About me
I am an Assistant Professor at the Institute for Mathematical and Computational Engineering (IMC) of the Pontificia Universidad Católica de Chile (UC). My research interests are Numerical Analysis and Scientific Computing.
Education
- Ph.D. Applied Mathematics, Brown University 2016
- M.Sc. Applied Mathematics Brown University 2012
- Ingeniero Civil Matematico, Universidad de Concepcion 2010
- B.Sc. Mathematical Engineering, Universidad de Concepcion 2010
Research Interests
Numerical Analysis and Scientific Computing.
Publications:
Führer, T. and Sánchez, M.A. Quasi-interpolators with application to postprocessing in finite element methods. *Submitted. 2024.
- Sanchez, M. A., Valenzuela, J. Symplectic Hamiltonian finite element methods for semilinear wave propagation. Journal of Scientific Computing. 99 (3), 62, 2024.
- Hojas, V. A., Pérez-Arancibia, C., Sánchez, M. A. Reflectionless discrete perfectly matched layers for higher-order finite difference schemes. Submitted. June 2023.
- Cockburn, B., Du, S., Sánchez, M. A. Combining finite element space-discretizations with symplectic time-marching schemes for linear Hamiltonian systems. Frontiers in Applied Mathematics and Statistics 9, 1165371. 2023.
- Calderer, M. C., Henao, D., Sánchez, M. A., Song, S., Siegel, R. A. A numerical scheme and validation of the asymptotic energy release rate formula for a 2D gel thin film debonding problem. Submitted. 2023.
- Cockburn, B., Du, S., Sánchez, M. A. A priori error analysis of new semidiscrete, Hamiltonian HDG methods for the time-dependent Maxwell’s equations. ESAIM: Mathematical Modelling and Numerical Analysis 57 (4), 2097-2129. 2023.
- Calderer, M. C., Henao, D., Sánchez, M. A., Song, S., Siegel, R. A. Gels: Energetics, Singularities and Cavitation. Accepted. Journal of Elasticity. 2022.
- Song, S., Siegel, R. A., Sánchez, M. A., Calderer, M. C., & Henao, D. Experiments, modelling, and simulations for a gel bonded to a rigid substrate. Journal of Elasticity. 1-29, 2022.
- Cockburn, B., Du, S. & Sánchez, M. Discontinuous Galerkin Methods with Time-Operators in Their Numerical Traces for Time-Dependent Electromagnetics. Computational Methods in Applied Mathematics. 2022. https://doi.org/10.1515/cmam-2021-0215
- Sánchez, M. A., Du, S., Cockburn, B., Nguyen, N. C., & Peraire, J. Symplectic Hamiltonian finite element methods for electromagnetics. Computer Methods in Applied Mechanics and Engineering. 396, 114969, 2022.
- Genaro Laymuns and Manuel A. Sánchez,. Corrected finite element methods on unfitted meshes for Stokes moving interface problem. Computers & Mathematics with Applications. 108, 159-174, 2022.
- MA Sánchez, B Cockburn, NC Nguyen, J Peraire. Symplectic Hamiltonian finite element methods for linear elastodynamics. Computer Methods in Applied Mechanics and Engineering, 381: 113843, 2021.
- M. Ainsworth, S Jiang, MA Sánchez. An $\mathcal O(p^3)$ $hp$-version FEM in two dimensions: Preconditioning and post-processing. Computer Methods in Applied Mechanics and Engineering. 350: 766-802, 2019.
- Bernardo Cockburn, Zhixing Fu, Allan Hungria, Liangyue Ji, Manuel A. Sánchez. Stormer-Numerov HDG methods for acoustic waves. Journal of Scientific Computing. 75 (2): 597-624, 2018.
- LH Nguyen, SKF Stoter, M Ruess, MA Sánchez, and D Schillinger. The diffuse Nitsche method: Dirichlet constraints on phase‐field boundaries. International Journal for Numerical Methods in Engineering. 113 (4): 601-633, 2017.
- MA Sánchez, C Ciuca, NC Nguyen, J Peraire, B Cockburn. Symplectic Hamiltonian HDG methods for wave propagation phenomena. Journal of Computational Physics. 350: 951-973, 2017.
- Bernardo Cockburn, Manuel A. Sánchez, Chunguang Xiong. Supercloseness of primal-dual Galerkin approximations for second order elliptic problems. Journal of Scientific Computing 75 (1): 376-394, 2018.
- Erik Burman, Johnny Guzmán, Manuel A. Sánchez, and Marcus Sarkis. Robust flux error estimation of an unfitted Nitsche method for high-contrast interface problems. IMA Journal of Numerical Analysis. 38 (2): 646-668, 2018.
