Zi Han^1,*, Zhentian Huang²

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.1, pp. 245-272, 2024, DOI:10.32604/cmes.2023.029708

Abstract In the context of global mean square error concerning the number of random variables in the representation, the Karhunen–Loève (KL) expansion is the optimal series expansion method for random field discretization. The computational efficiency and accuracy of the KL expansion are contingent upon the accurate resolution of the Fredholm integral eigenvalue problem (IEVP). The paper proposes an interpolation method based on different interpolation basis functions such as moving least squares (MLS), least squares (LS), and finite element method (FEM) to solve the IEVP. Compared with the Galerkin method based on finite element or Legendre polynomials, the main advantage of the… More > Graphic Abstract

Supriya Gupta^*, Aakanksha Sharaff, Naresh Kumar Nagwani

Computer Systems Science and Engineering, Vol.45, No.3, pp. 2333-2349, 2023, DOI:10.32604/csse.2023.030385

Abstract Text Summarization models facilitate biomedical clinicians and researchers in acquiring informative data from enormous domain-specific literature within less time and effort. Evaluating and selecting the most informative sentences from biomedical articles is always challenging. This study aims to develop a dual-mode biomedical text summarization model to achieve enhanced coverage and information. The research also includes checking the fitment of appropriate graph ranking techniques for improved performance of the summarization model. The input biomedical text is mapped as a graph where meaningful sentences are evaluated as the central node and the critical associations between them. The proposed framework utilizes the top… More >

J. Sladek¹, V. Sladek¹, P. Stanak¹, E. Pan²

CMES-Computer Modeling in Engineering & Sciences, Vol.64, No.3, pp. 267-298, 2010, DOI:10.3970/cmes.2010.064.267

Abstract The plate equations are obtained by means of an appropriate expansion of the mechanical displacement and electric potential in powers of the thickness coordinate in the variational equation of electroelasticity and integration through the thickness. The appropriate assumptions are made to derive the uncoupled equations for the extensional and flexural motion. The present approach reduces the original 3-D plate problem to a 2-D problem, with all the unknown quantities being localized in the mid-plane of the plate. A meshless local Petrov-Galerkin (MLPG) method is then applied to solve the problem. Nodal points are randomly spread in the mid-plane of the… More >

Z. D. Han¹, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 665-678, 2003, DOI:10.3970/cmes.2003.004.665

Abstract The numerical implementation of the truly Meshless Local Petrov-Galerkin (MLPG) type weak-forms of the displacement and traction boundary integral equations is presented, for solids undergoing small deformations. In the accompanying part I of this paper, the general MLPG/BIE weak-forms were presented [Atluri, Han and Shen (2003)]. The MLPG weak forms provide the most general basis for the numerical solution of the non-hyper-singular displacement and traction BIEs [given in Han, and Atluri (2003)], which are simply derived by using the gradients of the displacements of the fundamental solutions [Okada, Rajiyah, and Atluri (1989a,b)]. By employing the various types of test functions,… More >

S. N. Atluri¹, Z. D. Han¹, A. M. Rajendran²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.6, pp. 491-514, 2004, DOI:10.3970/cmes.2004.006.491

Abstract The Meshless Finite Volume Method (MFVM) is developed for solving elasto-static problems, through a new Meshless Local Petrov-Galerkin (MLPG) ``Mixed'' approach. In this MLPG mixed approach, both the strains as well as displacements are interpolated, at randomly distributed points in the domain, through local meshless interpolation schemes such as the moving least squares(MLS) or radial basis functions(RBF). The nodal values of strains are expressed in terms of the independently interpolated nodal values of displacements, by simply enforcing the strain-displacement relationships directly by collocation at the nodal points. The MLPG local weak form is then written for the equilibrium equations over… More >

Z. D. Han¹, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.2, pp. 169-188, 2004, DOI:10.3970/cmes.2004.006.169

Abstract Three different truly Meshless Local Petrov-Galerkin (MLPG) methods are developed for solving 3D elasto-static problems. Using the general MLPG concept, these methods are derived through the local weak forms of the equilibrium equations, by using different test functions, namely, the Heaviside function, the Dirac delta function, and the fundamental solutions. The one with the use of the fundamental solutions is based on the local unsymmetric weak form (LUSWF), which is equivalent to the local boundary integral equations (LBIE) of the elasto-statics. Simple formulations are derived for the LBIEs in which only weakly-singular integrals are included for a simple numerical implementation.… More >

Z. D. Han¹, S. N. Atluri²

CMC-Computers, Materials & Continua, Vol.1, No.2, pp. 129-140, 2004, DOI:10.3970/cmc.2004.001.129

Abstract A Meshless Local Petrov-Galerkin (MLPG) method has been developed for solving 3D elasto-dynamic problems. It is derived from the local weak form of the equilibrium equations by using the general MLPG concept. By incorporating the moving least squares (MLS) approximations for trial and test functions, the local weak form is discretized, and is integrated over the local sub-domain for the transient structural analysis. The present numerical technique imposes a correction to the accelerations, to enforce the kinematic boundary conditions in the MLS approximation, while using an explicit time-integration algorithm. Numerical examples for solving the transient response of the elastic structures… More >

S. Vahdati¹, D. Mirzaei²

CMES-Computer Modeling in Engineering & Sciences, Vol.109-110, No.3, pp. 247-262, 2015, DOI:10.3970/cmes.2015.109.247

Abstract In this paper we present a meshless collocation method based on the moving least squares (MLS) approximation for numerical solution of the multiasset (d-dimensional) American option in financial mathematics. This problem is modeled by the Black-Scholes equation with moving boundary conditions. A penalty approach is applied to convert the original problem to one in a fixed domain. In finite parts, boundary conditions satisfy in associated (d-1)-dimensional Black-Scholes equations while in infinity they approach to zero. All equations are treated by the proposed meshless approximation method where the method of lines is employed for handling the time variable. Numerical examples for… More >

Sang-Ri Yi¹, Boyoung Kim², Jun Won Kang^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.106, No.2, pp. 77-104, 2015, DOI:10.3970/cmes.2015.106.077

Abstract This study is concerned with the development of new mixed unsplitfield perfectly matched layers (PMLs) for the simulation of plane electromagnetic waves in heterogeneous unbounded domains. To formulate the unsplit-field PML, a complex coordinate transformation is introduced to Maxwell's equations in the frequency domain. The transformed equations are converted back to the time domain via the inverse Fourier transform, to arrive at governing equations for transient electromagnetic waves within the PML-truncated computational domain. A mixed finite element method is used to solve the PML-endowed Maxwell equations. The developed PML method is relatively simple and straightforward when compared to split-field PML… More >

M. Dehghan¹, M. Abbaszadeh², A. Mohebbi³

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.5, pp. 399-444, 2014, DOI:10.3970/cmes.2014.100.399

Abstract In this paper three numerical techniques are proposed for solving the system of N-coupled nonlinear Schrödinger (CNLS) equations. Firstly, we obtain a time discrete scheme by approximating the first-order time derivative via the forward finite difference formula, then for obtaining a full discretization scheme, we use the Kansa’s approach to approximate the spatial derivatives via radial basis functions (RBFs) collocation methodology. We introduce the moving least squares (MLS) approximation and radial point interpolation method (RPIM) with their shape functions, separately. It should be noted that the shape functions of RPIM unlike the shape functions of the MLS approximation have kronecker… More >