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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Parallel block preconditioning of the incompressible Navier-Stokes equations with weakly imposed boundary conditions

White, Raymon January 2016 (has links)
This project is concerned with the development and implementation of a novel preconditioning method for the iterative solution of linear systems that arise in the finite element discretisation of the incompressible Navier-Stokes equations with weakly imposed boundary conditions. In this context we studied an augmented approach where the Schur complement associated with the momentum block of the Navier-Stokes equations has special sparse structure. We follow the standard inf-sup stable method of discretising the Navier-Stokes equations by the Taylor-Hood elements with the Lagrange multiplier constraints discretised using the same order approximation on matching grids. The resulting system of nonlinear equations is solved iteratively by Newton's method. The spectrum of the linearised Oseen's problem, preconditioned by the exact augmentation preconditioner was analysed. Then we developed inexact versions of the preconditioner aimed at achieving optimal scaling of the algorithm in terms of computational resources and wall-clock times. The experimental evaluation of the methodology involve a number of benchmark problems in two and three spatial dimensions. The obtained results demonstrate efficiency, robustness and almost optimal scaling of the solution algorithm with respect to the discrete problem size. We used OOMPH-LIB as a testbed for our experiments. The preconditioning strategies were implemented using OOMPH-LIB's Parallel Block Preconditioning Framework. The initial version of the software was significantly upgraded during the course of this project with newly implemented functionalities to facilitate the rapid development of sophisticated hierarchical design of parallel block preconditioners. Parallel performance analysis of the newly introduced functionalities demonstrate negligible overhead in terms of wall-clock time and the framework demonstrate good weak and strong parallel scaling.

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