically Changing Point Configurations
(March 12 - 16, 2018)
This workshop focuses on fast algorithms for the generation of high quality point configurations and meshes such as hierarchical schemes combined with energy or geometrical optimization techniques. Energy methods utilizing appropriate potentials for a prescribed density on a given manifold have been effective in generating point configurations with good covering and packing properties. These methods rely on efficient energy, gradient, and potential computations which can be achieved by hierarchical algorithms that model a system in a recursively compressed (low-rank or low-dimensional) form where information is transmitted non-locally on a hierarchical tree structure. Different aspects of this technique can be found in the classical FFT, multigrid, and fast multipole method (FMM), as well as the recently developed fast direct solvers, multilevel models in statistics, and convolutional neural networks in deep learning.
Fast generation of point configurations and meshes for dynamically evolving systems is especially challenging. For example, in molecular dynamics simulations, the shape of the molecule changes at each time step, and many numerical methods require an underlying “mesh” (e.g., points in particle methods, or surface or volume elements in finite element and integral equation methods) at each time step. Among the essential considerations are the history dependency of the meshes for simulations where the mesh needs to be updated at each time step; coupling of the fast spatial algorithms with the state-of-the-art point and mesh generation tools; recursive algorithm implementation and parallelization; and applications in atmosphere, Earth, gravitational models, dynamics of biomolecular systems; fluid dynamics, and beyond.
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