primitive zero symmetric sign pattern matrices with the maximum base abstract in b cheng b liu the base sets of primitive zero symmetric sign pattern matrices linear algebra appl 428 2008 715 731 cheng and liu studied the bases of primitive zero symmetric sign pattern matrices the sharp upper bound of the bases was obtained in this paper we characterize the sign pattern matrices with the sharp bound

bounds on the local bases of primitive non powerful minimally strong signed digraphs abstract in this paper we study the local bases of primitive non powerful minimally strong signed digraphs of order n 7 we obtain the first two or three largest kth local bases depending on whether n is odd or even together with complete characterization of the equality cases for primitive non powerful minimally strong signed digraphs

on the exponent of a primitive digraph abstract we characterize the equality case of the upper bound d n s n 2 for the exponent of a primitive digraph in the case s 2 where n is the number of the vertices of the digraph d and s is the length of the shortest elementary circuit of d we also answer a question about the equality case when s 1 the exponent of an n n primitive nonnegative matrix a is the same as the exponent of the associated digraph d a of a so every theorem in this paper can be translated into a theorem about nonnegative matrices

the base sets of quasi primitive zero symmetric sign pattern matrices with zero trace abstract cheng and liu bo cheng bolian liu the base sets of primitive zero symmetric sign pattern matrices linear algebra appl 428 2008 715 731 showed that the base set of quasi primitive zero symmetric generalized sign pattern matrices is 1 2 2 n the matrices with zero trace play a prominent role in matrix theory in this paper we investigate the bases of quasi primitive zero symmetric generalized sign pattern matrices with zero trace and prove that the base set of such matrices is 2 3 2 n 1

strong coupling schemes for interaction of thin walled structures and incompressible flows the contribution addresses the specific physical sensitivity inherent in the interaction of slender structures like membranes or shells and instationary incompressible flows and its consequences for numerical solution schemes different partitioned strong coupling approaches are presented and compared with respect to their efficiency in addition to the classical block gauss seidel iteration and a newton krylov approach a two level coupling scheme is introduced it is based on a coarse grid predictor followed by the usual iterative fine scale solution the performance of the three coupling schemes is investigated applying a two dimensional model problem of a membrane roof three dimensional numerical examples demonstrate the mechanical and numerical sensitivity for these especially delicate fluid structure interaction problems copyright 2010 john wiley sons ltd

fluid structure interaction with large structural displacements the calculation of viscous flows inside deformable structures faces major difficulties when enforcing the kinematic compatibility at the fluid structure interface and updating the geometry of the domain this paper proposes to overcome these problems by considering the fluid and the structure as a unique continuous medium to be studied in a fixed reference configuration the resulting problem is then split into a fluid and a structural part through an additive decomposition of the space of kinematically admissible test functions this approach treats the structure in a fully lagrangian way and uses an associated arbitrary lagrangian eulerian ale formulation for the fluid such a strategy has three advantages which are detailed in the present paper it can be discretised in time by implicit stable energy conserving time integration schemes and solved by simple iterative uncoupled algorithms the fluid and the structural problems can be approximated by independent finite element spaces the most recent geometrically exact nonlinear shell models can be used for the structures the full strategy has been implemented into an industrial cfd code results obtained in the simulation of industrial hydraulic shock absorbers are presented at the end of the paper

bounds on the base of primitive nearly reducible sign pattern matrices abstract in j y shao l h you bound on the base of irreducible generalized sign pattern matrices discrete math in press shao and you extended the concept of the base from powerful sign pattern matrices to non powerful and generalized sign pattern matrices in this paper we study the base for primitive non powerful nearly reducible sign pattern and generalized sign pattern matrices we obtain sharp upper bounds together with complete characterization of the equality cases of the base for primitive nearly reducible sign pattern and generalized sign pattern matrices we also show that there exist gaps in the base set of the classes of such matrices

partitioned procedures for the transient solution of coupled aroelastic problems part i model problem theory and two dimensional application abstract in order to predict the dynamic response of a flexible structure in a fluid flow the equations of motion of the structure and the fluid must be solved simultaneously in this paper we present several partitioned procedures for time integrating this focus coupled problem and discuss their merits in terms of accuracy stability heterogeneous computing i o transfers subcycling and parallel processing all theoretical results are derived for a one dimensional piston model problem with a compressible flow because the complete three dimensional aeroelastic problem is difficult to analyze mathematically however the insight gained from the analysis of the coupled piston problem and the conclusions drawn from its numerical investigation are confirmed with the numerical simulation of the two dimensional transient aeroelastic response of a flexible panel in a transonic non linear euler flow regime

