Shane E. Sawyer

Shane E. Sawyer

Graduate Teaching Assistant

University of Tennessee, Knoxville

Biography

Shane Sawyer is an early PhD student in Mathematics at the University of Tennessee, Knoxville. He is a Graduate Teaching Assistant in the mathematics department working under the direction of Dr. Abner Salgado. His research interests include applying numerical analysis to fractional partial differential equations, developing algorithms to compute approximate solutions to PDEs, and investigating the underlying mathematical frameworks to understand the connections between approximation theory and deep neural networks.

Interests

  • Numerical Analysis
  • Numerical Solutions to (Fractional) PDEs
  • High Performance Scietific Computing
  • Applied and Computational Mathematics
  • Machine Learning
  • Fluid Dynamics

Education

  • Early PhD Student in Mathematics

    University of Tennessee, Knoxville

  • MEng in Computational Engineering

    University of Tennessee, Chattanooga

  • BSc in Applied Mathematics

    University of Tennessee, Chattanooga

Skills

Programming

Linux

Applied Mathematics

Recent Experience

 
 
 
 
 

Graduate Teaching Assistant

University of Tennessee, Knoxville

Aug 2020 – Present

Responsibilities include:

  • Leading synchronous lectures in College Algebra with a flipped class environment
  • Using Internet technology for student interaction and assessment
  • Hosting virtual office hours
 
 
 
 
 

Graduate Research Assistant

University of Tennessee, Knoxville

Aug 2019 – Jul 2020
Research areas of machine learning to investigate mathematical underpinnings.
 
 
 
 
 

Graduate Research Assistant

University of Tennessee, JICS

Aug 2017 – Aug 2019
Assisted in group research activities including continued development of a high performance implementation of bioinformatics code and assisting collaboration efforts with campus partners and other academic partners.

Accomplish­ments

Machine Learning

Coursera Jan 2018
Andrew Ng’s popular introductory course to Machine Learning that provides an overview of the basics of the field.

Heterogeneous Parallel Programming

Coursera Apr 2014
An introductory online course teaching the fundamentals of parallel programming algorithms and how to implement them on an Nvidia GPU using the CUDA framework.

Recent Posts

Some Preliminaries on the Fractional Laplacian

Suppose we have an orthonormal basis given by $\{ \phi_k \}_{k \geq 1}$ of $L^2(\Omega)$. This implies that we can write for all $w \in L^2(\Omega)$ as $$ w = \sum_{k=1}^{\infty} w_k \phi_k \, \, , \,\, \text{where} \,\, w_k = (w_k, \phi_k)_{L^2(\Omega)} = \int_{\Omega} w \phi_k \, dx \,\, .
Oct 21, 2020 2 min read

Projects

Understanding Fractional Pdes

In this project, I am beginning my journey on learning numerical analysis of Fractional PDEs.

Meet the Team

Research Assistants

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Jammers

Research Assistant

Playing with strings, Chittering at the birds, Hiding from strangers

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Logan

Research Assistant

Getting treats, Sleeping in my box, Harrassing Jammers

Past Research Assistants

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D

Past Research Assistant

Chasing the red dot, Yelling at any cat outside the window

Recent & Upcoming Talks

Featured Publications

Recent Publications

Quickly discover relevant content by filtering publications.

HPC-BLAST: Distributed BLAST for Modern HPC Clusters.

PDF DOI

HPC-BLAST: distributed BLAST for Xeon Phi clusters

Analysis and implementation of a high-order reconstruction algorithm for an unstructured finite volume flow solver

Computational Prediction of Forces and Moments for Transport Aircraft

Unstructured grid solutions of CAWAPI F-16XL by UT SimCenter

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