Papers in Journals

  • [32] Some solutions of minimaxmax problems for the torsional displacements of rectangular plates, ZAMM Journal of Applied Mathematics and Mechanics DOI: 10.1002/zamm.201800065 (2018) (with Filippo Gazzola).

  • [31] A numerical algorithm to reduce the ill conditioning in meshless methods for the Helmholtz equation, Numerical Algorithms 79 (3), 879-897 (2018).

  • [30] The Method of Fundamental Solutions applied to boundary value problems on the sphere, Computers & Mathematics with Applications, 75(7), 2365-2373 (2018). (with Carlos J. S. Alves)

  • [29] A nonlinear eigenvalue optimization problem: optimal potential functions, Nonlinear Analysis Series B: Real World Applications, 40, 307-327 (2018) (with Seyyed Abbas Mohammadi and Heinrich Voss)

  • [28] Reducing the ill conditioning in the Method of Fundamental Solutions, Advances in Computational Mathematics, 44(1), 351-365 (2018).

  • [27] Harmonic configurations of non-homogeneous membranes, Acta Acustica united with Acustica, 103(4), 596-606 (2017).

  • [26] Is it possible to tune a drum? Journal of Computational Physics 338, 91-106 (2017).

  • [25] Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives, Communications in Nonlinear Science and Numerical Simulation 48, 398-413 (2017), (with Rui A. C. Ferreira)

  • [24] Numerical minimization of Dirichlet-Laplacian eigenvalues of four-dimensional geometries, SIAM Journal of Scientific Computing 39(3), B508-B521 (2017). (with Édouard Oudet)

  • [23] Detection of holes in an elastic body based on eigenvalues and traces of eigenmodes, Journal of Computational Physics 333, 352-368 (2017). (with Cristian Barbarosie and Anca-Maria Toader)

  • [22] Maximal and minimal norm of Laplacian eigenfunctions in a given subdomain, Inverse Problems 32 (11), article id. 115003. (2016)

  • [21] Bounds and extremal domains for Robin eigenvalues with negative boundary parameter, Advances in Calculus of Variations do:10.1515/acv-2015-0045. (with Pedro Freitas and David Krejčiřík)

  • [20] Optimisation of eigenvalues of the Dirichlet Laplacian with a surface area restriction, Applied Mathematics and Optimization 73, 313-328 (2016). (with Pedro Freitas)

  • [19] An augmented-RBF method for solving fractional Sturm-Liouville eigenvalue problems, SIAM Journal of Scientific Computing 37 (1), A515-A535 (2015). (with Rui A. C. Ferreira)

  • [18] Critical behaviour for scalar nonlinear waves, Physica D: Nonlinear Phenomena, 292-293, 1-7 (2015). (with David Masoero and Andrea Raimondo)

  • [17] Optimal Bilaplacian eigenvalues, SIAM Journal on Control and Optimization 52 (4), 2250-2260 (2014).

  • [16] The Method of Fundamental Solutions applied to some inverse eigenproblems, SIAM Journal on Scientific Computing 35 (3), A1689-A1708 (2013). (with Carlos J. S. Alves)

  • [15] Optimal spectral rectangles and lattice ellipses, Proceedings of the Royal Society of London A 469(2150), 20120492, doi:10.1098/rspa.2012.0492 (2013). (with Pedro Freitas)

  • [14] Optimization of sums and quotients of Dirichlet-Laplacian eigenvalues, Applied Mathematics and Computation 219 (9), 4239-4254 (2013)

  • [13] Convex shape optimization for the least biharmonic Steklov eigenvalue, ESAIM - COCV 19 (2), 385-403 (2013). (with Filippo Gazzola)

  • [12] Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin Laplacian, ESAIM - COCV 19 (2), 438-459 (2013). (with Pedro Freitas and James B. Kennedy)

  • [11] On the role of spectral markers and stability in spine models, Journal of the Mechanical Behavior of Biomedical Materials 14, 19-28 (2012). (with Pedro Freitas)

  • [10] Numerical optimization of low eigenvalues of the Dirichlet and Neumann Laplacians, Journal of Optimization Theory and Applications, 154, 235-257 (2012). (with Pedro Freitas

  • [9] Numerical calculation of eigensolutions of 3D shapes using the Method of Fundamental Solutions, Numerical Methods for Partial Differential Equations 27(6), 1525-1550 (2011).

  • [8] On the buckling eigenvalue problem, Journal of Physics A: Mathematical and Theoretical (44), No. 21, 215205 (13 pp.) (2011).

