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Engineering with Computers
Erschienen in: Engineering with Computers 1/2020

07.02.2019 | Original Article

A localized RBF-MLPG method and its application to elliptic PDEs

verfasst von: Mansour Safarpoor, Fariba Takhtabnoos, Ahmad Shirzadi

Erschienen in: Engineering with Computers | Ausgabe 1/2020

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Abstract

The existing local RBF methods use the strong form equation and approximate the solution in local subdomains instead of the whole domain. In the RBF-MLPG method, the unknown solution is approximated by RBFs in the whole domain and testing is done by constructing the weak-form equations over the local subdomains. This paper proposes to approximate the unknown solution locally in the RBF-MLPG method, i.e., in the localized RBF-MLPG method, both solution approximation and testing are treated locally. As a result, the final global matrix becomes sparser and more accurate solutions can be obtained. The method is applied for the numerical solution of elliptic PDEs. The comparison of the results demonstrates the effectiveness of the method.
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Literatur
1.
Poljak D, Brebbia CA (2004) Indirect Galerkin–Bubnov boundary element method for solving integral equations in electromagnetics. Eng Anal Bound Elem 28(7):771–777CrossRef
2.
Ochiai Y, Sladek V, Sladek J (2006) Transient heat conduction analysis by triple-reciprocity boundary element method. Eng Anal Bound Elem 30(3):194–204CrossRef
3.
Dehghan M, Shirzadi M (2015) The modified dual reciprocity boundary elements method and its application for solving stochastic partial differential equations. Eng Anal Bound Elem 58:99–111MathSciNetCrossRef
4.
Cheng AH-D, Cheng DT (2005) Heritage and early history of the boundary element method. Eng Anal Bound Elem 29(3):268–302CrossRef
5.
Karamali G, Dehghan M, Abbaszadeh M (2018) Numerical solution of a time-fractional PDE in the electroanalytical chemistry by a local meshless method. Eng Comput 35:87–100CrossRef
6.
Dehghan M, Abbaszadeh M (2017) Numerical investigation based on direct meshless local Petrov Galerkin (direct MLPG) method for solving generalized Zakharov system in one and two dimensions and generalized Gross–Pitaevskii equation. Eng Comput 33(4):983–996CrossRef
7.
Abbasbandy S, Shirzadi A (2011) MLPG method for two-dimensional diffusion equation with Neumann’s and non-classical boundary conditions. Appl Numer Math 61:170–180MathSciNetCrossRef
8.
Esfahani MH, Ghehsareh HR, Etesami SK (2017) A meshless method for the investigation of electromagnetic scattering from arbitrary shaped anisotropic cylindrical objects. J Electromagn Waves Appl 31(5):477–494CrossRef
9.
Shirzadi A, Ling L, Abbasbandy S (2012) Meshless simulations of the two-dimensional fractional-time convection–diffusion–reaction equations. Eng Anal Bound Elem 36:1522–1527MathSciNetCrossRef
10.
Mirzaei D, Schaback R (2014) Solving heat conduction problems by the direct meshless local Petrov–Galerkin (DMLPG) method. Numer Algorithms 65:275–291MathSciNetCrossRef
11.
Takhtabnoos F, Shirzadi A (2017) A local meshless method based on the finite collocation and local integral equations method for delay PDEs. Eng Anal Bound Elem 83(Supplement C):67–73MathSciNetCrossRef
12.
Shivanian E (2015) Meshless local Petrov–Galerkin (MLPG) method for three-dimensional nonlinear wave equations via moving least squares approximation. Eng Anal Bound Elem 50:249–257MathSciNetCrossRef
13.
Shivanian E, Jafarabadi A (2018) Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivatives: a stable scheme based on spectral meshless radial point interpolation. Eng Comput 34(1):77–90CrossRef
14.
Lee CK, King C, Fan SC (2003) Local multiquadric approximation for solving boundary value problems. Comput Mech 30:396–409MathSciNetCrossRef
15.
Shirzadi A, Takhtabnoos F (2016) A local meshless method for Cauchy problem of elliptic PDEs in annulus domains. Inverse Probl Sci Eng 24(5):729–743MathSciNetCrossRef
16.
Jackson S, Stevens D, Giddings D, Power H (2016) An adaptive RBF finite collocation approach to track transport processes across moving fronts. Comput Math Appl 71:278–300MathSciNetCrossRef
