GPU and Krylov Based Parallel Model Order Reduction Algorithms for MIMO Circuit Reductions

Analysis of modern high-speed, high-density designs with multi physics-based formulations for signal, power and thermal integrity analysis is becoming increasingly challenging due to the need for mixed frequency and time analysis. The associated timing, memory and costs of solving large sets of circuit equations become prohibitively expensive. Simulation of such systems help designers to build, analyze and characterize circuits prior to their manufacturing. However, working with full-scale models can lead to circuits with millions of nodes incurring prohibitively excessive computational costs. To circumvent such problems, Model Order Reduction (MOR) schemes utilizing Krylov Subspace based projections such as the Passive Reduced Interconnect Modeling Algorithm (PRIMA) and Structure-Preserving Reduced-order Interconnect Macromodeling algorithm (SPRIM) have also been widely used. In this thesis, PRIMA and SPRIM algorithms are advanced to the emerging computing platforms of Graphics Processing Units (GPU) with Tensor Cores (TC), yielding significant speed-up compared to using the traditional multi-core CPUs.

Name thesis:degree_name

Master of Applied Science (M.App.Sc.)

Level thesis:degree_level

Master's

Discipline thesis:degree_discipline

Engineering, Electrical and Computer

Grantor dc:publisher

Carleton University

Year dc:date.issued

2026

Author dc:creator

• Ananda, Rayeed

Statement dc:rights

• Copyright © 2026 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, distribution to students, research and scholarship. Theses may only be shared by linking to the Carleton University Institutional Repository and no part may be copied without proper attribution to the author; no part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.

Language dc:language.iso

en

DOI

10.22215/etd/2026-17015

OAI identifier oai:identifier

oai:carleton.scholaris.ca:20.500.14718/45172