Assembly of multiscale linear PDE operators

Kuchta, Miroslav

doi:10.48550/arxiv.1912.09319

Cited by 2 publications

(2 citation statements)

References 22 publications

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“…The mesh of Γ then consists of facets of T h , see also Figure 2.1. The linear systems are assembled using the multiscale library FEniCS ii [38], a module built on top of cbc.block [44] and the FEniCS framework [42].…”

Section: Remark 22 (Common Setup Of Experiments) Throughout the Paper...mentioning

confidence: 99%

Robust preconditioning of monolithically coupled multiphysics problems

Holter,

Kuchta,

Mardal

2020

Preprint

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In many applications, one wants to model physical systems consisting of two different physical processes in two different domains that are coupled across a common interface. A crucial challenge is then that the solutions of the two different domains often depend critically on the interaction at the interface and therefore the problem cannot be easily decoupled into its subproblems.Here, we present a framework for finding robust preconditioners for a fairly general class of such problems by exploiting operators representing fractional and weighted Laplacians at the interface. Furthermore, we show feasibility of the framework for two common multiphysics problems; namely the Darcy-Stokes problem and a fluid-structure interaction problem. Numerical experiments that demonstrate the effectiveness of the approach are included.

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Section: Remark 22 (Common Setup Of Experiments) Throughout the Paper...mentioning

confidence: 99%

Robust preconditioning of monolithically coupled multiphysics problems

Holter,

Kuchta,

Mardal

2020

Preprint

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“…To discretize (4), we use lowest order (P2-P1) Taylor-Hood elements for the Stokes velocity and pressure, while piecewise quadratic elements (P2) were used for the Darcy pressure and piecewise constant elements (P0) for the Lagrange multiplier. Discretization is carried out in the FEniCS library [24], with coupling maps between the interface and domains and the fractional Laplacians being implemented by the extension FEniCS ii [25].…”

Section: Preliminariesmentioning

confidence: 99%

Robust preconditioning for coupled Stokes-Darcy problems with the Darcy problem in primal form

Holter¹,

Kuchta²,

Mardal³

2020

Preprint

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The coupled Darcy-Stokes problem is widely used for modeling fluid transport in physical systems consisting of a porous part and a free part. In this work we consider preconditioners for monolitic solution algorithms of the coupled Darcy-Stokes problem, where the Darcy problem is in primal form. We employ the operator preconditioning framework and utilize a fractional solver at the interface between the problems to obtain order optimal schemes that are robust with respect to the material parameters, i.e. the permeability, viscosity and Beavers-Joseph-Saffman condition. Our approach is similar to that of [1], but since the Darcy problem is in primal form, the mass conservation at the interface introduces some challenges. These challenges will be specifically addressed in this paper. Numerical experiments illustrating the performance are provided. The preconditioner is posed in non-standard Sobolev spaces which may be perceived as an obstacle for its use in applications. However, we detail the implementational aspects and show that the preconditioner is quite feasible to realize in practice.

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Assembly of multiscale linear PDE operators

Cited by 2 publications

References 22 publications

Robust preconditioning of monolithically coupled multiphysics problems

Robust preconditioning of monolithically coupled multiphysics problems

Robust preconditioning for coupled Stokes-Darcy problems with the Darcy problem in primal form

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