Manuel E. Solano

Manuel E. Solano

Associate Professor

Departamento de Ingeniería Matemática

Facultad de Ciencias Físicas y Matemáticas

Centro de Investigación en Ingeniería Matemática CI²MA

Universidad de Concepción

Research

- Numerical analysis
- Finite element methods
- Hybridizable discontinuous Galerkin method
- Scientific computing

Publications

[37] Jessika Camaño, Ricardo Oyarzúa, Miguel Serón and Manuel E. SolanoA conforming finite element method for a nonisothermal fluid-membrane interaction. Submitted (2023).

[36] Liliana Camargo, Bibiana López-Rodríguez, Mauricio Osorio and Manuel Solano. An adaptive and quasi-periodic HDG method for Maxwell's equations in heterogeneous media. Journal of Scientific Computing, Vol. 98, 7 (2024).

[35] Juan M. Cárdenas and Manuel Solano A high order unfitted hybridizable discontinuous Galerkin method for linear elasticity.. IMA Journal of Numerical Analysis, 44 (2), 945-979 (2024).

[34] Esteban Henríquez and Manuel E. SolanoAn unfitted HDG method for a distributed optimal control problem. Journal of Computational and Applied Mathematics, Vol. 441, 115703 (2023).

[33] Liliana Camargo and Manuel Solano A high order unfitted HDG method for the Helmholtz equation with first order absorbing boundary condition.. Submitted (2021).

[32] Nestor Sánchez, Tonatiuh Sánchez-Vizuet and Manuel E. Solano Afternote to Coupling at a distance: convergence analysis and a priori error estimates.. Computational Methods in Applied Mathematics, 22(4),945-970(2022).

[31] Jaime Manríquez, Ngoc-Cuong Nguyen and Manuel Solano A dissimilar non-matching HDG discretization for Stokes flows.. Computer Methods in Applied Mechanics and Engineering Volume 399, 1 September 2022, 115292.

[30] Ricardo Oyarzúa, Manuel Solano and Paulo Zúñiga. Analysis of an unfitted mixed finite element method for a class of quasi-Newtonian Stokes flow. Computers and Mathematics with Applications, Vol 114 , 225-243 (2022).

[29] Nestor Sánchez, Tonatiuh Sánchez-Vizuet and Manuel E. Solano Error analysis of an unfitted HDG method for a class of non-linear elliptic problems.. Journal of Scientific Computing, Vol. 90, 92 (2022).

[28] Manuel Solano and F. Vargas. An unfitted HDG method for Oseen equations. Journal of Computational and Applied Mathematics, Vol. 399, 113721 (2022).

[27] Ngoc-Cuong Nguyen, Jaime Peraire, Manuel Solano and Sébastien Terrana An HDG method for dissimlar meshes.. IMA Journal of Numerical Analysis, 42 (2), 1665–1699 (2022).

[26] Nestor Sánchez, Tonatiuh Sánchez-Vizuet and Manuel E. Solano A priori and a posteriori error analysis of an unfitted HDG method for semi-linear elliptic problems.. Numerische Mathematik, Vol. 148, 919-958 (2021).

[25] Ricardo Oyarzúa, Sander Rhebergen, Manuel Solano and Paulo Zúñiga. Error analysis of a conforming and locking-free four-field formulation for the stationary Biot's model. ESAIM: M2AN, Vol. 55, S475-S506 (2021).

[24] Peter Monk, Cinthya Rivas, Rodolfo Rodríguez and Manuel E. Solano An asymptotic model based on matching far and near field expansions for thin gratings problems. ESAIM: M2AN, Vol. 55, S507-S533 (2021)

[23] Liliana Camargo, Bibiana López-Rodríguez, Mauricio Osorio and Manuel Solano. An HDG method for Maxwell equations in heterogeneous media. Computer Methods in Applied Mechanics and Engineering. Vol. 368, 113178 (2020).

