Methods for Solving Large-scale Linear Systems in Scientific Computing
Preconditioners and Performance Portability
Time: Thu 2025-09-25 10.00
Location: Kollegiesalen, Brinellvägen 8, Stockholm
Video link: https://kth-se.zoom.us/j/65542778560
Language: English
Subject area: Computer Science
Doctoral student: Måns Andersson , Beräkningsvetenskap och beräkningsteknik (CST)
Opponent: Paolo Bientinesi, Umeå universitet, Umeå, Sverige
Supervisor: Professor Stefano Markidis, Beräkningsvetenskap och beräkningsteknik (CST); Niclas Jansson, Parallelldatorcentrum, PDC; Associate professor Ivy Bo Peng, Beräkningsvetenskap och beräkningsteknik (CST)
QC 20250827
Abstract
Large-scale simulations play a crucial role in scientific discovery and industrial applications. Many of these simulations require solving large linear systems, which commonly arise in the modeling of fluids, electromagnetic fields,and other physical phenomena. Solving such systems is often computationally expensive and time-consuming, making it a critical component in simulation performance.
This thesis focuses on two types of linear systems that frequently arise in modeling and optimization: saddle-point problems and large-scale Poisson equations. Saddle-point problems naturally occur in coupled systems, such as fluid dynamics involving velocity and pressure, and can often be reformulated as optimization problems. Poisson’s equation, on the other hand, frequently acts as a performance bottleneck in large simulations.
A Jacobi preconditioned Conjugate Gradient and a constraint preconditioned GMRES are evaluated on optimization problems arising in radiotherapy treatment planning; the methods demonstrate good convergence properties. Several preconditioners that were evaluated consider domain decomposition on distributed systems where the quality of the preconditioner is weighted against the communication costs.
A novel Anderson accelerated matrix-splitting method is proposed that behaves similarly to inexact left-preconditioned GMRES. Matrix splitting techniques are especially suitable for saddle-point problems as there are many natural splittings for such systems.
Beyond algorithmic choices, performance is also influenced by modern computing architectures, which are increasingly heterogeneous. Efficient use of these systems often requires hardware-specific implementations, which can be costly to develop and maintain. To address this, various strategies introduce portability layers that abstract away hardware details while maintaining performance.
This thesis presents two approaches for solving large-scale Poisson equations using different portability models. Both methods demonstrate promising results in terms of performance and portability.