Solving tri-diagonal linear systems using field programmable gate arrays

Warne, David, Kelson, Neil A., & Hayward, Ross F. (2012) Solving tri-diagonal linear systems using field programmable gate arrays. In 4th International Conference on Computational Methods (ICCM2012), 25-28 November 2012, Crowne Plaza, Gold Coast, QLD.


In this paper, we present the outcomes of a project on the exploration of the use of Field Programmable Gate Arrays(FPGAs) as co-processors for scientific computation. We designed a custom circuit for the pipelined solving of multiple tri-diagonal linear systems. The design is well suited for applications that require many independent tri diagonal system solves, such as finite difference methods for solving PDEs or applications utilising cubic spline interpolation. The selected solver algorithm was the Tri Diagonal Matrix Algorithm (TDMA or Thomas Algorithm). Our solver supports user specified precision thought the use of a custom floating point VHDL library supporting addition, subtraction, multiplication and division. The variable precision TDMA solver was tested for correctness in simulation mode. The TDMA pipeline was tested successfully in hardware using a simplified solver model. The details of implementation, the limitations, and future work are also discussed.

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ID Code: 54894
Item Type: Conference Paper
Refereed: Yes
Keywords: FPGA, Matrix Factorisation, Hardware Acceleration, Tri-diagonal Matrix Algorithm, Reconfigurable Computing
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Analysis (010301)
Australian and New Zealand Standard Research Classification > TECHNOLOGY (100000) > COMPUTER HARDWARE (100600) > Arithmetic and Logic Structures (100601)
Australian and New Zealand Standard Research Classification > TECHNOLOGY (100000) > COMPUTER HARDWARE (100600) > Logic Design (100603)
Divisions: Current > QUT Faculties and Divisions > Division of Technology, Information and Library Services
Current > Schools > School of Electrical Engineering & Computer Science
Past > QUT Faculties & Divisions > Faculty of Science and Technology
Current > Research Centres > High Performance Computing and Research Support
Copyright Owner: Copyright 2012 [please consult the authors]
Deposited On: 20 Nov 2012 01:36
Last Modified: 26 Feb 2013 09:09

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