Dr. Yi's Research Page

Fundings

Department of Energy (PI), DE-SC0024703, "Advanced Multi-Physics Machine Learning for Subsurface Energy Systems Across Scales," (10/15/2023--10/14/2026), $4,930,625
National Science Foundation (PI), DMS 2208426, "Collaborative Research: Physics-Preserving Adaptive Finite Element Methods for Thermo-Poroelasticity," (07/01/2022--06/30/2025), $250,518
College of Science Research Enhancement Fund (Co-PI), "Visualization and Analysis of Giant Virus Structure," (01/01/2015--07/31/2015), $20,000
National Science Foundation (PI), DMS 1217123, "A mixed finite element framework for Biot's consolidation model and its interface problems," (09/01/2012--08/31/2016), $263,569
The University Research Institute grant (PI), " Development, analysis and implementation of numerical methods for flow in deformable porous media," (01/01/2011--12/31/2011), $5,000
National Science Foundation (Co-PI), DMS 0707562, "Modeling, Analysis and Simulation of Multiscale Nonlinear Systems: Workshop at Oregon State University," (05/01/2007--04/30/2008). $27,634
Department of Energy (Senior Personnel), Office of Science, Multiscale Mathematics Initiative Project 98089, "Modeling, Analysis, and Simulation of Multiscale Preferential Flow," (08/15/2005--08/14/2008), $647,000

List of Publications

S.-Y. Yi and S. Lee, Physics-preserving enriched Galerkin method for a fully-coupled thermo-poroelasticity, Numerische Mathematik, accepted, 2024.
X. Hu, S. Lee, L. Mu, and S.-Y. Yi, Pressure-robust enriched Galerkin methods for the Stokes equations, Journal of Computational and Applied Mathematics, 436, 115449, 2024
F. Ballarin, S. Lee, and S.-Y. Yi, Projection-based reduced order modeling of a fixed-point iterative coupling scheme for thermo-poroelasticity, Results in Applied Mathematics, vol. 21, 100430, 2024
S. Lee and S.-Y. Yi, Locking-free and locally-conservative enriched Galerkin method for linear poroelasticity, Journal of Scientific Computing, vol. 94, article number 26, 2023
S.-Y. Yi, X. Hu, S. Lee, J.H. Adler, and L. Zikatanov, An enriched Galerkin method for the Stokes equations, Computers & Mathematics with Applications, vol. 120, pp. 115--131, 2022
S.-Y. Yi, S. Lee, and L. Zikatanov, Locking-free enriched Galerkin method for linear elasticity, SIAM Journal on Numerical Analysis, vol. 60, no.1, pp. 52-75, 2022
Y. Jeon and S.-Y. Yi, The immersed interface hybridized difference method for parabolic interface problems, Numerical Mathematics: Theory, Methods and Applications, vol. 15, no. 2, pp. 336--359, 2022
S.-Y. Yi and K. Lee, Numerical study for European option pricing equations with non-Levy jumps, Applicable Analysis, vol. 100, no. 7, pp. 1454--1470, 2021
M.L. Bean and S.-Y. Yi, A Monolithic Mixed Finite Element Method for a Fluid-Structure Interaction Problem, Applied Mathematics and Computation, vol. 363, 2019
S.-Y. Yi, A lowest-order weak Galerkin method for linear elasticity, Journal of Compuational and Applied Mathematics, vol. 350, pp. 286--298, 2019
S.-Y. Yi, A study of two modes of locking in poroelasticity, SIAM Journal on Numerical Analysis, vol. 55, no. 4, pp. 1915--1936, 2017
M. L. Bean, K. Lipnikov, S.-Y. Yi, A block-diagonal preconditioner for a four-field mixed fintie element method for Biot's equations, Applied Numerical Mathematics, vol. 122, pp. 1--13, 2017
S.-Y. Yi and M. L. Bean, Iteratively coupled solution strategies for a four-field mixed finite method for poroelasticity, International Journal for Numerial and Analytical Methods in Geomechanics, vol. 41, issue 2, pp. 159--179, 2017
A. Cesmelioglu, H. Lee, A. Quaini, K. Wang, and S.-Y. Yi, Optimization-based decoupling algorithms for fluid-poroelastic system, In Topics in Numerical Partial Differential Equations and Scientific Computing, The IMA Volumes in Mathematics and its Applications 160, S.C. Brenner (ed.), pp. 137-176, 2016
M. Peszynska, R. E. Showalter, and S.-Y. Yi, Flow and transport when scales are not separated: Numerical analysis and simulations of micro- and macro-models, International Journal of Numerical Analysis and Modeling, vol. 12, no. 3, pp. 476--515, 2015.
M. L. Bean and S.-Y. Yi, An Immersed Interface Method for a 1D Poroelasticity Problem with Discontinuous Coefficients, Journal of Computational and Applied Mathematics, vol. 272, pp. 81--96, 2014
S.-Y. Yi, Convergence analysis of a new mixed finite element method for Biot's consolidation model, Numerical Methods for Partial Differential Equations, Numerical Methods for Partial Differential Equations, vol.30, no.4, pp 1189-1210, 2014
S.-Y. Yi and S. Lee, An operator-splitting method for the forced Korteweg-de Vries equation, Applied Mathematics and Computation, vol. 230, pp. 276-289, 2014
S.-Y. Yi, Coupling of nonconforming and mixed finite element methods for Biot's consolidation model, Numerical Methods for Partial Differential Equations, vol. 29, pp. 1749-1777, 2013
S.-Y. Yi and J. Douglas, Jr., An experimental study of several multidimensional, locally conservative, Eulerian-Lagrangian finite element methods for a semilinear parabolic equation, International Journal of Numerical Analysis and Modeling Series B, vol. 4, no. 3, pp. 29-314, 2013.
S.-Y. Yi, M. Peszynska, and R. E. Showalter, Numerical upscaled model of transport with non-separated scaes, XVIII International Conference on Water Resources, CMWR 2010, J. Carreta (Ed), Barcelona, 2010
J. Douglas, Jr., A. M. Spagnuolo, and S.-Y. Yi, The Convergence of a multidimensional, locally conservative, Eulerian-Lagrangian finite element method for a semilinear parabolic equation, Math. Models Methods Appl. Sci., 20(2), pp. 315-348, 2010
M. Peszynska, R. E. Showalter, and S.-Y. Yi, Homogenization of pseudoparabolic systems, Applicable Analysis, 88(9), pp. 1265-1282, 2009
M. Peszynska and S.-Y. Yi, Numerical methods for unsaturated flow with dynamic capillary pressure in heterogeneous porous media, International Journal of Numerical Analysis and Modeling, 5, Supp., pp.126-149, 2008
S.-Y. Yi, A new nonconforming mixed finite element method for linear elasticity, Math. Models Methods Appl. Sci., 16(7), pp. 979-999, 2006
S.-Y. Yi, mixed finite element methods for llinear elasticity using rectangular elements in two and three dimensions, Calcolo, 42(2), pp. 115-133, 2005

