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Add smoothing based on Chebyshev polynomials of the fourth kind #856

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@MalachiTimothyPhillips MalachiTimothyPhillips commented Mar 14, 2023

Closes #862

Variant 2: Standard, 1st Kind Chebyshev smoothing with $D^{-1}A$. No restriction on the Chebyshev order.

Variant 3: 4th Kind Chebyshev smoother with $D^{-1}A$. No restriction on the Chebyshev order.

Variant 4: Optimized 4th Kind Chebyshev smoother with $D^{-1}A$. Chebyshev order must be in [1,16] due to needing to compute the $\beta_k$ coefficients.

Variants 3-4 are from https://arxiv.org/pdf/2202.08830.pdf.

These correspond to relaxation type 16.

In addition, relaxation type 19 has been implemented as a "no-op" smoother. This can be used in the case a user wishes to omit the post smoothing step, for example.

p.s.: I'm happy to walk through these changes "offline" on a zoom call.

Variant 2: Standard, 1st Kind Chebyshev smoothing with $D^{-1}A$.
No restriction on the Chebyshev order.

Variant 3: 4th Kind Chebyshev smoother with $D^{-1}A$.
No restriction on the Chebyshev order.

Variant 4: Optimized 4th Kind Chebyshev smoother with $D^{-1}A$.
Chebyshev order must be in [1,16] due to needing to compute the
$\beta_k$ coefficients.

Variants 3-4 are from https://arxiv.org/pdf/2202.08830.pdf.

These correspond to relaxation type 16.

In addition, relaxation type 19 has been implemented as a "no-op"
smoother. This can be used in the case a user wishes to omit the post
smoothing step, for example.
@MalachiTimothyPhillips MalachiTimothyPhillips changed the title Additional options for Chebyshev-accelerated Jacobi smoothing. Add smoothing based on Chebyshev polynomials of the fourth kind Mar 14, 2023
@liruipeng liruipeng self-assigned this Mar 16, 2023
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Implement Chebyshev polynomial smoothing of the fourth kind
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