We devise a hybrid approach for solving linear systems arising from interior point methods applied to linear programming problems. These systems are solved by preconditioned conjugate gradient method that works in two phases. During phase I it uses a kind of incomplete Cholesky preconditioner such that fill-in can be controlled in terms of available memory. As the optimal solution of the proble...

For the solution of large systems of linear equations, iterative solvers with preconditioners are typically employed. However, the design of preconditioners for the black-box case, in which no additional information about the underlying problem is known, is very difficult. The most commonly employed method of incomplete LU factorizations is a serial algorithm and thus not well suited for the ma...

Iterative solvers for sparse linear systems often benefit from using preconditioners. While there are implementations for many iterative methods that leverage the computing power of accelerators, porting the latest developments in preconditioners to accelerators has been challenging. In this paper we develop a selfadaptive multi-elimination preconditioner for graphics processing units (GPUs). T...

In this paper, we study the effect the choice of mesh quality metric, preconditioner, and sparse linear solver have on the numerical solution of elliptic partial differential equations (PDEs). We smoothe meshes on several geometric domains using various quality metrics and solve the associated elliptic PDEs using the finite element method. The resulting linear systems are solved using various c...

This routine solves a complex sparse non-Hermitian system of linear equations: Ax 1⁄4 b; using an RGMRES (Saad and Schultz (1986)), CGS (Sonneveld (1989)), Bi-CGSTAB(‘) (Van der Vorst (1989), Sleijpen and Fokkema (1993)), or TFQMR (Freund and Nachtigal (1991), Freund (1993)) method. F11DSF allows the following choices for the preconditioner: no preconditioning; Jacobi preconditioning (Young (19...

In this work we discuss parallel preconditioning techniques for the bidomain equations, a non-linear system of partial differential equations which is widely used for describing electrical activity in cardiac tissue. We focus on the solution of the linear system associated with the elliptic part of the bidomain model, since it dominates computation, with the preconditioned conjugate gradient me...

For a fast simulation of interconnect structures we consider preconditioned iterative solution methods for large complex valued linear systems. In many applications the discretized equations result in ill-conditioned matrices, and efficient preconditioners are indispensable to solve the linear systems accurately. We apply the dual threshold incomplete LU (ILUT) factorization as preconditioners ...

Monopole antennas are usually used for measurement of the shielding effectiveness of metallic enclosures. This paper presents an accurate numerical modeling for monopole antennas attached in shielded enclosures with apertures. The electric field integral equation (EFIE) is formulated for the induced currents on both the monopoles and enclosure. The precorrected-FFT accelerated method of moments...

When solving a linear system in parallel, a large overhead in using an incomplete LU factorization as a preconditioner may annihilate any gains made from the improved convergence. This overhead is due to the inherently sequential nature of such a preconditioning. Multicoloring of the subdomains assigned to processors is a common remedy for increasing the parallelism of a global ordering. Howeve...

In this paper, a block LU preconditioner for saddle point problems is presented. The main diierence between the approach presented here and that of other studies is that an explicit, accurate approximation of the Schur complement matrix is eeciently computed. This is used to compute a preconditioner to the Schur complement matrix that in turn deenes a preconditioner for a global iteration. The ...