Olshanskii, Maxim A.2020-06-02May 20202020-05May 2020https://hdl.handle.net/10657/6604Motivated by the numerical solution of the incompressible Navier-Stokes equations, this thesis studies numerical properties of threshold incomplete LU factorizations for nonsymmetric saddlepoint matrices. We consider preconditioned iterative Krylov-subspace methods, such as GMRES, to solve large and sparse linear algebraic systems that result from a Galerkin nite element (FE) discretizations of the linearized Navier-Stokes equations. The corresponding preconditioners are used to accelerate the convergence of the GMRES method. Stabilized and unstabilized nite element methods are used for the Navier-Stokes problem leading to systems of algebraic equations of a saddle point type, which has a 2 2-block structure. Numerical experiments for model problems of a driven cavity flow, and flow over a backward-facing step illustrate the performance of one-parameter and two-parameter ILU factorizations as preconditioners. We also introduce a Machine Learning (ML) based approach for building ILU factorizations for preconditioning. For this purpose, we use the tools well-developed in the scope of image segmentation. Image Segmentation is the process of partitioning an image into separate and distinct regions.The process has some similarities to building patterns for ILU-type preconditioner. In our interpretation, the segmented regions represent a non-zero pattern for L and U factors. We applied a convolutional neural network with the benchmark U-net architecture to predict non-zero patterns for ILU-type factorizations and further use the resulting preconditioners to solve the discrete linearized Navier-Stokes system.application/pdfengThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).MathematicsPreconditionerNavier-Stokes2020-06-02Thesisborn digital