Multigrid solution for the cauchy problem associated with helmholtz type equation on non uniform grids

Ghaffar, Fazal; Badshah, Noor; Islam, Shafiqul

doi:10.26480/msmk.02.2017.06.10

Cited by 3 publications

(3 citation statements)

References 26 publications

(42 reference statements)

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“…Multigrid method has been extensively used for several elliptic problems such as Poisson and Helmholtz equations 48–56 . We are using multigrid V‐cycle method to solve linear system arising from the discretization of HOC difference scheme.…”

Section: Multigrid Methodsmentioning

confidence: 99%

“…Multigrid method has been extensively used for several elliptic problems such as Poisson and Helmholtz equations. [48][49][50][51][52][53][54][55][56] We are using multigrid V-cycle method to solve linear system arising from the discretization of HOC difference scheme. To show the performance and to match the results of HOC scheme, we use the full weighting projection operator on uniform grids as proposed in the previous researches 44,[57][58][59] for Toeplitz matrices.…”

Section: Multigrid Methodsmentioning

confidence: 99%

See 1 more Smart Citation

A higher‐order unconditionally stable scheme for the solution of fractional diffusion equation

Ghaffar

Ullah

Badshah

et al. 2020

Math Methods in App Sciences

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In this paper, a higher‐order compact finite difference scheme with multigrid algorithm is applied for solving one‐dimensional time fractional diffusion equation. The second‐order derivative with respect to space is approximated by higher‐order compact difference scheme. Then, Grünwald–Letnikov approximation is used for the Riemann–Liouville time derivative to get an implicit scheme. The scheme is based on a heptadiagonal matrix with eighth‐order accurate local truncation error. Fourier analysis is used to analyze the stability of higher‐order compact finite difference scheme. Matrix analysis is used to show that the scheme is convergent with the accuracy of eighth‐order in space. Numerical experiments confirm our theoretical analysis and demonstrate the performance and accuracy of our proposed scheme.

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Section: Multigrid Methodsmentioning

confidence: 99%

Section: Multigrid Methodsmentioning

confidence: 99%

A higher‐order unconditionally stable scheme for the solution of fractional diffusion equation

Ghaffar

Ullah

Badshah

et al. 2020

Math Methods in App Sciences

Self Cite

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“…As an effective method for decreasing friction force, the ultrasonic friction reduction has been widely employed in materials production, the density uniformity of tantalum core can be improved by the friction force between tantalum powder particles and mould wall [15][16][17][18]. In this paper, a low frictional tantalum powder forming mould based on ultrasonic friction reduction is proposed to improve the density uniformity of tantalum core, which can be achieved by the three-wavelength exciting mode.…”

Section: Introductionmentioning

confidence: 99%

Design and Analysis of a Low Friction Tantalum Powder Forming Mould Utilizing Multi-Wavelength Exciting Mode

Li¹,

Yin²,

Gao³

et al. 2018

Topics in Chemical &Amp; Material Engineering

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Tantalum capacitor has been widely used in many fields of electrical, communications, automotive, military, aerospace, etc. This paper proposes a low frictional mould of tantalum capacitor, and the ultrasonic friction reduction is realized by an ultrasonic transducer driven by twelve rectangular piezoelectric plates. The forming pressing mould mainly contains top convex mould, top adjusting shim, ultrasonic transducer, bottom convex mould, and bottom adjusting shim. The rectangular piezoelectric plates are bonded to the opposite outside surfaces of ultrasonic transducer and the d31 working mode is adopted. The composite exciting method of the forming pressing mould is clarified in detail. The modal shape of the ultrasonic transducer is analyzed using Finite Element Method (FEM). The prototype is fabricated and tested. The testing results indicate that the vibration performance of the motor is in good agreement with the simulation results.

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A Relative Tolerance Relation of Rough Set (RTRS) for Potential Fish Yields in Indonesia

Saedudin

Kasim

Mahdin

et al. 2018

Journal of Coastal Research

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Multigrid solution for the cauchy problem associated with helmholtz type equation on non uniform grids

Cited by 3 publications

References 26 publications

A higher‐order unconditionally stable scheme for the solution of fractional diffusion equation

A higher‐order unconditionally stable scheme for the solution of fractional diffusion equation

Design and Analysis of a Low Friction Tantalum Powder Forming Mould Utilizing Multi-Wavelength Exciting Mode

A Relative Tolerance Relation of Rough Set (RTRS) for Potential Fish Yields in Indonesia

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