A second order accurate finite difference scheme for the heat equation on irregular domains and adaptive grids

Han Chen; Chohong Min; Frederic Gibou

A second order accurate finite difference scheme for the heat equation on irregular domains and adaptive grids

Han Chen, Chohong Min, Frederic Gibou

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We present a finite difference scheme for solving the variable coefficient heat equations with Dirichlet boundary conditions on irregular domains. A quadtree data structure is used to represent the non-graded adaptive Cartesian grids, and the interface is represented by the zero value points of the level set function. Numerical results in two spatial dimensions demonstrate second order accuracy for both the solution and its gradient in the L¹ and L^∞ norms.

Original language	English
Title of host publication	Amorphous and Polycrystalline Thin-Film Silicon Science and Technology - 2006
Pages	123-128
Number of pages	6
State	Published - 2007
Event	2006 MRS Spring Meeting - San Francisco, CA, United States Duration: 18 Apr 2006 → 21 Apr 2006

Publication series

Name	Materials Research Society Symposium Proceedings
Volume	910
ISSN (Print)	0272-9172

Conference

Conference	2006 MRS Spring Meeting
Country/Territory	United States
City	San Francisco, CA
Period	18/04/06 → 21/04/06

Cite this

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title = "A second order accurate finite difference scheme for the heat equation on irregular domains and adaptive grids",

abstract = "We present a finite difference scheme for solving the variable coefficient heat equations with Dirichlet boundary conditions on irregular domains. A quadtree data structure is used to represent the non-graded adaptive Cartesian grids, and the interface is represented by the zero value points of the level set function. Numerical results in two spatial dimensions demonstrate second order accuracy for both the solution and its gradient in the L1 and L∞ norms.",

author = "Han Chen and Chohong Min and Frederic Gibou",

year = "2007",

language = "English",

isbn = "1558998667",

series = "Materials Research Society Symposium Proceedings",

pages = "123--128",

booktitle = "Amorphous and Polycrystalline Thin-Film Silicon Science and Technology - 2006",

note = "2006 MRS Spring Meeting ; Conference date: 18-04-2006 Through 21-04-2006",

}

A second order accurate finite difference scheme for the heat equation on irregular domains and adaptive grids. / Chen, Han; Min, Chohong; Gibou, Frederic.
Amorphous and Polycrystalline Thin-Film Silicon Science and Technology - 2006. 2007. p. 123-128 (Materials Research Society Symposium Proceedings; Vol. 910).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - A second order accurate finite difference scheme for the heat equation on irregular domains and adaptive grids

AU - Chen, Han

AU - Min, Chohong

AU - Gibou, Frederic

PY - 2007

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N2 - We present a finite difference scheme for solving the variable coefficient heat equations with Dirichlet boundary conditions on irregular domains. A quadtree data structure is used to represent the non-graded adaptive Cartesian grids, and the interface is represented by the zero value points of the level set function. Numerical results in two spatial dimensions demonstrate second order accuracy for both the solution and its gradient in the L1 and L∞ norms.

AB - We present a finite difference scheme for solving the variable coefficient heat equations with Dirichlet boundary conditions on irregular domains. A quadtree data structure is used to represent the non-graded adaptive Cartesian grids, and the interface is represented by the zero value points of the level set function. Numerical results in two spatial dimensions demonstrate second order accuracy for both the solution and its gradient in the L1 and L∞ norms.

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M3 - Conference contribution

AN - SCOPUS:34249950435

SN - 1558998667

SN - 9781558998667

T3 - Materials Research Society Symposium Proceedings

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BT - Amorphous and Polycrystalline Thin-Film Silicon Science and Technology - 2006

T2 - 2006 MRS Spring Meeting

Y2 - 18 April 2006 through 21 April 2006

ER -

A second order accurate finite difference scheme for the heat equation on irregular domains and adaptive grids

Abstract

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Conference

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