Parallel Edge-Based Inexact Newton Solution of Steady Incompressible 3D Navier-Stokes Equations

• Published in: Euro-Par 2005 Parallel Processing pp. 1237 - 1245
• Main Authors: Elias, Renato N., Martins, Marcos A. D., Coutinho, Alvaro L. G. A.
• Format: Book Chapter Conference Proceeding
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2005; Springer
• Series: Lecture Notes in Computer Science
• Subjects: Applied sciences; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Exact sciences and technology; Finite Element Formulation; Inexact Newton Method; Message Passing Interface; Nonlinear Iteration; Parallel Solver; Software; High performance; Parallel algorithm; Grid; Krylov subspace method; Matrix product; Distributed system; Vector method; Distributed computing; Modeling; Partial differential equation; Finite element method; Communicating process; Message passing; Navier Stokes equation; Message passing interface; Matrix method; Edge detection; Newton method
• ISBN: 3540287000; 9783540287001
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/11549468_135

The parallel edge-based solution of 3D incompressible Navier-Stokes equations is presented. The governing partial differential equations are discretized using the SUPG/PSPG stabilized finite element method [5] on unstructured grids. The resulting fully coupled nonlinear system of equations is solved by the inexact Newton-Krylov method [1]. Matrix-vector products within GMRES are computed edge-by-edge, diminishing flop counts and memory requirements. The non-linear solver parallel implementation is based in message passing interface (MPI). Performance tests on several computers, such as the SGI Altix, the Cray XD1 and a mini-wireless cluster were carried out in representative problems and results have shown that edge-based schemes require less CPU time and memory than element-based solutions.