Papers in International Journals

• Alves, Carlos J. S.; Martins, Nuno F. M.; Silvestre, Ana Leonor (2022)  Numerical methods with particular solutions for nonhomogeneous Stokes and Brinkman systems . Advances in Computational Mathematics: 48(4), 44.

• Alves, Carlos J. S.; Martins, Nuno F. M.; Valtchev, Svilen S.  (2021)  Domain decomposition methods with fundamental solutions for Helmholtz problems with discontinuous source terms . Computers and Mathematics with Applications: 88, 16-32.

• Alves, Carlos J. S.; Antunes, Pedro R. S.; Martins, Nuno F. M.; Valtchev, Svilen S.  (2020)  Solving boundary value problems on manifolds with a plane waves method . Applied Mathematics Letters: 107, 106426.

• Alves, Carlos J. S.; Martins, Nuno F. M.; Valtchev, Svilen S.  (2018)  Trefftz methods with cracklets and their relation to BEM and MFS . Engineering Analysis and Boundary Elements: 95, 93-104.

• Alves, Carlos J. S.; Mamud, Roberto; Martins, Nuno F. M.; Roberty, Nilson C. (2017)  On Inverse Problems for Characteristic Sources in Helmholtz Equations . Mathematical Problems in Engineering: 2017, ID 2472060.

• Alves, Carlos J. S.; Martins, Nuno F. M.; Valtchev, Svilen S.  (2017)  Extending the method of fundamental solutions to non-homogeneous elastic wave problems . Applied Numerical Mathematics: 115, 299-313.

• Araújo, João; Kinyon, M.; Konieczny, J.; Martins, Nuno F. M. (2017)  Four notions of conjugacy for abstract semigroups . Proceedings of the Royal Society of Edinburgh Section A: Mathematics: volume 147, issue 6, 1169-1214.

• Martins, Nuno F. M.; Rebelo, Magda (2014)  Meshfree methods for nonhomogeneous Brinkman flows . Computers & Mathematics with Applications: 68(8), 872-886.

• Alves, Carlos J. S.; Martins, Nuno F. M.; Roberty, Nilson C. (2014)  Identification and Reconstruction of Elastic Body Forces . Inverse Problems: 30(5), 055015.

• Martins, Nuno F. M. (2014)  Detecting the Localization of Elastic Inclusions and Lame Coefficients . Inverse Problems and Imaging: 8(3), 779-794.

• Martins, Nuno F. M.; Rebelo, Magda (2013)  A Meshfree Method for Elasticity Problems with Interfaces . Applied Mathematics and Computation: 219(22), 10732-10745.

• Alves, Carlos J. S.; Martins, Nuno F. M. (2009)  The Direct Method of Fundamental Solutions and the Inverse Kirsch-Kress Method for the Reconstruction of Elastic Inclusions OR Cavities . Journal of Integral Equations and Applications: 21(2), 153-178.

• Alves, Carlos J. S.; Martins, Nuno F. M.; Roberty, Nilson C. (2009)  Full Identification of Acoustic Sources with Multiple Frequencies and Boundary Measurements . Inverse Problems and Imaging: 3(2), 275-294.

• Martins, Nuno F. M.; Silvestre, Ana Leonor (2008)  An Iterative MFS Approach for the Detection of Immersed Obstacles . Engineering Analysis with Boundary Elements: 32(6), 517-524.

• Alves, Carlos J. S.; Colaco, Marcelo J.; Leitao, Vitor M. A.; Martins, Nuno F. M.; Orlande, Helcio R. B.; Roberty, Nilson C. (2008)  Recovering the Source Term in a Linear Diffusion Problem by the Method of Fundamental Solutions . Inverse Problems in Science and Engineering: 16(8), PII 905240936.

Papers or Chapters in Edited Books

• Martins, Nuno F. M.; Valtchev, Svilen S.  (2025)  A Meshfree Method of Particular Solutions with Neuber-Papkovich Potentials for Nonhomogeneous Elastodynamic Problems . Numerical Mathematics and Advanced Applications, ENUMATH 2023 (Ed. Sequeira, A., et al.). Lecture Notes in Computational Science and Engineering, Vol. 154, Springer Cham, 162-171.

• Alves, Carlos J. S.; Martins, Nuno F. M. (2013)  Density results and the method of fundamental solutions for Cauchy data reconstruction . Advances in Boundary Element and Meshless Techniques XIV (A. Sellier and M.H. Aliabadi, Eds.): EC Ltd, Eastleigh, UK, pp. 323-328.

• Alves, Carlos J. S.; Martins, Nuno F. M. (2009)  On the Determination of a Robin Boundary Coefficient in an Elastic Cavity Using the MFS . Progress on Meshless Methods, Computational Methods in Applied Sciences, Springer Netherlands: 11, 125-139.

• Alves, Carlos J. S.; Martins, Nuno F. M. (2008)  Reconstruction of inclusions or cavities in potential problems using the MFS . The Method of Fundamental Solutions - A Meshless Method, Dynamic Publishers.

Communications in Conference Proceedings

• Valtchev, Svilen S. ; Martins, Nuno F. M. (2021)  Meshfree approximate solution of the Cauchy-Navier equations of elastodynamics . Proceedings of the 3nd International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA).

• Martins, Nuno F. M.; Morgado, M. Luísa; Rebelo, Magda (2014)  A meshfree numerical method for the time-fractional diffusion equation . Proceedings of the 14th International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE 2014): Vol III, 892-903.

• Valtchev, Svilen S. ; Alves, Carlos J. S.; Martins, Nuno F. M. (2014)  A Meshfree Method with Fundamental Solutions for Inhomogeneous Elastic Wave Problems . Proceedings of the 6th International Conference on Numerical Analysis (NumAn 2014), September 2-5, Chania,Greece.

• Martins, Nuno F. M. (2014)  Direct and optimization methods for the localization of obstacles in a porous media . Proceedings of the 4th International conference on engineering optimization, CRC Press 2014, 991-996.

• Martins, Nuno F. M.; Rebelo, Magda (2013)  A Stokeslets Approach for the Numerical Solution of Brinkman Systems . Proceedings of International Conference Numerical Analysis and Applied Mathematics, AIP Conference Proceedings (ICNAAM 2013), American Institute of Physics, New York: 1558, 746-749.

• Alves, Carlos J. S.; Colaço, M. J.; Martins, Nuno F. M.; Rainha, M. L.; Roberty, N. C. (2012)  Uncertainties on the inverse source problem for elliptic boundary value problems . ECCOMAS 2012 Congress (6th European Congress on ComputationalMethods in Applied Sciences and Engineering). September 10-14, 2012, Vienna, Austria, 5298-5311.

Thesis

• Martins, Nuno F. M. (2009)  Mathematical and numerical methods for inverse problems using fundamental solutions techniques . PhD Thesis, Instituto Superior Tecnico, University of Lisbon.