28 citations · 74 across the 10 of their papers we have counts for
4 papers · 2 filters
RBF-LOI: Augmenting Radial Basis Functions (RBFs) with Least Orthogonal Interpolation (LOI) for Solving PDEs on Surfaces
Varun Shankar, Akil Narayan, Robert M. Kirby
We present a new method for the solution of PDEs on manifolds of co-dimension one using stable scale-free radial basis function (RBF) interpolatio…
Hyperviscosity-Based Stabilization for Radial Basis Function-Finite Difference (RBF-FD) Discretizations of Advection-Diffusion Equations
Varun Shankar, Aaron L. Fogelson
We present a novel hyperviscosity formulation for stabilizing RBF-FD discretizations of the advection-diffusion equation. The amount of hyperviscosity is determined quasi-analytica…
Curvilinear Mesh Adaptation using Radial Basis Function Interpolation and Smoothing
Vidhi Zala, Varun Shankar, Shankar P. Sastry +1
We present a new iterative technique based on radial basis function (RBF) interpolation and smoothing for the generation and smoothing of curvilinear meshes from straight-sided or…
Mesh-free Semi-Lagrangian Methods for Transport on a Sphere Using Radial Basis Functions
Varun Shankar, Grady Wright
We present three new semi-Lagrangian methods based on radial basis function (RBF) interpolation for numerically simulating transport on a sphere. The methods are mesh-free and are…