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RESEARCH AREAS Numerical Methods for Partial Differential Equations and Integro-differential Equations: Theory (convergence, stability analysis) and Applications RESEARCH UNIT Centro de Matemática da Universidade de Coimbra Current Optical Coherence Elastography for imaging retina mechanical properties (FCT Research Project ICDT - SAICT/032162 - ElastoOCT) Efficient Simulation and Computation for Health, Sea and Industry (FCT Research Project POCI-01-0145-FEDER-028118) Past Numerical Analysis of Nonlinear Nonlocal Evolution Problems (Ministerio de Economía y Competitividad MTM2014-54710-P) additive.MILLING - Add Milling to Additive Manufacturing, (European Regional Development Fund through the Partnership Agreement PT2020, PT2020-POCISII& DT 3414) Reaction
Optical Modelling of the Human Retina in Health and Disease: from structure to function (FCT Research Project PTDC/SAU-ENB/119132/2010) Multiscale mathematical models for bone remodeling with applications in dentistry (L’Oréal Portugal Medals of Honor For Women in Science, 2010) S. Barbeiro, D. Lobo, Improved PDE models for image restoration through backpropagation , Preprint, 2019. J.A. Ferreira, S. Barbeiro, G. Pena, M. Wheeler (editors), Modelling and Simulation in Fluid Dynamics in Porous Media, Springer Proceedings in mathematics and Statistics, Volume 28, Springer, N.Y. 2013. S. Barbeiro, Accuracy of a coupled mixed and Galerkin finite element approximation for poroelasticity, Portugaliae Mathematica, 75 (3-4) (2018), pp. 249–265. DOI 10.4171/PM/2018. A. Araújo, S. Barbeiro, M. Khaksar Galati, Convergence of an explicit iterative leap-frog discontinuous Galerkin method for time-domain Maxwell’s equations in anisotropic materials,Journal of Mathematics in Industry, 8:9 (2018). DOI: https://doi.org/10.1186/s13362-018-0051-6. S. Barbeiro, S. Gh. Bardeji, J. A. Ferreira, L. Pinto, Non-Fickian convection-diffusion models in porous media, Numerische Mathematik, 138 (4) (2018), pp. 869–904. DOI: 10.1007/s00211-017- 0922-6 A. Araújo, S. Barbeiro, M. Khaksar Galati, Stability of a leap-frog discontinuous Galerkin method for time-domain Maxwell’s equations in anisotropic materials, Communications in Computational Physics, 21(5) (2017), pp. 1350–1375. DOI: 10.4208/cicp.OA-2016-0110 A. Araújo, S. Barbeiro, E. Cuesta, A. Durán, Cross-diffusion systems for image processing: II. The linear case, Journal of Mathematical Imaging and Vision, 58 (3) (2017), pp. 447–467. DOI:10.1007/ s10851-017-0720-x. A. Araújo, S. Barbeiro, E. Cuesta, A. Durán, Cross-diffusion systems for image processing: I. The linear case, Journal of Mathematical Imaging and Vision, 58 (3) (2017), pp. 447–467. DOI:10.1007/ s10851-017-0720-x. A. Araújo, S. Barbeiro, P. Serranho, Stability of finite difference schemes for nonlinear complex reaction-diffusion processes, IMA Journal of Numerical Analysis, 35 (3) (2015), pp. 1381–1401. DOI: https://doi.org/10.1093/ imanum/dru037 A. Araújo, S. Barbeiro, P. Serranho, Convergence of finite