Ewha Womans University Mathematics

 
홈

Research Areas

Prof. June-Yub Lee

Scientific Computing Lab

Faculty Introduction
Prof. June-Yub Lee
Prof. June-Yub Lee
Research Area
  • Fast Algorithm
  • Numerical PDE
  • Inverse Problem
  • Phase field Equation
Lab Introduction

The research topics of Prof. June-Yub Lee include numerical analysis, more specifically high-speed numerical methods based on the integral equations, and mathematical analysis of inverse problems using the high-speed methods. Among many research results, accelerating the non-uniform Fast Fourier Transform is a major research achievement that extends the FFT developed in 1965 and is one of the representative research achievements in the field of applied mathematics. The type3 NUFFT which extends the non-uniform Fourier transform technique, and MRI reconstruction technique using the NUFFT were studied. In addition, various studies on the inverse problem were conducted to develop the reconstruction formula, MREIT-related numerical technique, and the Equipotential method. And the polarization tensor and moment tensor methods that analyze the mathematical characteristics of the inverse problem were studied. Since 2014, research on the phase field equation such as the spectral method of the Allen-Cahn equation, the phase field crystal equation, the convex splitting RK method, and the 2nd order operator separation method are in progress. Recently, researches on scientific computation using artificial neural networks have been conducted.

Major research projects and Research achievements
Numerical Computation Tools including Elliptic PDE solver
Numerical Computation Tools including Elliptic PDE solver
  • Triple junction problem, Quasi-periodic direct, Parareal DC, Flux conservative
  • Prolate function, Non-Uniform FFT, Fast Sinc Trans.
  • Parallel Poisson solver, Poisson solver, Nonseparable elliptic PDE
  • Two-point BVP, Singularly Perturbed BVP, Rosenau-Burgers Eq.
Numerical Computation Tools including Elliptic PDE solver
Numerical Computation Tools including Elliptic PDE solver
  • Thin elastic inclusion, Polarization tensors, Electrical anomalies
  • Curl-J method, Equipotential line method, Forward Solver
  • High Contrast Composites, Cauchy problem, Elasticity
  • P-Laplacian, Free-boundary, Bernoulli type Eq.
Vortex Calculation, CFD, and Phase Field computation
Vortex Calculation, CFD, and Phase Field computation
  • Operator Splitting : Image-segment, Semi-Analytic, PF-Crystal, Epitaxial Thin Film
  • Energy-Stable Methods : CSRK, CSRK-R, cCS-vCH, CSRK-x-CH, ConvexGrad-RK
  • Phase-Field Models : PFC-CS_BF, Modified PFC, PFC-CSRK-LongTime
  • Long time Vortex sheet, Recirculating flow
Mathematical Education, Neural Networks (AI), and Miscellaneous
Mathematical Education, Neural Networks (AI), and Miscellaneous
  • Internet usage, Two-way communication, Graph Clustering
Selected research papers
Mathscinet
Mathscinet
  • Unconditionally stable methods for gradient flow using Convex Splitting Runge–Kutta scheme, Journal of Computational Physics, 2017
  • First and second order numerical methods based on a new convex splitting for phase-field crystal equation, Journal of Computational Physics, 2016
  • Electrostatics and heat conduction in high contrast composite materials, Journal of Computational Physics, 2006
  • Accelerating the non-uniform fast Fourier transform, SIAM Review, 2004 (Cited 449 times)
  • A reconstruction formula and uniqueness of conductivity in MREIT using two internal current distributions, Inverse Problems 2004
  • A direct adaptive Poisson solver of arbitrary order accuracy, J. Comp. Physics, 1996
Graduate Students
  • Chantara Tann Integrated Ph.D student
    Research Area: Numerical Differential Equations