Organizing Committee
Abstract

This workshop will provide a platform for researchers working on localized kernel-based methods to present and discuss their latest developments, as well as the current theoretical and practical challenges in the field. These methods, such as radial basis function-generated finite differences (RBF-FD) or RBF-generated partition of unity methods (RBF-PUM), promise to develop into general-purpose meshless techniques for the numerical solution of partial differential equations that inherit the ease of implementation of the finite difference method, and yet potentially possess a greater ability than the finite element method to fit any geometry or adapt to singularities or other features of the solution.

The numerical evidence collected in recent years by a rapidly growing community of researchers suggests that these methods combine numerical stability on irregular node layouts, high computational speed, high accuracy, easy local adaptive refinement, and excellent opportunities for large-scale parallel computing. Despite recent efforts to provide error bounds for local kernel-based methods, their theory is still in its infancy.

The key topics of the workshop will include the latest computational achievements for large-scale computing in the geosciences, the mathematical tools of analysis for providing a solid foundation for the development and exploitation of the methods, the applications that benefit the most from their meshless nature, and the ways for techniques developed within other numerical methods to be combined with localized kernel-based methods in order to optimize a model in terms of accuracy and computational cost.

The main aspects of localized kernel-based methods and their applications will be presented in a number of survey lectures and tutorials accessible to graduate students and other researchers with background in numerical analysis and scientific computation.

Image for "Localized Kernel-Based Meshless Methods for Partial Differential Equations"

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, August 7, 2017
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration121 South Main Street Providence RI 11th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome11th Floor Lecture Hall 
9:00 - 9:45am EDTRadial Basis Function-generated Finite Differences (RBF-FD)- Basic concepts and some applications - Bengt Fornberg, University of Colorado11th Floor Lecture Hall
10:00 - 10:45am EDTRadial Basis Function-Generated Finite Differences (RBF-FD)- New Computational Opportunities in the Geo-Fluid Modeling - Natasha Flyer, National Center for Atmospheric Research11th Floor Lecture Hall
11:00 - 11:30am EDTCoffee/ Tea Break11th Floor Collaborative Space 
11:30 - 12:05pm EDTNumerical Quadrature Over Smooth Closed Surfaces - Jonah Reeger, Airforce Institute of Technology11th Floor Lecture Hall
12:15 - 2:15pm EDTBreak for Lunch/ Free Time  
2:15 - 2:50pm EDTMicrocombustor modeling using the RBF-FD method - Manuel Kindelan, Universidad Carlos III de Madrid11th Floor Lecture Hall
3:00 - 3:35pm EDTRBF-FD approximations based on PHS with polynomial augmentation for the numerical solution of elliptic PDEs - Víctor Bayona, Universidad Carlos III de Madrid11th Floor Lecture Hall 
3:45 - 4:15pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
4:15 - 4:50pm EDTA Meshless Approach to Spectral Wave Modeling - Adrean Webb, University of Tokyo11th Floor Lecture Hall
5:00 - 6:30pm EDTWelcome Reception11th Floor Collaborative Space 
Tuesday, August 8, 2017
TimeEventLocationMaterials
9:00 - 9:45am EDTRadial basis function partition of unity methods for PDEs - Elisabeth Larsson, Uppsala University11th Floor Lecture Hall
10:00 - 10:45am EDTRBF-Partition of Unity Method- an overview of recent results - Alessandra De Rossi, University of Turin11th Floor Lecture Hall
11:00 - 11:30am EDTCoffee/ Tea Break11th Floor Collaborative Space 
11:30 - 12:05pm EDTThe RBF-FD method applied to two problems- Groundwater Flow Modelling and Solving PDEs on Arbitrary Surfaces. - Cécile Piret, Michigan Technical University11th Floor Lecture Hall 
12:10 - 12:15pm EDTGroup Photo11th Floor Lecture Hall 
12:15 - 2:15pm EDTBreak for Lunch/ Free Time11th Floor Collaborative Space 
2:15 - 2:50pm EDTLow-complexity and periodic minimal energy problems - Doug Hardin, Vanderbilt University11th Floor Lecture Hall 
3:00 - 3:35pm EDTMimetic Methods - Jose Castillo, Computational Science Research Center (San Diego State University)11th Floor Lecture Hall 
3:45 - 4:15pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
4:15 - 4:50pm EDTNumerical solution of surface PDEs with Radial Basis Functions - Andriy Sokolov, TU Dortmund11th Floor Lecture Hall 
Wednesday, August 9, 2017
TimeEventLocationMaterials
9:00 - 9:45am EDTTowards Error Bounds for Localized Kernel-Based Meshless Methods - Robert Schaback, Georg-August-Universität Göttingen11th Floor Lecture Hall
10:00 - 10:45am EDTConsistency estimates for generalized finite difference methods and selection of sets of influence. - Oleg Davydov, University of Giessen11th Floor Lecture Hall
11:00 - 12:15pm EDTPoster Session Coffee/ Tea Break11th Floor Collaborative Space 
12:15 - 2:15pm EDTBreak for Lunch/ Free Time11th Floor Collaborative Space 
2:15 - 2:50pm EDTReproducing kernel-based methods in generalized Besov spaces - Barbara Zwicknagl, Universität Würzburg11th Floor Lecture Hall 
3:00 - 3:35pm EDTKernel methods for partial differential equations with random input data - Christian Rieger, University of Bonn11th Floor Lecture Hall
3:45 - 4:15pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
4:15 - 4:50pm EDTSpace-time Localized RBF Collocation Methods for PDEs - Alfa Heryudono, University of Massachusetts Dartmouth11th Floor Lecture Hall
Thursday, August 10, 2017
TimeEventLocationMaterials
9:00 - 9:35am EDTMeshfree semi-Lagrangian methods for transport on spheres and other surfaces - Grady Wright, Boise State University11th Floor Lecture Hall
9:45 - 10:20am EDTEfficient high-order RBF-FD methods for advection-diffusion-reaction PDEs on irregular domains - Varun Shankar, University of Utah11th Floor Lecture Hall 
10:30 - 11:00am EDTCoffee/ Tea Break11th Floor Collaborative Space 
11:00 - 12:00pm EDTSoftware Session11th Floor Lecture Hall 
12:00 - 2:00pm EDTBreak for Lunch/ Free Time11th Floor Collaborative Space 
2:00 - 4:00pm EDTSoftware Session11th Floor Lecture Hall 
4:00 - 4:30pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
4:30 - 5:30pm EDTPanel Discussion11th Floor Lecture Hall 
Friday, August 11, 2017
TimeEventLocationMaterials
9:00 - 9:35am EDTComputing optimal sampling points for polynomial and kernel-based approximations - Rodrigo Platte, Arizona State University11th Floor Lecture Hall
9:45 - 10:20am EDTParameter-free radial basis functions for Eulerian and semi-Lagrangian discretizations on the sphere - Gregory Barnett, Sandia National Laboratories11th Floor Lecture Hall
10:30 - 11:00am EDTCoffee/ Tea Break11th Floor Collaborative Space 
11:00 - 11:35am EDTFinite Difference Approximations in the Presence of Noise for Identifying Discontinuities - Michael McCourt, SigOpt11th Floor Lecture Hall
11:45 - 12:20pm EDTCompatible spatial discretization using generalized moving least squares - Nathaniel Albert Trask, Sandia National Laboratory11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch/ Free Time11th Floor Collaborative Space 
2:30 - 3:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 

Lecture Videos

Mimetic Methods

Jose Castillo
Computational Science Research Center (San Diego State University)
August 8, 2017