analysis of the block gauss seidel solution procedure for a strongly coupled model problem with reference to fluid structure interaction the block gauss seidel procedure is widely used for the resolution of the strong coupling in the computer simulation of fluid structure interaction based on a simple model problem this work presents a detailed analysis of the convergence behaviour of the method in particular the model problem is used to highlight some aspects that arise in the context of the application of the block gauss seidel method to fsi problems thus the effects of the time integration schemes chosen of relaxation techniques of physical constraints and non linearities on the convergence of the iterations are investigated

the scrambling index set of primitive minimally strong digraphs abstract denote the scrambling index set of primitive minimally strong digraphs of order n by si n for n 13 we show that si n contains all integers in the interval 3 k 1 n where k 1 n n 2 12 n 13 8 if both n and n 1 2 are odd n 2 12 n 5 8 if n is odd and n 1 2 is even n 2 10 n 16 8 if n is even and n 2 is odd n 2 10 n 8 8 if both n and n 2 are even we also identify all elements of si n which are larger than n 2 6 n 13 2 n is odd or n 2 6 n 12 2 n is even it is shown that there exist more gaps in the set si n

coupled adjoint based sensitivities in large displacement fluid structure interaction using algorithmic differentiation summary a methodology for the calculation of gradients with respect to design parameters in general fluid structure interaction problems is presented it is based on fixed point iterations on the adjoint variables of the coupled system using algorithmic differentiation this removes the need for the construction of the analytic jacobian for the coupled physical problem which is the usual limitation for the computation of adjoints in most realistic applications the formulation is shown to be amenable to partitioned solution methods for the adjoint equations it also poses no restrictions to the nonlinear physics in either the fluid or structural field other than the existence of a converged solution to the primal problem from which to compute the adjoints we demonstrate the applicability of this procedure and the accuracy of the computed gradients on coupled problems involving viscous flows with geometrical and material non linearities in the structural domain this article is protected by copyright all rights reserved

an integration factor method for stochastic and stiff reaction diffusion systems stochastic effects are often present in the biochemical systems involving reactions and diffusions when the reactions are stiff existing numerical methods for stochastic reaction diffusion equations require either very small time steps for any explicit schemes or solving large nonlinear systems at each time step for the implicit schemes here we present a class of semi implicit integration factor methods that treat the diffusion term exactly and reaction implicitly for a system of stochastic reaction diffusion equations our linear stability analysis shows the advantage of such methods for both small and large amplitudes of noise direct use of the method to solving several linear and nonlinear stochastic reaction diffusion equations demonstrates good accuracy efficiency and stability properties this new class of methods which are easy to implement will have broader applications in solving stochastic reaction diffusion equations arising from models in biology and physical sciences

artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows this note investigates the so called arti cial added mass e ect which is responsible for devastating instabilities within sequentially staggered fluid structure interaction fsi simulations where incompressible fluids are considered a discrete representation of the added mass operatorma is given and instability conditions are evaluated for different temporal discretisation schemes it is proven that for every sequentially staggered scheme and given spatial discretisation of a problem a mass ratio between fluid and structural mass density can be found at which the coupled system becomes unstable the analysis is quite general and does not depend upon the particular spatial discretisation schemes used however here special attention is put on stabilised finite elements employed on the fluid partition numerical investigations further highlight the results

the kth lower bases of primitive non powerful signed digraphs abstract in j shao l you h shan bound on the bases of irreducible generalized sign pattern matrices linear algebra appl 427 2007 285 300 the authors extended the concept of the base from powerful sign pattern matrices to non powerful irreducible sign pattern matrices recently the k th local bases and the k th upper bases which are generalizations of the bases of primitive non powerful signed digraphs were introduced in this paper we introduce a new parameter called the k th lower bases of primitive non powerful signed digraphs and obtain some bounds for it for some cases the bounds we obtain are best possible and the extremal signed digraphs are characterized respectively moreover we show that there exist gaps in the k th lower bases set of primitive non powerful signed digraphs

