High-Order Basis Functions for the Moment Method Solution of Two-Dimensional Scattering Problems

2006 ◽  
Author(s):  
Jin-Ping Zhang ◽  
Yun-Sheng Xu ◽  
Wei-Dong Wang
Keyword(s):  
Moment Method ◽  
High Order ◽  
Basis Functions ◽  
Two Dimensional ◽  
Scattering Problems ◽  
The Moment

Inverse Scattering Scheme Based on the Moment Method in the Spectral Domain, Part I: Theory

1992 ◽  
Vol 14 (1) ◽  
pp. 16-28 ◽  
Author(s):  
Se-Yun Kim ◽  
Hyun-Chul Choi ◽  
Jae-Min Lee ◽  
Jung-Woong Ra
Keyword(s):  
Inverse Scattering ◽  
Basis Function ◽  
Moment Method ◽  
Spectral Domain ◽  
Scattering Problems ◽  
Actual Mechanism ◽  
Spectral Components ◽  
Key Factor ◽  
The Moment ◽  
Measurement Location

Recently, electromagnetic and ultrasonic imaging of inhomogeneous objects by applying the moment-method procedures of forward scattering problems in the reverse sequence have been developed. In this paper, the inverse scattering formulation has been modified to be applicable in the spectral domain. Compared to previous schemes, the suggested formulation illustrates clearly the actual mechanism of the inverse scattering process by explicit separation of the contributions from several variables, such as the measurement location, basis function, and geometry of objects. The ill-posedness inherent in inverse scattering problems was also explained easily in this spectral scheme by the exponentially-decaying behavior of high-frequency spectral components of the scattered field. It implies that enlargement of the discretized cell size is a key factor in regularizing the ill-posedness. In particular, since the singular kernel to be integrated on each cell became regular in the modified scheme, various types of basis functions instead of pulse function were adopted without additional difficulties. This advantage is expected to play an important role in regularizing the noise effect by selecting polynomial basis function on the enlarged cells of discretization in the spectral inverse scattering scheme.

scholarly journals Numerical Regularized Moment Method For High Mach Number Flow

2012 ◽  
Vol 11 (5) ◽  
pp. 1415-1438 ◽  
Author(s):  
Zhenning Cai ◽  
Ruo Li ◽  
Yanli Wang
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Moment Method ◽  
Arbitrary Order ◽  
High Order ◽  
Numerical Implementation ◽  
Moment System ◽  
Number Flow ◽  
High Mach ◽  
The Moment

AbstractThis paper is a continuation of our earlier work [SIAM J. Sci. Comput., 32(2010), pp. 2875-2907] in which a numerical moment method with arbitrary order of moments was presented. However, the computation may break down during the calculation of the structure of a shock wave with Mach number M0≥ 3. In this paper, we concentrate on the regularization of the moment systems. First, we apply the Maxwell iteration to the infinite moment system and determine the magnitude of each moment with respect to the Knudsen number. After that, we obtain the approximation of high order moments and close the moment systems by dropping some high-order terms. Linearization is then performed to obtain a very simple regularization term, thus it is very convenient for numerical implementation. To validate the new regularization, the shock structures of low order systems are computed with different shock Mach numbers.

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