difference schemes for nonlinear complex reaction-diffusion processes, SIAM Journal on Numerical Analysis 53 (1) (2015), pp. 228– 250. DOI:10.1137/130933642 . A. Correia, L. Pinto, A. Araújo, S. Barbeiro, F. Caramelo, P. Menezes, M. Morgado, P. Serranh, R. Bernardes, Monte Carlo simulation of diabetic macular edema changes on optical coherence tomography data, 2014 IEEE-EMBS International Conference on Biomedical and Health Informatics (BHI), pp. 724--727, 2014. DOI: 10.1109/BHI.2014.6864466 A. Correia, L. Pinto, A. Araújo, S. Barbeiro, P. Serranho, M. Morgado, F. Caramelo, P. Meneze, R. Bernardes, Simulation of DME changes on OCT, Acta Ophthalmologica, 92, 2014. DOI: 10.1111/j.1755-3768.2014.2443.x A. Araújo, S. Barbeiro, P. Serranho, Stability of finite difference schemes for nonlinear complex reaction-diffusion processes, IMA Journal of Numerical Analysis, 2014. DOI: 10.1093/imanum/dru037. S. Barbeiro, S. GH. Bardeji and J. Ferreira, Laplace transform – Finite element method for non Fickian flows, Computer Methods in Applied Mechanics and Engineering, vol. 261-262, pp. 16–23, 2013. A. Araújo, S. Barbeiro and P. Serranho, Stability of finite difference schemes for complex diffusion processes, SIAM J. Numer. Anal., vol. 50, n. 3, pp. 1284-1296, 2012. S. Barbeiro, J.A. Ferreira, L. Pinto, H1-second order convergent estimates for non Fickian models, Applied Numerical Mathematics, 61, 201–215, 2011. Rui Bernardes, Cristina Maduro, Pedro Serranho, Adérito Araújo, Sílvia Barbeiro, José Cunha-Vaz, Improved adaptive complex diffusion despeckling filter, Optics Express, Vol. 18, Issue 23, pp. 24048-24059, 2010. Sílvia Barbeiro, Mary F. Wheeler, A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability, Computational Geosciences, v. 14, n. 4, 755-768, 2010.
S. Barbeiro, J.A. Ferreira, Coupled vehicle-skin models for drug
release, Comput. Methods Appl. Mech. Engrg. 198, 2078-2086, 2009.
S. Barbeiro, Supraconvergent cell-centered scheme for two dimensional elliptic problems, Applied Numerical Mathematics, 59, 56-72, 2009.
S. Barbeiro, Discretely compact imbeddings in spaces of cell-centered grid functions, Numerical Functional analysis and Optimization, 29:5, 491-506, 2008.
S. Barbeiro, J.A. Ferreira, Integro-differential models for percutaneous drug absorption, International Journal of Computer Mathematics, 84, 451-467, 2007.
S. Barbeiro, J.A. Ferreira, R.D. Grigorieff, Supraconvergence of a finite difference scheme for solutions in H^s(0,L), IMA J. Numer. Anal., 25, 797-811, 2005.
S. Barbeiro, J.A. Ferreira, A superconvergent piecewise linear finite element method for elliptic systems of partial differential equations, J. Comput. Appl. Math., 177, 287-300, 2005. S. Barbeiro, J.A. Ferreira, J. Brandts, Superconvergence of piecewise linear semi-discretizations for parabolic problems with non uniform triangulations, J. Math. Fluid Mech., 7, 192-214, 2005.
S. Barbeiro, J.A. Ferreira, A nonstandard linear finite element method for a planar elasticity problem, Applied Numerical Mathematics 37, 331-340, 2001.
