Artículos

 

Load Balancing for Parallel Computations with the Finite Element Method

 

Balanceo de Cargas para Computación en Paralelo con el Método de Elementos Finitos

 

José Luis González García¹, Ramin Yahyapour¹, and Andrei Tchernykh²

 

¹ GWDG - Gesellschaft für wissenschaftliche Datenverarbeitung mbH Göttingen, Göttingen, Lower Saxony, Germany. jose-luis.gonzalez-garcia@gwdg.de, ramin.yahyapour@gwdg.de

² CICESE Research Center, Ensenada, Baja California, Mexico. chernykh@cicese.mx

 

Article received on 25/02/2013;
accepted on 27/07/2013.

 

Abstract

In this paper, we give an overview of efforts to improve current techniques of load-balancing and efficiency of finite element method (FEM) computations on large-scale parallel machines and introduce a multilevel load balancer to improve the local load imbalance. FEM is used to numerically approximate solutions of partial differential equations (PDEs) as well as integral equations. The PDEs domain is discretized into a mesh of information and usually solved using iterative methods. Distributing the mesh among the processors in a parallel computer, also known as the mesh-partitioning problem, was shown to be NP-complete. Many efforts are focused on graph-partitioning to parallelize and distribute the mesh of information. Data partitioning is important to efficiently execute applications in distributed systems. To address this problem, a variety of general-purpose libraries and techniques have been developed providing great effectiveness. But the load-balancing problem is not yet well solved. Today's large simulations require new techniques to scale on clusters of thousands of processors and to be resource aware due the increasing use of heterogeneous computing architectures as found in many-core computer systems. Existing libraries and algorithms need to be enhanced to support more complex applications and hardware architectures. We present trends in this field and discuss new ideas and approaches that take into account the new emerging requirements.

Keywords: Load balancing, FEM, HPC efficiency.

 

Resumen

En este artículo damos una vista general de los esfuerzos para mejorar las técnicas actuales de balanceo de cargas y eficiencia en el cómputo con el uso del método de elementos finitos (MEF o FEM por sus siglas en inglés) en máquinas paralelas de gran escala. Introducimos también un balanceo de cargas multinivel para mejorar las diferencias locales. El MEF es usado para aproximar numéricamente las soluciones a ecuaciones diferenciales parciales (EDP o PDE por sus siglas en inglés) o a ecuaciones integrales. El dominio de las EDP se hace discreto convirtiéndolo en una malla de información y usualmente se soluciona utilizando métodos iterativos. La distribución de la malla en los procesadores de una computadora paralela, también conocido como el problema de partición de la malla, es NP-completo. Muchos esfuerzos se enfocan en partición de grafos para paralelizar y distribuir la malla de información. La partición de la información es importante para ejecutar las aplicaciones eficientemente en sistemas distribuidos. Para abordar este problema, una variedad de librerías de propósito general y técnicas se han desarrollado proveyendo gran efectividad. Pero el problema del balanceo de cargas no está del todo solucionado. Las extensas simulaciones de hoy requieren nuevas técnicas para poder ser ejecutadas eficientemente en sistemas de miles de procesadores y para tomar en cuenta los recursos disponibles debido al extenso uso de arquitecturas heterogéneas en la actualidad. Las librerías y algoritmos actuales deben ser adaptados para ser capaces de manejar aplicaciones más complejas y diferentes arquitecturas de hardware. Nosotros presentamos las tendencias en este campo y discutimos nuevas ideas que consideran los requerimientos emergentes.

Palabras clave: Balanceo de cargas, método de elementos finitos, eficiencia en computación de alto desempeño.

 

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Acknowledgment

This work was partially supported by CONACYT under grant number 309370.

 

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