A multilayer method of fundamental solutions for Stokes flow problems

Boselli, Francesco; Obrist, Dominik; Kleiser, Leonhard

doi:10.1016/j.jcp.2012.05.023

Cited by 9 publications

(8 citation statements)

References 51 publications

(73 reference statements)

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“…Previous implementations of the MFS (monolayer MFS) considered source points positioned on a single layer with an arbitrary distance from the boundary. Recent works have shown that positioning the source points on multiple layers by greedy algorithms improves the accuracy and the convergence rate of the MFS and its robustness with respect to the user‐defined source layers. We consider here the multilayer MFS proposed in for Stokes flow problems.…”

Section: Multilayer Methods Of Fundamental Solutionsmentioning

confidence: 99%

“…Recent works have shown that positioning the source points on multiple layers by greedy algorithms improves the accuracy and the convergence rate of the MFS and its robustness with respect to the user‐defined source layers. We consider here the multilayer MFS proposed in for Stokes flow problems. The source points are positioned on several layers at different distances from the boundary (Figure ), and the linear system is solved in the least‐squares sense by the block greedy‐QR algorithm (BGQRa) proposed in .…”

Section: Multilayer Methods Of Fundamental Solutionsmentioning

confidence: 99%

“…We consider here the multilayer MFS proposed in for Stokes flow problems. The source points are positioned on several layers at different distances from the boundary (Figure ), and the linear system is solved in the least‐squares sense by the block greedy‐QR algorithm (BGQRa) proposed in . The BGQRa selects N < 3 M c appropriate columns of A to obtain a 3 M c × N suboptimal submatrix A opt that is then used instead of the full matrix A for computing the least‐squares solution of .…”

Section: Multilayer Methods Of Fundamental Solutionsmentioning

confidence: 99%

“…We found it natural to solve the resulting governing equations by the multilayer MFS . The MFS approximates the flow field as a superposition of Stokeslets with their singularities (source points) positioned outside the flow domain (Figure ).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A meshless boundary method for Stokes flows with particles: Application to canalithiasis

Boselli

Obrist

Kleiser

2013

Numer Methods Biomed Eng

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We propose to couple the method of fundamental solutions (MFS) to the force coupling method (FCM). The resulting method is an efficient, easy to program, meshless method for flows at low Reynolds numbers with finite-size particles. In such an approach, the flow domain is extended across the solid particle phase, and the flow is approximated by a superposition of singular Stokeslets positioned outside the flow domain and finite-size multipoles collocated with the particle. To improve the efficiency of the coupling, we propose new MFS quadratures for the computation of the volume integrals required for the FCM. These are exact and do not require the expensive evaluation of Stokeslets. The proposed method has been developed in the context of investigations of the fluid dynamics of canalithiasis, that is, a pathological condition of the semicircular canals of the inner ear. Numerical examples are presented to illustrate the applicability of the method.

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Section: Multilayer Methods Of Fundamental Solutionsmentioning

confidence: 99%

Section: Multilayer Methods Of Fundamental Solutionsmentioning

confidence: 99%

Section: Multilayer Methods Of Fundamental Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A meshless boundary method for Stokes flows with particles: Application to canalithiasis

Boselli

Obrist

Kleiser

2013

Numer Methods Biomed Eng

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“…Boselli and his colleagues [166,167] employed a combination of the multilayer MFS approach and the force coupling method for numerical investigation of the fluid dynamics of benign paroxysmal positional vertigo or canalithiasis conditions affecting the semicircular canals of the inner ear by solving the Stoke flow equations with finite-size particles. In [168], the authors employed a block greedy-QR algorithm that exploits the robustness of the multilayer MFS approach in a multilevel fashion and alleviates the over-head of multiple source layers thereby allowing the multilayer MFS to outperform the monolayer MFS.…”

Section: Deasmentioning

confidence: 99%

Meshfree and Particle Methods in Biomechanics: Prospects and Challenges

Zhang

Ademiloye

Liew

2018

Arch Computat Methods Eng

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The use of meshfree and particle methods in the field of bioengineering and biomechanics has significantly increased. This may be attributed to their unique abilities to overcome most of the inherent limitations of mesh-based methods in dealing with problems involving large deformation and complex geometry that are common in bioengineering and computational biomechanics in particular. This review article is intended to identify, highlight and summarize research works on topics that are of substantial interest in the field of computational biomechanics in which meshfree or particle methods have been employed for analysis, simulation or/and modeling of biological systems such as soft matters, cells, biological soft and hard tissues and organs. We also anticipate that this review will serve as a useful resource and guide to researchers who intend to extend their work into these research areas. This review article includes 333 references. Highlights  We present an up to date review of meshfree and particle methods, including their advantages and limitations.  We comprehensively discuss past and recent applications of meshfree and particle methods in bioengineering and biomechanics.  We identify research areas, directions, and opportunities for the application of meshfree and particle methods in bioengineering and biomechanics.

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Modelling shows that stimulation of the semicircular canals depends on the rotation centre

Goyens

2020

Hearing Research

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A multilayer method of fundamental solutions for Stokes flow problems

Cited by 9 publications

References 51 publications

A meshless boundary method for Stokes flows with particles: Application to canalithiasis

A meshless boundary method for Stokes flows with particles: Application to canalithiasis

Meshfree and Particle Methods in Biomechanics: Prospects and Challenges

Modelling shows that stimulation of the semicircular canals depends on the rotation centre

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