Members > Former Member

Francisco Bernal

Institutional Address

Instituto Superior Técnico (IST)
Av. Rovisco Pais 1
1049-001 LISBOA

Phone: | Email:


Post-Doctoral Fellow, Instituto Superior Técnico, Universidade de Lisboa


Applied and Numerical Analysis

Principal Area

stochastic numerics

Other Area

meshless methods


Master’s in Stock Markets and Financial Derivatives (UNED, 2009)

Ph.D. in Mathematical Engineering Universidad Carlos III (Madrid), 2008

Master’s in Finite Elements UNED University (Madrid), 2003
Licenciado in Physics (Spanish B.S. + M.S.) Universidad de Sevilla, 1998



Papers in International Journals

Mancini, Sara; Bernal, Francisco; Acebron, Juan (2014) An Efficient Algorithm for Accelerating Monte Carlo Approximations of the Solution to Boundary Value Problems. , (submitted).
Bernal, Francisco; Acebron, Juan; Anjam, Immanuel (2014) A Stochastic Algorithm Based on Fast Marching for Automatic Capacitance Extraction in Non-Manhattan Geometries. SIAM Journal on Imaging Sciences: 7(4), 2657-2674.
Bernal, Francisco; Backofen, R.; Voigt, A. (2010) Elastic interactions in phase-field crystal models: numerics and postprocessing . International Journal of Materials Research: 101(4), 467-472.
Kindelan, M.; Bernal, Francisco; González-Rodríguez, P.; Moscoso, M. (2010) Application of the RBF meshless method to the solution of the radiative transport equation. Journal of Computational Physics: 229(5), 1897–1908.
Bernal, Francisco; Kindelan, Manuel (2010) Radial Basis Function ( RBF) solution of the Motz problem.. Engineering Computations: 27(5), 606-620.
Bernal, Francisco; Kindelan, M. (2009) On the enriched RBF method for singular potential problems. Engineering Analysis with Boundary Elements: 33(8-9), 1062-1073.
Bernal, Francisco; Gutiérrez, G.; Kindelan, M. (2009) Use of singularity capturing functions in the solution of problems with discontinuous boundary conditions. Engineering Analysis with Boundary Elements: 33(2), 200-208.
Bernal, Francisco; Gutierrez, Gail (2009) Solving delay differential equations through RBF collocation.. Advances in Applied Mathematics and Mechanics: 1(2), 257-272.
Bernal, Francisco; Kindelan, Manuel (2007) RBF meshless modeling of Non-Newtonian Hele-Shaw flow.. Engineering Analysis with Boundary Elements: 31 (10), 863-874.

Papers or Chapters in Edited Books

Bernal, Francisco (2012) Solving Non-smooth Delay Differential Equations with Multiquadrics. Progress in Industrial Mathematics at ECMI 2010, Mathematics in Industry, Springer Berlin Heidelberg , 603-609.
Bernal, Francisco; Kindelan, Manuel (2010) Meshless solution of singular potential flows in strong formulation,. Progress in Industrial Mathematics at ECMI 2008, Mathematics in Industry, Springer Berlin Heidelberg, 727-732.
Bernal, Francisco; Kindelan, Manuel (2009) A meshless solution to the p-Laplace equation. Progress on Meshless Methods, Computational Methods in Applied Sciences, Springer Netherlands: 11, 17-35.
Bernal, Francisco; Kindelan, Manuel (2008) Meshless Simulation of Hele-Shaw Flow. Progress in Industrial Mathematics at ECMI 2006 , Mathematics in Industry, Springer Berlin Heidelberg: 12, 677-682.
Bernal, Francisco; Kindelan, Manuel (2007) An RBF meshless method for injection molding modelling. Lecture Notes in Computational Science and Engineering: 57, 41-56.


Euro PM2003 European Powder Metallurgy Conference. Valencia (Spain)  (Contributed Talk)
3rd International Workshop on Meshfree Methods for Partial Differential Equations. Bonn (Germany)  (Contributed Talk)
Recent Advances in Partial Differential Equations and Applications. Toledo (Spain)  (Poster)
ECMI 2006 14th European Conference on Mathematics for Industry Leganes (Spain)  (Contributed Talk)
ECCOMAS Thematic Conference on Meshless Methods. Porto (Portugal)  (Contributed Talk)
ECMI 2008 15th European Conference on Mathematics for Industry. London (United Kingdom)  (Contributed Talk)