Incomplete factorizations are used to approximate the factorization of a sparse coe cient matrix A, such that A = L̄Ū ⇡ LU , and are commonly used as preconditioners for iterative methods, such as GMRES [7]. The approximation is normally achieved by some combination of dropping small value and/or by not allowing fill-in, i.e., zero elements becoming nonzero during factorization, based on levels ...

We examine the scalability of the recently developed Albany/FELIX finite-element based code for the first-order Stokes momentum balance equations for ice flow. We focus our analysis on the performance of two possible preconditioners for the iterative solution of the sparse linear systems that arise from the discretization of the governing equations: (1) a preconditioner based on the incomplete ...

Motivated by the numerical solution of the linearized incompressible Navier–Stokes equations, we study threshold incomplete LU factorizations for non-symmetric saddle point matrices. The resulting preconditioners are used to accelerate the convergence of a Krylov subspace method applied to finite element discretizations of fluid dynamics problems in three space dimensions. The paper presents an...

In this chapter, we give a brief overview of a particular class of preconditioners known as incomplete factorizations. They can be thought of as approximating the exact LU factorization of a given matrix A (e.g. computed via Gaussian elimination) by disallowing certain ll-ins. As opposed to other PDE-based preconditioners such as multigrid and domain decomposition, this class of preconditioners...

Motivated by the numerical solution of the linearized incompressible Navier–Stokes equations, we study threshold incomplete LU factorizations for nonsymmetric saddle-point matrices. The resulting preconditioners are used to accelerate the convergence of a Krylov subspace method applied to finite element discretizations of fluid dynamics problems in three space dimensions. The paper presents and...

The efficient algorithm is presented for the analysis of electromagnetic scattering from composite structures with coexisting open and closed conductors. A hybrid combined-field integral equation-the improved electric-field integral equation (CFIE-IEFIE) formulation with the incomplete LU factorization (ILU) preconditioner is proposed. Numerical results are given to demonstrate that the efficie...

In this paper, we investigate GPU based parallel triangular solvers systematically. The parallel triangular solvers are fundamental to incomplete LU factorization family preconditioners and algebraic multigrid solvers. We develop a new matrix format suitable for GPU devices. Parallel lower triangular solvers and upper triangular solvers are developed for this new data structure. With these solv...