$\newcommand{\norm}[1]{\left\lVert#1\right\rVert} \newcommand{\sint}{\text{s}\kern-5pt\int} \newcommand{\powerset}{\mathcal{P}} \newcommand{\RR}{\mathbb{R}} \newcommand{\NN}{\mathbb{N}} \newcommand{\QQ}{\mathbb{Q}} \newcommand{\ZZ}{\mathbb{Z}} \newcommand{\CC}{\mathbb{C}} \newcommand{\SS}{\mathbb{S}} \newcommand{\MM}{\mathbb{M}} \newcommand{\LL}{\mathcal{L}} \renewcommand{\Re}{\operatorname{Re}} \renewcommand{\Im}{\operatorname{Im}} \renewcommand{\vec}[1]{\mathbf{#1}}$

Recent Changes

Last Meeting

Thursday April 20th, 2019

Sun Apr 21 18:10:20 2019

Discussed large eigenvalues in the projection method when using LOI.

Recent Articles

References for Thesis

Mon Jun 17 09:21:01 2019

This page lists the references for my Thesis. It's mostly just so I can copy them into the presentation slideshow.


Fri May 31 19:33:40 2019

This article outlines the RBF Orthogonal Gradients method for solving approximating surface operators as described in [1].

Using Plotly

Sat Mar 2 17:53:06 2019

This is to test the functionality of plotly in the context of sharing scientific data.

CSE 19 Poster Errata

Sat Mar 2 13:02:10 2019

This webpage shows the updated convergence plots for the Tangent Plane Method, Iterated RBF-FD, and Hermite RBF-FD.

Radial Basis Function

Thu Feb 7 13:14:42 2019

This article defines radial basis fuctions (RBFs), describes several types of RBF, and discusses their motivation and applications.

Recent Experiments

Experiment 001 - Time-Stepping

Sun Sep 16 22:13:31 2018

This experiment will test forward and backward Euler time-stepping. We will verify the order of the error.

Experiment 003 RBF Independent Error

Sat Sep 1 17:46:26 2018

It has been obsereved that when using iterated differentiation to solve the problem $\Delta_\SS u = -20Y_{4,-3}$ on the unit sphere, if the degree of the basis terms is 5 (i.e. one higher than the degree of the forcing function) then the error is independent of the choice of RBF. We attempt to explain this behavior.

Experiment 002 - RBF-FD on the Sphere

Mon Aug 27 10:02:13 2018

This experiment will set up code to quickly test many variations of RBF-FD on $\SS^2$. We will test many aspects of RBF-FD in this circumstance including how the number of polynomial/spherical harmonic terms affect stability and convergence rates for PHS RBFs and infinitely-differentiable RBFs.