The Interface Probing Technique in Domain Decomposition

Chan, Tony F.; Mathew, Tarek Poonithara Abraham

doi:10.1137/0613018

Cited by 65 publications

(52 citation statements)

References 15 publications

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“…The interface probing technique (see [7] and references therein) represents a more general approach for approximating the flow on the boundary. The aim is to approximate the Schur complement matrix S EE by a low-bandwidth matrixŜ EE , such that…”

Section: Probing Techniquementioning

confidence: 99%

Multiscale mass conservative domain decomposition preconditioners for elliptic problems on irregular grids

2011

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Multiscale methods can in many cases be viewed as special types of domain decomposition preconditioners. The localisation approximations introduced within the multiscale framework are dependent upon both the heterogeneity of the reservoir and the structure of the computational grid. While previous works on multiscale control volume methods have focused on heterogeneous elliptic problems on regular Cartesian grids, we have tested the multiscale control volume formulations on two-dimensional elliptic problems involving heterogeneous media and irregular grid structures. Our study shows that the tangential flow approximation commonly used within multiscale methods is not suited for problems involving rough grids. We present a more robust mass conservative domain decomposition preconditioner for simulating flow in heterogeneous porous media on general grids.

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Section: Probing Techniquementioning

confidence: 99%

Multiscale mass conservative domain decomposition preconditioners for elliptic problems on irregular grids

2011

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“…Since the Schur complement matrices themselves are too expensive to calculate, the bottom-up approach requires introducing low-rank approximations to the Schur complement (e.g. probing based techniques (Chan & Mathew, 1992)) at every stage in the succession. The class of domain decomposition methods known as substructuring methods is often formulated in terms of the bottom-up framework.…”

Section: Remark 4: For Local Discretizations the Direct Coupling Betwmentioning

confidence: 99%

Mass Conservative Domain Decomposition for Porous Media Flow

Nordbotten¹,

Keilegavlen²,

Sandvin³

2012

Finite Volume Method - Powerful Means of Engineering Design

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“…In [17], Chan and Mathew presented a quite simple idea for retrieving elements of an unassembled matrix E originated from a structured mesh. A set of probe vectors composed by zeros and ones forms a rectangular matrix W , for instance, when using three probe vectors…”

Section: Probementioning

confidence: 99%

Comparing Some Methods and Preconditioners for Hydropower Plant Flow Simulations

Carvalho

Fortes

Giraud

2008

High Performance Computing for Computational Science - VECPAR 2008

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Abstract. We describe some features of a three-dimensional numerical simulator currently under development for studying water physico-chemical properties during the flooding of hydroelectric plants reservoirs. The work is sponsored by the Brazilian Electric Energy National Agency (ANEEL) and conducted with Furnas Centrais Elétricas S. A., the leading Brazilian power utility company. An overview of the simulator requirements is given. The mathematical model, the software modules, and engineering solutions are briefly discussed, including the finite element based transport module. We compare methods, iterative methods and preconditioners used to solve the sparse linear systems which arise from the discretization of three-dimensional partial differential equations.

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The Interface Probing Technique in Domain Decomposition

Cited by 65 publications

References 15 publications

Multiscale mass conservative domain decomposition preconditioners for elliptic problems on irregular grids

Multiscale mass conservative domain decomposition preconditioners for elliptic problems on irregular grids

Mass Conservative Domain Decomposition for Porous Media Flow

Comparing Some Methods and Preconditioners for Hydropower Plant Flow Simulations

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