Localized Kernel-Based Meshless Methods for Partial Differential Equations
(August 7 - 11, 2017)

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Description

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.

Organizing Committee

  • Oleg Davydov
    (University of Giessen, Germany)
  • Greg Fasshauer
    (Colorado School of Mines)
  • Natasha Flyer
    (National Center for Atmospheric Research (NCAR))
  • Bengt Fornberg
    (University of Colorado-Boulder)
  • Elisabeth Larsson
    (Uppsala University, Sweden)

= speaker    = poster presenter

Monday August 7, 2017
Time Description Speaker Location Abstracts Slides
8:30 - 8:55Registration121 South Main Street Providence RI 11th Floor Collaborative Space
8:55 - 9:00Welcome11th Floor Lecture Hall
9:00 - 9:45Radial Basis Function-generated Finite Differences (RBF-FD)- Basic concepts and some applicationsBengt Fornberg, University of Colorado11th Floor Lecture Hall
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10:00 - 10:45Radial Basis Function-Generated Finite Differences (RBF-FD)- New Computational Opportunities in the Geo-Fluid ModelingNatasha Flyer, National Center for Atmospheric Research11th Floor Lecture Hall
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11:00 - 11:30Coffee/ Tea Break11th Floor Collaborative Space
11:30 - 12:05Numerical Quadrature Over Smooth Closed SurfacesJonah Reeger, Airforce Institute of Technology11th Floor Lecture Hall
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12:15 - 2:15Break for Lunch/ Free Time
2:15 - 2:50Microcombustor modeling using the RBF-FD methodManuel Kindelan, Universidad Carlos III de Madrid11th Floor Lecture Hall
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3:00 - 3:35RBF-FD approximations based on PHS with polynomial augmentation for the numerical solution of elliptic PDEsVíctor Bayona, Universidad Carlos III de Madrid11th Floor Lecture Hall
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3:45 - 4:15Coffee/ Tea Break11th Floor Collaborative Space
4:15 - 4:50A Meshless Approach to Spectral Wave ModelingAdrean Webb, University of Tokyo11th Floor Lecture Hall
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5:00 - 6:30Welcome Reception11th Floor Collaborative Space

Tuesday August 8, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 9:45Radial basis function partition of unity methods for PDEsElisabeth Larsson, Uppsala University11th Floor Lecture Hall
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10:00 - 10:45RBF-Partition of Unity Method- an overview of recent resultsAlessandra De Rossi, University of Turin11th Floor Lecture Hall
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11:00 - 11:30Coffee/ Tea Break11th Floor Collaborative Space
11:30 - 12:05The RBF-FD method applied to two problems- Groundwater Flow Modelling and Solving PDEs on Arbitrary Surfaces.Cécile Piret, Michigan Technical University11th Floor Lecture Hall
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12:10 - 12:15Group Photo11th Floor Lecture Hall
12:15 - 2:15Break for Lunch/ Free Time11th Floor Collaborative Space
2:15 - 2:50Generating quasi-uniform node sets via energy minimizationDoug Hardin, Vanderbilt University11th Floor Lecture Hall
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3:00 - 3:35High Order Compact Mimetic Finite DifferencesJose Castillo, Computational Science Research Center (San Diego State University)11th Floor Lecture Hall
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3:45 - 4:15Coffee/ Tea Break11th Floor Collaborative Space
4:15 - 4:50Numerical study of the RBF-FD level set based method for partial differential equations on evolving-in-time surfacesAndriy Sokolov, TU Dortmund11th Floor Lecture Hall
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Wednesday August 9, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 9:45Towards Error Bounds for Localized Kernel-Based Meshless MethodsRobert Schaback, Georg-August-Universität Göttingen11th Floor Lecture Hall
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10:00 - 10:45Consistency estimates for generalized finite difference methods and selection of sets of influence.Oleg Davydov, University of Giessen11th Floor Lecture Hall
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11:00 - 12:15Poster Session Coffee/ Tea Break11th Floor Collaborative Space
12:15 - 2:15Break for Lunch/ Free Time11th Floor Collaborative Space
2:15 - 2:50Reproducing kernel-based methods in generalized Besov spacesBarbara Zwicknagl, Universität Würzburg11th Floor Lecture Hall
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3:00 - 3:35Kernel methods for partial differential equations with random input dataChristian Rieger, University of Bonn11th Floor Lecture Hall
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3:45 - 4:15Coffee/ Tea Break11th Floor Collaborative Space
4:15 - 4:50Space-time Localized RBF Collocation Methods for PDEsAlfa Heryudono, University of Massachusetts Dartmouth11th Floor Lecture Hall
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Thursday August 10, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 9:35Meshfree semi-Lagrangian methods for transport on spheres and other surfacesGrady Wright, Boise State University11th Floor Lecture Hall
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9:45 - 10:20Efficient High-order RBF-FD Methods for Advection-Diffusion-Reaction Equations on Irregular DomainsVarun Shankar, University of Utah11th Floor Lecture Hall
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10:30 - 11:00Coffee/ Tea Break11th Floor Collaborative Space
11:00 - 12:00Software Session11th Floor Lecture Hall
12:00 - 2:00Break for Lunch/ Free Time11th Floor Collaborative Space
2:00 - 4:00Software Session11th Floor Lecture Hall
4:00 - 4:30Coffee/ Tea Break11th Floor Collaborative Space
4:30 - 5:30Panel Discussion11th Floor Lecture Hall

Friday August 11, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 9:35Computing optimal sampling points for polynomial and kernel-based approximationsRodrigo Platte, Arizona State University11th Floor Lecture Hall
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9:45 - 10:20Parameter-free radial basis functions for Eulerian and semi-Lagrangian discretizations on the sphereGregory Barnett, Sandia National Laboratories11th Floor Lecture Hall
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10:30 - 11:00Coffee/ Tea Break11th Floor Collaborative Space
11:00 - 11:35Finite Difference Approximations in the Presence of Noise for Identifying DiscontinuitiesMichael McCourt, SigOpt11th Floor Lecture Hall
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11:45 - 12:20Compatible spatial discretization using generalized moving least squaresNathaniel Albert Trask, Sandia National Laboratory11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch/ Free Time11th Floor Collaborative Space
2:30 - 3:00Coffee/ Tea Break11th Floor Collaborative Space