Conference proceedings and other publications A. Araújo, S. Barbeiro, E. Cuesta, A. Durán, A discrete cross-diffusion model for image restoration, Progress in Industrial Mathematics at ECMI 2016, Springer, ECMI book series of Mathematics in Industry. ISBN 978-3-319-63081-6 A. Araújo, S. Barbeiro, M. Khaksar Galati, Convergence of a leap-frog discontinuous Galerkinmethod for time-domain Maxwell’s equations in anisotropic materials, Progress in Industrial Mathematics at ECMI 2016, Springer, ECMI book series of Mathematics in Industry. ISBN 978-3-319-63081-6 S. Barbeiro, High order finite elements, CIM Bulletin, n.37, 26-32, outubro de 2016. ISSN: 2183-8062 M. Santos, A. Araújo, S. Barbeiro, F. Caramelo, A.L. Correia, I. Marques, L. Pinto, P. Serranho, R. Bernardes e M. Morgado, Simulation of Cellular Changes on Optical Coherence Tomography of Human Retina, 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Milan, August 2015, pp. 8147–8150. DOI: 10.1109/EMBC.2015.7320285 M. Santos, A. Arújo, S. Barbeiro, F. Caramelo, A. Correia, M.I. Marques, M. Morgado, L. Pinto, P. Serranho, R. Bernardes, Maxwell’s equations based 3D model of light scattering in the retina, IEEE 4th Portuguese Meeting on Bioengineering (ENBENG), Porto, February 2015, pp. 1–5. DOI: 10.1109/ENBENG.2015.7088869 A. Arújo, S. Barbeiro e M. Khaksar Ghalati, A discontinuous Galerkin scheme for solving 2D wave propagation in anisotropic materials, IEEE 4th Portuguese Meeting on Bioengineering (ENBENG), Porto, February 2015, pp. 1-4. DOI: 10.1109/ENBENG.2015.7088866 A. Correia, A. Araújo, S. Barbeiro, F. Caramelo, P. Serranho, M. Morgado e R. Bernardes, Simulation of DME changes on OCT, (abstract), Acta Ophthalmologica, Volume 92, Issue s253, September 2014. DOI: 10.1111/j.1755-3768.2014.2443.x A. Correia, L. Pinto, A. Araújo, S. Barbeiro, F. Caramelo, P. Menezes, M. Morgado, P. Serranho, R. Bernardes, Monte Carlo simulation of diabetic macular edema changes on optical coherence tomography data, IEEE-EMBS International Conference on Biomedical and Health Informatics (BHI), June 2014, pp. 724–727. DOI: 10.1109/BHI.2014.6864466 A. Araújo, S. Barbeiro, L. Pinto, F. Caramelo, A.L. Correia, M. Morgado, P. Serranho, A.S.C. Silva e R. Bernardes, Numerical solution of time-dependent Maxwell’s equations for modeling scattered electromagnetic wave’s propagation, Proceedings of the 13th International Conference on Computational and Mathematical Methods in Science and Engineering, vol. 1, CMMSE 2013, Almeria, Spain, 24-27 June 2013, Ian Hamilton & Jesús Vigo-Aguiar (Eds.), 2013, 121-129. ISBN: 978-84-616-2723-3 S. Barbeiro, Um desafio matemático em modelação multi-escala, Rua Larga, Imprensa da Universidade de Coimbra, n´umero 33, novembro de 2011. ISSN: 1645-765X S. Barbeiro, O problema de Mandel, Actas do Encontro Nacional da Sociedade Portuguesa de Matemática, 2010. A. Araújo, S. Barbeiro, J. Ferreira, Laboratory of Computational Mathematics: an interface between academia and industry, Proceedings of the Eimi Study Conference, Lisboa, de 19 a 23 de Abril, 2010. S. Barbeiro, F. Teodoro, Estimating the price elasticity of water, Portuguese Study Groups' Reports, 69th European Study Groupwith Industry, Coimbra, de 20 a 24 de Abril, 2009. S. Barbeiro, J.A. Ferreira, Elementos finitos lineares: estimativas de erro, Actas do VI Congresso de Mecânica Aplicada e Computacional, Universidade de Aveiro, Eds: Paulo M. M. Vila Real e José J. Grácio, 1597-1606, 2000. ISBN 972-8021-61-5 S. Barbeiro,Normas Duais Discretas em Problemas Elípticos , Phd Thesis, Universidade de Coimbra, 2005. S. Barbeiro, Supraconvêrgencia em Métodos de Diferenças Finitas Elípticos, Master Thesis, Universidade de Coimbra, 2000. |
