Malachi Phillips

Malachi Phillips

PhD in CS@UIUC

Publications

These are a few highlights from some recent papers. A biblatex file including all of my publications may be accessed here: references.bib

Optimal Chebyshev Smoothers and One-sided V-cycles

Published in arXiv, 2022

This paper considers the use of 4th-kind and optimized 4th-kind Chebyshev, polynomials as accelerators for multigrid smoothing. These methods are developed in James Lottes’s excellent paper, Optimal polynomial smoothers for multigrid V-cycles. We extend the analysis of Lottes to the case of one-sided V-cycles, and show that, for large values of the multigrid approximation constant, smoothing with $2k$-order Chebyshev polynomials on one-side yields superior convergence to smoothing with $k$-order Chebyshev polynomials on both sides.

Download here

Tuning Spectral Element Preconditioners for Parallel Scalability on GPUs

Published in SIAM PP 22 Proceeding, 2022

This paper is concerning runtime tuning spectral element preconditioners for parallel scalability on GPUs. A nascent tuning strategy is proposed to help alleviate the difficulty of choosing a reasonable preconditioner for a given problem. A variety of novel preconditioning schemes are also proposed, including $p$-multigrid with Chebyshev-accelerated Schwarz smoothers, low-order operator preconditioning, and even hybridizing the two approach by treating the low-order operator as the coarse grid operator.

Download here

pplacerDC: a new scalable phylogenetic placement method

Published in Proceedings of the 12th ACM Conference on Bioinformatics, Computational Biology, and Health Informatics, 2021

This paper presents a novel algorithm for phylogenetic placement that is scalable to large datasets. The general idea is to decompose a given tree using a centroid decomposition, and to apply recursively until the trees are small enough such that they may be solved using pplacer. From there, the results are merged together to produce a final placement.

Download here

Optimal Chebyshev Smoothers and One-sided V-cycles

Published in arXiv, 2022

This paper considers the use of 4th-kind and optimized 4th-kind Chebyshev, polynomials as accelerators for multigrid smoothing. These methods are developed in James Lottes’s excellent paper, Optimal polynomial smoothers for multigrid V-cycles. We extend the analysis of Lottes to the case of one-sided V-cycles, and show that, for large values of the multigrid approximation constant, smoothing with $2k$-order Chebyshev polynomials on one-side yields superior convergence to smoothing with $k$-order Chebyshev polynomials on both sides.

Download here

Tuning Spectral Element Preconditioners for Parallel Scalability on GPUs

Published in SIAM PP 22 Proceeding, 2022

This paper is concerning runtime tuning spectral element preconditioners for parallel scalability on GPUs. A nascent tuning strategy is proposed to help alleviate the difficulty of choosing a reasonable preconditioner for a given problem. A variety of novel preconditioning schemes are also proposed, including $p$-multigrid with Chebyshev-accelerated Schwarz smoothers, low-order operator preconditioning, and even hybridizing the two approach by treating the low-order operator as the coarse grid operator.

Download here

pplacerDC: a new scalable phylogenetic placement method

Published in Proceedings of the 12th ACM Conference on Bioinformatics, Computational Biology, and Health Informatics, 2021

This paper presents a novel algorithm for phylogenetic placement that is scalable to large datasets. The general idea is to decompose a given tree using a centroid decomposition, and to apply recursively until the trees are small enough such that they may be solved using pplacer. From there, the results are merged together to produce a final placement.

Download here