I am an incoming Mathematics PhD at the Courant Institute of Mathematical Sciences at NYU and current MS student at Stanford University studying Computational and Mathematical Engineering. My research interests surround developing high-order numerical methods and their applications modeling dynamical systems found in natural phenomena and engineering environments.

I studied computational science and applied mathematics with their surrounding uses in various scientific fields from Georgia Tech and UC Berkeley in undergrad. In the past, I have been fortunate to work with NASA Supercomputing, Julia Computing, and various university labs.

I have primarily worked in numerical mathematics, parallel programming, data science, pure mathematics, and web development. Check out the source code for this website!

04.15.2023

Accepted NYU Courant PhD offer in Mathematics

04.16.2023

Awarded NumFocus grant to develop documentation for CVXPY convex optimization library

04.05.2023

Funded through CA position for CS 246: Graduate Mining Massive Datasets

02.07.2023

Recieved NYU Courant PhD Offer in Mathematics

11.28.2022

Funded through CA position for CS 448B: Graduate Data Visualization

09.30.2022

Funded through CA position for CS 149: Parallel Programming

04.15.2022

Accepted Stanford MS Offer in ICME

03.15.2022

Recieved Rice PhD Offer, Stanford, NYU, UW MS Offers

Research-wise, my interests lie in the field of mathematical modeling and simulation, particularly surrounding the development of efficient high-order numerical methods. The simulation of large and complex systems with numerical methods in an accurate and efficient manner presents a lot of challenges I find intriguing.

From a mathematical standpoint, I am interested in studying better preconditioning, discretization, and meshing techniques that can be used for such numerical solvers. From an algorithmic perspective, I aim to study how different predictive methods may be used to accelerate similar simulations and thereby reduce computational cost.

Aside from numerics, I have touched on interesting topics in discrete simulation and data science in the past. Effective data analysis and interactive data visualization in computational journalism is likewise quite interesting.

1. High-Fidelity Numerical Methods

Mathematical formulations and tools towards developing efficient and accurate high-order numerical methods for continuous simulation of partial differential equations

2. Efficient Parallel Algorithms

Fast iterative methods and preconditioners as applied to large matrix computations using new parallel programming toolkits across both CPU and GPU systems

3. Unstructured Mesh Generation

Unstructured methods of developing curvlinear meshes for the use of high-order numerical methods, as well as associated adaptive mesh refinement procedures

4. Network Simulation

Optimizing communication networks with discrete event simulation of distributed edge computing architectures and induced compute load from IOT jobs

2023-Now

New York University

PhD Mathematics

2022-Now

Stanford University

MS Computational and Mathematical Engineering

2020-2022

Georgia Tech

BS Mathematics

2018-2020

UC Berkeley

2022-Now

Course Assistant, Department of CS

2021-2022

Modeling and Simulation Intern, JuliaSim

2021-2022

Teaching Assistant, Department of CSE

Course Grader, Department of Mathematics

2020-2021

Research Associate, Computational Aerosciences

2019-2021

Course Reader, Department of Mathematics

Research Assistant, Department of EECS

2018-2019

University of Arizona

Research Assistant, Department of Bioengineering

Now

Accelerated High-Order Discontinuous Galerkin Methods

(Stanford) Leveraged Jax to optimize Discontinuous Galerkin numerical method code, to understand methods of parallelizing numerical methods across CPUs/GPUs/TPUs using matrix computations to enable compiler-driven parallelism

Document
Codebase

2022

Task-based Parallel Multigrid and Adaptive Mesh Refinement FEM Solver

(Stanford) Developing a quadratic finite element solver with multigrid and adaptive mesh refinement accelerations using Regent, a Nvidia Legate based research task-based parallel language for proof of concept purposes

Document
Slideset

2022

Space Mission Logistics Discrete Event Simulation Framework

(Georgia Tech) Developed generalized discrete event simulation model of space mission timelines, providing logistical and risk analyses. Testing on a conceptual operation of a future Mars mission