  • [7] On the range of the first two Dirichlet and nontrivial Neumann eigenvalues of the Laplacian, Proceedings of the Royal Society of London A, 467 (2130), 1577-1603 (2011). (with Antoine Henrot)

  • [6] On the inverse spectral problem for Euclidean triangles, Proceedings of the Royal Society of London A, 467 (2130), 1546-1562 (2011). (with Pedro Freitas)

  • [5] A meshfree numerical method for acoustic wave propagation problems in planar domains with corners and cracks, Journal of Computational and Applied Mathematics 234, 2646-2662 (2010). (with Svilen S. Valtchev)

  • [4] The Method of Fundamental Solutions applied to the calculation of eigensolutions for 2D plates, International Journal for Numerical Methods in Engineering 77, 177-194 (2009). (with Carlos J. S. Alves)

  • [3] A numerical study of the spectral gap, Journal of Physics A: Mathematical and Theoretical (41), No. 5, 055201 (19 pp.) (2008). (with Pedro Freitas)

  • [2] New bounds for the principal Dirichlet eigenvalue of planar regions, Experimental Mathematics, Nº 15, pp. 333-342 (2006). (with Pedro Freitas)

  • [1] The Method of Fundamental Solutions applied to the calculation of eigenfrequencies and eigenmodes of 2D simply connected shapes, Computers, Materials & Continua Vol 2, No. 4, pp. 251-266 (2005). (with Carlos J. S. Alves)


Papers submitted

  • Parametric shape optimization using the support function (with Beniamin Bogosel)

  • Extremal p-Laplacian eigenvalues

  • A numerical method for the calculation of extremal Steklov and mixed Steklov eigenvalues


Books / Book chapters

  • The method of fundamental solutions applied to eigenproblems in PDE's, LAP Lambert Academic Publishing, ISBN-13:978-3-659-49122-1 (2013). 

  • Numerical determination of the resonance frequencies and eigenmodes using the MFS, in Computational Methods (Editors: G. R. Liu, V. B. C. Tan & X. Han), Springer, pp. 1385-1389 (2007). (with Carlos J. S. Alves)

  • On the range of the first two Dirichlet eigenvalues of the Laplacian with volume and perimeter constraint, Publ. RIMS, Kyoto University 1850 (2013), 66-78. (with Antoine Henrot)



Proceedings of International Conferences (with referee)


  1. Numerical determination of the resonance frequencies in a bounded domain using the MFS, in Proceedings of the International Workshop on Meshfree Methods - Lisbon (Editors: C. Alves, C. S. Chen & V. Leitão), pp. 139-144 (2003). (with Carlos J. S. Alves)

  2. Numerical determination of eigenfrequencies and eigenmodes using the Method of Fundamental Solutions, in Proceedings ICCES’04 – Madeira in CdRom (Editors S. N. Atluri & A. Tadeu) (2004). (with Carlos J. S. Alves)

  3. The Method of Fundamental Solutions applied to the numerical calculation of eigenfrequencies and eigenmodes for 3D simply connected domains, in Proceedings of ECCOMAS Thematic Conference on Meshless Methods - Lisboa (Editors: V. Leitão, C. Alves & C. Duarte), pp. C34.1- C34.6., ISBN 972-99289-1-6 (2005). (with Carlos J. S. Alves)

  4. Numerical calculation of eigenfrequencies and eigenmodes of 3D simply connected domains using the Method of Fundamental Solutions, in Proceedings of International Conference on Computational & Experimental Engineering and Sciences (ICCES’05) in CdRom – Chennai, India (2005). (with Carlos J. S. Alves)

  5. The Method of Fundamental Solutions applied to the calculation of the eigensolutions for simply connected plates, in Proceedings III European Conference on Computational Mechanics, Lisbon in CdRom (2006). (with Carlos J. S. Alves)

  6. The Method of Fundamental Solutions applied to the calculation of eigenfrequencies and eigenmodes of 2D simply connected shapes, in Proceedings of International Conference on Computational & Experimental Engineering and Sciences in CdRom – Miami, USA (Editors: Z. Han, S. W. Lee & M. Nakagaki) (2007). (with Carlos J. S. Alves)

  7. The Method of Fundamental Solutions applied to the calculation of eigensolutions in 2D plates, in Proceedings of ECCOMAS Thematic Conference on Meshless Methods 07- Porto (Editors: A Ferreira, E. Kansa, V. Leitão & G. Fasshauer), pp.18-24 (2007). (with Carlos J. S. Alves)

  8. Numerical solution of the magnetic Laplacian eigenvalue problem using radial basis functions, in Proceedings of Conference on Numerical Analysis NumAn2014 - Chania, Greece (Editors: G Akrivis, et al.), pp.17-22 (2014).