Solving tri-diagonal linear systems using field programmable gate arrays

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.

Solving tri-diagonal linear systems using field programmable gate arrays

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.

Comparison of high level FPGA hardware design for solving tri-diagonal linear systems

Reconfigurable computing devices can increase the performance of compute intensive algorithms by implementing application specific co-processor architectures. The power cost for this performance gain is often an order of magnitude less than that of modern CPUs and GPUs. Exploiting the potential of reconfigurable devices such as Field-Programmable Gate Arrays (FPGAs) is typically a complex and tedious hardware engineering task. Re- cently the major FPGA vendors (Altera, and Xilinx) have released their own high-level design tools, which have great potential for rapid development of FPGA based custom accelerators. In this paper, we will evaluate Altera’s OpenCL Software Development Kit, and Xilinx’s Vivado High Level Sythesis tool. These tools will be compared for their per- formance, logic utilisation, and ease of development for the test case of a Tri-diagonal linear system solver.

Calculation of volume from crank angle using reconfigurable hardware

Fast calculation of quantities such as in-cylinder volume and indicated power is important in internal combustion engine research. Multiple channels of data including crank angle and pressure were collected for this purpose using a fully instrumented diesel engine research facility. Currently, existing methods use software to post-process the data, first calculating volume from crank angle, then calculating the indicated work and indicated power from the area enclosed by the pressure-volume indicator diagram. Instead, this work investigates the feasibility of achieving real-time calculation of volume and power via hardware implementation on Field Programmable Gate Arrays (FPGAs). Alternative hardware implementations were investigated using lookup tables, Taylor series methods or the CORDIC (CoOrdinate Rotation DIgital Computer) algorithm to compute the trigonometric operations in the crank angle to volume calculation, and the CORDIC algorithm was found to use the least amount of resources. Simulation of the hardware based implementation showed that the error in the volume and indicated power is less than 0.1%.

Calculation of engine parameters using reconfigurable hardware

The feasibility of real-time calculation of parameters for an internal combustion engine via reconfigurable hardware implementation is investigated as an alternative to software computation. A detailed in-hardware field programmable gate array (FPGA)-based design is developed and evaluated using input crank angle and in-cylinder pressure data from fully instrumented diesel engines in the QUT Biofuel Engine Research Facility (BERF). Results indicate the feasibility of employing a hardware-based implementation for real-time processing for speeds comparable to the data sampling rate currently used in the facility, with acceptably low level of discrepancies between hardware and software-based calculation of key engine parameters.

Computation of ECG signal features using MCMC modelling in software and FPGA reconfigurable hardware

Computational optimisation of clinically important electrocardiogram signal features, within a single heart beat, using a Markov-chain Monte Carlo (MCMC) method is undertaken. A detailed, efficient data-driven software implementation of an MCMC algorithm has been shown. Initially software parallelisation is explored and has been shown that despite the large amount of model parameter inter-dependency that parallelisation is possible. Also, an initial reconfigurable hardware approach is explored for future applicability to real-time computation on a portable ECG device, under continuous extended use.