Coupling of the improved singular boundary method and dual reciprocity method for multi-term time-fractional mixed diffusion-wave equations

Safari, Farzaneh; Chen, Wen

doi:10.1016/j.camwa.2019.02.001

Cited by 30 publications

(7 citation statements)

References 43 publications

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“…where Π[P i ] = 𝜚 i . In Safari et al [32], ℜ l approximated by PhS. Consider the Euclidean distance between x and x i as r i and…”

Section: The 3d-lmfs Methodsmentioning

confidence: 99%

Approximation of three‐dimensional nonlinear wave equations by fundamental solutions and weighted residuals process

Safari

2023

Math Methods in App Sciences

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In this paper, the localized method of fundamental solutions (LMFS) with coupling the dual reciprocity method (DRM) is applied to simulate three‐space dimensional nonlinear wave equations. First, DRM, which is a popular meshless method based on polyharmonic splines (PhS), is applied to obtain the particular solution. After evaluating the particular solution, 3D‐LMFS method can be employed to evaluate the homogeneous solution. The proposed 3D‐LMFS algorithms construct 3D artificial surfaces where source points and then the collocation procedure propose by using the fundamental solutions in each 3D surface. Straightforwardly, a solution to the 3D wave equation is approximated by a sum of the combination of PhS and fundamental solutions using LMFS. Eventually, the scheme has been prosperously tested with selected examples.

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“…where Π[P i ] = 𝜚 i . In Safari et al [32], ℜ l approximated by PhS. Consider the Euclidean distance between x and x i as r i and…”

Section: The 3d-lmfs Methodsmentioning

confidence: 99%

Approximation of three‐dimensional nonlinear wave equations by fundamental solutions and weighted residuals process

Safari

2023

Math Methods in App Sciences

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“…Safari and Sun [12] solved a fractional Rayleigh-Stokes using an improved singular boundary and dual reciprocity methods. Safari and Chen [13] solved a multi-term time-fractional mixed diffusion-wave equations with coupling of the improved singular boundary and dual reciprocity methods. In [14], Safari et al used a meshless method to solve a variable-order fractional diffusion problems with fourthorder derivative term.…”

Section: Introductionmentioning

confidence: 99%

Solution of the Modified Time Fractional Coupled Burgers Equations Using Laplace Adomian Decompostion Method

Omame

Zaman

2023

Acta Mechanica Et Automatica

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In this work, a coupled system of time-fractional modified Burgers’ equations is considered. Three different fractional operators: Caputo, Caputo-Fabrizio and Atangana-Baleanu operators are implemented for the equations. Also, two different scenarios are examined for each fractional operator: when the initial conditions are u(x, y, 0) = sin(xy), v(x, y, 0) = sin(xy), and when they are u(x, y, 0) = e{−kxy}, v(x, y, 0) = e{−kxy}, where k, α are some positive constants. With the aid of computable Adomian polynomials, the solutions are obtained using Laplace Adomian decomposition method (LADM). The method does not need linearization, weak nonlinearity assumptions or perturbation theory. Simulations are also presented to support theoretical results, and the behaviour of the solutions under the three different fractional operators compared.

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“…Due to considering heat source, a domain integral appears in the boundary integral equation (BIE) of heat conduction. Several previous pieces of research applied the multiple reciprocity method (MRM) (Safari and Chen, 2019; Yan et al ., 2019) and radial integration method (RIM) (Cui et al ., 2018b) as integral dimension reduction method. In this research, the line integration method (LIM)-coupled BEM, that is, the LIBEM, is applied to reduce the domain integral dimensionally, and the domain integrals can be transferred into line integrals; hence, volume discretization is avoided successfully.…”

Section: Introductionmentioning

confidence: 99%

The fast multipole method–accelerated line integration boundary element method for 3D heat conduction analysis with heat source

Liu,

Wang,

Feng

et al. 2023

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Purpose3D steady heat conduction analysis considering heat source is conducted on the fundamental of the fast multipole method (FMM)-accelerated line integration boundary element method (LIBEM).Design/methodology/approachDue to considering the heat source, domain integral is generated in the traditional heat conduction boundary integral equation (BIE), which will counteract the well-known merit of the BEM, namely, boundary-only discretization. To avoid volume discretization, the enhanced BEM, the LIBEM with dimension reduction property is introduced to transfer the domain integral into line integrals. Besides, owing to the unsatisfactory performance of the LIBEM when it comes to large-scale structures requiring massive computation, the FMM-accelerated LIBEM (FM-LIBEM) is proposed to improve the computation efficiency further.FindingsAssuming N and M are the numbers of nodes and integral lines, respectively, the FM-LIBEM can reduce the time complexity from O(NM) to about O(N+ M), and a full discussion and verification of the advantage are done based on numerical examples under heat conduction.Originality/value(1) The LIBEM is applied to 3D heat conduction analysis with heat source. (2) The domain integrals can be transformed into boundary integrals with straight line integrals by the LIM. (3) A FM-LIBEM is proposed and can reduce the time complexity from O(NM) to O(N+ M). (4) The FM-LIBEM with high computational efficiency is exerted to solve 3D heat conduction analysis with heat source in massive computation successfully.

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Coupling of the improved singular boundary method and dual reciprocity method for multi-term time-fractional mixed diffusion-wave equations

Cited by 30 publications

References 43 publications

Approximation of three‐dimensional nonlinear wave equations by fundamental solutions and weighted residuals process

Approximation of three‐dimensional nonlinear wave equations by fundamental solutions and weighted residuals process

Solution of the Modified Time Fractional Coupled Burgers Equations Using Laplace Adomian Decompostion Method

The fast multipole method–accelerated line integration boundary element method for 3D heat conduction analysis with heat source

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