26 citations · 63 across the 17 of their papers we have counts for
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Solving the Incompressible Navier-Stokes Equations on Oriented Curved Surfaces Discretized by Point Clouds
Alejandra Foggia, Ivo F. Sbalzarini
We present a meshfree numerical solver for the incompressible Navier-Stokes equations on oriented curved surfaces that are represented by surface point clouds. On curved surfaces,…
An Overview of Meshfree Collocation Methods
Tomas Halada, Serhii Yaskovets, Abhinav Singh +3
We provide a comprehensive overview of meshfree collocation methods for numerically approximating differential operators on continuously labeled unstructured point clouds. Meshfree…
Multivariate Newton Interpolation in Downward Closed Spaces Reaches the Optimal Geometric Approximation Rates for Bos--Levenberg--Trefethen Functions
Michael Hecht, Phil-Alexander Hofmann, Damar Wicaksono +5
We extend the univariate Newton interpolation algorithm to arbitrary spatial dimensions and for any choice of downward-closed polynomial space, while preserving its quadratic runti…
Global Polynomial Level Sets for Numerical Differential Geometry of Smooth Closed Surfaces
Sachin K. Thekke Veettil, Gentian Zavalani, Uwe Hernandez Acosta +2
We present a computational scheme that derives a global polynomial level set parametrisation for smooth closed surfaces from a regular surface-point set and prove its uniqueness. T…
STENCIL-NET: Data-driven solution-adaptive discretization of partial differential equations
Suryanarayana Maddu, Dominik Sturm, Bevan L. Cheeseman +2
Numerical methods for approximately solving partial differential equations (PDE) are at the core of scientific computing. Often, this requires high-resolution or adaptive discretiz…
Stability selection enables robust learning of partial differential equations from limited noisy data
Suryanarayana Maddu, Bevan L. Cheeseman, Ivo F. Sbalzarini +1
We present a statistical learning framework for robust identification of partial differential equations from noisy spatiotemporal data. Extending previous sparse regression approac…