[22] Tonatiuh Sanchez-Vizuet, Antoine J. Cerfon and Manuel E. Solano Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad-Shafranov equation by extension from polygonal subdomains. Computer Physics Communications, Vol. 255, 107239, (2020).

[21] Ricardo Oyarzúa, Manuel Solano and Paulo Zúñiga. A priori and a posteriori error analyses of a high order unfitted mixed-FEM for Stokes flow. Computer Methods in Applied Mechanics and Engineering. Vol. 360, 112780 (2020).

[20] Rodolfo Araya, Manuel Solano and Patrick Vega. A posteriori error analysis of an HDG method for the Oseen problem. Applied Numerical Mathematics, Vol. 146, 291–308 (2019) .

[19] Manuel Solano and F. Vargas. A high order HDG method for Stokes flow in curved domains.. J. Sci Comput., Vol. 79, Issue 3, pp 1505–1533 (2019)

[18] Ricardo Oyarzúa, Manuel Solano and Paulo Zúñiga. A high order mixed-FEM for diffusion problems on curved domains. J. Sci Comput. , Vol. 79, 1, pp. 49-78 (2019)

[17] Ariel Lombardi, Rommel Bustinza and Manuel Solano An anisotropic a priori error analysis for a convection--dominated diffusion problem using the HDG method.. Computer Methods in Applied Mechanics and Engineering, Vol. 345, pp. 382-401 (2019)

[16] Tonatiuh Sánchez-Vizuet and Manuel E. Solano A Hybridizable Discontinuous Galerkin solver for the Grad-Shafranov equation.. Computer Physics Communications, Vol. 235, pp 120-132, (2019).

[15] Jay Gopalakrishnan, Manuel E. Solano and Felipe Vargas. Dispersion analysis of HDG methods . Journal of Scientific Computing, Vol. 77 (3), pp. 1703-1735, (2018).

[14] R. Araya, Manuel Solano and P. Vega. Analysis of an adaptive HDG method for the Brinkman problem. , IMA Journal of Numerical Analysis, vol. 39, 3, pp. 1502-1528, (2019).

[13] C. Rivas, R. Rodríguez and Manuel E. Solano. A perfectly matched layer for finite-element calculations of diffraction by metallic surface-relief gratings.. Wave Motion, Vol. 78, pp. 68-82, (2018).

[12] C. Rivas, Manuel E. Solano, R. Rodríguez, P. B. Monk and A. Lakhtakia. Asymptotic model for finite-element calculations of diffraction by shallow metallic surface-relief gratings.. J. Opt. Soc. Am. A. Vol. 34, Issue 1, pp. 68-79 (2017)

[11] H. Chen, W. Qiu, K. Shi and Manuel Solano A superconvergent HDG method for the Maxwell equations.. J. Sci Comput. , Vol. 70, 3, pp. 1010-1029 (2017) .

[10] W. Qiu ,Manuel Solano and Patrick Vega. A high order HDG method for curved-interface problems via approximations from straight triangulations.. J. Sci Comput., Vol. 69, 3, pp. 1384-1407 (2016) .

[9] Manuel E. Solano, Greg D. Barber, Akhlesh Lakhtakia, Muhammad Faryad, Peter B. Monk and Thomas E. Mallouk. Buffer layer between a planar optical concentrator and a solar cell. AIP Advances 5, 097150 (2015)

[8] Mikhail V. Shuba, Muhammad Faryad, Manuel E. Solano, Peter B. Monk and Akhlesh Lakhtakia. Adequacy of the rigorous coupled-wave approach for thin-film silicon solar cells with periodically corrugated metallic backreflectors: spectral analysis. J. Opt. Soc. Am. A. Vol. 32, Issue 7, pp. 1222-1230 (2015)

[7] Manuel E. Solano, Muhammad Faryad, Akhlesh Lakhtakia, and Peter B. Monk. Comparison of rigorous coupled-wave approach and finite element method for photovoltaic devices with periodically corrugated metallic back reflector. JOSA A, Vol. 31, Issue 10, pp. 2275-2284 (2014)

