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A Second Order Finite-Difference Ghost-Point Method for Elasticity Problems on unbounded domains with Applications to Volcanology

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Communications in Computational Physics 2014年第9期16卷 983-1009页

作者： Armando Coco Gilda Currenti Ciro Del Negro Giovanni Russo Dipartimento di Scienze della Terra e Geoambientali Universita di Bari Aldo MoroBariItaly. Bristol University Queens RoadBristol BS81RJUnited Kingdom. Istituto Nazionale di Geofisica e Vulcanologia Italy. Dipartimento di Matematica e Informatica Universita di CataniaCataniaItaly

We propose a finite-difference ghost-point approach for the numerical solution of Cauchy-Navier equations in linear elasticity problems on arbitrary unbounded *** technique is based on a smooth coordinate transformation,which maps an unbounded domain into a unit *** geometries are defined by suitable level-set *** equations are discretized by classical nine-point stencil on interior points,while boundary conditions and high order reconstructions are used to define the field variables at ghost-points,which are grid nodes external to the domain with a neighbor inside the *** linear system arising from such discretization is solved by a multigrid *** approach is then applied to solve elasticity problems in volcanology for computing the displacement caused by pressure *** method is suitable to treat problems in which the geometry of the source often changes(explore the effects of different scenarios,or solve inverse problems in which the geometry itself is part of the unknown),since it does not require complex re-meshing when the geometry is *** numerical tests are successfully performed,which asses the effectiveness of the present approach.

关键词： Linear elasticity Cauchy-Navier equations ground deformation unbounded domain coordinate transformation method Cartesian grid ghost points level-set methods multigrid.

Pullback attractors for the non-autonomous Benjamin-Bona-Mahony equation in unbounded domains

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Science China Mathematics 2011年第4期54卷 741-752页

作者： PARK Jong Yeoul PARK Sun Hye Department of Mathematics Pusan National University

The existence of a pullback attractor is proven for the non-autonomous Benjamin-Bona-Mahony equation in unbounded *** asymptotic compactness of the solution operator is obtained by the uniform estimates on the tails o... 详细信息

关键词： Benjamin-Bona-Mahony equation pullback attractor unbounded domain

Some Recent Advances on SpectralMethods for unbounded domains

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Communications in Computational Physics 2009年第2期5卷 195-241页

作者： Jie Shen Li-Lian Wang Department of Mathematics Purdue UniversityWest LafayetteIN47907USA Division of Mathematical Sciences School of Physical and Mathematical SciencesNanyang Technological University637616Singapore

We present in this paper a unified framework for analyzing the spectral methods in unbounded domains using mapped Jacobi,Laguerre and Hermite functions.A detailed comparison of the convergence rates of these spectral methods for solutions with typical decay behaviors is carried out,both theoretically and computationally.A brief review on some of the recent advances in the spectral methods for unbounded domains is also presented.

关键词： Spectral method unbounded domain orthogonal polynomials rational functions Hermite functions Laguerre functions

Numerical Method for the Deterministic Kardar-Parisi-Zhang Equation in unbounded domains

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Communications in Computational Physics 2006年第3期1卷 479-493页

作者： Zhenli Xu Houde Han Xiaonan Wu Department of Mathematics University of Science and Technology of ChinaHefei 230026P.R.China Department of Mathematical Sciences Tsinghua UniversityBeijing 100084P.R.China Department of Mathematics Hong Kong Baptist UniversityKowloon TongHong Kong

We propose an artificial boundary method for solving the deterministic Kardar-Parisi-Zhang equation in one-,two-and three dimensional unbounded *** exact artificial boundary conditions are obtained on the artificial *** the original problems are reduced to equivalent problems in bounded domains.A fi-nite difference method is applied to solve the reduced problems,and some numerical examples are provided to show the effectiveness of the method.

关键词： Quasilinear parabolic equation artificial boundary condition viscous Hamilton-Jacobi equation unbounded domain

ARTIFICIAL BOUNDARY METHOD FOR BURGERS＇ EQUATION USING NONLINEAR BOUNDARY CONDITIONS

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Journal of Computational Mathematics 2006年第3期24卷 295-304页

作者： Hou-de Han Xiao-nan Wu Zhen-li Xu Department of Mathematical Sciences Tsinghua University Beijing 100084. China Department of Mathematics Hong Kong Baptist University Kowloon Tong Hong Kong Department of Mathematics University of Science and Technology of China Hefei 230026 China

This paper discusses the numerical solution of Burgers＇ equation on unbounded domains. Two artificial boundaries are introduced and boundary conditions are obtained on the artificial boundaries, which are in nonlinear forms. Then the original problem is reduced to an equivalent problem on a bounded domain. Finite difference method is applied to the reduced problem, and some numerical examples are given to show the effectiveness of the new approach.

