Publication

Mathematical Research

[1] Park, J.-H., Salgado, A. J., & Wise, S. M. (2021). Preconditioned accelerated gradient descent methods for locally Lipschitz smooth objectives with applications to the solution of nonlinear PDEs. J. Sci. Comput., 89(1), Paper No. 17, 37. https://doi.org/10.1007/s10915-021-01615-8

[2] Park, J.-H., Salgado, A. J., & Wise, S. M. (2023). Benchmark computations of the phase field crystal and functionalized Cahn-Hilliard equations via fully implicit, Nesterov accelerated schemes. Communications in Computational Physics, 33(2), 367–398. https://doi.org/10.4208/cicp.OA-2022-0117

[3] Park, J.-H., Salgado, A. J., & Wise, S. M. (In progress) Perturbed preconditioned gradient descent method for Cahn-Hilliard equation with variable mobility.

[4] Park, J.-H., Salgado, A. J., & Wise, S. M. (in progress) Nondegenerate convergence of generic local Lipschitz smooth functionals beyond Sobolev embedding.

Pedagogical Research

[5] Park, J. (2014) A Case-Study on Creative Exploring Activities for Uncomplicated Routine Problems. Korea National University of Education. Thesis for Master of Education. 

Research Statement

Here is a summary of what I have done and future plan.

Organized by research directions

Optimization and its applications 

Study convergence of optimization methods and confirm it with useful examples.

Related publications: [1]

Computational study of real world problems

Develop, analyze, and compare efficient numerical methods for real world problems 

Related publications: [2, 3]

Theoretical Numerical Analysis

Study finer theoretical tools to better tackle numerical methods.

Related publications: [4]

TALKS/PRESENTATIONS

• SAIM Conference on Mathematical Aspects of Material Science. (Abstract submitted, Pittsburgh, PA, 05/19/2024 - 05/24/2024)
  Perturbed preconditioned gradient descent method for Cahn-Hilliard equation with variable mobility.

• 6th Annual Meeting of SIAM Central States Section: MiniSymposium-8: Recent Advances in Numerical Methods for Partial Differential Equations (University of Kansas - online, 10/02/2021).
  Preconditioned Accelerated Gradient Descent Methods for Locally Lipschitz Smooth Objectives with Applications to the Solution of Nonlinear Partial Differential Equations.

• Departmental PDE/Data Science/Applied Math Semiar (UC Santa Barbara, 10/02/2021)
  Preconditioned Nesterov’s acceleration for locally Lipschitz functions and its applications to phase field models.

• SAIM Conference on Mathematical Aspects of Material Science (online, 05/2021)
  Stable and Fast Adaptive Solvers for the Functionalized Cahn-Hilliard (FCH) Equation

• Hong Kong Polytechnic University, (online--Hong Kong, 03/01/2021)
  Numerical Comparison of Some Semi-implicit and Fully Implicit Solvers for Functionalized Cahn-Hilliard and Phase Field Crystal Equations

• Sayas Numerics Seminar (online, 11/10/2020)
  Preconditioned accelerated gradient descent methods for locally Lipschitz smooth objectives with applications to the solution of nonlinear PDEs.

• Southern University of Science and Technology Numerical Seminar (online--China, 10/21/2020)
  Preconditioned accelerated gradient descent methods for locally Lipschitz smooth objectives with applications to the solution of nonlinear PDEs.

• Illinois Institute of Technology Numerical Seminar (online, 10/16/2020)
  Preconditioned accelerated gradient descent methods for locally Lipschitz smooth objectives with applications to the solution of nonlinear PDEs.

• The 43rd Annual Meeting SIAM Southeastern Atlantic Section Mini-symposium (University of Tennessee, 09/21/2019)
  Preconditioned Nesterov’s Accelerated Gradient Descent Method For Strongly Convex, Lipschitz Smooth Objectives

• Departmental graduate research showcase for early-year graduate students’ directions (University of Tennessee, 11/21/2019)
  A generic picture of research in numerical PDE: modeling, analysis, discrete analysis, and solver development (with the example of Cahn-Hilliard equation)

• Oral specialty exam (University of Tennessee, 01/09/2019)
  A mixed method for some fourth order elliptic equations related to Cahn-Hilliard equation.

• Departmental Computational and Applied Mathematics Seminar (University of Tennessee, 10/02/2019)
  An ODE model for Nesterov’s accelerated gradient descent method for Lipschitz smooth, strongly convex objective functionals

• Departmental Computational and Applied Mathematics Seminar (University of Tennessee, 09/11/2019)
  Nesterov’s Acceleration

• Departmental Computational and Applied Mathematics Seminar (University of Tennessee, 02/14/2018)
  Discrete Gagliardo-Nirenberg inequality

• Departmental Computational and Applied Mathematics Seminar (University of Tennessee, 12/06/2017, presentation of reading)
  Finite element approximation of p–Laplacian

• Class Project Presentation -- Quantum computing (University of Tennessee, 04/21/2020 )
  Berry phase estimation in gate-based adiabatic quantum simulation

• Class Project Presentation -- Advanced methods in numerical PDE (University of Tennessee, 11/29/2018)
  Interpolation spaces

• Class Project Presentation -- Statistics (University of Tennessee, 11/28/2017)
  Hamiltonian Monte Carlo – theory and application

CONFERENCES/SEMINARS ATTENDED

• PDE/Data Science/Applied Math Semiar -- UC Santa Barbara, 10/02/2021-present

• SIAM Annual Meeting and Joint Conference on Applied Mathematics Education -- Online, 07/11/2022-07/15/2022

• The 50th Barrett Lectures: Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models -- University of Tennessee Koxville (online), 05/17/2021-05/19/2021

• Finite Element Circus -- Online, 11/06/2020–11/07/2020

• Second Symposium on Machine Learning and Dynamical Systems -- Online, 10/21/2020–10/30/2020

• AMS Fall Sectional Meeting (East) -- Online, 10/03/2020–10/04/2020

• Sayas Numerics Seminar (weekly) -- Online, 09/2020–12/2020

• Springer Nature PDE and Applications Webinar (weekly) -- Online, 08/2020–10/2020

• SIAM/CAIMS Annual Meeting -- Online, 07/06/2020–07/17/2020

• Householder lecture -- University of Tennessee, 11/16/2018

• Finite Element Circus -- University of Tennessee, 03/16/2018–03/17/2018

• Householder lecture -- Oak Ridge National Laboratory, 10/25/2017

• Departmental Computational and Applied Mathematics Seminar (weekly) -- University of Tennessee, 08/2017–present