Position Openings

I have position openings for one postdoc research associate and two graduate research assistants to work on my current NSF and DOE projects. Please, contact me if you're interested.

Research Interests

My general research interests are in Numerical Analysis and Scientific Computing. My primary research interests include

Numerical methods for partial differential equations

Flow and transport in porous media

Computational solid mechanics

Modeling of multi-scale and multi-physics problems

Fundings

Department of Energy (PI), DE-SC0024703, "Advanced Multi-Physics Machine Learning for Subsurface Energy Systems Across Scales," (10/15/2023--10/14/2026), $4,930,625

National Science Foundation (PI), DMS 2208426, "Collaborative Research: Physics-Preserving Adaptive Finite Element Methods for Thermo-Poroelasticity," (07/01/2022--06/30/2025), $250,518

College of Science Research Enhancement Fund (Co-PI), "Visualization and Analysis of Giant Virus Structure," (01/01/2015--07/31/2015), $20,000

National Science Foundation (PI), DMS 1217123, "A mixed finite element framework for Biot's consolidation model and its interface problems," (09/01/2012--08/31/2016), $263,569

The University Research Institute grant (PI), " Development, analysis and implementation of numerical methods for flow in deformable porous media," (01/01/2011--12/31/2011), $5,000

National Science Foundation (Co-PI), DMS 0707562, "Modeling, Analysis and Simulation of Multiscale Nonlinear Systems: Workshop at Oregon State University," (05/01/2007--04/30/2008). $27,634

Department of Energy (Senior Personnel), Office of Science, Multiscale Mathematics Initiative Project 98089, "Modeling, Analysis, and Simulation of Multiscale Preferential Flow," (08/15/2005--08/14/2008), $647,000

List of Publications

S.-Y. Yi and S. Lee, Physics-preserving enriched Galerkin method for a fully-coupled thermo-poroelasticity, Numerische Mathematik, accepted, 2024.

