A Spatially Fourth-Order Cartesian Grid Method for Fast Solutions of Elliptic and Parabolic Problems on Irregular Domains with Sharply Curved Boundaries

doi:10.1007/s10915-025-02909-x

	A Spatially Fourth-Order Cartesian Grid Method for Fast Solutions of Elliptic and Parabolic Problems on Irregular Domains with Sharply Curved Boundaries
	Li, Chuan 1; Zhao, Shan 2; Pentecost, Benjamin 1; Ren, Yiming 2; Guan, Zhen 3
	2025-06-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	103 期号:3 页码:35
摘要	This work aims to develop a fast and spatially fourth-order Cartesian grid finite difference method for solving elliptic and parabolic problems over two-dimensional irregular domains with sharply curved boundaries, under the assumptions that the boundary is C1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C<^>1$$\end{document}-continuous and the solution is sufficiently smooth up to the boundary. The proposed Augmented Matched Interface and Boundary (AMIB) method inherits its predecessor's speed and accuracy advantages, such as maintaining the Fast Fourier-Transform (FFT) efficiency and being fourth-order accuracy in handling any boundary conditions (Dirichlet, Neumann, Robin, or their combinations). To accommodate sharply curved boundaries, the proposed adaptive AMIB method features two significant improvements. First, an adaptive ray-casting Matched Interface and Boundary (MIB) scheme was developed to overcome the difficulties of generating fictitious values at some grid points where the boundary is sharply curved by reusing previously calculated fictitious values at nearby grid points. Second, several stabilizers, which include a new preconditioner for the resulting augmented system and proper grid selection requirements to interpolate the fictitious values and approximate derivative jumps in the MIB scheme, were designed to ensure the stability of the AMIB method. Numerical experiments have been conducted to validate the proposed AMIB method for solving boundary and initial value problems with sharply curved boundaries.
关键词	Elliptic boundary value problem Parabolic initial-and-boundary value problems Irregular domains Robin boundary condition High order finite difference Augmented matched interface and boundary (AMIB) Fast Fourier transform
DOI	10.1007/s10915-025-02909-x
收录类别	SCI
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:001485846100001
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://119.78.100.204/handle/2XEOYT63/42382
专题	中国科学院计算技术研究所期刊论文_英文
通讯作者	Li, Chuan
作者单位	1.West Chester Univ Penn, Dept Math, W Chester, PA 19383 USA 2.Univ Alabama, Dept Math, Tuscaloosa, AL 35487 USA 3.Chinese Acad Sci, Inst Comp Technol, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Li, Chuan,Zhao, Shan,Pentecost, Benjamin,et al. A Spatially Fourth-Order Cartesian Grid Method for Fast Solutions of Elliptic and Parabolic Problems on Irregular Domains with Sharply Curved Boundaries[J]. JOURNAL OF SCIENTIFIC COMPUTING,2025,103(3):35.
APA	Li, Chuan,Zhao, Shan,Pentecost, Benjamin,Ren, Yiming,&Guan, Zhen.(2025).A Spatially Fourth-Order Cartesian Grid Method for Fast Solutions of Elliptic and Parabolic Problems on Irregular Domains with Sharply Curved Boundaries.JOURNAL OF SCIENTIFIC COMPUTING,103(3),35.
MLA	Li, Chuan,et al."A Spatially Fourth-Order Cartesian Grid Method for Fast Solutions of Elliptic and Parabolic Problems on Irregular Domains with Sharply Curved Boundaries".JOURNAL OF SCIENTIFIC COMPUTING 103.3(2025):35.