Papers in International Journals

• Antunes, Pedro R. S.; Calunga, Hernani; Serranho, Pedro (2024)  Improving the conditioning of the Method of Fundamental Solutions for the Helmholtz equation on domains in polar or elliptic coordinates . Applied Mathematics and Computation: 482, 128969.

• 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.; Antunes, Pedro R. S. (2019)  Determination of elastic resonance frequencies and eigenmodes using the method of fundamental solutions . Engineering Analysis and Boundary Elements: 101, 330-342.

• Alves, Carlos J. S.; Antunes, Pedro R. S. (2018)  The method of fundamental solutions applied to boundary value problems on the surface of a sphere . Computers and Mathematics with Applications: 75 (7), 2365-2373.

• Antunes, Pedro R. S.; Rui A. C. Ferreira (2015)  An augmented-RBF method for solving fractional Sturm-Liouville eigenvalue problems . SIAM Journal of Scientific Computing: 37(1), A515-A535.

• Masoero, David; Raimondo, Andrea; Antunes, Pedro R. S. (2015)  Critical behaviour for scalar nonlinear waves . Physica D: Nonlinear Phenomena: 292–293, 1-7.

• Antunes, Pedro R. S. (2014)  Optimal Bilaplacian eigenvalues . SIAM Journal on Control and Optimization: 52, 2250–2260.

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

• Antunes, Pedro R. S. (2013)  Optimization of sums and quotients of Dirichlet-Laplacian eigenvalues . Applied Mathematics and Computation: 219, 4239-4254.

• Antunes, Pedro R. S.; Freitas, Pedro; Kennedy, James B. (2013)  Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin Laplacian . ESAIM: Control, Optimisation and Calculus of Variations: 19, 438-459.

• Alves, Carlos J. S.; Antunes, Pedro R. S. (2013)  The Method of Fundamental Solutions Applied to Some Inverse Eigenproblems . SIAM Journal on Scientific Computing: 35(3), A1689-A1708.

• Antunes, Pedro R. S.; Freitas, Pedro (2013)  Optimal spectral rectangles and lattice ellipses . Proceedings of the Royal Society A: 469, 2012-0492.

• Antunes, Pedro R. S.; Gazzola, Filippo (2013)  Convex shape optimization for the least biharmonic Steklov eigenvalue . ESAIM: Control, Optimisation and Calculus of Variations: 19, 385-403.

• Antunes, Pedro R. S.; Freitas, Pedro (2012)  On the role of spectral markers and stability in spine models . Journal of the Mechanical Behavior of Biomedical Materials: 14, 19-28.

• Antunes, Pedro R. S.; Freitas, Pedro (2012)  Numerical optimization of low eigenvalues of the Dirichlet and Neumann Laplacians . Journal of Optimization Theory and Applications: 154, 235-257.

• Antunes, Pedro R. S.; Henrot, Antoine (2011)  On the range of the first two Dirichlet and nontrivial Neumann eigenvalues of the Laplacian . Proceedings of the Royal Society A: 467, 1577-1603.

• Antunes, Pedro R. S. (2011)  Numerical calculation of eigensolutions of 3D shapes using the Method of Fundamental Solutions . Numerical Methods for Partial Differential Equations: 27, 1525-1550.

• Antunes, Pedro R. S. (2011)  On the buckling eigenvalue problem . Journal of Physics A: Mathematical and Theoretical: 44, 215-205.

• Antunes, Pedro R. S.; Freitas, Pedro (2011)  On the inverse spectral problem for Euclidean triangles . Proceedings of the Royal Society A: 467, 1546-1562.

• Antunes, Pedro R. S.; Valtchev, Svilen S.  (2010)  A Meshfree Numerical Method for Acoustic Wave Propagation Problems in Planar Domains with Corners and Cracks . Journal of Computational and Applied Mathematics: 234(9), 2646-2662.

• Alves, Carlos J. S.; Antunes, Pedro R. S. (2009)  The method of fundamental solutions applied to the calculation of eigensolutions for 2D plates . International Journal for Numerical Methods in Engineering: 77(2), 177–194.

• Antunes, Pedro R. S.; Freitas, Pedro (2008)  A Numerical Study of the Spectral Gap . Journal of Physics A-Mathematical and Theoretical: 41(5), 055201.

• Antunes, Pedro R. S.; Freitas, Pedro (2006)  New Bounds for the Principal Dirichlet Eigenvalue of Planar Regions . Experimental Mathematics: 15(3), 333-342.

• Alves, Carlos J. S.; Antunes, Pedro R. S. (2005)  The Method of Fundamental Solutions Applied to the Calculation of Eigenfrequencies and Eigenmodes of 2D Simply Connected Shapes . CMC-Computers Materials & Continua: 2(4), 251-265.

Papers or Chapters in Edited Books

• Alves, Carlos J. S.; Antunes, Pedro R. S. (2006)  Numerical Determination of the Resonance Frequencies and Eigenmodes Using the MFS . Computational Methods, Ed. Liu, GR et al.: ISBN 978-1-4020-3953-9, 1385-1389.

Communications in Conference Proceedings

• Alves, Carlos J. S.; Antunes, Pedro R. S. (2007)  The Method of Fundamental Solutions Applied to the Calculation of Eigensolutions in 2D Plates . Proceedings of the 2nd ECOMMAS Thematic Conference on Meshless Methods, Porto, 8-14.

• Alves, Carlos J. S.; Antunes, Pedro R. S. (2005)  The method of fundamental solutions applied to the numerical calculation of eigenfrequencies and eigenmodes of 3D simply connected domains . Proceedings of the ECCOMAS Thematic Conference on Meshless Methods (Editors: Leitão,V. et al). IST, Lisboa, B34.1-6.

• Alves, Carlos J. S.; Antunes, Pedro R. S. (2004)  Numerical determination of eigenfrequencies and eigenmodes using the method of fundamental solutions . Proceedings of the International Conference in Engineering & Science 2004 (Editors: Atluri, S.; Tadeu, A.), in CD. Tech Science Press, Los Angeles.

Thesis

• Antunes, Pedro R. S. (2008)  Meshless Methods for Eigenproblems in PDEs . PhD Thesis, Instituto Superior Tecnico, University of Lisbon.