- Johnny Guzmán, Manuel A. Sánchez, and Marcus Sarkis. A finite element method for high-contrast interface problems with error estimates independent of contrast. Journal of Scientific Computing. 73 (1): 330-365, 2017
- Johnny Guzmán, Manuel A. Sánchez, and Marcus Sarkis. Higher-order finite element methods for elliptic problems with interfaces. ESAIM: Mathematical Modelling and Numerical Analysis. 50 (5): 1561-1583, 2016.
- Mark Ainsworth and Manuel A. Sánchez. Computing the Bezier control points of the Lagrangian interpolant in arbitrary dimension. SIAM Journal on Scientific Computing. 38 (3): A1682-A1700, 2016.
- Johnny Guzmán, Manuel A. Sánchez, and Marcus Sarkis. On the accuracy of finite element approximations to a class of interface problems. Mathematics of Computations. 85 (301): 2071-2098, 2016.
- Johnny Guzmán and Manuel A. Sánchez. Max-norm stability of low order Taylor–Hood elements in three dimensions. Journal of Scientific Computing. 65 (2): 598-621, 2015.
- Gabriel N. Gatica, Antonio Márquez, and Manuel A. Sánchez. Pseudostress-based mixed finite element methods for the Stokes problem in $\mathbb R^n$ with Dirichlet boundary conditions. I: A priori error analysis. Communications in Computational Physics, 12 (1): 109-134, 2012.
- Gabriel N. Gatica, Antonio Márquez, and Manuel A. Sánchez. A priori and a posteriori error analyses of a velocity-pseudostress formulation for a class of quasi-Newtonian Stokes flows. Computer Methods in Applied Mechanics and Engineering. 200 (17-20): 1619-1636, 2011.
- Gabriel N. Gatica, Antonio Márquez, and Manuel A. Sánchez. Analysis of a velocity–pressure–pseudostress formulation for the stationary Stokes equations. Computer Methods in Applied Mechanics and Engineering, 199 (17-20): 1064-1079, 2010.
Students
- Diego Vera, Master of Mathematical and Computational Engineering, IMC UC. August 2024-.
- Sebastian Ferra, Master of Mathematical and Computational Engineering, IMC UC. August 2023-.
- Cristhian Nuñez, Ph.D. in Mathematics, UC. 2022-.
- Vicente Hojas, Master of Engineering Sciences, UC. Graduated January 2024.
- Pablo Cortes, Master of Engineering Sciences, UC. 2021-.
- Joaquin Valenzuela, Master of Engineering Sciences, UC. Graduated July 2023.
- Genaro Laymuns. Master of Engineering Sciences, UC. Graduated July 2021.
Follow this link to learn more about current and past students’ projects, including undergraduate research projects. Research opportunities for students (undergraduate and graduate) are also available.
Teaching
UC
- 2024 - II. IMT3410 Métodos para Ecuaciones Diferenciales
- 2024 - I. Algebra Lineal Numérica IMT2111
- 2024 - I. Algebra Lineal MAT1203
- 2023 - II. IMT3410 Métodos para Ecuaciones Diferenciales
- 2023 - I. Modulo Analisis Numerico, Introduccion a la Ingenieria Matematica IMT1001
- 2023 - I. Algebra Lineal Numerica IMT2111
- 2023 - I. Ecuaciones Diferenciales Ordinarias MAT1640
- 2022 - II. IMT3410 Métodos para Ecuaciones Diferenciales
- 2022 - I. Algebra Lineal Numerica IMT2111
- 2022 - I. Cálculo I MAT 1610
- 2021 - I. Ecuaciones Diferenciales Ordinarias MAT1640 Youtube channel
- 2021 - I. Algebra Lineal Numerica IMT2111
- 2020 - II. Topicos Avanzados de Ingenieria Matematica, IMT 3800
- 2020 - II. Calculo Cientifico I, MAT2605
- 2020 - I. Álgebra Lineal Numérica, IMT 2111
- 2019 - II. Introducción al Álgebra, MAT 1206
- 2019 - II. Tópicos Avanzados de Análisis Numérico, IMT 3810
- 2019 - I. Álgebra Lineal Numérica, IMT 2111
- 2019 - I. Cálculo I MAT 1610
- 2018 - II. Taller de Matemáticas Aplicadas IMT 2116
University of Minnesota
- Spring 2018 Calculus II
- Fall 2017 Calculus I
Contact me
email: manuel.sanchez at uc.cl
mailing address:
Instituto de Ingenieria Matematica y Computacional
Edificio Hernan Briones, 2do piso, Campus San Joaquin UC
Avda. Vicuna Mackenna 4860, Macul, Santiago, Chile.