Explicit preconditioned domain decomposition schemes for solving nonlinear boundary value problems

AbstractA new class of inner-outer iterative procedures in conjunction with Picard-Newton methods based on explicit preconditioning iterative methods for solving nonlinear systems is presented. Explicit preconditioned iterative schemes, based on the explicit computation of a class of domain decomposition generalized approximate inverse matrix techniques are presented for the efficient solution of nonlinear boundary value problems on multiprocessor systems. Applications of the new composite scheme on characteristic nonlinear boundary value problems are discussed and numerical results are given

A three-dimensional explicit preconditioned solver

AbstractA new class of Generalized Approximate Inverse Matrix (GAIM) techniques, based on the concept of LU-sparse factorization procedures, is introduced for computing explicitly generalized approximate inverses of large sparse unsymmetric matrices of regular structure, without inverting the decomposition factors. Explicit preconditioned iterative methods, in conjunction with modified forms of the GAIM techniques, are presented for solving numerically boundary value problems in three dimensions. The numerical implementation of these algorithms is presented and Fortran subroutines are give

Normalized explicit finite element approximate inverse preconditioning

Normalized explicit approximate inverse matrix techniques for computing explicitly various families of normalized approximate inverses based on normalized approximate factorization procedures for solving sparse linear systems, which are derived from the finite difference and finite element discretization of partial differential equations are presented. Normalized explicit preconditioned conjugate gradient-type schemes in conjunction with normalized approximate inverse matrix techniques are presented for the efficient solution of linear and non-linear systems. Theoretical estimates on the rate of convergence and computational complexity of the normalized explicit preconditioned conjugate gradient method are also presented. Applications of the proposed methods on characteristic linear and non-linear problems are discussed and numerical results are given. © 2004 Elsevier Ltd. All rights reserved

Normalized explicit approximate inverse preconditioning for solving 3D boundary value problems on uniprocessor and distributed systems

Normalized explicit approximate inverse matrix techniques, based on normalized approximate factorization procedures, for solving sparse linear systems resulting from the finite difference discretization of partial differential equations in three space variables are introduced. Normalized explicit preconditioned conjugate gradient schemes in conjunction with normalized approximate inverse matrix techniques are presented for solving sparse linear systems. The convergence analysis with theoretical estimates on the rate of convergence and computational complexity of the normalized explicit preconditioned conjugate gradient method are also derived. A Parallel Normalized Explicit Preconditioned Conjugate Gradient method for distributed memory systems, using message passing interface (MPI) communication library, is also given along with theoretical estimates on speedups, efficiency and computational complexity. Application of the proposed method on a three-dimensional boundary value problem is discussed and numerical results are given for uniprocessor and multicomputer systems. Copyright © 2005 John Wiley & Sons, Ltd

Solving Non-linear Finite Difference Systems by Normalized Approximate Inverses

A class of inner-outer isomorphic iterative procedures in conjunction with Picard/Newton methods based on normalized explicit approximate inverse matrix techniques for solving efficiently sparse non-linear finite difference systems is presented. Applications on characteristic non-linear boundary value problems in three dimensions are discussed and numerical results are given. © Springer-Verlag 2004

Optimal server resource reservation policies for priority classes of users under cyclic non-homogeneous markov modeling

Resource availability optimization is studied on a server-client system where different users are partitioned into priority classes. The aim is to provide higher resource availability according to the priority of each class. For this purpose, resource reservation is modeled by a homogeneous continuous time Markov chain (CTMC), but also by a cyclic non-homogeneous Markov chain (CNHMC) as there is a cyclic behavior of the users' requests for resources. The contribution of the work presented consists in the formulation of a multiobjective optimization problem for both the above cases that aims to determine the optimal resource reservation policy providing higher levels of resource availability for all classes. The optimization problem is solved either with known methods or with a proposed kind of heuristic algorithm. Finally, explicit generalized approximate inverse preconditioning methods are adopted for solving efficiently sparse linear systems that are derived, in order to compute resource availability.Server resources Priority classes Resource availability modeling Non-homogeneous Markov chains Optimization Approximate inverse matrix algorithms Preconditioning

Parallel and systolic solution of normalized explicit approximate inverse preconditioning

A new class of normalized approximate inverse matrix techniques, based on the concept of sparse normalized approximate factorization procedures are introduced for solving sparse linear systems derived from the finite difference discretization of partial differential equations. Normalized explicit preconditioned conjugate gradient type methods in conjunction with normalized approximate inverse matrix techniques are presented for the efficient solution of sparse linear systems. Theoretical results on the rate of convergence of the normalized explicit preconditioned conjugate gradient scheme and estimates of the required computational work are presented. Application of the new proposed methods on two dimensional initial/boundary value problems is discussed and numerical results are given. The parallel and systolic implementation of the dominant computational part is also investigated. © 2004 Kluwer Academic Publishers

Manifold spirals, disc-halo interactions, and the secular evolution in N-body models of barred galaxies

The manifold theory of barred-spiral structure provides a dynamical mechanism explaining how spiral arms beyond the ends of galactic bars can be supported by chaotic flows extending beyond the bar's corotation zone. We discuss its applicability to N-body simulations of secularly evolving barred galaxies. In these simulations, we observe consecutive 'incidents' of spiral activity, leading to a time-varying disc morphology. Besides disc self-excitations, we provide evidence of a newly noted excitation mechanism related to the 'off-centring' effect: particles ejected in elongated orbits at major incidents cause the disc centre-of-mass to recoil and be set in a wobble-type orbit with respect to the halo centre of mass. The time-dependent m = 1 perturbation on the disc by the above mechanism correlates with the excitation of new incidents of non-axisymmetric activity beyond the bar. At every new excitation, the manifolds act as dynamical avenues attracting particles which are directed far from corotation along chaotic orbits. The fact that the manifolds evolve morphologically in time, due to varying non-axisymmetric perturbations, allows to reconcile manifolds with the presence of multiple patterns and frequencies in the disc. We find a time-oscillating pattern speed profilep(R) at distances R between the bar's corotation, at resonance with the succession of minima and maxima of the non-axisymmetric activity beyond the bar. Finally, we discuss disc thermalization, i.e. the evolution of the disc velocity dispersion profile and its connection with disc responsiveness to manifold spirals. © 2019 The Author(s)