X. Hu, S. Lee, L. Mu, and S.-Y. Yi, Pressure-robust enriched Galerkin methods for the Stokes equations, Journal of Computational and Applied Mathematics, 436, 115449, 2024

F. Ballarin, S. Lee, and S.-Y. Yi, Projection-based reduced order modeling of a fixed-point iterative coupling scheme for thermo-poroelasticity, Results in Applied Mathematics, vol. 21, 100430, 2024

S. Lee and S.-Y. Yi, Locking-free and locally-conservative enriched Galerkin method for linear poroelasticity, Journal of Scientific Computing, vol. 94, article number 26, 2023

S.-Y. Yi, X. Hu, S. Lee, J.H. Adler, and L. Zikatanov, An enriched Galerkin method for the Stokes equations, Computers & Mathematics with Applications, vol. 120, pp. 115--131, 2022

S.-Y. Yi, S. Lee, and L. Zikatanov, Locking-free enriched Galerkin method for linear elasticity, SIAM Journal on Numerical Analysis, vol. 60, no.1, pp. 52-75, 2022

Y. Jeon and S.-Y. Yi, The immersed interface hybridized difference method for parabolic interface problems, Numerical Mathematics: Theory, Methods and Applications, vol. 15, no. 2, pp. 336--359, 2022

S.-Y. Yi and K. Lee, Numerical study for European option pricing equations with non-Levy jumps, Applicable Analysis, vol. 100, no. 7, pp. 1454--1470, 2021

M.L. Bean and S.-Y. Yi, A Monolithic Mixed Finite Element Method for a Fluid-Structure Interaction Problem, Applied Mathematics and Computation, vol. 363, 2019

S.-Y. Yi, A lowest-order weak Galerkin method for linear elasticity, Journal of Compuational and Applied Mathematics, vol. 350, pp. 286--298, 2019

S.-Y. Yi, A study of two modes of locking in poroelasticity, SIAM Journal on Numerical Analysis, vol. 55, no. 4, pp. 1915--1936, 2017

M. L. Bean, K. Lipnikov, S.-Y. Yi, A block-diagonal preconditioner for a four-field mixed fintie element method for Biot's equations, Applied Numerical Mathematics, vol. 122, pp. 1--13, 2017

S.-Y. Yi and M. L. Bean, Iteratively coupled solution strategies for a four-field mixed finite method for poroelasticity, International Journal for Numerial and Analytical Methods in Geomechanics, vol. 41, issue 2, pp. 159--179, 2017

M. Peszynska, R. E. Showalter, and S.-Y. Yi, Flow and transport when scales are not separated: Numerical analysis and simulations of micro- and macro-models, International Journal of Numerical Analysis and Modeling, vol. 12, no. 3, pp. 476--515, 2015.

M. L. Bean and S.-Y. Yi, An Immersed Interface Method for a 1D Poroelasticity Problem with Discontinuous Coefficients, Journal of Computational and Applied Mathematics, vol. 272, pp. 81--96, 2014

S.-Y. Yi, Convergence analysis of a new mixed finite element method for Biot's consolidation model, Numerical Methods for Partial Differential Equations, Numerical Methods for Partial Differential Equations, vol.30, no.4, pp 1189-1210, 2014

S.-Y. Yi and S. Lee, An operator-splitting method for the forced Korteweg-de Vries equation, Applied Mathematics and Computation, vol. 230, pp. 276-289, 2014

S.-Y. Yi, Coupling of nonconforming and mixed finite element methods for Biot's consolidation model, Numerical Methods for Partial Differential Equations, vol. 29, pp. 1749-1777, 2013

S.-Y. Yi and J. Douglas, Jr., An experimental study of several multidimensional, locally conservative, Eulerian-Lagrangian finite element methods for a semilinear parabolic equation, International Journal of Numerical Analysis and Modeling Series B, vol. 4, no. 3, pp. 29-314, 2013.

S.-Y. Yi, M. Peszynska, and R. E. Showalter, Numerical upscaled model of transport with non-separated scaes, XVIII International Conference on Water Resources, CMWR 2010, J. Carreta (Ed), Barcelona, 2010

J. Douglas, Jr., A. M. Spagnuolo, and S.-Y. Yi, The Convergence of a multidimensional, locally conservative, Eulerian-Lagrangian finite element method for a semilinear parabolic equation, Math. Models Methods Appl. Sci., 20(2), pp. 315-348, 2010

M. Peszynska, R. E. Showalter, and S.-Y. Yi, Homogenization of pseudoparabolic systems, Applicable Analysis, 88(9), pp. 1265-1282, 2009

M. Peszynska and S.-Y. Yi, Numerical methods for unsaturated flow with dynamic capillary pressure in heterogeneous porous media, International Journal of Numerical Analysis and Modeling, 5, Supp., pp.126-149, 2008

S.-Y. Yi, A new nonconforming mixed finite element method for linear elasticity, Math. Models Methods Appl. Sci., 16(7), pp. 979-999, 2006

S.-Y. Yi, mixed finite element methods for llinear elasticity using rectangular elements in two and three dimensions, Calcolo, 42(2), pp. 115-133, 2005

Position Openings

I have position openings for one postdoc research associate and two graduate research assistants to work on my current NSF and DOE projects. Please, contact me if you're interested.