Two sides tangential filtering decomposition

AbstractIn this paper we study a class of preconditioners that satisfy the so-called left and/or right filtering conditions. For practical applications, we use a multiplicative combination of filtering based preconditioners with the classical ILU(0) preconditioner, which is known to be efficient. Although the left filtering condition has a more sound theoretical motivation than the right one, extensive tests on convection–diffusion equations with heterogeneous and anisotropic diffusion tensors reveal that satisfying left or right filtering conditions lead to comparable results. On the filtering vector, these numerical tests reveal that e=[1,…,1]T is a reasonable choice, which is effective and can avoid the preprocessing needed in other methods to build the filtering vector. Numerical tests show that the composite preconditioners are rather robust and efficient for these problems with strongly varying coefficients

Graphene under bichromatic driving: Commensurability and spatio-temporal symmetries

We study the non-linear current response of a Dirac model that is coupled to two time-periodic electro-magnetic fields with different frequencies. We distinguish between incommensurable and commensurable frequencies, the latter characterized by their ratio p/q with co-prime integers p and q. Coupling the (effective) two-level system to a dissipative bath ensures a well-defined long-time solution for the reduced density operator and, thus, the current. We then analyze the spatio-temporal symmetries that force certain current components to vanish and close with conclusions for directed average currents.Comment: 8 pages, 5 figure

Modified Tangential Frequency Filtering Decomposition and its Fourier Analysis

In this paper, a modified tangential frequency filtering decomposition (MTFFD) preconditioner is proposed. The optimal order of the modification and the optimal relaxation parameter are determined by Fourier analysis. With this choice of the optimal order of modification, the Fourier results show that the condition number of the preconditioned matrix is ${\cal O}(h^{-\frac{2}{3}})$, and the spectrum distribution of the preconditioned matrix can be predicted by the Fourier results. The performance of MTFFD is compared with tangential frequency filtering (TFFD) preconditioner on a variety of large sparse matrices arising from the discretization of PDEs with discontinuous coefficients. The numerical results show that the MTFFD preconditioner is much more efficient than the TFFD preconditioner

Two sides tangential filtering decomposition

Dans ce papier nous introduisons la decomposition bas\'{e}e sur un filtrage tangentiel \`{a} gauche et de deux c\^{o}t\'{e}s. Le pr\'{e}conditionnement obtenu par ce filtrage est combin\'{e} avec le pr\'{e}conditionnement classique $\mathbf{ILU(0)}$ de mani\`{e}re multiplicative. Notre analyse montre que le pr\'{e}conditionnement compos\'{e} h\'{e}rite des avantages de chacun des préconditionnements. Pour le vecteur de filtrage, nous montrons que $ones$ est un choix efficace et peut \'{e}viter la phase de pretraitement n\'{e}cessaire par les autres m\'{e}thodes pour \'{e}tablir ce vecteur. Les r\'{e}sultats num\'{e}riques montrent que le pr\'{e}conditionnement compos\'{e} est robuste et efficace pour les systèmes lin\'{e}aires avec une structure bloc tridiagonal résultant de la discr\'{e}tisation des \'{e}quations diff\'{e}rentielles partielles avec des coefficients fortement variables

G-CSC Report 2010

The present report gives a short summary of the research of the Goethe Center for Scientific Computing (G-CSC) of the Goethe University Frankfurt. G-CSC aims at developing and applying methods and tools for modelling and numerical simulation of problems from empirical science and technology. In particular, fast solvers for partial differential equations (i.e. pde) such as robust, parallel, and adaptive multigrid methods and numerical methods for stochastic differential equations are developed. These methods are highly adanvced and allow to solve complex problems.. The G-CSC is organised in departments and interdisciplinary research groups. Departments are localised directly at the G-CSC, while the task of interdisciplinary research groups is to bridge disciplines and to bring scientists form different departments together. Currently, G-CSC consists of the department Simulation and Modelling and the interdisciplinary research group Computational Finance