[Paper Review] Domain Decomposition Based High Performance Parallel Computing

Mandhapati Raju, Siddhartha Kumar Khaitan|ArXiv.org|Nov 4, 2009

Matrix Theory and Algorithms16 references14 citations

TL;DR

This paper proposes a domain decomposition approach to enhance the scalability of parallel sparse direct solvers in finite element-based Navier-Stokes simulations. By integrating the high-performance solver PARDISO with domain decomposition, the authors achieve improved parallel efficiency for both Newton and modified Newton algorithms, overcoming the limited scalability of traditional parallel sparse direct solvers in large-scale CFD applications.

ABSTRACT

The study deals with the parallelization of finite element based Navier-Stokes codes using domain decomposition and state-ofart sparse direct solvers. There has been significant improvement in the performance of sparse direct solvers. Parallel sparse direct solvers are not found to exhibit good scalability. Hence, the parallelization of sparse direct solvers is done using domain decomposition techniques. A highly efficient sparse direct solver PARDISO is used in this study. The scalability of both Newton and modified Newton algorithms are tested.

Motivation & Objective

• To address the poor scalability of parallel sparse direct solvers in large-scale finite element simulations.
• To improve the performance of Newton and modified Newton methods in solving large sparse linear systems arising from Navier-Stokes equations.
• To leverage domain decomposition techniques to enable efficient parallelization of the sparse direct solver PARDISO.
• To evaluate the scalability and efficiency of the proposed approach on high-performance computing architectures.

Proposed method

• Application of domain decomposition to partition the computational domain into subdomains for parallel processing.
• Use of the PARDISO sparse direct solver for solving the local linear systems within each subdomain.
• Implementation of iterative solution strategies based on Newton and modified Newton methods within the domain-decomposed framework.
• Distribution of the global system matrix and right-hand side vector across processors using domain decomposition partitioning.
• Synchronization and communication of interface degrees of freedom between subdomains to maintain solution consistency.
• Optimization of data distribution and solver configuration to minimize communication overhead and maximize parallel efficiency.

Experimental results

Research questions

• RQ1 Can domain decomposition effectively improve the scalability of parallel sparse direct solvers in finite element simulations?
• RQ2 How does the performance of Newton and modified Newton methods scale when combined with domain decomposition and PARDISO?
• RQ3 What is the impact of domain decomposition on the convergence behavior and computational cost of solving large sparse linear systems in Navier-Stokes simulations?
• RQ4 To what extent does the proposed approach mitigate the inherent scalability limitations of parallel sparse direct solvers?

Key findings

• The proposed domain decomposition-based approach significantly improves the scalability of the PARDISO solver in parallel finite element simulations.
• Both Newton and modified Newton algorithms demonstrated enhanced parallel efficiency when combined with domain decomposition and PARDISO.
• The study confirms that domain decomposition enables effective load balancing and reduces communication bottlenecks in large-scale simulations.
• The integration of PARDISO with domain decomposition leads to faster convergence and reduced solution time compared to standard parallel sparse direct solvers.