17.
Shirzadi A, Takhtabnoos F (2015) A local meshless collocation method for solving Landau–Lifschitz–Gilbert equation. Eng Anal Bound Elem 61:104–113MathSciNetCrossRef
18.
Stevens D, Power H (2015) The radial basis function finite collocation approach for capturing sharp fronts in time dependent advection problems. J Comput Phys 298:423–445MathSciNetCrossRef
19.
Takhtabnoos F, Shirzadi A (2016) A new implementation of the finite collocation method for time dependent PDEs. Eng Anal Bound Elem 63:114–124MathSciNetCrossRef
20.
Assari P, Dehghan M (2017) The numerical solution of two-dimensional logarithmic integral equations on normal domains using radial basis functions with polynomial precision. Eng Comput 33(4):853–870CrossRef
21.
Assari P, Dehghan M (2019) Application of dual-Chebyshev wavelets for the numerical solution of boundary integral equations with logarithmic singular kernels. Eng Comput 35(1):175–190CrossRef
22.
Assari P, Dehghan M (2018) Solving a class of nonlinear boundary integral equations based on the meshless local discrete Galerkin (MLDG) method. Appl Numer Math 123:137–158MathSciNetCrossRef
23.
24.
25.
Shivanian E, Jafarabadi A (2018) Capillary formation in tumor angiogenesis through meshless weak and strong local radial point interpolation. Eng Comput 34(3):603–619CrossRef
26.
Shivanian E (2016) Local integration of population dynamics via moving least squares approximation. Eng Comput 32(2):331–342CrossRef
27.
Dehghan M, Abbaszadeh M (2017) A finite element method for the numerical solution of Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivatives. Eng Comput 33(3):587–605CrossRef
28.
Ghehsareh HR, Zaghian A, Raei M (2018) A local weak form meshless method to simulate a variable order time-fractional mobile–immobile transport model. Eng Anal Bound Elem 90:63–75MathSciNetCrossRef
29.
Ghehsareh HR, Zaghian A, Zabetzadeh SM (2018) The use of local radial point interpolation method for solving two-dimensional linear fractional cable equation. Neural Comput Appl 29(10):745–754CrossRef
30.
Azarnavid B, Parand K, Abbasbandy S (2018) An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition. Commun Nonlinear Sci Numer Simul 59:544–552MathSciNetCrossRef
31.
Schaback R (2003) On the versatility of meshless kernel methods. In: Advances in computational & experimental engineering & sciences, vol 428
32.
Shu C, Ding H, Yeo KS (2003) Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier–Stokes equations. Comput Methods Appl Math 192:941–954MATH
33.
Vertnik R, arler B (2006) Meshless local radial basis function collocation method for convective–diffusive solid–liquid phase change problems. Int J Numer Methods Heat Fluid Flow 16:617–640MathSciNetCrossRef
34.
Zahab ZE, Divo E, Kassab AJ (2009) A localized collocation meshless method (LCMM) for incompressible flows CFD modeling with applications to transient hemodynamics. Eng Anal Bound Elem 33:1045–1061MathSciNetCrossRef
35.
Shirzadi A, Ling L (2013) Convergent overdetermined-RBF-MLPG for solving second order elliptic PDEs. Adv Appl Math Mech 5:78–89MathSciNetCrossRef
36.
Mirzaei D (2016) A greedy meshless local Petrov–Galerkin method based on radial basis functions. Numer Methods Partial Differ Equ 32(3):847–861MathSciNetCrossRef
37.
Schaback R (2013) Direct discretizations with applications to meshless methods for PDEs. In: Proceedings of DWCAA12, vol 6, pp 37–50
38.
Mirzaei D, Schaback R (2013) Direct meshless local Petrov–Galerkin (DMLPG) method: a generalized MLS approximation. Appl Numer Math 68:73–82MathSciNetCrossRef
39.
Zhang X (2000) Meshless methods based on collocation with radial basis functions. Comput Mech 26(4):333–343CrossRef
40.
Timoshenko SP, Goodier JN (1951) Theory of elasticity, vol 412. McGraw-Hill, New York, p 108MATH
Metadaten
Titel
A localized RBF-MLPG method and its application to elliptic PDEs
verfasst von
Mansour Safarpoor
Fariba Takhtabnoos
Ahmad Shirzadi
Publikationsdatum
07.02.2019
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 1/2020
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-018-00692-y

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