Finite element modelling of three dimensional elasticity problems gives rise to large sparse matrices. Various preconditioning methods are developed for use in preconditioned conjugate gradient iterative solution techniques. Incomplete factorizations based on levels of fill, drop tolerance, and a two level hierarchical basis are developed. Various techniques for ensuring that the incomplete fac...

In this paper we deal with performance analysis of Monte Carlo algorithm for large linear algebra problems. We consider applicability and efficiency of the Markov chain Monte Carlo for large problems, i.e., problems involving matrices with a number of non-zero elements ranging between one million and one billion. We are concentrating on analysis of the almost Optimal Monte Carlo (MAO) algorithm...

We present structure-preserving numerical methods for the eigenvalue problem of complex palindromic pencils. Such problems arise in control theory, as well as from palindromic linearizations of higher degree palindromic matrix polynomials. A key ingredient of these methods is the development of an appropriate condensed form — the anti-triangular Schur form. Ill-conditioned problems with eigenva...

We present a finite-element simulation tool for calculating light fields in 3D nano-optical devices. This allows to solve challenging problems on a standard personal computer. We present solutions to eigenvalue problems, like Bloch-type eigenvalues in photonic crystals and photonic crystal waveguides, and to scattering problems, like the transmission through finite photonic crystals. The discre...

a r t i c l e i n f o The study here highlights the potential that analytical methods based on Knowledge Discovery in Databases (KDD) methodologies have to aid both the resolution of unstructured marketing/business problems and the process of scholarly knowledge discovery. The authors present and discuss the application of KDD in these situations prior to the presentation of an analytical metho...

Advanced Krylov subspace methods are investigated for the solution of large sparse linear systems arising from stiff adjoint-based aerodynamic shape optimization problems. A special attention is paid to flexible inner–outer GMRES strategy combined with most relevant preconditioning and deflation techniques. The choice this specific class solvers challenging problems based on its outstanding con...