- Finite element methods
- Hybridizable discontinuous Galerkin method
- Scientific computing
 Ricardo Oyarzúa, Manuel Solano and Paulo Zúñiga. A high order mixed-FEM for diffusion problems on curved domains. Submitted.
 Jay Gopalakrishnan, M. E. Solano and Felipe Vargas. Dispersion analysis of HDG methods equation. Submitted.
 Tonatiuh Sánchez-Vizuet and M. E. Solano A Hybridizable Discontinuous Galerkin solver for the Grad-Shafranov equation. Submitted.
 Ariel Lombardi, Rommel Bustinza and M. Solano and F. Vargas. An anisotropic a priori error analysis for a convection--dominated diffusion problem using the HDG method.. Submitted.
 M. Solano and F. Vargas. A high order HDG method for Stokes flow in curved domains.. Submitted.
 R. Araya, M. Solano and P. Vega. Analysis of an adaptive HDG method for the Brinkman problem. Accepted.
 C. Rivas, R. Rodriguez 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. Rodriguez, 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 M. Solano A superconvergent HDG method for the Maxwell equations.. J. Sci Comput. , Vol. 70, 3, pp. 1010-1029 (2017) .
 W. Qiu ,M. Solano and P. 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)
 B. Cockburn and M. Solano. Solving convection-diffusion problems on curved domains by extensions from subdomains. J. Sci Comput., Vol. 59, pp. 512-543 (2014)
 B. Cockburn, W. Qiu and M. 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)
M. Solano, M. Faryad, P. Monk, Thomas Mallouk and A. Lakhtakia. Periodically multilayered planar optical concentrator for photovoltaic solar cells. Applied Physics Letters, Vol. 103, 191115 (2013)
M. Solano, M. Faryad, A. Hall, T. Mallouk, P. Monk, and A. 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 M. Solano. Solving
Dirichlet Boundary-value Problems on Curved
Domains by Extensions from Subdomains. SIAM J. Sci.
Comput. 34, pp. A497-A519 (2012)
 B. Cockburn,
F.-J. Sayas and M. 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 Rodolfo Rodríguez. 2014 - present.
 Patrick Vega. Title: Hybridizable Discontinuous Galerkin method in fluid mechanics. In collaboration with Weifenq Qiu and Rodolfo Araya. 2016 - present.
 Felipe Vargas. Title: Discontinuous Galerkin methods in continuum mechanics . In collaboration with Jay Gopalakrishnan. 2016 - present.
 Paulo Zúñiga. Title: High order mixed method in fluid mechanics . In collaboration with Ricardo Oyarzúa. 2017 - present.
Undergraduate Program in Civil Mathematical Engineering, Universidad de Concepción
 Juan Manuel Cárdenas. Title: An HDG method for linear elasticity in curved domains. 2017 - present.
 Alejandra Barrios. Title: An HDG method for the biharmonic. 2017 - present.
Ph.D. Program in Mathematical Sciences, Universidad Nacional de Colombia, Medellín campus
 Liliana Camargo. Title: An HDG method applied to light harvesting devices. In collaboration with Mauricio Osorio and Bibiana López Rodríguez 2017 - present.