ANALYSIS OF THE FICTITIOUS DOMAIN METHOD FOR EXTERIOR HELMHOLTZ PROBLEM

被引：0
|
作者：
ATAMIAN, C [1 ]
JOLY, P [1 ]
机构：
[1] INRIA,F-78153 LE CHESNAY,FRANCE
来源：
RAIRO-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 1993年 / 27卷 / 03期
关键词：
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The fictitious domain method has been conceived in order to solve partial differential equations in exterior domains. It consists in extending the equation in the interior domain by replacing the obstacle by a right hand side, with support contained in the interior domain, which becomes a control that we try to adjust in order to satisfy the boundary condition. We apply this approach to a diffraction problem for a harmonic wave. The problem is formulated as an optimal control problem that we analyse with the help of the Lagrange multiplier's theory. A link with the classical potential theory is established. We then show the convergence of a regularisation-penalisation method that we illustrate numerically,
引用
收藏
页码：251 / 288
页数：38
相关论文
共 50 条
  • [1] A Fictitious Domain Spectral Method for Solving the Helmholtz Equation in Exterior Domains
    Gu, Yiqi
    Shen, Jie
    JOURNAL OF SCIENTIFIC COMPUTING, 2023, 94 (03)
  • [2] A Fictitious Domain Spectral Method for Solving the Helmholtz Equation in Exterior Domains
    Yiqi Gu
    Jie Shen
    Journal of Scientific Computing, 2023, 94
  • [3] A domain decomposition method for the exterior Helmholtz problem
    Susan-Resiga, RF
    Atassi, HM
    JOURNAL OF COMPUTATIONAL PHYSICS, 1998, 147 (02) : 388 - 401
  • [4] An Overlapping Domain Decomposition Method for the Helmholtz Exterior Problem
    Savchenko, Alexander
    Petukhov, Artem
    NUMERICAL ANALYSIS AND ITS APPLICATIONS (NAA 2016), 2017, 10187 : 591 - 598
  • [5] A blended fictitious/real domain decomposition method for partially axisymmetric exterior Helmholtz problems with Dirichlet boundary conditions
    Hetmaniuk, U
    Farhat, C
    RECENT DEVELOPMENTS IN DOMAIN DECOMPOSITION METHODS, 2002, 23 : 1 - 26
  • [6] A parallel fictitious domain method for the three-dimensional Helmholtz equation
    Heikkola, E
    Rossi, T
    Toivanen, J
    SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2003, 24 (05): : 1567 - 1588
  • [7] 3D Helmholtz wave equation by fictitious domain method
    Kuznetsov, Yu. A.
    Lipnikov, K.N.
    Russian Journal of Numerical Analysis and Mathematical Modelling, 13 (05): : 371 - 387
  • [8] A fictitious domain method for a unilateral contact problem
    Bécache, E
    Joly, P
    Scarella, G
    MATHEMATICAL AND NUMERICAL ASPECTS OF WAVE PROPAGATION, WAVES 2003, 2003, : 431 - 436
  • [9] A FICTITIOUS DOMAIN METHOD FOR DIRICHLET PROBLEM AND APPLICATIONS
    GLOWINSKI, R
    PAN, TW
    PERIAUX, J
    COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1994, 111 (3-4) : 283 - 303
  • [10] The fictitious domain method as applied to the signorini problem
    Stepanov, VD
    Khludnev, AM
    DOKLADY MATHEMATICS, 2003, 68 (02) : 163 - 166
12345