71 citations · 365 across the 27 of their papers we have counts for
6 papers · 1 filter
Asymptotic and numerical analysis of a stochastic PDE model of volume transmission
Sean D. Lawley, Varun Shankar
Volume transmission is an important neural communication pathway in which neurons in one brain region influence the neurotransmitter concentration in the extracellular space of a d…
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…
Robust Node Generation for Meshfree Discretizations on Irregular Domains and Surfaces
Varun Shankar, Robert M. Kirby, Aaron L. Fogelson
We present a new algorithm for the automatic one-shot generation of scattered node sets on irregular 2D and 3D domains using Poisson disk sampling coupled to novel parameter-free,…
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…