Research

My research interests are within applied and computational mathematics with inverse coefficient problems in ordinary and partial differential equations (PDE) and an emphasis on numerical analysis of the identification of various parameters in variational problems of PDE. I am also interested in the approximation of solutions of various linear elliptic problems with non-trivial boundary conditions and their applications to problems from classical field theories and engineering.

AMS-SIMONS Grant 2024-2027.

Publications

Schroedinger-Steklov eigenproblems and representations of solutions of elliptic partial differential equations(PDEs).

M.Cho, M. Rivas , On the $L^2-$ orthogonality of Steklov eigenfunctions, Electronic Journal of Differential Equations, Conference 26, (2022), pp. 45-58.
M. Cho, "A novel efficient numerical solution of Laplace equation with mixed boundary conditions", International Journal of Computer Mathematics, DOI: 10.1080/00207160.2021.1967939.
M. Cho "Steklov expansion method for regularized harmonic boundary problems", Numerical Functional Analysis and Optimization, https://doi.org/10.1080/01630563.2020.1845728.
M. Cho, "Steklov approximations of Green's functions for Laplace equations", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, (2020), Vol. 39 No. 4, pp. 991-1003, https://doi.org/10.1108/COMPEL-09-2019-0357.
M. Cho, "Highly accurate and efficient numerical methods for a problem of heat conduction", Mathematics and Mechanics of Solids, (2019), 24(11), 3410–3417.
G. Auchmuty and M. Cho, "Steklov approximations of harmonic boundary value problems on planar regions", Journal of Computational and Applied Mathematics, 321 (2017), 302-313.
G. Auchmuty and M. Cho, "Boundary integrals and approximations of harmonic functions", Numerical Functional Analysis and Optimization, 36 (2015), 687-703.
Steklov eigenproblems and approximations of harmonic functions, PhD Thesis (2014), University of Houston.

Optimization methods for elliptic inverse problems with PDE constraints and inverse elasticity problem.

M. Cho, A. A. Khan, T. Malvsheva, M. Sama, L. White, Stability Analysis of the Inverse Problem of Parameter Identification in Mixed Variational Problems, Applications of Nonlinear Analysis, p. 61-100, 2018.
M. Cho, B. Jadamba, A. A. Khan, A. A. Oberai, and M. Sama, Identification in Mixed Variational Problems by Adjoint Methods with Applications, MOPTA, p. 65-84, 2017.
M. Cho, B. Jadamba, R. Kahler, A. A. Khan, and M. Sama, First-order and second-order adjoint methods for the inverse problem of identifying nonlinear parameters in PDEs, Industrial Mathematics and Complex systems, p. 147-163, 2017.