Domain Decomposition Methods in Computational Fluid Dynamics

PAZ RODRIGO; STORTI MARIO; DALCÍN LISANDRO; GUSTAVO A. RÍOS RODRIGUEZ

Cluster Computing: Tools, Techniques and Applications

Nova Publishers

Lugar: Hauppauge, New York, USA; Año: 2009;

In this work, the development of a parallelizable preconditioner fordomain decomposition methods in the context of Finite Element so-lution of partial differential equations arising in the context of CFDproblems is studied. The preconditioner is based on solving a problemin a narrow strip around the interface of the partitioned problem. Thetheoretical basis and concepts that inspired the proposition of this in-terface strip preconditioner (ISP) are presented. The performance ofthis preconditioner (that has been implemented in a FEM productioncode called PETSC-FEM) is assessed with an analytical study of Schurcomplement matrix eigenvalues and numerical experiments conductedin a parallel computational environment. Also, we compare the con-vergence to the analytical solution or measured data for problems thathave been considered as ‘benchmarks’ in the computational fluid dy-namic literature. For this purpose, we study the solution obtained viaparallelized iterative methods that have been extensively used (e.g. pre-conditioned CG and GMRES global iteration and its variants, AdditiveSchwarz preconditioners) in CFD computations and those obtained withthe Interface Strip preconditioner for the Schur Complement method.