Accelerating Implicit Finite Difference Schemes Using a Hardware Optimized Tridiagonal Solver for FPGAs
We present a design and implementation of the Thomas algorithm optimized for hardware acceleration on an FPGA, the Thomas Core. The hardware-based algorithm combined with the custom data flow and low level parallelism available in an FPGA reduces the overall complexity from 8N down to 5N serial arithmetic operations, and almost halves the overall latency by parallelizing the two costly divisions. Combining this with a data streaming interface, we reduce memory overheads to 2 N-length vectors per N-tridiagonal system to be solved. The Thomas Core allows for multiple independent tridiagonal systems to be continuously solved in parallel, providing an efficient and scalable accelerator for many numerical computations. Finally we present applications for derivatives pricing problems using implicit finite difference schemes on an FPGA accelerated system and we investigate the use and limitations of fixed-point arithmetic in our algorithm.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
ADI finite difference schemes for the Heston-Hull-White PDE
In this paper we investigate the effectiveness of Alternating Direction Implicit (ADI) time discretization schemes in the numerical solution of the three-dimensional Heston-Hull-White partial differential equation, which…
Stochastic Multivariate Universal-Radix Finite-State Machine: a Theoretically and Practically Elegant Nonlinear Function Approximator
Nonlinearities are crucial for capturing complex input-output relationships especially in deep neural networks. However, nonlinear functions often incur various hardware and compute overheads. Meanwhile, stochastic compu…
A Machine Learning accelerated geophysical fluid solver
Machine learning methods have been successful in many areas, like image classification and natural language processing. However, it still needs to be determined how to apply ML to areas with mathematical constraints, lik…
Image ClassificationLiquidGEMM: Hardware-Efficient W4A8 GEMM Kernel for High-Performance LLM Serving
Quantization is a critical technique for accelerating LLM inference by reducing memory footprint and improving computational efficiency. Among various schemes, 4-bit weight and 8-bit activation quantization (W4A8) offers…
Computational EfficiencyTime-adaptive high-order compact finite difference schemes for option pricing in a family of stochastic volatility models
We propose a time-adaptive, high-order compact finite difference scheme for option pricing in a family of stochastic volatility models. We employ a semi-discrete high-order compact finite difference method for the spatia…