Two regularization methods for the Cauchy problems of the Helmholtz equation

被引：41

作者：

Qin, H. H. ^{[1
]}

Wei, T. ^{[1
]}

机构：

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China

来源：

APPLIED MATHEMATICAL MODELLING | 2010年 / 34卷 / 04期

关键词：

Cauchy problems; Helmholtz equation; Two regularization methods; Convergence estimates; BOUNDARY KNOT METHOD; FUNDAMENTAL-SOLUTIONS; HEAT-EQUATION;

D O I：

10.1016/j.apm.2009.07.008

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, the Cauchy problems for the Helmholtz equation are investigated. We propose two regularization methods to solve them. Convergence estimates are presented under an a-priori bounded assumption for the exact solution. Finally, the numerical examples show that the proposed numerical methods work effectively. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：947 / 967

页数：21

共 28 条

[1]

[Anonymous], 1977, NEW YORK

[2] Dual formulation of multiple reciprocity method for the acoustic mode of a cavity with a thin partition [J].

Chen, JT ;

Wong, FC .

JOURNAL OF SOUND AND VIBRATION, 1998, 217 (01) :75-95

[3] The detection of surface vibrations from interior acoustical pressure [J].

DeLillo, T ;

Isakov, V ;

Valdivia, N ;

Wang, LJ .

INVERSE PROBLEMS, 2003, 19 (03) :507-524

[4] The detection of the source of acoustical noise in two dimensions [J].

Delillo, T ;

Isakov, V ;

Valdivia, N ;

Wang, LJ .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2001, 61 (06) :2104-2121

[5] Wavelet and Fourier methods for solving the sideways heat equation [J].

Eldén, L ;

Berntsson, F ;

Reginska, T .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2000, 21 (06) :2187-2205

[6] Simplified Tikhonov and Fourier regularization methods on a general sideways parabolic equation [J].

Fu, CL .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 167 (02) :449-463

[7]

Hadamard J, 1923, LECT CAUCHY PROBLEM

[8] A boundary element investigation of irregular frequencies in electromagnetic scattering [J].

Hall, WS ;

Mao, XQ .

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 1995, 16 (03) :245-252

[9]

Harari I, 1998, INT J NUMER METH ENG, V41, P1105, DOI 10.1002/(SICI)1097-0207(19980330)41:6<1105::AID-NME327>3.0.CO

[10]

2-0

← 1 2 3 →