DocumentCode
1815574
Title
Examining the accuracy and the precision of PDEs for FPGA computations
Author
Kiss, András ; Nagy, Zoltán ; Csik, Arpad ; Szolgay, Péter
Author_Institution
Comput. & Autom. Res. Inst., Budapest, Hungary
fYear
2012
fDate
29-31 Aug. 2012
Firstpage
1
Lastpage
5
Abstract
There are a large number of problems which can be accelerated by using architectures on Field Programmable Gate Arrays (FPGA). However sometimes the complexity of a problem does not allow to map it onto a specific FPGA. In that case analysis of precision of the arithmetic unit which may solve the computational problem can be a good attempt to fit the architecture and to accelerate its computation. Numerical algorithm can be implemented using fixed-point or floating point arithmetic (or mixed (both)) with different precision. The aim of the article is not to optimize the numerical algorithm but to find a smaller arithmetic unit precision, which results enough accuracy and fits to smaller FPGA-s. In the paper, one particular problem type is investigated, namely the accuracy of the solution of a simple Partial Differential Equation (PDE). The accuracy measurement is done on an FPGA with different bit width. The solution of the advection equation is analyzed using first and second order discretization methods. As a result we managed to find an optimal bit width for the solution on a specific FPGA.
Keywords
computational complexity; field programmable gate arrays; fixed point arithmetic; floating point arithmetic; partial differential equations; FPGA computation; PDE accuracy measurement; PDE precision analysis; advection equation; arithmetic unit precision analysis; field programmable gate arrays; first-order discretization method; fixed point arithmetic; floating point arithmetic; numerical algorithm; optimal bit width; partial differential equation; problem complexity; second-order discretization method; Accuracy; Computer architecture; Equations; Field programmable gate arrays; Libraries; Mathematical model; Testing;
fLanguage
English
Publisher
ieee
Conference_Titel
Cellular Nanoscale Networks and Their Applications (CNNA), 2012 13th International Workshop on
Conference_Location
Turin
ISSN
2165-0160
Print_ISBN
978-1-4673-0287-6
Type
conf
DOI
10.1109/CNNA.2012.6331439
Filename
6331439
Link To Document