A Vanka-type multigrid solver for complex-shifted Laplacian systems from diagonalization-based parallel-in-time algorithms

He, Yunhui; Li, Jun

doi:10.48550/arxiv.2203.11154

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Local Fourier Analysis2

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2022

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“…From this point onward, let us drop the subscript h, unless it is necessary. The element-wise Vanka-type smoother has been successfully applied to complex-shifted Laplacian systems arising from optimal control problem [23]. Here, we consider an element-wise additive Vanka smoother applied to (6).…”

Section: Local Fourier Analysismentioning

confidence: 99%

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A Vanka-based parameter-robust multigrid relaxation for the Stokes-Darcy Brinkman problems

He¹

2022

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We propose a block-structured multigrid relaxation scheme for solving the Stokes-Darcy Brinkman equations discretized by the marker and cell scheme. An element-based additive Vanka smoother is used to solve the corresponding shifted Laplacian operator. Using local Fourier analysis, we present the stencil for the additive Vanka smoother and derive an optimal smoothing factor for Vanka-based Braess-Sarazin relaxation for the Stokes-Darcy Brinkman equations. Although the optimal damping parameter is dependent on meshsize and physical parameter, it is very close to one. Numerical results of two-grid and V(1,1)-cycle are presented, which show high efficiency of the proposed relaxation scheme and its robustness to physical parameters and the meshsize. Using a damping parameter equal to one gives almost the same results as these for the optimal damping parameter at a lower computational overhead.

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Section: Local Fourier Analysismentioning

confidence: 99%

“…Next, we compare ψ(−1, −1) (see (23)) and ψ(0, 0) (see (25)) to determine the maximum. Using (15), we have…”

Section: Local Fourier Analysismentioning

confidence: 99%

A Vanka-based parameter-robust multigrid relaxation for the Stokes-Darcy Brinkman problems

He¹

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

A Vanka-type multigrid solver for complex-shifted Laplacian systems from diagonalization-based parallel-in-time algorithms

Cited by 1 publication

References 20 publications

A Vanka-based parameter-robust multigrid relaxation for the Stokes-Darcy Brinkman problems

A Vanka-based parameter-robust multigrid relaxation for the Stokes-Darcy Brinkman problems

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