이준엽 교수는 수학전공 교수로서 수치해석과 과학계산을 전공하고 있다. 뉴욕대학교(NYU) Courant Institute에서 박사학위를 취득하였으며, <SIAM Review>, <Inverse Problems>, <J. of Computation Physics> 등을 포함하는 SCI 저널에 역문제의 수치해법 및 수치미분방정식의 고속해법 관련한 40여 편의 논문을 게재하였다.
대외적으로는 한국연구재단 자연과학단장, 한국산업응용수학회(KSIAM)의 부회장, 총무이사, 편집이사 등과 대한수학회(KMS)의 전산이사와 사업이사 등을 역임하였고, 교내에서는 관리처장, 입학관리부처장, 수리물리과학부 학부장과 중점연구소인 수리과학연구소장 직을 수행하였다.
이외에도 학술적으로는 1~13회 AMF 조직위원, ICM 2014 전산위원장, 1~6회 ICIP 조직위원 등을 맡았으며, 중등수학과 관련하여는 수학능력시험 출제위원, IMO 2000 출제위원, 교과서 심의위원 등을 역임하였다.
A High-Order and Unconditionally Energy Stable Scheme for the Conservative Allen-Cahn Equation with a Nonlocal Lagrange MultiplierJOURNAL OF SCIENTIFIC COMPUTING, 2022, v.90 no.1, 51
Energy quadratization Runge-Kutta method for the modified phase field crystal equationModelling and Simulation in Materials Science and Engineering, 2022, v.30 no.2, 24004
Energy quadratization Runge–Kutta scheme for the conservative Allen–Cahn equation with a nonlocal Lagrange multiplierApplied Mathematics Letters, 2022, v.132, 108161
Long-time simulation of the phase-field crystal equation using high-order energy-stable CSRK methodsComputer Methods in Applied Mechanics and Engineering, 2020, v.364, 112981
A constrained convex splitting scheme for the vector-valued Cahn-Hilliard equationJournal of the Korean Society for Industrial and Applied Mathematics, 2019, v.23 no.1, 1-18
First- and second-order energy stable methods for the modified phase field crystal equationComputer Methods in Applied Mechanics and Engineering, 2017, v.321, 1-17
HIGHER ORDER OPERATOR SPLITTING FOURIER SPECTRAL METHODS FOR THE ALLEN–CAHN EQUATIONJournal of the Korean Society for Industrial and Applied Mathematics, 2017, v.21 no.1, 1~16
Analysis and computational method based on quadratic B-spline FEM for the Rosenau-Burgers equationNumerical Methods for Partial Differential Equations, 2016, v.32 no.3, 877-895
First and second order numerical methods based on a new convex splitting for phase-field crystal equationJournal of Computational Physics, 2016, v.327, 519-542
A second order operator splitting method for Allen-Cahn type equations with nonlinear source termsPhysica A: Statistical Mechanics and its Applications, 2015, v.432, 24-34
A NUMERICAL METHOD FOR THE MODIFIED VECTOR-VALUED ALLEN–CAHN PHASE-FIELD MODEL AND ITS APPLICATION TO MULTIPHASE IMAGE SEGMENTATIONJournal of the Korean Society for Industrial and Applied Mathematics, 2014, 제18권 1호, 27-41
A fast direct solver for scattering from periodic structures with multiple material interfaces in two dimensionsJOURNAL OF COMPUTATIONAL PHYSICS, 2014, v.258, 738-751
An enhanced parareal algorithm based on the deferred correction methods for a stiff systemJOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2014, v.255, 297-305
[학술지논문] A High-Order and Unconditionally Energy Stable Scheme for the Conservative Allen-Cahn Equation with a Nonlocal Lagrange Multiplier
JOURNAL OF SCIENTIFIC COMPUTING, 2022, v.90
no.1
, 51-51
SCIE
[학술지논문] Energy quadratization Runge-Kutta scheme for the conservative Allen-Cahn equation with a nonlocal Lagrange multiplier
APPLIED MATHEMATICS LETTERS, 2022, v.132
no.108161
, 1-10
SCI
[학술지논문] An energy stable Runge-Kutta method for convex gradient problems
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2020, v.367
no.1
, 112455-112455
SCI
[학술지논문] Long-time simulation of the phase-field crystal equation using high-order energy-stable CSRK methods
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2020, v.364
no.0
, 112981-112981
SCI
[학술지논문] A High-Order Convex Splitting Method for a Non-Additive Cahn-Hilliard Energy Functional
MATHEMATICS, 2019, v.7
no.12
, 1242-1242
SCIE
[학술지논문] A constrained convex splitting scheme for the vector-valued Cahn-Hilliard equation
Journal of the Korean Society for Industrial and Applied Mathematics, 2019, v.23
no.1
, 1-18