Papers in Journals

*[33] Determination of elastic resonance frequencies and eigenmodes using the method of fundamental solutions, to appear in Engineering Analysis with Boundary Elements (2019)*(with Carlos J. S. Alves)*[32]**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).*[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]

*Bounds and extremal domains for Robin eigenvalues with negative boundary parameter,*Advances in Calculus of Variations 10, 357-379 (2017). (with Pedro Freitas and David Krejčiřík)[21]

*Maximal and minimal norm of Laplacian eigenfunctions in a given subdomain,*Inverse Problems 32 (11), article id. 115003. (2016)[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).[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)*Numerical results for extremal problem for eigenvalues of the Laplacian, in Shape optimization and spectral theory, 2017, 398-411, Antoine Henry (ed.), De Gruyter*(with Édouard Oudet)

Proceedings of International Conferences (with referee)

*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)*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)*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)*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)*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)*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)*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)*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).