On the choice of source points in the method of fundamental solutions

Alves, Carlos J.S.

doi:10.1016/j.enganabound.2009.05.007

Cited by 142 publications

(56 citation statements)

References 26 publications

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“…However, this can be addressed by using an adaptation of the practical algorithm presented in [13], see also [1]. Also, as mentioned in [3] the systems resulting from the MFS-K discretization suffer from ill-conditioning.…”

Section: Discussionmentioning

confidence: 99%

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Efficient Kansa-type MFS algorithm for elliptic problems

Karageorghis

2009

Numer Algor

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In this study we propose an efficient Kansa-type method of fundamental solutions (MFS-K) for the numerical solution of certain problems in circular geometries. In particular, we consider problems governed by the inhomogeneous Helmholtz equation in disks and annuli. The coefficient matrices in the linear systems resulting from the MFS-K discretization of these problems possess a block circulant structure and can thus be solved by means of a matrix decomposition algorithm and fast Fourier Transforms. Several numerical examples demonstrating the efficacy of the proposed algorithm are presented.

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Section: Discussionmentioning

confidence: 99%

“…In (2.3), H (1) 0 denotes the Hänkel function of the first kind and order zero. The singularities Q n are fixed on the boundary ∂˜ of a disk˜ concentric to (see, e.g.…”

Section: The Dirichlet Problemmentioning

confidence: 99%

Efficient Kansa-type MFS algorithm for elliptic problems

Karageorghis

2009

Numer Algor

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“…, N are distinct source points placed on an admissible source set (see e.g. [1]). For instance, when Ω is bounded and simply connected, we can take the boundary ∂ Ω of an enclosing open set Ω ⊃ Ω.…”

Section: Brief Description Of the Numerical Methodsmentioning

confidence: 99%

Convex shape optimization for the least biharmonic Steklov eigenvalue

Antunes

Gazzola

2013

ESAIM: COCV

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Abstract. The least Steklov eigenvalue d1 for the biharmonic operator in bounded domains gives a bound for the positivity preserving property for the hinged plate problem, appears as a norm of a suitable trace operator, and gives the optimal constant to estimate the L 2 -norm of harmonic functions. These applications suggest to address the problem of minimizing d1 in suitable classes of domains. We survey the existing results and conjectures about this topic; in particular, the existence of a convex domain of fixed measure minimizing d1 is known, although the optimal shape is still unknown. We perform several numerical experiments which strongly suggest that the optimal planar shape is the regular pentagon. We prove the existence of a domain minimizing d1 also among convex domains having fixed perimeter and present some numerical results supporting the conjecture that, among planar domains, the disk is the minimizer.

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“…As for the choice for the source points positions, we follow Alves [12] and take these points along the discrete normal direction, so we put y …”

Section: Formulation Of the Methodsmentioning

confidence: 99%

On the efficiency of the method of fundamental solutions for acoustic scattering by a poroelastic material

Nennig

Perrey-Debain

Chazot

2010

Boundary Elements and Other Mesh Reduction Methods XXXII

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The Method of Fundamental Solutions is now a well established technique that has proved to be reliable for a specific range of wave problems such as the scattering of acoustic and elastic waves by obstacles and inclusions of regular shapes. The goal of this paper is to show that the technique can be extended in order to solve transmission problems whereby an incident acoustic pressure wave impinges on a poroelastic material of finite dimension. For homogeneous and isotropic materials, the wave equation for the fluid phase and solid phase displacements are found to be decoupled thanks to the Helmholtz decomposition. This allows a systematic way for obtaining an analytic expression for the fundamental solution describing the wave displacement field in the material. The efficiency of the technique relies on choosing an appropriate set of fundamental solutions as well as properly imposing the transmission conditions at the air-porous interface.In this paper, we address this issue showing results involving bidimensional scatterers of various shapes. In particular, it is shown that reliable error indicators can be used to assess the quality of the results. Comparisons with results computed using a mixed pressure-displacement finite element formulation illustrate the great advantage of this new technique both in terms of computational resources and mesh preparation.

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On the choice of source points in the method of fundamental solutions

Cited by 142 publications

References 26 publications

Efficient Kansa-type MFS algorithm for elliptic problems

Efficient Kansa-type MFS algorithm for elliptic problems

Convex shape optimization for the least biharmonic Steklov eigenvalue

On the efficiency of the method of fundamental solutions for acoustic scattering by a poroelastic material

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