A spectral method for the Stokes problem in three-dimensional unbounded domains

Halpern, Laurence

doi:10.1090/s0025-5718-01-01269-8

Cited by 6 publications

(5 citation statements)

References 12 publications

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“…This ends the proof of (24). Now, let a 1 , ..., a n be the real vertices of T i and h i its altitude vector.…”

Section: The Polygonal Inversion and Polygonal Kelvin Transformmentioning

confidence: 60%

“…Reviewing the available strategies for solving PDEs in unbounded domains, we find a variety of methods having various degrees of accuracy, flexibility and sophistication. However, most of the existing methods rely -either on an integral representation of the exact solution and the use of Boundary Elements (see, e.g., [15,22,23,32,[34][35][36]); -or on replacing the unbounded domain by a sufficiently large bounded domain enclosed by a Perfectly Matched Layer (PML) (see [5,6]), or on the boundary of which an artificial boundary condition is prescribed; -or on a polar expansion of the solution like in spectral methods (see, e.g., [12,24]) or in infinite elements methods (see, e.g., [7,11,16,18,19,28]). …”

Section: Introductionmentioning

confidence: 99%

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Inverted finite elements: a new method for solving elliptic problems in unbounded domains

Boulmezaoud

2005

ESAIM: M2AN

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Abstract.In this paper, we propose a new numerical method for solving elliptic equations in unbounded regions of R n . The method is based on the mapping of a part of the domain into a bounded region. An appropriate family of weighted spaces is used for describing the growth or the decay of functions at large distances. After exposing the main ideas of the method, we analyse carefully its convergence. Some 3D computational results are displayed to demonstrate its efficiency and its high performance.Mathematics Subject Classification. 35J, 35J05, 65Jxx, 65Nxx, 65Rxx.

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“…This ends the proof of (24). Now, let a 1 , ..., a n be the real vertices of T i and h i its altitude vector.…”

Section: The Polygonal Inversion and Polygonal Kelvin Transformmentioning

confidence: 60%

Section: Introductionmentioning

confidence: 99%

Inverted finite elements: a new method for solving elliptic problems in unbounded domains

Boulmezaoud

2005

ESAIM: M2AN

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“…Define H div (O) = {w ∈ H 1 (O) : ∇•w = 0}. Following [21,22], introduce the transparent operator T on H 1/2 (∂O) defined by…”

Section: Reconstruction Methodmentioning

confidence: 99%

“…According to [22], the operator T is continuous from H 1/2 (∂O) to H −1/2 (∂O). It is self-adjoint, and…”

Section: Reconstruction Methodmentioning

confidence: 99%

A method of biological tissues elasticity reconstruction using magnetic resonance elastography measurements

et al. 2007

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Magnetic resonance elastography (MRE) is an approach to measuring material properties using external vibration in which the internal displacement measurements are made with magnetic resonance. A variety of simple methods have been designed to recover mechanical properties by inverting the displacement data. Currently, the remaining problems with all of these methods are that, in general, the homogeneous Helmholtz equation is used and therefore it fails at interfaces between tissues of different properties. The purpose of this work is to propose a new method for reconstructing both the shape and the shear modulus of a small anomaly with Lamé parameters different from the background ones using internal displacement measurements. 1. Introduction. Changes in tissue elasticity are generally correlated with pathological phenomena. Many cancers appear as extremely hard nodules.

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“…In this section, we perform some numerical tests to compare the three methods: the direct method in [11], the Stokesian Dynamics in [5] and the correction method. Recall that in the case of two particles, the correction method and the Stokesian Dynamics are exactly the same.…”

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confidence: 99%

Numerical Determination of Truncation Orders in the Correction Method for Stokes Equations

Tran

Nguyen

2018

J. ADV. ENG. COMPUT.

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Abstract. In [15], the authors propose an accurate method, namely the correction method, for computing hydrodynamic interaction between very closed spherical particles in a Stokes uid. The accuracy of this method depends on two truncation parameters for approximating the Neumann to Dirichlet matrix and the velocity correction respectively. In this paper, we establish a numerical determination to estimate these parameters. We perform some numerical experiments to present our method.

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A spectral method for the Stokes problem in three-dimensional unbounded domains

Cited by 6 publications

References 12 publications

Inverted finite elements: a new method for solving elliptic problems in unbounded domains

Inverted finite elements: a new method for solving elliptic problems in unbounded domains

A method of biological tissues elasticity reconstruction using magnetic resonance elastography measurements

Numerical Determination of Truncation Orders in the Correction Method for Stokes Equations

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