a survey on bases of sign pattern matrices abstract an n n sign pattern matrix has entries in 1 1 0 this paper surveys the following problems concerning the bases of sign pattern matrices base and base set of sign pattern matrices the generalizations of the base of sign pattern matrices other indices of sign pattern matrices several open problems are identified

two level algorithms for partitioned fluid structure interaction computations abstract in this paper we use the multigrid algorithm commonly used to improve the efficiency of the flow solver to improve the efficiency of partitioned fluid structure interaction iterations coupling not only the structure with the fine flow mesh but also with the coarse flow mesh often present due to the multigrid scheme leads to a significant efficiency improvement as solution of the flow equations typically takes much longer than the structure solve and as multigrid is not standard in structure solvers we do not coarsen the structure or the interface as a result the two level method can be easily implemented into existing solvers two types of two level algorithms were implemented 1 coarse grid correction of the partitioning error and 2 coarse grid prediction or full multigrid to generate a better initial guess the resulting schemes are combined with a fourth order runge kutta implicit time integration scheme for the linear one dimensional piston problem with compressible flow the superior stability accuracy and efficiency of the two level algorithms is shown the parameters of the piston problem were chosen such that both a weak and a strong interaction case were obtained even the strong interaction case with a flexible structure could be solved with our new two level partitioned scheme with just one iteration on the fine grid this is a major accomplishment as most weakly coupled methods fail in this case of the two algorithms the coarse grid prediction or full multigrid method was found to perform best the resulting efficiency gain for our one dimensional problem is around a factor of ten for the coarse to intermediate time steps at which the high order time integration methods should be run for two and three dimensional problems the efficiency gain is expected to be even larger

the generalized competition indices of primitive minimally strong digraphs abstract let d be a primitive digraph of order n and 1 m n the m competition index of d is the smallest positive integer k such that every pair of vertices x and y of d have at least m common preys in d k in this paper the upper bound of m competition indices 1 m n 1 for primitive minimally strong digraphs of order n is obtained furthermore it is shown that for 1 m n 1 there exist gaps in the m competition index set of primitive minimally strong digraphs of order n

a computational framework for fluid structure interaction finite element formulation and applications abstract this work is concerned with the modelling of the interaction of fluid flow with flexibly supported rigid bodies the fluid flow considered is governed by the incompressible navier stokes equations and modelled by employing stabilised low order velocity pressure finite elements the motion of the fluid domain is accounted for by an arbitrary lagrangian eulerian ale strategy the rigid body motion excited by the fluid flow is restricted by the elastic and damping properties of the supports for the temporal discretisation the discrete implicit generalised method is employed the resulting strongly coupled set of nonlinear equations is solved by means of a novel partitioned solution procedure which is based on the newton raphson methodology and incorporates full linearisation of the overall incremental problem the strong coupling is resolved and optimal convergence of the residuals is achieved several numerical examples are presented to demonstrate the robustness and efficiency of the methodology the examples clearly capture the phenomena of vortex induced oscillations and galloping

the base sets of primitive zero symmetric sign pattern matrices abstract in j y shao l h you bound on the base of irreducible generalized sign pattern matrices discrete math in press shao and you extended the concept of the base from powerful sign pattern matrices to non powerful and generalized sign pattern matrices in this paper we study the bases of primitive zero symmetric sign pattern and generalized sign pattern matrices sharp upper bounds of the bases are obtained we also show that there exist no gaps in the base sets of the classes of such matrices

irreducible sign k potent sign pattern matrices abstract the sign pattern matrix a is called sign k potent if k is the smallest positive integer such that a k 1 a the structure of irreducible sign k potent pattern matrices was characterized by stuart et al j stuart c eschenbach s kirkland linear algebra appl 294 1999 85 92 we extend those results to the reducible case providing necessary conditions that characterize the structure of each off diagonal block of the frobenius normal form of a reducible sign k potent matrix

on the period and base of a sign pattern matrix abstract a square sign pattern matrix a whose entries are or 0 is said to be powerful if all the powers a 1 a 2 a 3 are unambiguously defined for a powerful pattern a if a l a l p with l and p minimal then l is called the base of a and p is called the period of a we characterize irreducible powerful sign pattern matrices and investigate the period and base of a powerful sign pattern matrix we also consider some connections with real matrices and give some significant classes of powerful patterns