关键词： Burgers' equation unbounded domain Artificial boundary condition.

Approximate Analytical Solutions for a Class of Laminar Boundary-Layer Equations

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Chinese Physics Letters 2007年第7期24卷 1981-1984页

作者： Seripah Awang Kechil Ishak Hashim Sim Slaw Jiet Department of Mathematics Univer'siti Teknologi MARA 40450 Shah Alam Selangor Malaysia School of Mathematical Sciences Universiti Kebangsaan Malaysia 43600 UKM Bangi Selangor Malaysia

A simple and efficient approximate analytical technique is presented to obtain solutions to a class of two-point boundary value similarity problems in fluid mechanics. This technique is based on the decomposition method which yields a genera/analytic solution in the form of a convergent infinite series with easily computable terms. Comparative study is carried out to show the accuracy and effectiveness of the technique.

关键词： ADOMIAN DECOMPOSITION METHOD COMPARING NUMERICAL-METHODS GA-SB SYSTEM MARANGONI CONVECTION unbounded domain ALGORITHM SURFACE FLOWS

Well-posedness and dynamics of fractional Fitz Hugh-Nagumo systems on R^(N) driven by nonlinear noise

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Science China Mathematics 2021年第11期64卷 2395-2436页

作者： Renhai Wang Boling Guo Bixiang Wang Institute of Applied Physics and Computational Mathematics Beijing 100088China Department of Mathematics New Mexico Institute of Mining and TechnologySocorroNM 87801USA

This article is concerned with the well-posedness as well as long-term dynamics of a wide class of non-autonomous,non-local,fractional,stochastic Fitz Hugh-Nagumo systems driven by nonlinear noise defined on the entire space *** well-posedness is proved for the systems with polynomial drift terms of arbitrary order as well as locally Lipschitz nonlinear diffusion terms by utilizing the pathwise and mean square uniform *** mean random dynamical system generated by the solution operators is proved to possess a unique weak pullback mean random attractor in a Bochner *** existence of invariant measures is also established for the autonomous systems with globally Lipschitz continuous diffusion *** idea of uniform tail-estimates of the solutions in the appropriate spaces is employed to derive the tightness of a family of probability distributions of the solutions in order to overcome the non-compactness of the standard Sobolev embeddings on RNas well as the lack of smoothing effect on one component of the *** results of this paper are new even when the fractional Laplacian is replaced by the standard Laplacian.

关键词： fractional Fitz Hugh-Nagumo system weak pullback mean random attractor invariant measure nonlinear noise unbounded domain

Split Local Artificial Boundary Conditions for the Two-Dimensional Sine-Gordon Equation on R^(2)

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Communications in Computational Physics 2011年第10期10卷 1161-1183页

作者： Houde Han Zhiwen Zhang Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China.

In this paper the numerical solution of the two-dimensional sine-Gordon equation is *** local artificial boundary conditions are obtained by the operator splitting *** the original problem is reduced to an initial boundary value problem on a bounded computational domain,which can be solved by the finite *** numerical examples are provided to demonstrate the effectiveness and accuracy of the proposed method,and some interesting propagation and collision behaviors of the solitary wave solutions are observed.

关键词： Sine-Gordon equation operator splitting method artificial boundary condition soliton unbounded domain

Regularity and finite dimensionality of attractor for plate equation on R^n

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Applied Mathematics and Mechanics(English Edition) 2010年第11期31卷 1453-1462页

作者：肖海滨 Department of Mathematics Ningbo University Department of Mathematics Nanjing University

This paper addresses the regularity and finite dimensionality of the global attractor for the plate equation on the unbounded domain. The existence of the attractor in the phase space has been established in an earlier work of the author. It is shown that the attractor is actually a bounded set of the phase space and has finite fractal dimensionality.

关键词： global attractor plate equation regularity finite dimensionality unbounded domain