Effective Preconditioners for Mixed-Dimensional Scalar Elliptic Problems

被引：1

作者：

Hu, Xiaozhe ^{[1
,2
]}

Keilegavlen, Eirik ^{[2
]}

Nordbotten, Jan M. ^{[2
]}

机构：

[1] Tufts Univ, Dept Math, Medford, MA USA

[2] Univ Bergen, Ctr Modeling Coupled Subsurface Dynam, Dept Math, Bergen, Norway

来源：

WATER RESOURCES RESEARCH | 2023年 / 59卷 / 01期

基金：

美国国家科学基金会;

关键词：

fractured porous media; linear solvers; mixed-dimensional models; numerical modeling; FLOW; APPROXIMATION; JUMPS;

D O I：

10.1029/2022WR032985

中图分类号：

X [环境科学、安全科学];

学科分类号：

08 ; 0830 ;

摘要：

Discretization of flow in fractured porous media commonly lead to large systems of linear equations that require dedicated solvers. In this work, we develop an efficient linear solver and its practical implementation for mixed-dimensional scalar elliptic problems. We design an effective preconditioner based on approximate block factorization and algebraic multigrid techniques. Numerical results on benchmarks with complex fracture structures demonstrate the effectiveness of the proposed linear solver and its robustness with respect to different physical and discretization parameters.

引用

页数：9

共 33 条

[1] An introduction to multipoint flux approximations for quadrilateral grids [J].

Aavatsmark, I .

COMPUTATIONAL GEOSCIENCES, 2002, 6 (3-4) :405-432

[2] Verification benchmarks for single-phase flow in three-dimensional fractured porous media [J].

Berre, Inga ;

Boon, Wietse M. ;

Flemisch, Bernd ;

Fumagalli, Alessio ;

Glaeser, Dennis ;

Keilegavlen, Eirik ;

Scotti, Anna ;

Stefansson, Ivar ;

Tatomir, Alexandru ;

Brenner, Konstantin ;

Burbulla, Samuel ;

Devloo, Philippe ;

Duran, Omar ;

Favino, Marco ;

Hennicker, Julian ;

Lee, I-Hsien ;

Lipnikov, Konstantin ;

Masson, Roland ;

Mosthaf, Klaus ;

Nestola, Maria Giuseppina Chiara ;

Ni, Chuen-Fa ;

Nikitin, Kirill ;

Schadle, Philipp ;

Svyatskiy, Daniil ;

Yanbarisov, Ruslan ;

Zulian, Patrick .

ADVANCES IN WATER RESOURCES, 2021, 147

[3] Flow in Fractured Porous Media: A Review of Conceptual Models and Discretization Approaches [J].

Berre, Inga ;

Doster, Florian ;

Keilegavlen, Eirik .

TRANSPORT IN POROUS MEDIA, 2019, 130 (01) :215-236

[4] Functional analysis and exterior calculus on mixed-dimensional geometries [J].

Boon, Wietse M. ;

Nordbotten, Jan M. ;

Vatne, Jon E. .

ANNALI DI MATEMATICA PURA ED APPLICATA, 2021, 200 (02) :757-789

[5] ROBUST DISCRETIZATION OF FLOW IN FRACTURED POROUS MEDIA [J].

Boon, Wietse M. ;

Nordbotten, Jan M. ;

Yotov, Ivan .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2018, 56 (04) :2203-2233

[6] An improved convergence analysis of smoothed aggregation algebraic multigrid [J].

Brezina, Marian ;

Vanek, Petr ;

Vassilevski, Panayot S. .

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2012, 19 (03) :441-469

[7] MIXED-DIMENSIONAL AUXILIARY SPACE PRECONDITIONERS [J].

Budisa, Ana ;

Boon, Wietse M. ;

Hu, Xiaozhe .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2020, 42 (05) :A3367-A3396

[8] Block preconditioners for mixed-dimensional discretization of flow in fractured porous media [J].

Budisa, Ana ;

Hu, Xiaozhe .

COMPUTATIONAL GEOSCIENCES, 2021, 25 (02) :671-686

[9] Robust multigrid methods for nonsmooth coefficient elliptic linear systems [J].

Chan, TF ;

Wan, WL .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 123 (1-2) :323-352

[10] FLOW SIMULATION IN THREE-DIMENSIONAL DISCRETE FRACTURE NETWORKS [J].

Erhel, Jocelyne ;

De Dreuzy, Jean-Raynald ;

Poirriez, Baptiste .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2009, 31 (04) :2688-2705

← 1 2 3 4 →