- Wave scattering problems in exterior domains with the method of fundamental solutions, accepted in Numerische Mathematik (2024) (with Carlos J. S. Alves).
- A well conditioned Method of Fundamental Solutions for Laplace equation, Numerical Algorithms 91, 1381-1405 (2022).
- Modelling silicosis: dynamics of a model with piecewise constant rate coefficients, Journal of Dynamics and Differential Equations, (2022) (with Fernando P. da Costa, João T. Pinto and Rafael Sasportes).
- Parametric shape optimization using the support function, to Computational Optimization an Applications 82, 107-138 (2022). (with Beniamin Bogosel).
- Numerical calculation of extremal Steklov eigenvalues in 3D and 4D, Computers and Mathematics with Applications 104, 50-58 (2021).
- 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)
- Bound states in semi-Dirac semi-metals, Physics Letters A, 386, 126991 (2021) (with David Krejcirik)
- 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) - Extremal p-Laplacian eigenvalues, Nonlinearity 32, 5087-5109 (2019).
- 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)
- 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)
- 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)
- A numerical algorithm to reduce the ill conditioning in meshless methods for the Helmholtz equation, Numerical Algorithms 79 (3), 879-897 (2018)
- 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)
- A nonlinear eigenvalue optimization problem: Optimal potential functions. Nonlinear Analysis: Real World Applications 40, 307-327, (2018). (with Seyyed Abbas Mohammadi and Heinrich Voss)
- Reducing the ill conditioning in the Method of Fundamental Solutions, Advances in Computational Mathematics 44 (1), 351-365 (2018).
- Harmonic configurations of non-homogeneous membranes, Acta Acustica united with acustica 103 (4), 596-606 (2017).
- Is it possible to tune a drum?, Journal of Computational Physics 338, 91-106 (2017).
- 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)
- Numerical shape optimization of four-dimensional geometries, SIAM Journal on Scientific Computing 39 (3), B508-B521 (2017). (with Édouard Oudet)
- 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)
- 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)
- 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.
- Optimisation of eigenvalues of the Dirichlet Laplacian with a surface area restriction, Applied Mathematics & Optimization, 73, 313-328 (2016). (with Pedro Freitas)
- 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)
- Critical behaviour for scalar nonlinear waves, Physica D: Nonlinear Phenomena, 292-293, 1-7 (2015). (with Davide Masoero and Andrea Raimondo)
- Optimal Bilaplacian eigenvalues, SIAM Journal on Control and Optimization 52(4), 2250-2260 (2014).
- 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)
- 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)
- Convex shape optimization for the least biharmonic Steklov eigenvalue, ESAIM - Control, Optimisation and Calculus of Variations 19 (2), 385-403 (2013). (with Filippo Gazzola)
- Optimization of sums and quotients of Dirichlet-Laplacian eigenvalues, Applied Mathematics and Computation 219 (9), 4239-4254 (2013).
- 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)
- 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)
- Numerical optimization of low eigenvalues of the Dirichlet and Neumann Laplacians, Journal of Optimization Theory and Applications, 154, 235-257 (2012). (with Pedro Freitas)
- Numerical calculation of eigensolutions of 3D shapes using the Method of Fundamental Solutions, Numerical Methods for Partial Differential Equations 27 (6), 1525-1550 (2011).
- On the buckling eigenvalue problem, Journal of Physics A: Mathematical and Theoretical 44, (21), 215205 (13 pp.) (2011).
- 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)

- 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)
- 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)

- 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)
- A numerical study of the spectral gap, Journal of Physics A: Mathematical and Theoretical (41), 5, 055201 (19 pp.) (2008). (with Pedro Freitas)
- New bounds for the principal Dirichlet eigenvalue of planar regions, Experimental Mathematics, 15, 333-342 (2006). (with Pedro Freitas)
- 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)

Papers submitted for publication

- Optimization of the Steklov-Lamé eigenvalues with respect to the domain (with Beniamin Bogosel)