The numerical solution of large sparse linear systems lies at the heart of many large-scale scientific and engineering computations. These large linear systems frequently arise from the discretization and linearization of partial differential equations. Iterative solution techniques have become a powerful tool in solving these problems, because they have minimal storage requirements and generally need less computing time than direct solvers.
Iterative techniques are also good if only a limited accuracy is required.
Usually the linear system is preconditioned in order to accelerate the convergence of the associated iterative scheme. The incomplete factorization is one of the more effective preconditioners of conjugate gradient type methods used for the solution of large sparse linear systems. Most of the preconditioned iterative schemes involve the solution of triangular sparse systems. The focus of this thesis is to look at ways to solve triangular systems on parallel architectures. I will be looking at the case of blocked bidiagonal systems that occurs in the peconditioning step of the linear system that arises from the five-point discretization of Laplace's second order differential equation.