4,920 research outputs found
Optimising Sparse Matrix Vector multiplication for large scale FEM problems on FPGA
Sparse Matrix Vector multiplication (SpMV) is an important kernel in many scientific applications. In this work we propose an architecture and an automated customisation method to detect and optimise the architecture for block diagonal sparse matrices. We evaluate the proposed approach in the context of the spectral/hp Finite Element Method, using the local matrix assembly approach. This problem leads to a large sparse system of linear equations with block diagonal matrix which is typically solved using an iterative method such as the Preconditioned Conjugate Gradient. The efficiency of the proposed architecture combined with the effectiveness of the proposed customisation method reduces BRAM resource utilisation by as much as 10 times, while achieving identical throughput with existing state of the art designs and requiring minimal development effort from the end user. In the context of the Finite Element Method, our approach enables the solution of larger problems than previously possible, enabling the applicability of FPGAs to more interesting HPC problems
Lecture 03: Hierarchically Low Rank Methods and Applications
As simulation and analytics enter the exascale era, numerical algorithms, particularly implicit solvers that couple vast numbers of degrees of freedom, must span a widening gap between ambitious applications and austere architectures to support them. We present fifteen universals for researchers in scalable solvers: imperatives from computer architecture that scalable solvers must respect, strategies towards achieving them that are currently well established, and additional strategies currently being developed for an effective and efficient exascale software ecosystem. We consider recent generalizations of what it means to “solve” a computational problem, which suggest that we have often been “oversolving” them at the smaller scales of the past because we could afford to do so. We present innovations that allow to approach lin-log complexity in storage and operation count in many important algorithmic kernels and thus create an opportunity for full applications with optimal scalability
Lecture 03: Hierarchically Low Rank Methods and Applications
As simulation and analytics enter the exascale era, numerical algorithms, particularly implicit solvers that couple vast numbers of degrees of freedom, must span a widening gap between ambitious applications and austere architectures to support them. We present fifteen universals for researchers in scalable solvers: imperatives from computer architecture that scalable solvers must respect, strategies towards achieving them that are currently well established, and additional strategies currently being developed for an effective and efficient exascale software ecosystem. We consider recent generalizations of what it means to “solve” a computational problem, which suggest that we have often been “oversolving” them at the smaller scales of the past because we could afford to do so. We present innovations that allow to approach lin-log complexity in storage and operation count in many important algorithmic kernels and thus create an opportunity for full applications with optimal scalability
Optimizing Bit-Serial Matrix Multiplication for Reconfigurable Computing
Matrix-matrix multiplication is a key computational kernel for numerous
applications in science and engineering, with ample parallelism and data
locality that lends itself well to high-performance implementations. Many
matrix multiplication-dependent applications can use reduced-precision integer
or fixed-point representations to increase their performance and energy
efficiency while still offering adequate quality of results. However, precision
requirements may vary between different application phases or depend on input
data, rendering constant-precision solutions ineffective. BISMO, a vectorized
bit-serial matrix multiplication overlay for reconfigurable computing,
previously utilized the excellent binary-operation performance of FPGAs to
offer a matrix multiplication performance that scales with required precision
and parallelism. We show how BISMO can be scaled up on Xilinx FPGAs using an
arithmetic architecture that better utilizes 6-LUTs. The improved BISMO
achieves a peak performance of 15.4 binary TOPS on the Ultra96 board with a
Xilinx UltraScale+ MPSoC.Comment: Invited paper at ACM TRETS as extension of FPL'18 paper
arXiv:1806.0886
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