Stokes flow around cylinders in a bounded two-dimensional domain using multipole-accelerated boundary element methods

Mammoli, Andrea; Ingber, M. S.

doi:10.1002/(sici)1097-0207(19990310)44:7<897::aid-nme530>3.0.co;2-s

Cited by 41 publications

(19 citation statements)

References 8 publications

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“…[25]) has been employed to compute the cluster integrals in (15)- (18). This procedure starts with computing integrals over each cell with its own pole (at its mid-point).…”

Section: ð12þmentioning

confidence: 99%

“…The f i num in Eqs. (25), (26) for this problem are the unspecified values on oB, i.e. u on the lower and q on the upper half circle, respectively.…”

Section: Problem 2: Mixed Problem In An Unit Diskmentioning

confidence: 99%

“…The CPU times required to form the system matrices (formation time) and the error measure defined by Eq. (25), for the various discretizations, for both the usual BNM and the BNMM, are given in Table 4 (see, also, Fig. 10).…”

Section: Speed-up Studiesmentioning

confidence: 99%

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Application of an accelerated boundary-based mesh-free method to two-dimensional problems in potential theory

Kulkarni

Telukunta

Mukherjee

2003

Computational Mechanics

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The boundary node method (BNM) is a boundary-only meshfree method based on boundary integral equations (BIE). One drawback of the usual BNM, however, is that it typically requires much more computer time than the usual boundary element method (BEM). The multipole method (MM) has been demonstrated, in the context of the n body problem, and the BEM, to greatly accelerate these methods while still maintaining sufficient accuracy. The present paper explores, for the first time, a coupling of the BNM with the MM (called the BNMM) in the context of 2-D potential theory. Numerical results (for selected problems) from the BNM are compared with those from the BNMM with regard to accuracy and computational efficiency. Introduction Domain-based meshfree methodsMeshfree (also called meshless) methods, that only require points rather than elements to be specified in the physical domain, have tremendous potential advantages over methods such as the finite element method (FEM) that require discretization of a body into elements.The idea of moving least squares (MLS) interpolants, for curve and surface fitting, is described in a book by [21].[29] proposed a coupling of MLS interpolants with Galerkin procedures in order to solve boundary value problems. They called their method the diffuse element method (DEM) and applied it to two-dimensional (2-D) problems in potential theory and linear elasticity.During the relatively short span of less than a decade, great progress has been made in solid mechanics applications of domain-based meshfree methods. Some of these methods are: The element-free Galerkin (EFG) method [4], the reproducing kernel particle method (RKPM) [23], h À p clouds [31] the meshless local Petrov-Galerkin (MLPG) approach [2], the extended finite element method (X-FEM) [12], the finite cloud method (FCM) [1] and the point interpolation method (PIM) [24]. The boundary element methodAnother approach towards alleviating meshing difficulties associated with the FEM is the use of the boundary element method (BEM) (e.g. [26,3,7,6]). The standard BEM is a very mature method for the analysis of a broad class of problems in science and engineering. For linear problems, the BEM has the well known dimensionality advantage in that only the 2-D bounding surface of a 3-D body needs to be meshed when this method is used. Boundary-based meshfree methodsS. Mukherjee, together with his research collaborators, has recently proposed a new computational approach called the boundary node method (BNM) [27,20,9,8,10,11,14]. Other examples of boundary-based meshless methods are the local BIE (LBIE) approach [36,35] and the boundary point interpolation method (BPIM) [18]. The LBIE, however, is not strictly a boundary method since it requires evaluation of integrals over certain surfaces (called L s in [36]) that can be regarded as ''closure surfaces'' of boundary elements. [22] have very recently proposed a boundary only method called the boundary cloud method (BCM). This method is very similar to the BNM in that scattered points are used f...

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“…[25]) has been employed to compute the cluster integrals in (15)- (18). This procedure starts with computing integrals over each cell with its own pole (at its mid-point).…”

Section: ð12þmentioning

confidence: 99%

“…The f i num in Eqs. (25), (26) for this problem are the unspecified values on oB, i.e. u on the lower and q on the upper half circle, respectively.…”

Section: Problem 2: Mixed Problem In An Unit Diskmentioning

confidence: 99%

See 1 more Smart Citation

Application of an accelerated boundary-based mesh-free method to two-dimensional problems in potential theory

Kulkarni

Telukunta

Mukherjee

2003

Computational Mechanics

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“…The main goal was to reduce the CPU time in FMM accelerated BEM to O(N). Thereafter this new technique was applied for solving elasticity [3] and fluids [4] problems in large-scale. Some years after, [5] announced the FMM as one of the top algorithms in scientific computing that were developed in the 20th century.…”

Section: Introductionmentioning

confidence: 99%

Optimization Using Topological Derivative and Boundary Element Method With Fast Multipole

Braga¹,

Anflor²,

Albuquerque³

2014

Proceedings of 10th World Congress on Computational Mechanics

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Abstract. The objective of this work is to compare topologies resulting from direct BEM (Boundary Element Method) with a BEM accelerated by Fast Multipole Method (FMM). A formulation of fast multipole boundary element (FMBEM) is introduced in order to turn the optimization process more attractive in the point of view of the computational cost. The formulation of the fast multipole is briefly summarized. A topological-shape sensitivity approach is used to select the points showing the lowest sensitivities, where material is removed by opening a cavity. As the iterative process evolves, the original domain has holes progressively removed, until a given stop criteria is achieved. A benchmark is investigated by

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“…Passively rotating cylinders between actively rotating confining cylinders have been investigated in Ref. [23] using multipole-accelerated boundary-element methods. Rotating cylinders and rotlets (infinitesimal cylinders) with fixed axis have been studied in Refs.…”

Section: Introductionmentioning

confidence: 99%

Dynamic self-assembly and directed flow of rotating colloids in microchannels

Götze

Gompper

2011

Phys. Rev. E

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Nonequilibrium structure formation and dynamics in suspensions of superparamagnetic colloids driven by an external rotating magnetic field are studied by particle-based mesoscale hydrodynamics simulations in confined geometry. We address the fundamental question how the rotation of the colloids about their own axes can be converted into a translational motion by breaking the symmetry of the confining geometry. We study a two-dimensional system of colloids with short-range repulsive interactions, which mimics flow in shallow microchannels. In straight channels, we observe a two-way traffic but-for symmetry reasons-no net transport. However, by keeping some colloids fixed near one of the two walls, net transport can be achieved. This approach allows the control and switchability of the flow in complex microchannel networks. A minimal geometry that fulfills the requirement of broken symmetry are ring channels. We determine the translational velocity of the spinning colloids and study its dependence on the channel width for various median radii. We conclude that spinning colloids present a promising alternative for flow generation and control in microfluidic devices.

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Stokes flow around cylinders in a bounded two-dimensional domain using multipole-accelerated boundary element methods

Cited by 41 publications

References 8 publications

Application of an accelerated boundary-based mesh-free method to two-dimensional problems in potential theory

Application of an accelerated boundary-based mesh-free method to two-dimensional problems in potential theory

Optimization Using Topological Derivative and Boundary Element Method With Fast Multipole

Dynamic self-assembly and directed flow of rotating colloids in microchannels

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