کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6915328 1447395 2018 58 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Superconvergent gradient smoothing meshfree collocation method
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
Superconvergent gradient smoothing meshfree collocation method
چکیده انگلیسی
A superconvergent meshfree collocation method with smoothed nodal gradients is presented. In this method, the first order smoothed gradients of meshfree shape function are constructed through a meshfree interpolation of the standard derivatives of meshfree shape function, while the second order smoothed gradients are computed through directly differentiating the first order smoothed gradients. It is noted that the second order smoothed gradients evaluated at meshfree nodes can be conveniently expressed as two successive first order gradient smoothing operations on the meshfree shape function, which facilitates a trivial numerical implementation. Subsequently, an employment of the second order smoothed gradients in the strong form of a given problem leads to the gradient smoothing meshfree collocation method purely using nodes as the collocation points. Based upon a local truncation error analysis, it is systematically shown that the proposed meshfree collocation method yields superconvergent solutions for odd degree basis functions. A key ingredient attributed to this superconvergence property is that the second order smoothed gradients meet the consistency conditions which go one order beyond the original basis degree of meshfree approximation. Another interesting fact is that the present formulation enables a convergent collocation scheme when the linear basis function is used in meshfree approximation, which is non-feasible in the conventional collocation formulation. The effectiveness of the proposed methodology is validated by numerical examples for both potential and elasticity problems. Numerical results well demonstrate the superconvergence and higher efficiency of the present gradient smoothing meshfree collocation method.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Methods in Applied Mechanics and Engineering - Volume 340, 1 October 2018, Pages 728-766
نویسندگان
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