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Optimal spectral rectangles and lattice ellipses
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 withExpand
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Numerical Optimization of Low Eigenvalues of the Dirichlet and Neumann Laplacians
TLDR
We perform a numerical optimization of the first ten nontrivial eigenvalues of the Neumann Laplacian for planar Euclidean domains. Expand
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A numerical study of the spectral gap
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-standingExpand
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Optimisation of Eigenvalues of the Dirichlet Laplacian with a Surface Area Restriction
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, weExpand
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The method of fundamental solutions applied to the calculation of eigensolutions for 2D plates
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 connectedExpand
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New Bounds for the Principal Dirichlet Eigenvalue of Planar Regions
TLDR
We present a numerical study for the first Dirichlet eigenvalue of certain classes of planar regions. Expand
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On the range of the first two Dirichlet and Neumann eigenvalues of the Laplacian
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 firstExpand
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The Method of Fundamental Solutions Applied to Some Inverse Eigenproblems
TLDR
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. Expand
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A meshfree numerical method for acoustic wave propagation problems in planar domains with corners and cracks
TLDR
We address the numerical solution of Boundary Value Problems (BVP) for the Helmholtz equation, modelling physical phenomena from the fields of room acoustics and acoustic resonance. Expand
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Optimization of sums and quotients of Dirichlet-Laplacian eigenvalues
TLDR
We study some shape optimization problems related to sums and quotients of Dirichlet Laplacian eigenvalues @l"n for planar domains. Expand
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