An unconditionally convergent RSCSCS iteration method for Riesz space fractional diffusion equations with variable coefficients

She, Zi-Hang; Qiu, Li-Min; Qu, Wei

doi:10.1016/j.matcom.2022.07.003

Cited by 6 publications

(4 citation statements)

References 30 publications

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“…To solve the systems resulting from the BEM discretization in the current study, we employed Zan et al's stable communication avoidance S-step-generalized minimal residual approach (SCAS-GMRES) to reduce the number of iterations and computation time [39]. Table 1 compares the SCAS-GMRES [39], fast modified diagonal, and toeplitz splitting (FMDTS) of Xin and Chong [40] and the unconditionally convergent-scaled circulant and skew-circulant splitting (UC-RSCSCS) of Zi et al [41] during our solution of the current problem. This table displays the number of iterations (Iter.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

BEM Modeling for Stress Sensitivity of Nonlocal Thermo-Elasto-Plastic Damage Problems

Fahmy

2024

Computation

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The main objective of this paper is to propose a new boundary element method (BEM) modeling for stress sensitivity of nonlocal thermo-elasto-plastic damage problems. The numerical solution of the heat conduction equation subjected to a non-local condition is described using a boundary element model. The total amount of heat energy contained inside the solid under consideration is specified by the non-local condition. The procedure of solving the heat equation will reveal an unknown control function that governs the temperature on a specific region of the solid’s boundary. The initial stress BEM for structures with strain-softening damage is employed in a boundary element program with iterations in each load increment to develop a plasticity model with yield limit deterioration. To avoid the difficulties associated with the numerical calculation of singular integrals, the regularization technique is applicable to integral operators. To validate the physical correctness and efficiency of the suggested formulation, a numerical case is solved.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

BEM Modeling for Stress Sensitivity of Nonlocal Thermo-Elasto-Plastic Damage Problems

Fahmy

2024

Computation

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“…By using the same technique of Fahmy [31], the radial point interpolation method (RPIM) and Cartesian transformation method (CTM) [33][34][35][36] are used to treat the domain integrals in Equation (45), which results from the fractional-order temperature-dependent heat conduction in Equation (22).…”

Section: Boundary Element Implementationmentioning

confidence: 99%

“…Case D is shown by the dash-dot line, which represents temperature-independent non-smart nanomaterials (f = 0).In the present paper, to solve linear systems generated by BEM discretization efficiently, we used the stable communication avoiding S-step-generalized minimal residual method (SCAS-GMRES) of Zan et al[43] to reduce the number of iterations and computation time. The SCAS-GMRES method[43], fast modified diagonal and toeplitz splitting (FMDTS) method of Xin and Chong[44], and unconditionally convergent-respectively scaled circulant and skew-circulant splitting (UC-RSCSCS) method of Zi et al[45] were compared when considering the solution of the current problem, as shown in Table2. This table shows the number of iterations (Iter.…”

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confidence: 99%

Fractional Temperature-Dependent BEM for Laser Ultrasonic Thermoelastic Propagation Problems of Smart Nanomaterials

Fahmy

2023

Fractal Fract

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The major goal of this work is to present a novel fractional temperature-dependent boundary element model (BEM) for solving thermoelastic wave propagation problems in smart nanomaterials. The computing performance of the suggested methodology was demonstrated by using stable communication avoiding S-step—generalized minimal residual method (SCAS-GMRES) to solve discretized linear BEM systems. The benefits of SCAS-GMRES are investigated and compared to those of other iterative techniques. The numerical results are graphed to demonstrate the influence of fractional, piezoelectric, and length scale characteristics on total force-stresses. These findings also demonstrate that the BEM methodology is practical, feasible, effective, and has superiority over domain methods. The results of the present paper help to develop the industrial uses of smart nanomaterials.

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“…In the present paper, to solve linear systems generated by BEM discretization efficiently, we used stable communication avoiding S-step -generalized minimal residual method (SCAS-GMRES) of Zan et al [43] to reduce the number of iterations and computation time. The SCAS-GMRES) [43], fast modified fast modified diagonal and toeplitz splitting (FMDTS) of Xin and Chong [44], and unconditionally convergent -respectively scaled circulant and skew-circulant splitting (UC-RSCSCS) of Zi et al [45] were compared during our solution of the current problem in Table 2. This table shows the number of iterations (Iter.…”

Section: 𝝀 = 𝟒𝟎𝟎 𝟏 − 𝑻 𝟔𝟎𝟎𝟎mentioning

confidence: 99%

Fractional Temperature-Dependent BEM for Laser Ultrasonic Thermoelastic Propagation Problems of Smart Nanomaterials

Fahmy¹

2023

Preprint

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The major goal of this work is to present a novel fractional temperature-dependent boundary element model (BEM) for solving thermoelastic wave propagation problems in smart nanomaterials. The computing performance of the suggested methodology was demonstrated by using stable communication avoiding S-step – generalized minimal residual method (SCAS-GMRES) to solve discretized linear BEM systems. The benefits of SCAS-GMRES are investigated and compared to those of other iterative techniques. The numerical results are graphed to demonstrate the influence of fractional, piezoelectric, and length scale characteristics on total force-stresses. These findings also demonstrate that the BEM methodology is practical, feasible, effective, and has superiority over domain methods. The results of the present paper help to develop the industrial uses of smart nanomaterials.

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An unconditionally convergent RSCSCS iteration method for Riesz space fractional diffusion equations with variable coefficients

Cited by 6 publications

References 30 publications

BEM Modeling for Stress Sensitivity of Nonlocal Thermo-Elasto-Plastic Damage Problems

BEM Modeling for Stress Sensitivity of Nonlocal Thermo-Elasto-Plastic Damage Problems

Fractional Temperature-Dependent BEM for Laser Ultrasonic Thermoelastic Propagation Problems of Smart Nanomaterials

Fractional Temperature-Dependent BEM for Laser Ultrasonic Thermoelastic Propagation Problems of Smart Nanomaterials

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