Mixed-Hybrid Formulation of Multidimensional Fracture Flow

Březina, Jan; Hokr, Milan

doi:10.1007/978-3-642-18466-6_14

Cited by 9 publications

(10 citation statements)

References 5 publications

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“…In this section, we recall the main ideas of the discrete model of the flow in fractured porous media that is based on connection of meshes of different dimensions as described in [30]. Let us denote the full domain by Ω 3 = Ω.…”

Section: Modelling Of Fracturesmentioning

confidence: 99%

“…The formulation and discussion of the continuous problem can be found in [30]. Let us consider spaces…”

Section: Modelling Of Fracturesmentioning

confidence: 99%

“…We take advantage of the special structure of the blocks in matrix (1) studied in detail in [26,28,29]. In particular, the nonzero structure of block C resulting from a combination of meshes with different spatial dimensions is considered in [30]. We describe our parallel implementation of the method and study its performance on several benchmark and real-world problems.…”

Section: Introductionmentioning

confidence: 99%

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BDDC for mixed‐hybrid formulation of flow in porous media with combined mesh dimensions

Šístek

Březina

Sousedík

2015

Numerical Linear Algebra App

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SUMMARYWe extend the Balancing Domain Decomposition by Constraints (BDDC) method to flows in porous media discretised by mixed-hybrid finite elements with combined mesh dimensions. Such discretisations appear when major geological fractures are modelled by 1D or 2D elements inside three-dimensional domains. In this set-up, the global problem as well as the substructure problems have a symmetric saddle-point structure, containing a 'penalty' block due to the combination of meshes. We show that the problem can be reduced by means of iterative substructuring to an interface problem, which is symmetric and positive definite. The interface problem can thus be solved by conjugate gradients with the BDDC method as a preconditioner. A parallel implementation of this algorithm is incorporated into an existing software package for subsurface flow simulations. We study the performance of the iterative solver on several academic and real-world problems. Numerical experiments illustrate its efficiency and scalability. Preprint version.

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Section: Modelling Of Fracturesmentioning

confidence: 99%

“…The formulation and discussion of the continuous problem can be found in [30]. Let us consider spaces…”

Section: Modelling Of Fracturesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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BDDC for mixed‐hybrid formulation of flow in porous media with combined mesh dimensions

Šístek

Březina

Sousedík

2015

Numerical Linear Algebra App

Self Cite

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show abstract

“…The procedure was originally invented for and tested on the base of Flow123d simulator [4,5,15] results. Flow123d is a software for a simulation of a water flow, reactive solute transport and heat transfer in a heterogeneous porous and fractured medium.…”

Section: Methodsmentioning

confidence: 99%

“…The proposed procedure is designed for the computation of the functional based on outputs of the Flow123d simulation software [4,5,15].…”

Section: Fig1: Test Case a -Geometrymentioning

confidence: 99%