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Publications Influence

Optimal spectral rectangles and lattice ellipses

- Pedro R. S. Antunes, P. Freitas
- Mathematics
- Proceedings of the Royal Society A: Mathematical…
- 8 February 2013

We consider the problem of minimizing the kth eigenvalue of rectangles with unit area and Dirichlet boundary conditions. This problem corresponds to finding the ellipse centred at the origin with… Expand

30 9

Numerical Optimization of Low Eigenvalues of the Dirichlet and Neumann Laplacians

- Pedro R. S. Antunes, P. Freitas
- Mathematics, Computer Science
- J. Optim. Theory Appl.
- 10 January 2012

TLDR

63 7

A numerical study of the spectral gap

- Pedro R. S. Antunes, P. Freitas
- Mathematics
- 23 January 2008

We present a numerical study of the spectral gap of the Dirichlet Laplacian, γ(K) = λ2(K) − λ1(K), of a planar convex region K. Besides providing supporting numerical evidence for the long-standing… Expand

26 4

Optimisation of Eigenvalues of the Dirichlet Laplacian with a Surface Area Restriction

- Pedro R. S. Antunes, P. Freitas
- Mathematics
- 1 April 2016

We perform a numerical optimisation of the low frequencies of the Dirichlet Laplacian with perimeter and surface area restrictions, in two and 3-dimensions, respectively. In the former case, we… Expand

19 4

The method of fundamental solutions applied to the calculation of eigensolutions for 2D plates

- C. Alves, Pedro R. S. Antunes
- Mathematics
- 8 January 2009

In this paper we study the application of the method of fundamental solutions (MFS) to the numerical calculation of the eigenvalues and eigenfunctions for the 2D bilaplacian in simply connected… Expand

36 3- PDF

New Bounds for the Principal Dirichlet Eigenvalue of Planar Regions

- Pedro R. S. Antunes, P. Freitas
- Computer Science, Mathematics
- Exp. Math.
- 1 January 2006

TLDR

31 3- PDF

On the range of the first two Dirichlet and Neumann eigenvalues of the Laplacian

- Pedro R. S. Antunes, A. Henrot
- Mathematics
- Proceedings of the Royal Society A: Mathematical…
- 8 June 2011

In this paper, we study the set of points in the plane defined by {(x, y)=(λ1(Ω), λ2(Ω)), |Ω|=1}, where (λ1(Ω), λ2(Ω)) are either the first two eigenvalues of the Dirichlet–Laplacian, or the first… Expand

11 2

The Method of Fundamental Solutions Applied to Some Inverse Eigenproblems

- C. Alves, Pedro R. S. Antunes
- Computer Science, Mathematics
- SIAM J. Sci. Comput.
- 25 June 2013

TLDR

19 1

A meshfree numerical method for acoustic wave propagation problems in planar domains with corners and cracks

- Pedro R. S. Antunes, S. Valtchev
- Mathematics, Computer Science
- J. Comput. Appl. Math.
- 1 September 2010

TLDR

28 1- PDF

Optimization of sums and quotients of Dirichlet-Laplacian eigenvalues

- Pedro R. S. Antunes
- Mathematics, Computer Science
- Appl. Math. Comput.
- 2013

TLDR

4 1- PDF