Document
Codebase

2022

Intersectional Demographic Regression Analysis of University Employee Salaries

(Georgia Tech) Regression analyses on individual and intersectional demographic factors affecting faculty salaries to determine best predictors across five public university systems

Document
Codebase
Poster

2021

Portable OpenMP CPU/GPU Parallelization of Iterative Methods

(NASA Supercomputing) Developed CPU and GPU portable iterative method solvers with new OpenMP implementations across different specialized compilers. Performance profiling and optimization across different pragmas and strategies

Document
Notes

2021

Correlative Analysis and Visualization of Transportation Ecosystems

(Georgia Tech) Used confounding factors within historical congestion data to develop predictive autoregressive integrated moving average (ARIMA) analyses, modeling the cyclic nature of transit demand

Document
Codebase
Poster

2021

Buzzbook Course Discovery Platform

(Georgia Tech) Developing a one-stop course planning platform to aggregate a course catalog, a requirements planner, visualized grading distributions, enrollment histories, a schedule optimizer, a ratings system, a course recommender, and an exam/syllabi database.

Website
Codebase

2020

Efficient Computational Methods for Kelvin-Helmholtz Instabilities

(UC Berkeley) Implemented and formulated efficient variations of the Uzawa and GMRES algorithms applied to the matrix computations arising from the numerical solution to the instabilities observed from the 2d Euler Equations for inviscid flows

2020

Natural Convection Boundary-Layer Flow Analysis

(UC Berkeley) Finite-difference method numerical modeling of hydrodynamically and thermally developed convective flow of different fluids in various geometries and analysis of their behaviors, comparison of scheme efficacies with dimensionless quantities

Document

2019

Time-Harmonic Wave Propagation Simulation in Waveguides

(UC Berkeley) Rigorous formulation and implementation of quadratic finite elements and custom meshing algorithm to simulate frequency response and resonance phenomena of a waveguide using the 2D Helmholtz Equation with Sommerfeld radiation conditions

Document
Codebase

2019

Optimal Traffic Signal Timing with a Continuum Flow Congestion Model

(UC Berkeley) Rigorous implementation of finite volume schemes (Godunov, Roe) in evaluating the Lighthill-Whitham-Richards traffic model, a flow-based traffic congestion model based on vehicle density that accounts for disturbance shocks

Document
Codebase

2019

Efficiency of a Domain-based Fog Computing Architecture

(UC Berkeley) Devised and implemented a discrete event simulation of a domain-based fog architecture model and demonstrated different queuing methods (FCFS, EDF, CR) to improve QoS for fog networks, formulating and modeling a discrete-event simulation based on various constraints on job size, deadline, and location.

Document
Codebase
Poster

2018

A Method of Modeling Asteroid Intercept Trajectory

(Independent) Developed a 3D N-body simulation of the solar system and modeled possible intercept trajectories to a celestial object using convex optimization strategies with a time-iterating RK4 approximation method.

Document

Sp 2023

Course Assistant, Graduate Mining Massive Datasets

Wi 2023

Course Assistant, Graduate Data Visualization

Au 2022

Course Assistant, Parallel Computing

Sp 2022

Math 6321 (Georgia Tech)

Grader, Graduate Complex Analysis

Sp 2022

Head Teaching Assistant, Graduate Data and Visual Analytics

Fa 2021

CSE 6242 (Georgia Tech)

Teaching Assistant, Graduate Data and Visual Analytics

Fa 2021

Math 121A (Berkeley)

Grader, Mathematical Methods for Physical Sciences

Sp 2021

Grader, Mathematical Methods for Physical Sciences

Fa 2020

Grader, Introduction to Complex Analysis

Math

Mathematical Methods Mathematical Programming Introductory Analysis Algebra FEM

Physics

Classical Mechanics Tensor Calculus

CS

Julia Fundamentals Database Systems Webdev

edhschen [at] stanford [dot] edu

Website

edhschen [dot] info

Last Update

Jan 18, 2023