Analysis of the fully discrete fat boundary method

Bertoluzza, Silvia; Ismaïl, Mourad; Maury, Bertrand

doi:10.1007/s00211-010-0317-4

Cited by 34 publications

(31 citation statements)

References 32 publications

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“…We choose to present in this work two types of FDM-like methods : (i) the penalty method which is probably the oldest and the simplest one (from the point of view of implementation) in this category (see [22,40] for example) and (ii) the Fat Boundary Method (FBM) which is more technical but has the great advantage to conserve the optimal order in the sense of classical finite element, and this, by adding an auxiliary local problem around the real boundaries [8,9,30,39].…”

Section: Some Fictitious Domain-like Methodsmentioning

confidence: 99%

“…The Fat Boundary Method was introduced in [39] to solve elliptic problems in perforated domains and extended to complex fluid simulations in [9,30]. As far as we know, it is known to be the only fictitious domain-like method that conserves the optimal order (see [8,9]).…”

Section: The Fat Boundary Methodsmentioning

confidence: 99%

“…As far as we know, it is known to be the only fictitious domain-like method that conserves the optimal order (see [8,9]). …”

Section: The Fat Boundary Methodsmentioning

confidence: 99%

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Feel++ : A computational framework for Galerkin Methods and Advanced Numerical Methods

Prud'Homme

Chabannes²,

Doyeux³

et al. 2012

ESAIM: Proc.

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Abstract. This paper presents an overview of a unified framework for finite element and spectral element methods in 1D, 2D and 3D in C ++ called FEEL++. The article is divided in two parts. The first part provides a digression through the design of the library as well as the main abstractions handled by it, namely, meshes, function spaces, operators, linear and bilinear forms and an embedded variational language. In every case, the closeness between the language developed in FEEL++ and the equivalent mathematical objects is highlighted. In the second part, examples using the mortar, Schwartz (non)overlapping, three fields and two fictitious domain-like methods (the Fat Boundary Method and the Penalty Method) are presented and numerically solved in the scope of the library.

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Section: Some Fictitious Domain-like Methodsmentioning

confidence: 99%

Section: The Fat Boundary Methodsmentioning

confidence: 99%

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Feel++ : A computational framework for Galerkin Methods and Advanced Numerical Methods

Prud'Homme

Chabannes²,

Doyeux³

et al. 2012

ESAIM: Proc.

Self Cite

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“…Concerning the penalty parameter ", it is known that it would deteriorate the precondition number ( [30]). The corresponding penalty problem is solved using a fictitious domain-like method with an order around 1/2 (see [24,[30][31][32]). Hence, the error of the method is dominated by the mesh discretization, and taking epsilon very small doesn't necessarily improve the accuracy.…”

Section: Remarkmentioning

confidence: 99%

A necklace model for vesicles simulations in 2D

Ismaïl

Lefebvre-Lepot

2014

Numerical Methods in Fluids

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The aim of this paper is to propose a new numerical model to simulate 2D vesicles interacting with a newtonian fluid. The inextensible membrane is modeled by a chain of circular rigid particles which are maintained in cohesion by using two different type of forces. First, a spring force is imposed between neighboring particles in the chain. Second, in order to model the bending of the membrane, each triplet of successive particles is submitted to an angular force.Numerical simulations of vesicles in shear flow have been run using Finite Element Method and the FreeFem++[1] software. Exploring different ratios of inner and outer viscosities, we recover the well known "Tank-Treading" and "Tumbling" motions predicted by theory and experiments. Moreover, for the first time, 2D simulations of the "Vacillating-Breathing" regime predicted by theory in [2] and observed experimentally in [3] are done without special ingredient like for example thermal fluctuations used in [4].

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“…Immersed boundaries (between one physical domain and one supplementary domain): the immersed boundary method (IBM) [26,27], the truncated domain method or cut-cell method [28,29], the direct forcing method [30,31], the fictitious domain methods with surface Lagrange multipliers [32,33] or the distributed (volume) Lagrange multipliers [34], the penalty methods [16,35,36], the finite cell method [21], the ghost-cell method [37], the fat boundary method [38,39], the fictitious domain with spread interface [2], the diffuse domain approach [40], the embedded finite-difference method [41], the X-FEM-based FDMs [42,43], and so on. Immersed interfaces (between two physical domains): the immersed interface method (IIM) [44,45], the ghost-fluid method [46], the matched interface and boundary method (MIB) [47], the algebraic immersed interface and boundary method [48], the FDM with immersed jumps [3,49], and so on.…”

Section: The Fictitious Domain Conceptmentioning

confidence: 99%

Fictitious domain methods for two‐phase flow energy balance computations in nuclear components

Belliard

Ramière

2011

Numerical Methods in Fluids

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This paper is dedicated to the numerical simulation of nuclear components (Cores and Steam Generators-SG) by fictitious domain methods. The fictitious domain approach consists in immersing the physical domain under study in a Cartesian domain, called the fictitious domain, and in performing the numerical resolution on this fictitious domain. The calculation times are then efficiently reduced by the use of fast solvers. In counterpart, one has to handle with an immersed boundary, generally non-aligned with the Cartesian mesh, which can be non-trivial. The two fictitious domain methods compared here on industrial simulations and developed by Ramière and coworkers, deal with an approximate immersed interface directly derived from the uniform Cartesian mesh. All the usual immersed boundary conditions (Dirichlet, Robin, Neumann), possibly mixed, are handled through a unique formulation of the fictitious problem. This kind of approximation leads to firstorder methods in space that exhibit a good ratio of the precision of the approximate solution over the CPU time, which is very important for industrial simulations. After a brief recall of the fictitious domain method with spread interface (Ramière et al., CMAME 2007) and the fictitious domain method with immersed jumps (Ramière et al., JCP 2008), we will focus on the numerical results provided by these methods applied to the energy balance equation in a SG. The advantages and drawbacks of each 1 method will be pointed out. Generally speaking, the two methods confirm their very good efficiency in term of precision, convergence and calculation time in an industrial context.

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Analysis of the fully discrete fat boundary method

Cited by 34 publications

References 32 publications

Feel++ : A computational framework for Galerkin Methods and Advanced Numerical Methods

Feel++ : A computational framework for Galerkin Methods and Advanced Numerical Methods

A necklace model for vesicles simulations in 2D

Fictitious domain methods for two‐phase flow energy balance computations in nuclear components

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