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

We consider the problem of minimizing the k th eigenvalue of rectangles with unit area and Dirichlet boundary conditions. This problem corresponds to finding the ellipse centred at the origin with… (More)

- Pedro R. S. Antunes, Pedro Freitas
- J. Optimization Theory and Applications
- 2012

We perform a numerical optimization of the first ten nontrivial eigenvalues of the Neumann Laplacian for planar Euclidean domains. The optimization procedure is done via a gradient method, while the… (More)

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… (More)

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… (More)

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… (More)

- Pedro R. S. Antunes, Pedro Freitas
- Experimental Mathematics
- 2006

We present a numerical study for the first Dirichlet eigenvalue of certain classes of planar regions. Based on this, we propose new types of bounds and establish several conjectures regarding the… (More)

- Pedro R. S. Antunes, Antoine Henrot
- Proceedings of the Royal Society A: Mathematical…
- 2010

In this paper we study the set of points, in the plane, defined by $\{(x,y)=(\lambda_1(\Omega),\lambda_2(\Omega)),\ |\Omega|=1\},$ where $(\lambda_1(\Omega),\lambda_2(\Omega))$ are either the two… (More)

- Pedro R. S. Antunes, Pedro Freitas
- Proceedings of the Royal Society A: Mathematical…
- 2010

We consider the inverse spectral problem for the Laplace operator on triangles with Dirichlet boundary conditions, providing numerical evidence to the effect that the eigenvalue triplet ( λ 1 , λ 2 ,… (More)

- Carlos J. S. Alves, Pedro R. S. Antunes
- SIAM J. Scientific Computing
- 2013

In this work we address the application of the method of fundamental solution (MFS) as a forward solver in some shape optimization problems in two- and three-dimensional domains. It is well known… (More)

In this work, we study the application of the Method of Fundamental Solutions (MFS) for the calculation of eigenfrequencies and eigenmodes in two and three-dimensional domains. We address some… (More)