1. Optimization of the Steklov-Lamé eigenvalues with respect to the domain, to appear in Journal of Differential Equations (2025) (with Beniamin Bogosel)

  2. The MFS-SVD method for the Laplace equation In three dimensions, to appear in SIAM Journal on Scientific Computing (2025) (with Vinicius Santos and Pedro Serranho).

  3. Improving the conditioning of the Method of Fundamental Solutions for the Helmholtz equation on domains in polar and elliptic coordinates, Applied Mathematics and Computation 482, 128969 (2024).
  4. Numerical optimisation of Dirac eigenvalues, Journal of Physics A: Mathematical and Theoretical 57(47), 475203 (2024) (with Francisco Bento and David Krejcirik).
  5. Wave scattering problems in exterior domains with the method of fundamental solutions, Numerische Mathematik 156(2), 375-394 (2024) (with Carlos J. S. Alves).
  6. Modelling silicosis: dynamics of a model with piecewise constant rate coefficients, Journal of Dynamics and Differential Equations 36(2), 1285-1310 (2024) (with Fernando P. da Costa, João T. Pinto and Rafael Sasportes).
  7. A well conditioned Method of Fundamental Solutions for Laplace equation, Numerical Algorithms 91, 1381-1405 (2022).
  8. Parametric shape optimization using the support function, to Computational Optimization an Applications 82, 107-138 (2022). (with Beniamin Bogosel).
  9. Numerical calculation of extremal Steklov eigenvalues in 3D and 4D, Computers and Mathematics with Applications 104, 50-58 (2021).
  10. A variational formulation for Dirac operators in bounded domains. Applications to spectral geometric inequalities, Communications in Mathematical Physics 386, 781-818 (2021) (with Rafael D. Benguria, Vladimir Lotoreichik and Thomas Ourmières-Bonafos)
  11. Bound states in semi-Dirac semi-metals, Physics Letters A, 386, 126991 (2021) (with David Krejcirik)
  12. Solving boundary value problems on manifolds with a plane wave method, Applied Mathematics Letters, 106426 (2020).
    (with Carlos J. S. Alves, Nuno F. M. Martins and Svilen S. Valtchev)
  13. Extremal p-Laplacian eigenvalues, Nonlinearity 32, 5087-5109 (2019).
  14. On the behaviour of clamped plates under large compression, SIAM Journal on Applied Mathematics 79 (5), 1872-1891 (2019). (with Pedro Freitas and Davide Buoso)
  15. Determination of elastic resonance frequencies and eigenmodes using the method of fundamental solutions, Engineering Analysis with Boundary Elements 101, 330-342 (2019). (with Carlos J. S. Alves)
  16. Some solutions of minimaxmax problems for the torsional displacements of rectangular plates, ZAMM Journal of Applied Mathematics and Mechanics 98 (11), 1974-1991 (2018). (with Filippo Gazzola)
  17. A numerical algorithm to reduce the ill conditioning in meshless methods for the Helmholtz equation, Numerical Algorithms 79 (3), 879-897 (2018)
  18. The method of fundamental solutions applied to boundary value problems on the surface of a sphere, Computers and Mathematics with Applications 75 (1), 2365-2373 (2018). (with Carlos J. S. Alves)
  19. A  nonlinear eigenvalue optimization problem: Optimal potential functions. Nonlinear Analysis: Real World Applications 40, 307-327, (2018). (with Seyyed Abbas Mohammadi and Heinrich Voss)
  20. Reducing the ill conditioning in the Method of Fundamental Solutions, Advances in Computational Mathematics 44 (1), 351-365 (2018).
  21. Harmonic configurations of non-homogeneous membranes, Acta Acustica united with acustica 103 (4), 596-606 (2017).
  22. Is it possible to tune a drum?, Journal of Computational Physics 338, 91-106 (2017).
  23. 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 shape optimization of four-dimensional geometries, SIAM Journal on Scientific Computing 39 (3),  B508-B521 (2017). (with Édouard Oudet)
  25. 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)
  26. Bounds and extremal domains for Robin eigenvalues with negative boundary parameter, Advances in Calculus of Variations, 10 (4), 357-379 (2017). (with Pedro Freitas and David Krejcirik)
  27. Maximal and minimal norm of Laplacian eigenfunctions in a given domain, Inverse Problems 32, (11), 115003 (2016), doi: 10.1088/0266-5611/32/11/115003.
  28. Optimisation of eigenvalues of the Dirichlet Laplacian with a surface area restriction, Applied Mathematics & Optimization, 73, 313-328 (2016). (with Pedro Freitas)
  29. 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)
  30. Critical behaviour for scalar nonlinear waves, Physica D: Nonlinear Phenomena, 292-293, 1-7 (2015). (with Davide Masoero and Andrea Raimondo)
  31. Optimal Bilaplacian eigenvalues, SIAM Journal on Control and Optimization 52(4), 2250-2260 (2014).
  32. 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)
  33. Optimal spectral rectangles and lattice ellipses, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469 (2150), 20120492, doi:10.1098/rspa.2012.0492 (2013).  (with Pedro Freitas)
  34. Convex shape optimization for the least biharmonic Steklov eigenvalue, ESAIM - Control, Optimisation and Calculus of Variations 19 (2), 385-403 (2013). (with Filippo Gazzola)
  35. Optimization of sums and quotients of Dirichlet-Laplacian eigenvalues, Applied Mathematics and Computation 219 (9), 4239-4254 (2013).
  36. Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin Laplacian, ESAIM - Control, Optimisation and Calculus of Variations 19 (2), 438-459 (2013).  (with Pedro Freitas and James B. Kennedy)
  37. 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)
  38. Numerical optimization of low eigenvalues of the Dirichlet and Neumann Laplacians, Journal of Optimization Theory and Applications, 154, 235-257 (2012). (with Pedro Freitas)
  39. Numerical calculation of eigensolutions of 3D shapes using the Method of Fundamental Solutions, Numerical Methods for Partial Differential Equations 27 (6), 1525-1550 (2011).
  40. On the buckling eigenvalue problem, Journal of Physics A: Mathematical and Theoretical 44, (21), 215205 (13 pp.) (2011).
  41. On the range of the first two Dirichlet and nontrivial Neumann eigenvalues of the Laplacian, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 467 (2130), 1577-1603 (2011). (with Antoine Henrot)
  42. On the inverse spectral problem for Euclidean triangles, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 467 (2130), 1546-1562 (2011). (with Pedro Freitas)
  43. 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)
  44. 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)
  45. A numerical study of the spectral gap, Journal of Physics A: Mathematical and Theoretical (41), 5, 055201 (19 pp.) (2008). (with Pedro Freitas)
  46. New bounds for the principal Dirichlet eigenvalue of planar regions, Experimental Mathematics, 15, 333-342 (2006). (with Pedro Freitas)
  47. The Method of Fundamental Solutions applied to the calculation of eigenfrequencies and eigenmodes of 2D simply connected shapes, Computers, Materials & Continua 2 (4), 251-266 (2005). (with Carlos J. S. Alves)