Preconditioned iterative solvers have the potential to solve very large sparse linear systems with a fraction of the memory used by direct methods. However, the effectiveness and performance of most preconditioners is not only problem dependent, but also fairly sensitive to the choice of their tunable parameters. As a result, a typical practitioner is faced with an overwhelming number of choice...

The availability of large-scale computing platforms comprised of tens of thousands of multicore processors motivates the need for the next generation of highly scalable sparse linear system solvers. These solvers must optimize parallel performance, processor (serial) performance, as well as memory requirements, while being robust across broad classes of applications and systems. In this paper, ...

This paper presents a performance comparison of sparse linear solvers based on iterative and direct methods for power system applications implemented on parallel computing platform. The iterative sparse linear solver evaluated in this paper is based on the conjugate gradient algorithm with a Jacobi pre-conditioner executed on a general purpose graphic processing unit (GPGPU). The direct solvers...

Discrete body of revolution (DBOR) codes can accelerate moment method (MoM) solutions for scattering geometries possessing discrete circular symmetry. Traditional DBOR formulations require modifications to the incident field, such as decomposition into circular modes. While appropriate for methods employing direct solvers, approaches employing iterative solvers are disadvantaged by this dramati...

In this chapter we will present an overview of a number of related iterative methods for the solution of linear systems of equations. These methods are so-called Krylov projection type methods and they include popular methods as Conjugate Gradients, Bi-Conjugate Gradients, LSQR and GMRES. We will sketch how these methods can be derived from simple basic iteration formulas, and how they are inte...