OpenCL parallel integration of ordinary differential equations: Applications in computational dynamics

Rodríguez, Marcos; Blesa, Fernando; Barrio, Roberto

doi:10.1016/j.cpc.2015.02.013

Cited by 11 publications

(8 citation statements)

References 28 publications

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“…We remark that we can take advantage of the latest computation devices such as multi-core CPUs, GPGPUs, Many Integrated Core coprocessors, etcetera. For computing the plots we have used a NVIDIA Tesla C2075 GPU-card, generating the data around 90 times faster than using a single core 37 .…”

Section: Methodsmentioning

confidence: 99%

Control strategies of 3-cell Central Pattern Generator via global stimuli

Rojo

Rodríguez

Barrio

2016

Sci Rep

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The study of the synchronization patterns of small neuron networks that control several biological processes has become an interesting growing discipline. Some of these synchronization patterns of individual neurons are related to some undesirable neurological diseases, and they are believed to play a crucial role in the emergence of pathological rhythmic brain activity in different diseases, like Parkinson’s disease. We show how, with a suitable combination of short and weak global inhibitory and excitatory stimuli over the whole network, we can switch between different stable bursting patterns in small neuron networks (in our case a 3-neuron network). We develop a systematic study showing and explaining the effects of applying the pulses at different moments. Moreover, we compare the technique on a completely symmetric network and on a slightly perturbed one (a much more realistic situation). The present approach of using global stimuli may allow to avoid undesirable synchronization patterns with nonaggressive stimuli.

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Section: Methodsmentioning

confidence: 99%

Control strategies of 3-cell Central Pattern Generator via global stimuli

Rojo

Rodríguez

Barrio

2016

Sci Rep

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“…The main aim of this section-besides presenting some results through diagrams-is to demonstrate the efficiency of the code. Instead of the direct comparison of the runtime between CPUs and GPUs which is a common test process [66,83,84], the utilization of the streaming multiprocessors (SMs) and arithmetic function units are presented. They are obtained via the NVIDIA Visual Profiler (release 7.5).…”

Section: Discussion: Test Cases Performances and Profilingmentioning

confidence: 99%

Modular, general purpose ODE integration package to solve large number of independent ODE systems on GPUs

Hegedűs¹

2018

Preprint

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A general purpose, modular program package for the integration of large number of independent ordinary differential equation systems capable of using professional graphics cards is presented. The available numerical schemes are the explicit and adaptive Runge-Kutta-Cash-Karp algorithm and the explicit fourth order Runge-Kutta method with fixed time step. In order to harness the huge processing power of graphics cards, the intermediate points of the computed trajectories are not stored. As a compensate, with pre-declared device functions, the required special features or properties of a solution can be easily extracted and stored each into a dedicated variable. For instance, the maximum and minimum values and/or their time instances. Event handling is also incorporated into the package in order to detect special points which can be stored as well. Moreover, again with pre-declared device function calls at such special points, the efficient handling of nonsmooth dynamics-e.g. impact dynamics-is possible. Several test cases are presented to demonstrate the flexibility of the pre-declared device functions and the strength of the program package. The applied models are the simple Duffing oscillator, the more complex Keller-Miksis equation known in bubble dynamics, and a system describing the behaviour of a pressure relief valve that can exhibit impact dynamics.

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“…Therefore, we intend to make a user-friendly tool that will enable users to easily use hardware description languages by simply rewriting the differential equations. Moreover, we are now investigating the use of OpenCL [31] to combine different devices such as CPUs, GPUs, DSPs, and FPGAs to achieve faster calculation. Until now we obtained that FPGA (Terasic DE5-Net) is 15 times faster than CPU (one core of Intel Xeon E5-2697) and GPU (NVIDIA Quadro 410) is 6 times faster than the FPGA using Open CL.…”

Section: Resultsmentioning

confidence: 99%

Development of nonlinear analysis tools on FPGA

Shogo

Kohno

2017

NOLTA

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Many mathematical models in various scientific fields are represented by complicated differential equations, and such models cannot be solved analytically. Therefore, numerical analysis using computers is essential. However, when a system is more complicated, the analysis time is longer. In this study, we propose a fast numerical analysis method using a field programmable gate array (FPGA). The FPGA is a reconfigurable integrated circuit, and it is good at parallel processing. We developed the calculators of bifurcation diagrams and basins of attraction on an FPGA board. As a result, we constructed calculators that were at most 2.8 times faster and that consumed 95.2% less power than the conventional method using a CPU.

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OpenCL parallel integration of ordinary differential equations: Applications in computational dynamics

Cited by 11 publications

References 28 publications

Control strategies of 3-cell Central Pattern Generator via global stimuli

Control strategies of 3-cell Central Pattern Generator via global stimuli

Modular, general purpose ODE integration package to solve large number of independent ODE systems on GPUs

Development of nonlinear analysis tools on FPGA

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