Domain decomposition interface preconditioners for fourth-order elliptic problems

Tony F. Chan; Weinan E; Jiachang Sun

doi:10.1016/0168-9274(91)90072-8

Domain decomposition interface preconditioners for fourth-order elliptic problems

Tony F. Chan, Weinan E, Jiachang Sun

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We present preconditioners for the interface system arising from solving fourth-order elliptic equations with domain decomposition methods. These preconditioners are derived from a Fourier analysis of the interface operator. We show that the condition number of the interface Schur complement is of order O(h^-3), where h is the grid size. Precise estimates concerning the decay properties of the elements of the Schur complement are also obtained. Relationships between interface preconditioners for second-order problems and fourth-order problems are established. Analytical as well as numerical results are given to assess the performance of these preconditioners.

Original language	English (US)
Pages (from-to)	317-331
Number of pages	15
Journal	Applied Numerical Mathematics
Volume	8
Issue number	4-5
DOIs	https://doi.org/10.1016/0168-9274(91)90072-8
State	Published - Nov 1991

All Science Journal Classification (ASJC) codes

Numerical Analysis
Computational Mathematics
Applied Mathematics

Keywords

Domain decomposition
Schur complement
biharmonic equation
interface preconditioner.

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10.1016/0168-9274(91)90072-8

Cite this

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title = "Domain decomposition interface preconditioners for fourth-order elliptic problems",

abstract = "We present preconditioners for the interface system arising from solving fourth-order elliptic equations with domain decomposition methods. These preconditioners are derived from a Fourier analysis of the interface operator. We show that the condition number of the interface Schur complement is of order O(h-3), where h is the grid size. Precise estimates concerning the decay properties of the elements of the Schur complement are also obtained. Relationships between interface preconditioners for second-order problems and fourth-order problems are established. Analytical as well as numerical results are given to assess the performance of these preconditioners.",

keywords = "Domain decomposition, Schur complement, biharmonic equation, interface preconditioner.",

author = "Chan, {Tony F.} and Weinan E and Jiachang Sun",

note = "Funding Information: * This work was supported in part by the Department of Energy under contract DEFGO3-87-ER-25037 and the Army Research Office under contract DAAL03-88-K-0085. The third author was also supported by the National Science Foundation of China and a computer grant from Minnesota Supercomputer Institute.",

year = "1991",

month = nov,

doi = "10.1016/0168-9274(91)90072-8",

language = "English (US)",

volume = "8",

pages = "317--331",

journal = "Applied Numerical Mathematics",

issn = "0168-9274",

publisher = "Elsevier",

number = "4-5",

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TY - JOUR

T1 - Domain decomposition interface preconditioners for fourth-order elliptic problems

AU - Chan, Tony F.

AU - E, Weinan

AU - Sun, Jiachang

N1 - Funding Information: * This work was supported in part by the Department of Energy under contract DEFGO3-87-ER-25037 and the Army Research Office under contract DAAL03-88-K-0085. The third author was also supported by the National Science Foundation of China and a computer grant from Minnesota Supercomputer Institute.

PY - 1991/11

Y1 - 1991/11

N2 - We present preconditioners for the interface system arising from solving fourth-order elliptic equations with domain decomposition methods. These preconditioners are derived from a Fourier analysis of the interface operator. We show that the condition number of the interface Schur complement is of order O(h-3), where h is the grid size. Precise estimates concerning the decay properties of the elements of the Schur complement are also obtained. Relationships between interface preconditioners for second-order problems and fourth-order problems are established. Analytical as well as numerical results are given to assess the performance of these preconditioners.

AB - We present preconditioners for the interface system arising from solving fourth-order elliptic equations with domain decomposition methods. These preconditioners are derived from a Fourier analysis of the interface operator. We show that the condition number of the interface Schur complement is of order O(h-3), where h is the grid size. Precise estimates concerning the decay properties of the elements of the Schur complement are also obtained. Relationships between interface preconditioners for second-order problems and fourth-order problems are established. Analytical as well as numerical results are given to assess the performance of these preconditioners.

KW - Domain decomposition

KW - Schur complement

KW - biharmonic equation

KW - interface preconditioner.

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DO - 10.1016/0168-9274(91)90072-8

M3 - Article

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SN - 0168-9274

VL - 8

SP - 317

EP - 331

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

IS - 4-5

ER -

Domain decomposition interface preconditioners for fourth-order elliptic problems

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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