- Finite element methods
- Hybridizable discontinuous Galerkin method
- Scientific computing
 Ngoc-Cuong Nguyen, Jaime Peraire, Manuel Solano and Sébastien Terrana An HDG method for non-matching meshes.. Submitted.
 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.. Submitted.
 Manuel Solano and F. Vargas. An unfitted HDG method for Oseen equations. Submitted.
 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).
 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)
 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).
 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).
 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).
 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) .
 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)
 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)
 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)
 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).
 Jay Gopalakrishnan, Manuel E. Solano and Felipe Vargas. Dispersion analysis of HDG methods . Journal of Scientific Computing, Vol. 77 (3), pp. 1703-1735, (2018).
 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).
 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).
 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)
 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) .
 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) .
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)
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)
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)
 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)
 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)
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)
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)
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)
 Bernardo Cockburn,
Francisco Javier Sayas and Manuel Solano. Coupling at a Distance HDG and BEM. SIAM J. Sci. Comput. 34, pp
Ph.D. Program in Applied Sciences with major in Mathematical Engineering, Universidad de Concepción
 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.
 Patrick Vega. Title: Hybridizable Discontinuous Galerkin method in fluid mechanics. In collaboration with Dr. Weifenq Qiu and Dr.Rodolfo Araya. 2016 - December 2018.
 Felipe Vargas. Title: Discontinuous Galerkin methods in continuum mechanics . In collaboration with Dr. Jay Gopalakrishnan. 2016 - January 2019.
 Paulo Zúñiga. Title: High order mixed method in fluid mechanics . In collaboration with Dr. Ricardo Oyarzúa. 2017 - 2019.
 Nestor Sánchez. Title: Development of numerical methods with
applications in plasma physics. In collaboration with Dr. Tonatiuh Sáncez-Vizuet. 2019 - present.
Undergraduate Program in Civil Mathematical Engineering, Universidad de Concepción
 Juan Manuel Cárdenas. Title: An HDG method for linear elasticity in curved domains. April 2017 - March 2018.
 Alejandra Barrios. Title: An HDG method for the biharmonic. March 2017 - November 2018.
 Fernando Peña. Title: A discontinuous Galerkin method for the heat equation in non poligonal domains. March 2018 - May 2020.
 Jaime Manríquez. Title: A hybridizable discontinuous Galerkin method for the Stokes problem in non-mathcing meshes. March 2020 - present.