Yiguo Chen^1,2,3,*, Congjun Feng^1,2, Yonghong He³, Zhijun Chen³, Xiaowei Fan³, Chao Wang³, Xinmin Ge⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 2451-2463, 2023, DOI:10.32604/cmes.2023.021145 - 09 March 2023

Abstract The low-field nuclear magnetic resonance (NMR) technique has been used to probe the pore size distribution and the fluid composition in geophysical prospecting and related fields. However, the speed and accuracy of the existing numerical inversion methods are still challenging due to the ill-posed nature of the first kind Fredholm integral equation and the contamination of the noises. This paper proposes a novel inversion algorithm to accelerate the convergence and enhance the precision using empirical truncated singular value decompositions (TSVD) and the linearized Bregman iteration. The L1 penalty term is applied to construct the objective More > Graphic Abstract

Arezoo Emdadi¹, Edward J. Kansa², Nicolas Ali Libre^1,3, Mohammad Rahimian¹, Mohammad Shekarchi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.25, No.1, pp. 23-42, 2008, DOI:10.3970/cmes.2008.025.023

Abstract We present a new method based upon the paper of Volokh and Vilney (2000) that produces highly accurate and stable solutions to very ill-conditioned multiquadric (MQ) radial basis function (RBF) asymmetric collocation methods for partial differential equations (PDEs). We demonstrate that the modified Volokh-Vilney algorithm that we name the improved truncated singular value decomposition (IT-SVD) produces highly accurate and stable numerical solutions for large values of a constant MQ shape parameter, c, that exceeds the critical value of c based upon Gaussian elimination. More >

Nicolas Ali Libre^1,2, Arezoo Emdadi², Edward J. Kansa^3,4, Mohammad Rahimian², Mohammad Shekarchi²

CMES-Computer Modeling in Engineering & Sciences, Vol.24, No.1, pp. 61-80, 2008, DOI:10.3970/cmes.2008.024.061

Abstract The numerical solution of partial differential equations (PDEs) with Neumann boundary conditions (BCs) resulted from strong form collocation scheme are typically much poorer in accuracy compared to those with pure Dirichlet BCs. In this paper, we show numerically that the reason of the reduced accuracy is that Neumann BC requires the approximation of the spatial derivatives at Neumann boundaries which are significantly less accurate than approximation of main function. Therefore, we utilize boundary treatment schemes that based upon increasing the accuracy of spatial derivatives at boundaries. Increased accuracy of the spatial derivative approximation can be… More >

B. Jin^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.3, pp. 253-262, 2004, DOI:10.3970/cmes.2004.006.253

Abstract In this paper, we propose a new numerical scheme for the solution of the Laplace and biharmonic equations subjected to noisy boundary data. The equations are discretized by the method of fundamental solutions. Since the resulting matrix equation is highly ill-conditioned, a regularized solution is obtained using the truncated singular value decomposition, with the regularization parameter given by the L-curve method. Numerical experiments show that the method is stable with respect to the noise in the data, highly accurate and computationally very efficient. More >