28 citations · 30 across the 3 of their papers we have counts for
8 papers · 1 filter
A high-order, meshless, Lagrangian--Eulerian RBF-FD method for advection--diffusion--reaction on moving manifolds
Matthew Lowery, Grady B. Wright, Varun Shankar
We present a high-order radial basis function-generated finite difference (RBF-FD) method for partial differential equations on moving manifolds o…
MGM: A meshfree geometric multilevel method for systems arising from elliptic equations on point cloud surfaces
Grady B. Wright, Andrew M. Jones, Varun Shankar
We develop a new meshfree geometric multilevel (MGM) method for solving linear systems that arise from discretizing elliptic PDEs on surfaces represented by point clouds. The metho…
An Efficient High-Order Meshless Method for Advection-Diffusion Equations on Time-Varying Irregular Domains
Varun Shankar, Grady B. Wright, Aaron L. Fogelson
We present a high-order radial basis function finite difference (RBF-FD) framework for the solution of advection-diffusion equations on time-varying domains. Our framework is based…
A Robust Hyperviscosity Formulation for Stable RBF-FD Discretizations of Advection-Diffusion-Reaction Equations on Manifolds
Varun Shankar, Grady B. Wright, Akil Narayan
We present a new hyperviscosity formulation for stabilizing radial basis function-finite difference (RBF-FD) discretizations of advection-diffusion-reaction equations on manifolds…
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…