An efficient RBF-FD method using polyharmonic splines alongside polynomials for the numerical solution of two-dimensional PDEs held on irregular domains and subject to Dirichlet and Robin boundary conditions

سال انتشار: 1403
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 39

فایل این مقاله در 12 صفحه با فرمت PDF قابل دریافت می باشد

استخراج به نرم افزارهای پژوهشی:

لینک ثابت به این مقاله:

شناسه ملی سند علمی:

JR_IJNAA-15-4_015

تاریخ نمایه سازی: 25 اسفند 1402

چکیده مقاله:

In the present paper, the relatively new method of Radial Basis Function-Generated Finite Difference (RBF-FD) is used to solve a class of Partial Differential Equations (PDEs) with Dirichlet and Robin boundary conditions. For this approximation, Polyharmonic Splines (PHS) are used alongside Polynomials. This combination has many benefits. On the other hand, Polyharmonic Splines have no shape parameter and therefore relieve us of the hassle of calculating the optimal shape parameter. As the first problem, a two-dimensional Poisson equation with the Dirichlet boundary condition is investigated in various domains. Then, an elliptic PDE with the Robin boundary condition is solved by the proposed method. The results of numerical studies indicate the excellent efficiency, accuracy and high speed of the method, while for these studies, very fluctuating and special test functions have been used.

نویسندگان

Asghar Rahimi

Department of Applied Mathematics, Imam Khomeini International University, Qazvin, ۳۴۱۴۹-۱۶۸۱۸, Iran

Elyas Shivanian

Department of Applied Mathematics, Imam Khomeini International University, Qazvin, ۳۴۱۴۸-۹۶۸۱۸, Iran

مراجع و منابع این مقاله:

لیست زیر مراجع و منابع استفاده شده در این مقاله را نمایش می دهد. این مراجع به صورت کاملا ماشینی و بر اساس هوش مصنوعی استخراج شده اند و لذا ممکن است دارای اشکالاتی باشند که به مرور زمان دقت استخراج این محتوا افزایش می یابد. مراجعی که مقالات مربوط به آنها در سیویلیکا نمایه شده و پیدا شده اند، به خود مقاله لینک شده اند :
  • S. Abbasbandy, E. Shivanian, K. Hammood AL-Jizani, and S.N. Atluri, ...
  • M. Abbaszadeh, M. Dehghan, Simulation flows with multiple phases and ...
  • P. Assari, H. Adibi, and M. Dehghan, A meshless discrete ...
  • P. Assari and M. Dehghan, A meshless discrete collocation method ...
  • A.G. Atta, W.M. Abd-Elhameed, G.M. Moatimid, and Y.H. Youssri, Modal ...
  • A.G. Atta and Y.H. Youssri, Advanced shifted first-kind Chebyshev collocation ...
  • A.G. Atta, W.M. Abd-Elhameed, G.M. Moatimid, and Y.H.Youssri, A fast ...
  • A.G. Atta, W.M. Abd-Elhameed, and Y.H. Youssri, Shifted fifth-kind Chebyshev ...
  • G.A. Barnett, A robust RBF-FD formulation based on polyharmonic splines ...
  • G. Barton, Elements of Green’s Functions and Propagation: Potentials, Diffusion, ...
  • V. Bayona, M. Moscoso, M. Carretero, and M. Kindelan, RBF-FD ...
  • V. Bayona, M. Moscoso, and M. Kindelan, Optimal constant shape ...
  • V. Bayona, M. Moscoso, and M. Kindelan, Optimal variable shape ...
  • V. Bayona, M. Moscoso, and M. Kindelan, Gaussian RBF-FD weights ...
  • V. Bayona, N. Flyer, B. Fornberg, and G.A. Barnett, On ...
  • V. Bayona, An insight into RBF-FD approximations augmented with polynomials, ...
  • V. Bayona, N. Flyer, and B. Fornberg, On the role ...
  • M. Dehghan and V. Mohammadi, A numerical scheme based on ...
  • H. Ding, C. Shu, D. B. Tang, Error estimates of ...
  • W. Fang, Y. Wang, and Y. Xu, An implementation of ...
  • G.E. Fasshauer, Meshfree Approximation Methods with MATLAB, Interdisciplinary Mathematical Sciences ...
  • G.E. Fasshauer and J.G. Zhang, On choosing “optimal” shape parameters ...
  • N. Flyer, B. Fornberg, V. Bayona, and G.A. Barnett, On ...
  • N. Flyer, G.A. Barnett, and L.J. Wicker, Enhancing finite differences ...
  • B. Fornberg and G. Wright, Stable computation of multiquadric interpolants ...
  • B. Fornberg and C. Piret, On choosing a radial basis ...
  • B. Fornberg and N. Flyer, A Primer on Radial Basis ...
  • B. Fornberg and N. Flyer, Solving PDEs with radial basis ...
  • D. Gunderman, N. Flyer, and B. Fornberg, Transport schemes in ...
  • R.L. Hardy, Multiquadric equations of topography and other irregular surfaces, ...
  • J. Helsing and A. Karlsson, An explicit kernel-split panel-based Nystrom ...
  • E.J. Kansa, Multiquadrics—a scattered data approximation scheme with applications to ...
  • E.J. Kansa, Multiquadrics-a scattered data approximation scheme with applications to ...
  • H.R. Khodabandehlo, E. Shivanian, and S. Abbasbandy, Numerical solution of ...
  • G. Liu and Y. Gu, An Introduction to Meshfree Methods ...
  • R. Nittka, Elliptic and parabolic problems with Robin boundary conditions ...
  • D.T. Oanh, O. Davydov, and H.X. Phu, Adaptive RBF-FD method ...
  • Y. Qiao, S. Zhai, and X. Feng, RBF-FD method for ...
  • A. Rahimi, C.A.E. Shivanian, and S. Abbasbandy, Analysis of new ...
  • J. Rashidinia and M.N. Rasoulizadeh, Numerical methods based on radial ...
  • D. Rostamy, M. Emamjome, and S. Abbasbandy, A meshless technique ...
  • R. Schaback, Error estimates and condition numbers for radial basis ...
  • V. Shankar, G.B. Wright, R.M. Kirby, and A.L. Fogelson, A ...
  • E. Shivanian, Pseudospectral meshless radial point hermit interpolation versus pseudospectral ...
  • E. Shivanian, A. Rahimi, and M. Hosseini, Meshless local radial ...
  • C. Shu, H. Ding, K.S. Yeo, Local radial basis function-based ...
  • F. Soleymani, M. Barfeie, and F.K. Haghani, Inverse multi-quadric RBF ...
  • M. Tillenius, E. Larsson, E. Lehto, and N. Flyer, A ...
  • A.I. Tolstykh, On using RBF-based differencing formulas for unstructured and ...
  • A.I. Tolstykh and D. A. Shirobokov, On using radial basis ...
  • I. Tominec, P.F. Villard, E. Larsson, V. Bayona, and N. ...
  • G.B. Wright, Radial basis function interpolation: Numerical and analytical developments, ...
  • G.B. Wright and B. Fornberg, Scattered node compact finite difference-type ...
  • Y.H. Youssri, Two Fibonacci operational matrix pseudospectral schemes for nonlinear ...
  • نمایش کامل مراجع