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Restricted Additive Schwarz Algorithm with Schur Complement for Bound-Preserving Solution of Geological Carbon Sequestration.

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Title: Restricted Additive Schwarz Algorithm with Schur Complement for Bound-Preserving Solution of Geological Carbon Sequestration.
Authors: Jiang, Lei1 (AUTHOR) leijiang@hnu.edu.cn, Yang, Haijian2 (AUTHOR) haijianyang@hnu.edu.cn, Shi, Lijuan1 (AUTHOR) lijuanshi@hnu.edu.cn, Tu, Jiali1 (AUTHOR) jltu@hnu.edu.cn
Source: SIAM Journal on Scientific Computing. 2026, Vol. 48 Issue 3, pB440-B465. 26p.
Subjects: Schur complement, Geological carbon sequestration, Domain decomposition methods, Nonlinear equations, Carbon sequestration, Multiphase flow, Parallel programming
Abstract: High-resolution reservoir simulation of multiphase and multicomponent porous media flows, arising from geological carbon sequestration, requires solving large, sparse nonlinear and linear systems efficiently on parallel computers. This multiphysical process involves a compositional flow model with multiple wells and corner-point grid geometry, which demands efficient and scalable solvers optimized for high-performance computing. In the study, we present a nonstandard restricted additive Schwarz preconditioner with Schur complement, called SchurRAS, to mitigate slow convergence and stagnation in solving sparse linear systems. Our hybrid preconditioning approach combines overlapping domain decomposition for parallel scalability with localized Schur complement approximations to enhance solver efficiency on distributed-memory systems equipped with multicore nodes. Moreover, a minimum-type semismooth Newton algorithm is proposed to enhance nonlinear convergence and enforce physical constraints. Large-scale simulations are conducted on geological reservoir benchmarks and real-field carbon sequestration projects. The parallel performance evaluation on a supercomputer demonstrates the scalability of our approach to thousands of processor cores and shows that SchurRAS outperforms standard RAS in both iteration count and computational time. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:High-resolution reservoir simulation of multiphase and multicomponent porous media flows, arising from geological carbon sequestration, requires solving large, sparse nonlinear and linear systems efficiently on parallel computers. This multiphysical process involves a compositional flow model with multiple wells and corner-point grid geometry, which demands efficient and scalable solvers optimized for high-performance computing. In the study, we present a nonstandard restricted additive Schwarz preconditioner with Schur complement, called SchurRAS, to mitigate slow convergence and stagnation in solving sparse linear systems. Our hybrid preconditioning approach combines overlapping domain decomposition for parallel scalability with localized Schur complement approximations to enhance solver efficiency on distributed-memory systems equipped with multicore nodes. Moreover, a minimum-type semismooth Newton algorithm is proposed to enhance nonlinear convergence and enforce physical constraints. Large-scale simulations are conducted on geological reservoir benchmarks and real-field carbon sequestration projects. The parallel performance evaluation on a supercomputer demonstrates the scalability of our approach to thousands of processor cores and shows that SchurRAS outperforms standard RAS in both iteration count and computational time. [ABSTRACT FROM AUTHOR]
ISSN:10648275
DOI:10.1137/25M1780183