Published

2019-07-01

GPU Parallelization Nested Decomposition Method for Solving Large Linear Systems in Reservoir Numerical Simulation

Método de descomposición anidada a través de paralelización con Unidades de Procesamiento Gráfico para resolver Sistemas Lineales Grandes en la simulación numérica de yacimientos

DOI:

https://doi.org/10.15446/esrj.v23n3.81669

Keywords:

Nested decomposition, GPU parallel, Linear solution, CPR, (en)
Descomposición anidada, GPU paralela, solución lineal, CPR. (es)

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Authors

  • Xin Shi Peking University - College of Engineering
  • Yuan Di Peking University - College of Engineering
This paper designs a highly parallel Nested Factorization (NF) to solve large linear equations generated in reservoir numerical simulation problems. The NF method is a traditional linear solution preprocessing method for reservoir numerical simulation problems, and has regained attention in recent years due to its potential to extend to parallel architectures such as GPUs (Graphics Processor Units). The parallel algorithm of this paper is based on the MPNF (Massively Parallel Nested Factorization) framework proposed by Appleya (Appleyard, Appleyard, Wakefield, & Desitter, 2011). The MPNF algorithm designed in this paper focuses on its efficient implementation on the GPU parallel architecture. Its features include: using a custom matrix structure to achieve merge access, improving access bottlenecks and improving the efficiency of the SpMV algorithm. It is also applicable to the two-stage preprocessing method CPR. (Constrain Pressure Residual) pressure solution and global preprocessing stage; the MPNF method is extended to the solution of 2.5-dimensional unstructured grid problem. The parallel algorithm in this paper has been integrated into the reservoir numerical simulator. For the SPE10 (million grid, highly heterogeneous) standard example, the GPU-based parallel NF algorithm is in the structured grid model and the equivalent 2.5-dimensional non- On the structured grid model, compared with the serial version of the NF method, the acceleration ratios of 19.8 and 17.0 times were obtained respectively; compared with the mainstream serial solution method, the efficiency was also improved by 2 to 3 times.
Este artículo diseña una Factorización Anidada (NF) altamente paralela para resolver grandes ecuaciones lineales generadas en problemas de simulación numérica de yacimientos. El método NF es un método tradicional de preprocesamiento de solución lineal para problemas de simulación numérica de yacimientos, y ha recuperado atención en los últimos años debido a su potencial para extenderse a arquitecturas paralelas como las GPU (Unidades de Procesador de Gráficos). El algoritmo paralelo de este documento se basa en el marco de MPNF (Factorización Anidada Masivamente Paralela) propuesto por Appleya (Appleyard, Appleyard, Wakefield, & Desitter, 2011). El algoritmo MPNF diseñado en este documento se enfoca en su implementación eficiente en la arquitectura paralela de GPU. Sus características incluyen: usar una estructura de matriz personalizada para lograr un acceso combinado, mejorar los accesos de cuellos de botella y mejorar la eficiencia del algoritmo SpMV. También es aplicable al método de preprocesamiento en dos etapas CPR (solución de presión residual de restricción) presión solución y etapa de preprocesamiento global; el método MPNF se extiende a la solución del problema de cuadrícula no estructurada de 2.5 dimensiones. El algoritmo paralelo en este documento se ha integrado en el simulador numérico de yacimiento. Para el ejemplo estándar de SPE10 (millones de cuadrículas, altamente heterogéneo), el algoritmo NF paralelo basado en GPU está en el modelo de cuadrícula estructurada y el equivalente de 2.5-no dimensional- en el modelo de cuadrícula estructurada, en comparación con la versión en serie del método NF, los índices de aceleración de 19.8 y 17.0 veces se obtuvieron respectivamente; en comparación con el método de solución serial convencional, la eficiencia también se mejoró de 2 a 3 veces.

References

Appleyard, J., Appleyard, J., Wakefield, M., & Desitter, A. (2011). Accelerating reservoir simulators using GPU technology. SPE Reservoir Simulation Symposium. Society of Petroleum Engineers.

Appleyard, J. (2016). Method and apparatus for estimating the state of a system: U.S. Patent 9, 396, 162. 2016-7-19.

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How to Cite

APA

Shi, X. and Di, Y. (2019). GPU Parallelization Nested Decomposition Method for Solving Large Linear Systems in Reservoir Numerical Simulation. Earth Sciences Research Journal, 23(3), 249–257. https://doi.org/10.15446/esrj.v23n3.81669

ACM

[1]
Shi, X. and Di, Y. 2019. GPU Parallelization Nested Decomposition Method for Solving Large Linear Systems in Reservoir Numerical Simulation. Earth Sciences Research Journal. 23, 3 (Jul. 2019), 249–257. DOI:https://doi.org/10.15446/esrj.v23n3.81669.

ACS

(1)
Shi, X.; Di, Y. GPU Parallelization Nested Decomposition Method for Solving Large Linear Systems in Reservoir Numerical Simulation. Earth sci. res. j. 2019, 23, 249-257.

ABNT

SHI, X.; DI, Y. GPU Parallelization Nested Decomposition Method for Solving Large Linear Systems in Reservoir Numerical Simulation. Earth Sciences Research Journal, [S. l.], v. 23, n. 3, p. 249–257, 2019. DOI: 10.15446/esrj.v23n3.81669. Disponível em: https://revistas.unal.edu.co/index.php/esrj/article/view/81669. Acesso em: 1 aug. 2024.

Chicago

Shi, Xin, and Yuan Di. 2019. “GPU Parallelization Nested Decomposition Method for Solving Large Linear Systems in Reservoir Numerical Simulation”. Earth Sciences Research Journal 23 (3):249-57. https://doi.org/10.15446/esrj.v23n3.81669.

Harvard

Shi, X. and Di, Y. (2019) “GPU Parallelization Nested Decomposition Method for Solving Large Linear Systems in Reservoir Numerical Simulation”, Earth Sciences Research Journal, 23(3), pp. 249–257. doi: 10.15446/esrj.v23n3.81669.

IEEE

[1]
X. Shi and Y. Di, “GPU Parallelization Nested Decomposition Method for Solving Large Linear Systems in Reservoir Numerical Simulation”, Earth sci. res. j., vol. 23, no. 3, pp. 249–257, Jul. 2019.

MLA

Shi, X., and Y. Di. “GPU Parallelization Nested Decomposition Method for Solving Large Linear Systems in Reservoir Numerical Simulation”. Earth Sciences Research Journal, vol. 23, no. 3, July 2019, pp. 249-57, doi:10.15446/esrj.v23n3.81669.

Turabian

Shi, Xin, and Yuan Di. “GPU Parallelization Nested Decomposition Method for Solving Large Linear Systems in Reservoir Numerical Simulation”. Earth Sciences Research Journal 23, no. 3 (July 1, 2019): 249–257. Accessed August 1, 2024. https://revistas.unal.edu.co/index.php/esrj/article/view/81669.

Vancouver

1.
Shi X, Di Y. GPU Parallelization Nested Decomposition Method for Solving Large Linear Systems in Reservoir Numerical Simulation. Earth sci. res. j. [Internet]. 2019 Jul. 1 [cited 2024 Aug. 1];23(3):249-57. Available from: https://revistas.unal.edu.co/index.php/esrj/article/view/81669

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