On a general filter regularization method for the 2D and 3D Poisson equation in physical geodesy

被引：3

作者：

Nguyen Huy Tuan ^{[1
]}

Binh Thanh Tran ^{[2
]}

Le Dinh Long ^{[3
]}

机构：

[1] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam

[2] Sai Gon Univ, Dept Math & Applicat, Ho Chi Minh City, Vietnam

[3] Inst Computat Sci & Technol, Environm Sci Lab, Ho Chi Minh City, Vietnam

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2014年

关键词：

Poisson equation; Cauchy problem; ill-posed problem; convergence estimates; CAUCHY-PROBLEM; LAPLACE;

D O I：

10.1186/1687-1847-2014-258

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a Cauchy problem for the Poisson equation with nonhomogeneous source. The problem is shown to be ill-posed as the solution exhibits unstable dependence on the given data function. Using a new method, we regularize the given problem and obtain some new results. Two numerical examples are given to illustrate the effectiveness of our method.

引用

页数：21

共 50 条

[1] On a general filter regularization method for the 2D and 3D Poisson equation in physical geodesy
Nguyen Huy Tuan
Binh Thanh Tran
Le Dinh Long
Advances in Difference Equations, 2014
[2] Recovery of inclusions in 2D and 3D domains for Poisson's equation
Ito, Kazufumi
Liu, Ji-Chuan
INVERSE PROBLEMS, 2013, 29 (07)
[3] Effective 2D and 3D crack propagation with local mesh refinement and the screened Poisson equation
Areias, P.
Reinoso, J.
Camanho, P. P.
Cesar de Sa, J.
Rabczuk, T.
ENGINEERING FRACTURE MECHANICS, 2018, 189 : 339 - 360
[4] Solving 2D and 3D Poisson equations and biharmonic equations by the Haar wavelet method
Shi, Zhi
Cao, Yong-yan
Chen, Qing-jiang
APPLIED MATHEMATICAL MODELLING, 2012, 36 (11) : 5143 - 5161
[5] Solving Eikonal equation in 2D and 3D by generalized finite difference method
Salete, Eduardo
Flores, Jesus
Garcia, Angel
Negreanu, Mihaela
Vargas, Antonio M.
Urena, Francisco
COMPUTATIONAL AND MATHEMATICAL METHODS, 2021, 3 (06)
[6] A METHOD OF GENERAL MOMENTS FOR ORIENTING 2D PROJECTIONS OF UNKNOWN 3D OBJECTS
SALZMAN, DB
COMPUTER VISION GRAPHICS AND IMAGE PROCESSING, 1990, 50 (02): : 129 - 156
[7] A Multithreaded Solver for the 2D Poisson Equation
Vidal, Andres
Kassab, Alain
Mota, Daniel
Dechev, Damian
HIGH PERFORMANCE COMPUTING SYMPOSIUM 2012 (HPC 2012), 2012, 44 (06): : 9 - 17
[8] A "LEARN 2D, APPLY 3D" METHOD FOR 3D DECONVOLUTION MICROSCOPY
Soulez, Ferreol
2014 IEEE 11th International Symposium on Biomedical Imaging (ISBI), 2014, : 1075 - 1078
[9] Fourier method with Nitsche-mortaring for the Poisson equation in 3D
Heinrich, Bernd
Jung, Beate
NUMERICAL MATHEMATICS AND ADVANCED APPLICATIONS, 2006, : 467 - +
[10] 3D multidomain BEM for a Poisson equation
Ramsak, Matjaz
Skerget, Leopold
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2009, 33 (05) : 689 - 694

← 1 2 3 4 5 →