scholarly journals HotSpot Thermal Floorplan Solver Using Conjugate Gradient to Speed Up

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Zhonghua Jiang ◽  
Ning Xu
Keyword(s):  
Simulated Annealing ◽  
Conjugate Gradient ◽  
Decomposition Method ◽  
Sparse Matrix ◽  
Lu Decomposition ◽  
Ratio Curve ◽  
Resistance Model ◽  
Speed Up ◽  
Iterative Framework ◽  
Conjugate Gradient Solver

We proposed to use the conjugate gradient method to effectively solve the thermal resistance model in HotSpot thermal floorplan tool. The iterative conjugate gradient solver is suitable for traditional sparse matrix linear systems. We also defined the relative sparse matrix in the iterative thermal floorplan of Simulated Annealing framework algorithm, and the iterative method of relative sparse matrix could be applied to other iterative framework algorithms. The experimental results show that the running time of our incremental iterative conjugate gradient solver is speeded up approximately 11x compared with the LU decomposition method for case ami49, and the experiment ratio curve shows that our iterative conjugate gradient solver accelerated more with increasing number of modules.

Thermal Floorplan Base on Conjugate Gradient Solver in HotSpot

2014 ◽  
Vol 608-609 ◽  
pp. 908-912
Author(s):  
Zhong Hua Jiang ◽  
Ning Xu ◽  
Chun Xiang Wu
Keyword(s):  
Linear System ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Decomposition Method ◽  
Sparse Matrix ◽  
Linear Equations ◽  
Sparse Linear Systems ◽  
Vlsi Physical Design ◽  
Conjugate Gradient Solver

In this paper, we introduce an effective iterative method to solve the thermal linear system in HotSpot thermal floorplan, the iterative Conjugate Gradient Method is suitable to solve the traditional sparse matrix linear equations. We define a class of dummy sparse linear systems in iterative thermal floorplan algorithm, the iterative methods for linear system can be extended to apply to other iterative framework algorithm. We apply the conjugate gradient method to solve the thermal model in floorplan of VLSI physical design. The experiments' result shows that thermal floorplan using Conjugate gradient method is effective. The running time of our incremental conjugate gradient thermal solver with Jocabi Precondition is approximate 0.59 comparing with LU decomposition method.

Special parallel processor for lu decomposition of a large-scale sparse matrix

1987 ◽  
Vol 18 (6) ◽  
pp. 89-99 ◽  
Author(s):  
Hideki Asai ◽  
Mitsuo Asai ◽  
Mamoru Tanaka
Keyword(s):  
Large Scale ◽  
Sparse Matrix ◽  
Lu Decomposition ◽  
Parallel Processor

scholarly journals Request, Coalesce, Serve, and Forget: Miss-Optimized Memory Systems for Bandwidth-Bound Cache-Unfriendly Applications on FPGAs

2022 ◽  
Vol 15 (2) ◽  
pp. 1-33
Author(s):  
Mikhail Asiatici ◽  
Paolo Ienne
Keyword(s):  
Large Scale ◽  
Sparse Matrix ◽  
Memory Systems ◽  
Graph Analytics ◽  
Matrix Vector Multiplication ◽  
Area Reduction ◽  
Cache Line ◽  
Speed Up ◽  
Memory Accesses ◽  
On Chip

Applications such as large-scale sparse linear algebra and graph analytics are challenging to accelerate on FPGAs due to the short irregular memory accesses, resulting in low cache hit rates. Nonblocking caches reduce the bandwidth required by misses by requesting each cache line only once, even when there are multiple misses corresponding to it. However, such reuse mechanism is traditionally implemented using an associative lookup. This limits the number of misses that are considered for reuse to a few tens, at most. In this article, we present an efficient pipeline that can process and store thousands of outstanding misses in cuckoo hash tables in on-chip SRAM with minimal stalls. This brings the same bandwidth advantage as a larger cache for a fraction of the area budget, because outstanding misses do not need a data array, which can significantly speed up irregular memory-bound latency-insensitive applications. In addition, we extend nonblocking caches to generate variable-length bursts to memory, which increases the bandwidth delivered by DRAMs and their controllers. The resulting miss-optimized memory system provides up to 25% speedup with 24× area reduction on 15 large sparse matrix-vector multiplication benchmarks evaluated on an embedded and a datacenter FPGA system.

scholarly journals GPU-Based Conjugate Gradient Solver for Lattice QCD with Domain-Wall Fermions

2011 ◽  
Author(s):  
Yao-Yuan Mao ◽  
Ting-Wai Chiu ◽  
Tung-Han Hsieh ◽  
Kenji Ogawa
Keyword(s):  
Domain Wall ◽  
Lattice Qcd ◽  
Conjugate Gradient ◽  
Domain Wall Fermions ◽  
Conjugate Gradient Solver

scholarly journals Hybrid Genetic Algorithm and Simulated Annealing for Function Optimization

2017 ◽  
Vol 1 (2) ◽  
pp. 82 ◽  
Author(s):  
Tirana Noor Fatyanosa ◽  
Andreas Nugroho Sihananto ◽  
Gusti Ahmad Fanshuri Alfarisy ◽  
M Shochibul Burhan ◽  
Wayan Firdaus Mahmudy
Keyword(s):  
Genetic Algorithm ◽  
Simulated Annealing ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Hybrid Genetic Algorithm ◽  
Optimal Solution ◽  
Function Optimization ◽  
Non Linear ◽  
Speed Up ◽  
Linear Problems

The optimization problems on real-world usually have non-linear characteristics. Solving non-linear problems is time-consuming, thus heuristic approaches usually are being used to speed up the solution’s searching. Among of the heuristic-based algorithms, Genetic Algorithm (GA) and Simulated Annealing (SA) are two among most popular. The GA is powerful to get a nearly optimal solution on the broad searching area while SA is useful to looking for a solution in the narrow searching area. This study is comparing performance between GA, SA, and three types of Hybrid GA-SA to solve some non-linear optimization cases. The study shows that Hybrid GA-SA can enhance GA and SA to provide a better result

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