Organizing Committee
Abstract

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.

Image for "Fast Algorithms for Generating Static and Dynamically Changing Point Configurations"
3D point cloud of the workshop group photo. Right click the link and choose save to download the file. Use MeshLab to view it in 3D.

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, March 12, 2018
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration121 South Main Street Providence RI 11th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45am EDTAn introduction to the Fast Multipole Method - Per-Gunnar Martinsson, University of Oxford11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break 11th Floor Collaborative Space 
10:30 - 11:15am EDTBuilding a better non-uniform fast Fourier transform - Alex Barnett, Flatiron Institute11th Floor Lecture Hall
11:30 - 12:15pm EDTGPU algorithms for hierarchical matrix operations - George Turkiyyah, American University of Beirut11th Floor Lecture Hall
12:15 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTImproving Particle Methods - Robert Krasny, University of Michigan11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break 11th Floor Collaborative Space 
4:00 - 4:45pm EDTFast algorithms for data visualization - Manas Rachh, Yale University11th Floor Lecture Hall
5:00 - 6:30pm EDTWelcome Reception11th Floor Collaborative Space 
Tuesday, March 13, 2018
TimeEventLocationMaterials
9:00 - 5:00pm EDTBrown University/ ICERM Closed  
Wednesday, March 14, 2018
TimeEventLocationMaterials
8:30 - 8:50am EDTTBA - Doug Hardin, Vanderbilt University11th Floor Lecture Hall 
8:55 - 9:40am EDTNew Methods and Models for Condensed Phase Simulation - Teresa Head-Gordon, University of California, Berkeley11th Floor Lecture Hall
9:50 - 10:15am EDTCoffee/Tea Break 11th Floor Collaborative Space 
10:15 - 11:00am EDTFast Ewald summation for electrostatic potentials with arbitrary periodicity - Anna-Karin Tornberg, KTH Royal Institute of Technology11th Floor Lecture Hall
11:10 - 11:55am EDTRapid Point Reconfiguration for High-dimensional Interactions: Algorithms & Emerging Applications - Xiaobai Sun, Duke University11th Floor Lecture Hall 
12:05 - 1:30pm EDTLunch provided at ICERM  
1:30 - 2:00pm EDTMesh-Free Applications for Static and Dynamically Changing Node Configurations - Natasha Flyer, NCAR11th Floor Lecture Hall
2:10 - 2:55pm EDTLayer potentials for diffusion MRI modeling and simulation - Jing-Rebecca Li, INRIA11th Floor Lecture Hall
3:05 - 3:25pm EDTCoffee/Tea Break 11th Floor Collaborative Space 
3:25 - 4:10pm EDTMolecular surface meshing and applications in numerical simulation - Benzhuo Lu, Chinese Academy of Sciences11th Floor Lecture Hall
4:20 - 5:05pm EDTHigh-dimensional node generation with variable density - Oleksandr Vlasiuk, Vanderbilt University11th Floor Lecture Hall
5:10 - 5:55pm EDTFast multipole methods in arbitrary dimensions - George Biros, The University of Texas at Austin11th Floor Lecture Hall
Thursday, March 15, 2018
TimeEventLocationMaterials
9:00 - 9:45am EDTAn Introduction to Integral Equations - Adrianna Gillman, Rice University11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break 11th Floor Collaborative Space 
10:30 - 11:15am EDTIntegral equation methods for the Laplace-Beltrami problem - Mike O'Neil, Courant Institute, NYU11th Floor Lecture Hall
11:30 - 12:15pm EDTAdaptive grids for embedded integral equation based solvers - Travis Askham, University of Washington11th Floor Lecture Hall
12:25 - 12:35pm EDTWorkshop Group Photo11th Floor Lecture Hall 
12:35 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTA fast direct solver for boundary value problems on locally perturbed geometries. - Yabin Zhang, Rice University11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break 11th Floor Collaborative Space 
4:00 - 4:45pm EDTEfficient and Accurate Discretization of Singular Integral Operators on Surfaces - James Bremer, University of California, Davis11th Floor Lecture Hall
Friday, March 16, 2018
TimeEventLocationMaterials
9:00 - 9:45am EDTOn the Hierarchical Modeling Technique with Applications - Jingfang Huang, The University of North Carolina at Chapel Hill11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break 11th Floor Collaborative Space 
10:30 - 11:15am EDTOn the solution of the biharmonic equation on regions with corners - Kirill Serkh, New York University11th Floor Lecture Hall
11:30 - 12:15pm EDTFrom Kaczmarz algorithm to minimal energy problems - Xuemei Chen, University of San Francisco11th Floor Lecture Hall
12:15 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTCollaborative Time Collaborative Space 
3:30 - 4:00pm EDTCoffee/Tea Break 11th Floor Collaborative Space 
4:00 - 4:45pm EDTCollaborative Time Collaborative Space 

Associated Semester Workshops

Optimal and Random Point Configurations
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Lecture Videos