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The discrete Orthogonal Polynomial least squares Method for Approximation and Solving Partial Differential Equations

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Communications in Computational Physics 2008年第3期3卷 734-758页

作者： Anne Gelb Rodrigo B.Platte W.Steven Rosenthal Department of Mathematics and Statistics Arizona State UniversityTempeArizona 85287USA

We investigate numerical approximations based on polynomials that are orthogonal with respect to a weighted discrete inner product and develop an algorithm for solving time dependent differential *** focus on the family of super Gaussian weight functions and derive a criterion for the choice of parameters that provides good accuracy and stability for the time evolution of partial differential *** results show that this approach circumvents the problems related to the Runge phenomenon on equally spaced nodes and provides high accuracy in *** time stability,small corrections near the ends of the interval are computed using local polynomial *** numerical experiments illustrate the performance of the method.

关键词： discrete least-squares orthogonal polynomials spectralmethods high order numerical methods uniform grid.

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Numerical Analysis of Crack-Tip Fields using a Meshless Method in Linear Elastic Materials

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Advances in Applied Mathematics and Mechanics 2022年第6期14卷 1509-1534页

作者： Zahra Sheikhi Akbar Ghanbari Mohammad Karkon Soleyman Ghouhestani Department of Civil Engineering Larestan BranchIslamic Azad UniversityLarestanIran Department of Civil Engineering Fasa UniversityFasaIran

In this paper,the discrete least squares Meshless(DLSM)method is developed to determine crack-tip *** DLSM,the problem domain and its boundary are discretized by unrelated field nodes used to introduce the shape functions by the moving least-squares(MLS)*** method aims to minimize the sum of squared residuals of the governing differential equations at any nodal *** high-continuity shape functions are used,some necessary treatments,including the visibility criterion,diffraction,and transparency approaches,are employed in the DLSM to introduce strong discontinuities such as *** stress extrapolation and J-integral methods are used to calculate stress intensity *** classic numerical examples using three approaches to defining discontinuities in the irregular distribution of nodal points are considered to investigate the effectiveness of the DLSM *** numerical tests indicated that the proposed method effectively employed the approaches to defining discontinuities to deal with discontinuous *** was also demonstrated that the diffraction approach obtained higher accuracy than the other techniques.

关键词： Numerical analysis partial differential equations fracture mechanics meshless method discrete least-squares modification of weight function approaches to defining discontinuities stress intensity factors.

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