Block Preconditioners for Mixed-dimensional Discretization of Flow in Fractured Porous Media

Budiša, Ana; Hu, Xiaozhe

doi:10.48550/arxiv.1905.13513

Cited by 2 publications

(3 citation statements)

References 31 publications

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“…Thus, the MFB framework is favourable for 1) highly heterogeneous parts of the media where subdomain solves are affected by heterogeneities, 2) those fractures affected by strong non-linearities, and 3) lower permeable or blocking fractures where a coarse mortar space can be used without sacrificing accuracy. Otherwise, a robust preconditioner [7,18] can be used in the Krylov method, as well as a coarse mortar space that is compensated by taking higher order mortars [9,55].…”

Section: Form the Multiscale Flux Basis For Subdomainmentioning

confidence: 99%

Robust linear domain decomposition schemes for reduced non-linear fracture flow models

Ahmed¹,

Fumagalli²,

Budiša³

et al. 2019

Preprint

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In this work, we consider compressible single-phase flow problems in a porous media containing a fracture. In the latter, a non-linear pressure-velocity relation is prescribed. Using a non-overlapping domain decomposition procedure, we reformulate the global problem into a non-linear interface problem. We then introduce two new algorithms that are able to efficiently handle the non-linearity and the coupling between the fracture and the matrix, both based on linearization by the so-called L-scheme. The first algorithm, named MoLDD, uses the L-scheme to resolve the non-linearity, requiring at each iteration to solve the dimensional coupling via a domain decomposition approach. The second algorithm, called ItLDD, uses a sequential approach in which the dimensional coupling is part of the linearization iterations. For both algorithms, the computations are reduced only to the fracture by pre-computing, in an offline phase, a multiscale flux basis (the linear Robin-to-Neumann co-dimensional map), that represent the flux exchange between the fracture and the matrix. We present extensive theoretical findings and in particular, the stability and the convergence of both schemes are obtained, where usergiven parameters are optimized to minimise the number of iterations. Examples on two important fracture models are computed with the library PorePy and agree with the developed theory.

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Section: Form the Multiscale Flux Basis For Subdomainmentioning

confidence: 99%

Robust linear domain decomposition schemes for reduced non-linear fracture flow models

Ahmed¹,

Fumagalli²,

Budiša³

et al. 2019

Preprint

Self Cite

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“…where c 1,q , c 1,p , c 2,q , and c 2,p are positive constants independent of discretization and physical parameters. Following [9,23] and using Theorem 6.1 and (6.12), the condition number of M D A can be directly estimated as…”

Section: Block Preconditioners Based On Auxiliary Space Preconditioningmentioning

confidence: 99%

“…It can be proven that M L and M U are so-called field-of-value (FoV) equivalent preconditioners based on the well-posdeness conditions (6.9) and proper inner product induced by M D . We refer the reader to [1,2,9,22] for a more detailed theoretical analysis on these preconditioners and restrict our focus on their numerical performances in the next section.…”

Section: Block Preconditioners Based On Auxiliary Space Preconditioningmentioning

confidence: 99%

Mixed-Dimensional Auxiliary Space Preconditioners

Budiša¹,

Boon²,

Hu³

2019

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This work introduces nodal auxiliary space preconditioners for discretizations of mixeddimensional partial differential equations. We first consider the continuous setting and generalize the regular decomposition to this setting. With the use of conforming mixed finite element spaces, we then expand these results to the discrete case and obtain a decomposition in terms of nodal Lagrange elements. In turn, nodal preconditioners are proposed analogous to the auxiliary space preconditioners of Hiptmair and Xu [16]. Numerical experiments show the performance of this preconditioner in the context of flow in fractured porous media.

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Block Preconditioners for Mixed-dimensional Discretization of Flow in Fractured Porous Media

Cited by 2 publications

References 31 publications

Robust linear domain decomposition schemes for reduced non-linear fracture flow models

Robust linear domain decomposition schemes for reduced non-linear fracture flow models

Mixed-Dimensional Auxiliary Space Preconditioners

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