The electric field integral equation (EFIE) is a well-established tool to solve electromagnetic scattering problems. However, the development of efficient and easy-to-implement preconditioners remains an active research area. In recent years, operator preconditioning approaches have become popular for EFIE, where boundary regularized by multiplication with another convenient operator. A particu...

A class of preconditioners is introduced to enhance geometry optimisation and transition state search of molecular systems. We start from the Hessian of molecular mechanical terms, decompose it and retain only its positive definite part to construct a sparse preconditioner matrix. The construction requires only the computation of the gradient of the corresponding molecular mechanical terms that...

In this paper, we study the use of an incomplete Cholesky factorization (ICF) as a preconditioner for solving dense symmetric positive definite linear systems. This method is suitable for situations where matrices cannot be explicitly stored but each column can be easily computed. Analysis and implementation of this preconditioner are discussed. We test the proposed ICF on randomly generated sy...

Adaptive Block FSAI (ABF) is a novel and promising preconditioner for the efficient parallel solution of linear systems and eigenproblems arising from subsurface applications. However, one of its main drawbacks stems from the reduced scalability, as the iteration count to converge tends to grow increasing the number of processors. Graph partitioning techniques can help improve both the precondi...

We study a block triangular preconditioner for finite element approximations of the linearized Navier–Stokes equations. The preconditioner is based on the augmented Lagrangian formulation of the problem and was introduced by the authors in [SIAM J. Sci. Comput., 28 (2006), pp. 2095–2113]. In this paper we prove field-of-values type estimates for the preconditioned system which lead to optimal c...

The numerical study of exterior acoustics problems is usually carried out in the frequency domain. Finite element analyses often require the solution of large scale algebraic linear systems. For very large problems, sometimes the time domain is used. Implicit time integration requires linear system solves, but these are often far easier than those from the frequency domain. This paper shows a c...