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2014•SIAM Journal on Numerical AnalysisRequires access

A Robin-type Domain Decomposition Method with Red-Black Partition

Yongxiang Liu, Xuejun Xu

Open publisher page 8 citations

Abstract

In this paper, we present a new Robin-type nonoverlapping domain decomposition (DD) preconditioner. The unknown variables to be solved in this preconditioned algebraic system are the Robin transmission data on the interface, which are different from the well-known DD methods like substructuring nonoverlapping DD method and FETI method. Through choosing suitable parameter on each subdomain boundary and using the tool of energy estimate, for the second-order elliptic problem, we prove that the condition number of the preconditioned system is $C(1+\log(\frac{H}{h}))^2$, where $H$ is the coarse mesh size and $h$ is the fine mesh size. Moreover, in this paper, we always assume that there is a red-black partition for the whole domain $\Omega$. Numerical results are given to illustrate the efficiency of our DD preconditioner.

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What this paper is about

In this paper, we present a new Robin-type nonoverlapping domain decomposition (DD) preconditioner. The unknown variables to be solved in this preconditioned algebraic system are the Robin transmission data on the interface, which are different from the well-known DD methods like substructuring nonoverlapping DD method and FETI method. Through choosing suitable parameter on each subdomain boundary and using the tool of energy estimate, for the second-order elliptic problem, we prove that the condition number of the preconditioned system is $C(1+\log(\frac{H}{h}))^2$, where $H$ is the coarse mesh size and $h$ is the fine mesh size. Moreover, in this paper, we always assume that there is a red-black partition for the whole domain $\Omega$. Numerical results are given to illustrate the efficiency of our DD preconditioner.

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Available abstract

In this paper, we present a new Robin-type nonoverlapping domain decomposition (DD) preconditioner. The unknown variables to be solved in this preconditioned algebraic system are the Robin transmission data on the interface, which are different from the well-known DD methods like substructuring nonoverlapping DD method and FETI method. Through choosing suitable parameter on each subdomain boundary and using the tool of energy estimate, for the second-order elliptic problem, we prove that the condition number of the preconditioned system is $C(1+\log(\frac{H}{h}))^2$, where $H$ is the coarse mesh size and $h$ is the fine mesh size. Moreover, in this paper, we always assume that there is a red-black partition for the whole domain $\Omega$. Numerical results are given to illustrate the efficiency of our DD preconditioner.

Key concepts: Preconditioner, Domain decomposition methods, Mathematics, FETI, Partition (number theory), Condition number, Type (biology), Algebraic number

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