Improving performance of iterative solvers on modern architectures

Over the past decade or two massive changes have occurred both in terms of hardware and software for high performance computing. Large heterogeneous machines are commonly in use today, presenting new challenges for scientific algorithms. In this thesis we will focus on the performance of iterative algorithms and explore several different aspects of working on modern architectures. In the first part we present a novel halo exchange library that is designed specifically for modern heterogeneous architectures and illustrate how it is not only easy to use but also flexible and, most importantly, highly performant. In the second chapter we consider various relaxation schemes for preconditioning a GMRES solver for the Stokes equations, with a particular focus on their performance on GPUs. We present a few different schemes but mostly focus on two of them, Vanka and Braess-Sarazin. We show how, when carefully designed, Vanka is capable of outperforming Braess-Sarazin on the GPU, something that to our knowledge has never been achieved before. In the final part we move from the Stokes equations to the Reynolds-Averaged Navier-Stokes equations that arise in the context of wind turbine modeling. Our focus is on an algorithm that has been of renewed interest in recent years, restricted additive Schwarz (RAS) paired with ILU. After analyzing our implementation of RAS and ILU, we design a new solver that incorporates RAS+ILU as relaxation scheme for an AMG cycle. The AMG cycle is then used as preconditioning for some of the GMRES solves as part of a new solver we design to solve the RANS equations. We conclude by extending our solver with homotopy, making it capable of self-tuning for finding a possible continuation path for solving hard problems.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2024

Author dc:creator

• Spies, Lukas

Contributors dc:contributor

• Olson, Luke
• Gropp, William
• Fischer, Paul
• MacLachlan, Scott

• Heterogeneous
• Gpu
• Halo Exchange
• Relaxation Schemes
• Stokes
• Vanka
• Braess-sarazin
• Navier-stokes
• Rans
• Ras
• Amg
• Homotopy
• Reynolds Number
• Turbulence
• Firedrake
• Hypre
• Petsc

Statement dc:rights

• Copyright 2024 Lukas Spies

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/125547

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F125547