Fictitious Domain Methods for the Numerical Solution of Two-Dimensional Scattering Problems

1998 ◽  
Vol 145 (1) ◽  
pp. 89-109 ◽  
Author(s):  
Erkki Heikkola ◽  
Yuri A. Kuznetsov ◽  
Pekka Neittaanmäki ◽  
Jari Toivanen
Keyword(s):  
Numerical Solution ◽  
Fictitious Domain ◽  
Two Dimensional ◽  
Scattering Problems ◽  
Fictitious Domain Methods

FICTITIOUS DOMAIN METHODS FOR THE NUMERICAL SOLUTION OF THREE-DIMENSIONAL ACOUSTIC SCATTERING PROBLEMS

1999 ◽  
Vol 07 (03) ◽  
pp. 161-183 ◽  
Author(s):  
ERKKI HEIKKOLA ◽  
YURI A. KUZNETSOV ◽  
KONSTANTIN N. LIPNIKOV
Keyword(s):  
Boundary Value Problem ◽  
Numerical Solution ◽  
Boundary Value ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Fictitious Domain ◽  
Scattering Problems ◽  
Element Discretization ◽  
Fictitious Domain Methods ◽  
Acoustic Scattering Problems

Efficient iterative methods for the numerical solution of three-dimensional acoustic scattering problems are considered. The underlying exterior boundary value problem is approximated by truncating the unbounded domain and by imposing a non-reflecting boundary condition on the artificial boundary. The finite element discretization of the approximate boundary value problem is performed using locally fitted meshes, and algebraic fictitious domain methods with separable preconditioners are applied to the solution of the resultant mesh equations. These methods are based on imbedding the original domain into a larger one with a simple geometry (for example, a sphere or a parallelepiped). The iterative solution method is realized in a low-dimensional subspace, and partial solution methods are applied to the linear systems with the preconditioner. The results of numerical experiments demonstrate the efficiency and accuracy of the approach.

The Best Perturbation Method for the Parameter Inversion of Two-Dimension Convection-Diffusion Equation

2013 ◽  
Vol 380-384 ◽  
pp. 1143-1146
Author(s):  
Xiang Guo Liu
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Perturbation Method ◽  
Numerical Simulations ◽  
Numerical Solution ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Parameter Inversion ◽  
Parametric Inversion

The paper researches the parametric inversion of the two-dimensional convection-diffusion equation by means of best perturbation method, draw a Numerical Solution for such inverse problem. It is shown by numerical simulations that the method is feasible and effective.

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