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2023•Demonstratio MathematicaOpen access

A dimension expanded preconditioning technique for block two-by-two linear equations

Wei‐Hua Luo, Bruno Carpentieri, Jun Guo

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Abstract

Abstract In this article, we introduce a novel block preconditioner for block two-by-two linear equations by expanding the dimension of the coefficient matrix. Theoretical results on the eigenvalues distribution of the preconditioned matrix are obtained, and a feasible implementation is discussed. Some numerical examples, including the solution of the Navier-Stokes equations, are presented to support the theoretical findings and demonstrate the preconditioner’s efficiency.

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Abstract In this article, we introduce a novel block preconditioner for block two-by-two linear equations by expanding the dimension of the coefficient matrix. Theoretical results on the eigenvalues distribution of the preconditioned matrix are obtained, and a feasible implementation is discussed. Some numerical examples, including the solution of the Navier-Stokes equations, are presented to support the theoretical findings and demonstrate the preconditioner’s efficiency.

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Available abstract

Abstract In this article, we introduce a novel block preconditioner for block two-by-two linear equations by expanding the dimension of the coefficient matrix. Theoretical results on the eigenvalues distribution of the preconditioned matrix are obtained, and a feasible implementation is discussed. Some numerical examples, including the solution of the Navier-Stokes equations, are presented to support the theoretical findings and demonstrate the preconditioner’s efficiency.

Key concepts: Preconditioner, Mathematics, Coefficient matrix, Dimension (graph theory), Eigenvalues and eigenvectors, Block (permutation group theory), Matrix (chemical analysis), Applied mathematics

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