PETSc Users Manual (Rev. 3.4)

Balay, Satish; Brown, Judith M.; Buschelman, K.; Eijkhout, Victor; Gropp, William; Kaushik, D.; Knepley, Matthew G.; McInnes, Lois Curfman; Barry, Smith; Zhang, H.

doi:10.2172/1178104

Cited by 309 publications

(291 citation statements)

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“…The FFTs are performed using the FFTW library [12]. Whatever the discretization method, we obtain a finite dimensional eigenvalue problem, which we then solve numerically by a Krylov iteration method, as efficiently implemented in the Petsc and Slepc libraries [13,3].…”

Section: Laplace Operatormentioning

confidence: 99%

Approximation of the Laplace and Stokes operators with Dirichlet boundary conditions through volume penalization: a spectral viewpoint

2014

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Abstract. We report the results of a detailed study of the spectral properties of Laplace and Stokes operators, modified with a volume penalization term designed to approximate Dirichlet conditions in the limit when a penalization parameter, η, tends to zero. The eigenvalues and eigenfunctions are determined either analytically or numerically as functions of η, both in the continuous case and after applying Fourier or finite difference discretization schemes. For fixed η, we find that only the part of the spectrum corresponding to eigenvalues λ η −1 approaches Dirichlet boundary conditions, while the remainder of the spectrum is made of uncontrolled, spurious wall modes. The penalization error for the controlled eigenfunctions is estimated as a function of η and λ. Surprisingly, in the Stokes case, we show that the eigenfunctions approximately satisfy, with a precision O(η), Navier slip boundary conditions with slip length equal to √ η. Moreover, for a given discretization, we show that there exists a value of η, corresponding to a balance between penalization and discretization errors, below which no further gain in precision is achieved. These results shed light on the behavior of volume penalization schemes when solving the Navier-Stokes equations, outline the limitations of the method, and give indications on how to choose the penalization parameter in practical cases.

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Section: Laplace Operatormentioning

confidence: 99%

Approximation of the Laplace and Stokes operators with Dirichlet boundary conditions through volume penalization: a spectral viewpoint

2014

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“…To solve Eq. (3) the "PETSc" suite (Balay et al (2011(Balay et al ( , 2010(Balay et al ( , 1997) with an LU decomposition is used, the convex hull is calculated using "qhull" (Barber et al (1996)), and the cell cycle model is provided by "Chaste" (Mirams et al (2013); Pitt-Francis et al (2009)). …”

Section: Initial Conditions and Implementationmentioning

confidence: 99%

A computational model of nuclear self-organisation in syncytial embryos

Koke

Kanesaki

Großhans

et al. 2014

Journal of Theoretical Biology

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“…We implement a fully coupled finite element scheme (see, for example, Eriksson (1996)). The resulting discretized system of nonlinear algebraic equations are solved using the PETSc libraries (Balay et al, 1997(Balay et al, , 2010(Balay et al, , 2011. The finite element basis used in space is continuous, piecewise linear and the scheme is fully implicit in time.…”

Section: Description and Validation Of The Schemementioning

confidence: 99%

On a poroviscoelastic model for cell crawling

et al. 2014

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In this paper a minimal, one-dimensional, two-phase, viscoelastic, reactive, flow model for a crawling cell is presented. Two-phase models are used with a variety of constitutive assumptions in the literature to model cell motility. We use an upperconvected Maxwell model and demonstrate that even the simplest of two-phase, viscoelastic models displays features relevant to cell motility. We also show care must be exercised in choosing parameters for such models as a poor choice can lead to an ill-posed problem. A stability analysis reveals that the initially stationary, spatially uniform strip of cytoplasm starts to crawl in response to a perturbation which breaks the symmetry of the network volume fraction or network stress. We also demonstrate numerically that there is a steady travelling-wave solution in which the crawling velocity has a bell-shaped dependence on adhesion strength, in agreement with biological observation.

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PETSc Users Manual (Rev. 3.4)

Abstract: Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

Cited by 309 publications

References 0 publications

Approximation of the Laplace and Stokes operators with Dirichlet boundary conditions through volume penalization: a spectral viewpoint

Approximation of the Laplace and Stokes operators with Dirichlet boundary conditions through volume penalization: a spectral viewpoint

A computational model of nuclear self-organisation in syncytial embryos

On a poroviscoelastic model for cell crawling

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