[6] Bernardo Cockburn and Manuel Solano. Solving convection-diffusion problems on curved domains by extensions from subdomains. J. Sci Comput., Vol. 59, pp. 512-543 (2014)

[5] Bernardo Cockburn, Weifeng Qiu and Manuel Solano. A priori error analysis for HDG methods using extensions from subdomains to achieve boundary-conformity. Math. Comp., Vol. 82, 286, pp. 665-699 (2014)

[4] Manuel Solano, Muhammad Faryad, Peter Monk, Thomas Mallouk and Akhlesh Lakhtakia. Periodically multilayered planar optical concentrator for photovoltaic solar cells. Applied Physics Letters, Vol. 103, 191115 (2013)

[3] Manuel Solano, Muhamamd Faryad, Anthony S. Hall, Thomas Mallouk, Peter Monk, and Akhlesh Lakhtakia. Optimization of the absorption efficiency of an amorphous-silicon thin-film tandem solar cell backed by a metallic surface-relief grating. Applied Optics, Vol. 52, Issue 5, pp. 966-979 (2013)

[2] Bernardo Cockburn and Manuel Solano. Solving Dirichlet Boundary-value Problems on Curved Domains by Extensions from Subdomains. SIAM J. Sci. Comput. 34, pp. A497-A519 (2012)

[1] Bernardo Cockburn, Francisco Javier Sayas and Manuel Solano. Coupling at a Distance HDG and BEM. SIAM J. Sci. Comput. 34, pp A28-A47 (2012)

Students

Ph.D. Program in Applied Sciences with major in Mathematical Engineering, Universidad de Concepción

[1] Cinthya Rivas. Title: Efficient computation of electromagnetic fields in solar cells. In collaboration with Dr. Rodolfo Rodríguez and Dr. Peter Monk. April 2014 - September 2018.

[2] Patrick Vega. Title: Hybridizable Discontinuous Galerkin method in fluid mechanics. In collaboration with Dr. Weifenq Qiu and Dr.Rodolfo Araya. 2016 - December 2018.

[3] Felipe Vargas. Title: Discontinuous Galerkin methods in continuum mechanics . In collaboration with Dr. Jay Gopalakrishnan. 2016 - January 2019.

[4] Paulo Zúñiga. Title: High order mixed method in fluid mechanics . In collaboration with Dr. Ricardo Oyarzúa. 2017 - 2019.

[5] Nestor Sánchez. Title: Development of numerical methods with applications in plasma physics. In collaboration with Dr. Tonatiuh Sáncez-Vizuet. 2019 - September 2021.

[6] Isaac Bermúdez. Title: Discontinuous Galerkin methods for interface problems: application to water desalination processes. In collaboration with Dra. Jessika Camaño. September 2022-present.

Undergraduate Program in Civil Mathematical Engineering, Universidad de Concepción

[1] Juan Manuel Cárdenas. Title: An HDG method for linear elasticity in curved domains. April 2017 - March 2018.

[2] Alejandra Barrios. Title: An HDG method for the biharmonic. March 2017 - November 2018.

[3] Fernando Peña. Title: A discontinuous Galerkin method for the heat equation in non poligonal domains. March 2018 - May 2020.

[4] Jaime Manríquez. Title: A hybridizable discontinuous Galerkin method for the Stokes problem in non-mathcing meshes. March 2020 - December 2020.

[5] Esteban Henríquez. Title: An unfitted hybridizable discontinuous Galerkin method in shape optimization. December 2021-December 2022.

[6] Víctor Burgos. Title: Desarrollo y análisis de un método numérico para un modelo fenomenológico de osmosis inversa . In collaboration with Dr. Ricardo Oyarzúa, Universidad del Bío-Bío. Enero 2023-present.