GPU Implementation of Finite Difference Solvers

Giles, Michael B.; Laszlo, Endre; Reguly, István Z.; Appleyard, Jeremy; Demouth, Julien

doi:10.1109/whpcf.2014.10

Cited by 16 publications

(18 citation statements)

References 12 publications

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“…7,11,[19][20][21] The second is our proposal, where our designed data structure seeks to eliminate all non-coalesced memory operations when computing the numerical solution for the PDE with the Laplacian. The first is the classic sliding window approach, which is based on simple row major order.…”

Section: Laplacian Implementation On a Gpumentioning

confidence: 99%

“…7,11,21 For each new time step, the GPU computes thousands of points in parallel, solving Equation (5) on each point in the mesh, where the only dependency is temporal. 7,11,21 For each new time step, the GPU computes thousands of points in parallel, solving Equation (5) on each point in the mesh, where the only dependency is temporal.…”

Section: Laplacian Implementation On a Gpumentioning

confidence: 99%

“…[7][8][9]11,19,21 This happens because, although using row-major order enables some coalesced memory accesses for block warps, all blocks in the grid will compete for space in the cache. However, as each thread within a block will need its own data plus its six neighbors, this may lead to data access redundancy.…”

Section: Figurementioning

confidence: 99%

“…This means that the chance of a cache miss increases as the grid size grows. [7][8][9]11,21 In CUDA, threads of the same block can communicate with each other through shared memory, which is a low-latency memory, but limited in total storage. According to Equation (5), at the time thread k asks for data in position (x + 1, y, z), thread k + 1 had requested this same data already, so it should be in cache memory.…”

Section: Figurementioning

confidence: 99%

“…using FDM 7,11,21. Bartocci et al 11 evaluated GPU implementations for cardiac tissue models with different complexities.…”

mentioning

confidence: 99%

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Accelerating simulations of cardiac electrical dynamics through a multi‐GPU platform and an optimized data structure

Vasconcellos

Clua

Fenton

et al. 2019

Concurrency and Computation

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Simulations of cardiac electrophysiological models in tissue, particularly in 3D require the solutions of billions of differential equations even for just a couple of milliseconds, thus highly demanding in computational resources. In fact, even studies in small domains with very complex models may take several hours to reproduce seconds of electrical cardiac behavior.Today's Graphics Processor Units (GPUs) are becoming a way to accelerate such simulations, and give the added possibilities to run them locally without the need for supercomputers.Nevertheless, when using GPUs, bottlenecks related to global memory access caused by the spatial discretization of the large tissue domains being simulated, become a big challenge. For simulations in a single GPU, we propose a strategy to accelerate the computation of the diffusion term through a data-structure and memory access pattern designed to maximize coalescent memory transactions and minimize branch divergence, achieving results approximately 1.4 times faster than a standard GPU method. We also combine this data structure with a designed communication strategy to take advantage in the case of simulations in multi-GPU platforms.We demonstrate that, in the multi-GPU approach performs, simulations in 3D tissue can be just 4× slower than real time. KEYWORDScardiac electrophysiology models, GPU Computing, memory access optimization, parallel cardiac dynamics simulations INTRODUCTIONThe large increase of computational power over the last years shifted the bottleneck of different algorithms to the memory bandwidth and memory management. 1 One typical solution employed by hardware assemblers to minimize this issue is hardware hierarchical memory and memory locality optimization.Computational systems organize hierarchical memory system into levels. In the on-chip level, the registers are the fastest memory, with a high cost per byte and low capacity. Next, there are different cache levels according to the hardware architecture, typically called L1, L2, and so on.The main memory is the next level; here, the cost per byte is less than cache or registers, but latency is high. The last level is the secondary memory that has the highest latency with the lowest cost per byte. Overall, the cost per byte of each level determines the capacity and latency, which directly impact in performance.As each level of the hierarchical memory system has a different storage capacity and data is usually kept at the lowest memory level, computational systems must choose for each level which data will be prioritized to stay in memory and which will be removed when that memory level fills up. To do so, the computer memory system employs two fundamental principles, ie, temporal and spatial locality. 2 In general, these strategies aim to keep the most recently used data in the same memory level, since having to access higher memory levels drastically increases the time of the search.Based on the memory hierarchical principles, some researchers have tried to minimize memory system bottlenecks through s...

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Section: Laplacian Implementation On a Gpumentioning

confidence: 99%

Section: Laplacian Implementation On a Gpumentioning

confidence: 99%

Section: Figurementioning

confidence: 99%

Section: Figurementioning

confidence: 99%

“…using FDM 7,11,21. Bartocci et al 11 evaluated GPU implementations for cardiac tissue models with different complexities.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Accelerating simulations of cardiac electrical dynamics through a multi‐GPU platform and an optimized data structure

Vasconcellos

Clua

Fenton

et al. 2019

Concurrency and Computation

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GPU Memory Access Optimization for 2D Electrical Wave Propagation Through Cardiac Tissue and Karma Model Using Time and Space Blocking

Pires

Vasconcellos

Clua

2020

Computational Science and Its Applications – ICCSA 2020

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Abnormal heart function is one of the largest causes of death in the world. Understanding and simulating its contraction and relaxation movements may reduce this mortality and improve specific treatments. Due the high processing time to compute propagation of an electrical wave through cardiac tissue, interactive and real time simulations are a challenge, making unable corrective treatments on the fly. In this paper we propose an approach to reduce the electrophysiology models simulation computational time using the finite difference method to solve the laplacian operator, required by the karma model. Our solution optimizes accesses to global memory by storing more than one instant of time in shared memory within each GPU kernel call. We present tests that validate our proposal and show an increase performance close to when compared with available GPU implementations.

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