英文标题：
《Accelerating Implicit Finite Difference Schemes Using a Hardware
Optimized Tridiagonal Solver for FPGAs》
---
作者：
Samuel Palmer
---
最新提交年份：
2015
---
英文摘要：
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.
---
中文摘要：
我们提出了一种在FPGA上优化硬件加速的Thomas算法的设计和实现，即Thomas Core。基于硬件的算法与FPGA中的自定义数据流和低级别并行相结合，将总体复杂度从8N降低到5N串行算术运算，并通过将两个代价高昂的分区并行化，将总体延迟几乎减半。将其与数据流接口相结合，我们将内存开销减少到每N个待解决的三对角系统2个N长度向量。Thomas Core允许多个独立的三对角系统连续并行求解，为许多数值计算提供了一个高效且可扩展的加速器。最后，我们在FPGA加速系统上展示了隐式有限差分格式在衍生品定价问题中的应用，并研究了不动点算法在我们算法中的使用和局限性。
---
分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
--

---
PDF下载：
-->