- Finite element methods
- Hybridizable discontinuous Galerkin method
- Scientific computing
 M. Solano and F. Vargas. A high order HDG method for Stokes flow in curved domains.. Submitted.
 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