On The Acceleration Of Ill-Conditioned Linear Systems: A Pod-Based Deflation Method For The Simulation Of Two-Phase Flow

Gabriela Diaz Cortes; Jan Dirk Jansen; Kees Vuik

doi:10.3997/2214-4609.201802122

On The Acceleration Of Ill-Conditioned Linear Systems: A Pod-Based Deflation Method For The Simulation Of Two-Phase Flow

Gabriela Diaz Cortes, Jan Dirk Jansen, Kees Vuik

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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Abstract

We explore and develop POD-based deflation methods to accelerate the solution of large-scale linear systems resulting from two-phase flow simulation. The techniques here presented collect information from the system in a POD basis, which is later used in a deflation scheme. The snapshots required to obtain the POD basis are captured in two ways: a moving window approach, where the most recently computed solutions are used, and a training phase approach, where a full pre-simulation is run. We test this methodology in highly heterogeneous porous media: a full SPE 10 model containing O(10^6) cells, and in an academic layered problem presenting a contrast in permeability layers up to 10^6. Among the experiments, we study cases including gravity and capillary pressure terms. With the POD-based deflated procedure, we accelerate the convergence of a Preconditioned Conjugate Gradient (PCG) method, reducing the required number of iterations to around 10-30 %, i.e., we achieve speed-ups of factors three to ten.

Original language	English
Title of host publication	ECMOR XVI
Editors	D. Gunasekera
Place of Publication	Barcelona
Publisher	EAGE
Pages	1-22
Number of pages	22
ISBN (Print)	9789462822603
DOIs	https://doi.org/10.3997/2214-4609.201802122
Publication status	Published - 2018
Event	16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018: 3–6 September 2018, Barcelona, Spain - Barcelona, Spain Duration: 3 Sept 2018 → 6 Sept 2018 Conference number: 16 https://events.eage.org/en/2018/ecmorxvi

Conference

Conference	16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018
Abbreviated title	ECMOR 2018
Country/Territory	Spain
City	Barcelona
Period	3/09/18 → 6/09/18
Internet address	https://events.eage.org/en/2018/ecmorxvi

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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10.3997/2214-4609.201802122

Mo A2 02Final published version, 2.39 MB

1 Dissertation (TU Delft)

POD-Based Deflation Method For Reservoir Simulation
Diaz Cortes, G., 2019, Delft, the Netherlands. 156 p.
Research output: Thesis › Dissertation (TU Delft)

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Cite this

@inproceedings{dab7725e80624d5cbc9d18e7028f8da3,

title = "On The Acceleration Of Ill-Conditioned Linear Systems: A Pod-Based Deflation Method For The Simulation Of Two-Phase Flow ",

abstract = "We explore and develop POD-based deflation methods to accelerate the solution of large-scale linear systems resulting from two-phase flow simulation. The techniques here presented collect information from the system in a POD basis, which is later used in a deflation scheme. The snapshots required to obtain the POD basis are captured in two ways: a moving window approach, where the most recently computed solutions are used, and a training phase approach, where a full pre-simulation is run. We test this methodology in highly heterogeneous porous media: a full SPE 10 model containing O(10^6) cells, and in an academic layered problem presenting a contrast in permeability layers up to 10^6. Among the experiments, we study cases including gravity and capillary pressure terms. With the POD-based deflated procedure, we accelerate the convergence of a Preconditioned Conjugate Gradient (PCG) method, reducing the required number of iterations to around 10-30 %, i.e., we achieve speed-ups of factors three to ten. ",

author = "{Diaz Cortes}, Gabriela and Jansen, {Jan Dirk} and Kees Vuik",

note = "Green Open Access added to TU Delft Institutional Repository {\textquoteleft}You share, we take care!{\textquoteright} – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.; 16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018 : 3–6 September 2018, Barcelona, Spain, ECMOR 2018 ; Conference date: 03-09-2018 Through 06-09-2018",

year = "2018",

doi = "10.3997/2214-4609.201802122",

language = "English",

isbn = "9789462822603",

pages = "1--22",

editor = "D. Gunasekera",

booktitle = "ECMOR XVI",

publisher = "EAGE",

url = "https://events.eage.org/en/2018/ecmorxvi",

}

Diaz Cortes, G, Jansen, JD & Vuik, K 2018, On The Acceleration Of Ill-Conditioned Linear Systems: A Pod-Based Deflation Method For The Simulation Of Two-Phase Flow . in D Gunasekera (ed.), ECMOR XVI., Mo A2 02, EAGE, Barcelona, pp. 1-22, 16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018, Barcelona, Spain, 3/09/18. https://doi.org/10.3997/2214-4609.201802122

On The Acceleration Of Ill-Conditioned Linear Systems: A Pod-Based Deflation Method For The Simulation Of Two-Phase Flow . / Diaz Cortes, Gabriela; Jansen, Jan Dirk ; Vuik, Kees.
ECMOR XVI. ed. / D. Gunasekera. Barcelona: EAGE, 2018. p. 1-22 Mo A2 02.

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

TY - GEN

T1 - On The Acceleration Of Ill-Conditioned Linear Systems

T2 - 16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018

AU - Diaz Cortes, Gabriela

AU - Jansen, Jan Dirk

AU - Vuik, Kees

N1 - Conference code: 16

PY - 2018

Y1 - 2018

N2 - We explore and develop POD-based deflation methods to accelerate the solution of large-scale linear systems resulting from two-phase flow simulation. The techniques here presented collect information from the system in a POD basis, which is later used in a deflation scheme. The snapshots required to obtain the POD basis are captured in two ways: a moving window approach, where the most recently computed solutions are used, and a training phase approach, where a full pre-simulation is run. We test this methodology in highly heterogeneous porous media: a full SPE 10 model containing O(10^6) cells, and in an academic layered problem presenting a contrast in permeability layers up to 10^6. Among the experiments, we study cases including gravity and capillary pressure terms. With the POD-based deflated procedure, we accelerate the convergence of a Preconditioned Conjugate Gradient (PCG) method, reducing the required number of iterations to around 10-30 %, i.e., we achieve speed-ups of factors three to ten.

AB - We explore and develop POD-based deflation methods to accelerate the solution of large-scale linear systems resulting from two-phase flow simulation. The techniques here presented collect information from the system in a POD basis, which is later used in a deflation scheme. The snapshots required to obtain the POD basis are captured in two ways: a moving window approach, where the most recently computed solutions are used, and a training phase approach, where a full pre-simulation is run. We test this methodology in highly heterogeneous porous media: a full SPE 10 model containing O(10^6) cells, and in an academic layered problem presenting a contrast in permeability layers up to 10^6. Among the experiments, we study cases including gravity and capillary pressure terms. With the POD-based deflated procedure, we accelerate the convergence of a Preconditioned Conjugate Gradient (PCG) method, reducing the required number of iterations to around 10-30 %, i.e., we achieve speed-ups of factors three to ten.

U2 - 10.3997/2214-4609.201802122

DO - 10.3997/2214-4609.201802122

M3 - Conference contribution

SN - 9789462822603

SP - 1

EP - 22

BT - ECMOR XVI

A2 - Gunasekera, D.

PB - EAGE

CY - Barcelona

Y2 - 3 September 2018 through 6 September 2018

ER -

On The Acceleration Of Ill-Conditioned Linear Systems: A Pod-Based Deflation Method For The Simulation Of Two-Phase Flow

Abstract

Conference

Bibliographical note

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Research output

POD-Based Deflation Method For Reservoir Simulation

Cite this