numerical discretization of a darcy forchheimer model we solve a steady darcy forchheimer flow in a bounded region by means of piecewise constant velocities and nonconforming piecewise mathbb p 1 pressures for the computation we solve the nonlinearity by an alternating directions algorithm and we decouple the computation of the velocity from that of the pressure by a gradient algorithm we prove a priori error estimates of the scheme and convergence of the alternating directions algorithm

a semi analytic porosity evolution scheme for simulating wormhole propagation with the darcy brinkman forchheimer model abstract in this paper we consider numerical simulation of wormhole propagation with the darcy brinkman forchheimer model matrix acidization in carbonate reservoirs is a widely practiced technique in the product enhancement of the oil and gas reservoir a wormhole i e a flow channel with high porosity is generated during reactive dissolution of carbonates by the action of the injected acid in the wormhole forming process the porosity changes non uniformly in space and it even becomes close to unity in the central regions of a wormhole the darcy brinkman forchheimer model accounts for both the porous media and clear fluid area so it can be used to model wormhole propagation perfectly this model however strongly depends on porosity therefore the time schemes for solving the evolutionary equation of porosity have a significant effect on accuracy and stability of the numerical simulation for wormhole propagation we propose a semi analytic time scheme which solves the porosity equation analytically at each time step for given acid concentration the proposed numerical method can improve the accuracy and stability of numerical simulation significantly for theoretical analysis of the proposed time scheme for the wormhole simulation we first reconstruct the analytical functions of porosity to analyze the time error of the porosity and on the basis of error estimates of porosity we employ a coupled analysis approach to achieve the estimates of pressure velocity and solute concentration the time error estimates for velocity pressure concentration and porosity are obtained in different norms finally numerical results are provided to verify the effectiveness of the proposed scheme

maintaining lu factors of a general sparse matrix abstract the authors describe a set of procedures for computing and updating an lu factorization of a sparse matrix a where a may be square possibly singular or rectangular the procedures include a markowitz factorization and a bartels golub update similar to those of reid 1976 1982 the updates provided are addition deletion or replacement of a row or column of a and rank one modification previously column replacement has been the only update available various design features of the implementation lusol are described and computational comparisons are made with the la05 and ma28 packages of reid 1976 and duff 1977 keywords sparse matrix lu factors matrix factorization matrix updates rank one modification fortran software lower and upper triangular

dynamics of continuous time quantum walks in restricted geometries we study quantum transport on finite discrete structures and we model the process by means of continuous time quantum walks a direct and effective comparison between quantum and classical walks can be attained based on the average displacement of the walker as a function of time indeed a fast growth of the average displacement can be advantageously exploited to build up efficient search algorithms by means of analytical and numerical investigations we show that the finiteness and the inhomogeneity of the substrate jointly weaken the quantum walk performance we further highlight the interplay between the quantum walk dynamics and the underlying topology by studying the temporal evolution of the transfer probability distribution and the lower bound of long time averages

dissimilar behaviors of coherent exciton transport on scale free networks with identical degree sequence conventional wisdom is that the power law degree sequence has a profound impact on diverse dynamical processes taking place on scale free networks here we show that power law degree distribution alone is not sufficient to determine the behaviors of coherent exciton transport on scale free networks for this purpose we study coherent exciton transport on a class of scale free networks controlled by a tunable parameter q which have the same degree sequence independent of q but are very different in other structural properties determined by q such as average distance and fractality first through numerical determination of the time evolutions of return probabilities we compare in detail the dissimilarities in oscillation periods and oscillation amplitudes between two limiting cases of q 0 and q 1 second we demonstrate that in the network of q 0 up to the third generation the quantum transport problem between node groups partitioned by node degrees can be mapped onto a line furthermore we show that in the case of long time limit the transition probabilities in the networks of q 0 and q 1 exhibit different characteristic patterns with identical values finally we find that the degree averaged return probability decreases when the parameter q increases from 0 to 1 indicating that the stronger localization can be found in those networks with lower values of q our results suggest that it is far from enough to characterize the behaviors of coherent exciton transport on scale free networks merely by power law degree distribution

continuous time quantum walks on one dimensional regular networks in this paper we consider continuous time quantum walks ctqws on a one dimensional ring lattice of n nodes in which every node is connected to its 2m nearest neighbors m on either side in the framework of the bloch function ansatz we calculate the space time transition probabilities between two nodes of the lattice we find that the transport of ctqws between two different nodes is faster than that of the classical continuous time random walks ctrws the transport speed which is defined by the ratio of the shortest path length and propagating time increases with the connectivity parameter m for both ctqws and ctrws for fixed parameter m the transport of ctrws gets slower with the increase of the shortest distance while the transport speed of ctqws turns out to be a constant value in the long time limit depending on the network size n and connectivity parameter m the limiting probability distributions of ctqws show various patterns when the network size n is an even number the probability of being at the original node differs from that of being at the opposite node which also depends on the precise value of parameter m

slow transport by continuous time quantum walks continuous time quantum walks ctqws do not necessarily perform better than their classical counterparts the continuous time random walks ctrws for one special graph where a recent analysis showed that in a particular direction of propagation the penetration of the graph is faster by ctqws than by ctrws we demonstrate that in another direction of propagation the opposite is true in this case a ctqw initially localized at one site displays a slow transport we furthermore show that when the ctqw s initial condition is a totally symmetric superposition of states of equivalent sites the transport gets to be much more rapid

mixed finite elements for elliptic problems with tensor coefficients as cell centered finite differences we present an expanded mixed finite element approximation of second order elliptic problems containing a tensor coefficient the mixed method is expanded in the sense that three variables are explicitly approximated namely the scalar unknown the negative of its gradient and its flux the tensor coefficient times the negative gradient the resulting linear system is a saddle point problem in the case of the lowest order raviart thomas elements on rectangular parallelepipeds we approximate this expanded mixed method by incorporating certain quadrature rules this enables us to write the system as a simple cell centered finite difference method requiring the solution of a sparse positive semidefinite linear system for the scalar unknown for a general tensor coefficient the sparsity pattern for the scalar unknown is a 9 point stencil in two dimensions and 19 points in three dimensions existing theory shows that the expanded mixed method gives optimal order approximations in the l 2 and h s norms and superconvergence is obtained between the l 2 projection of the scalar variable and its approximation we show that these rates of convergence are retained for the finite difference method if h denotes the maximal mesh spacing then the optimal rate is o h the superconvergence rate o h 2 is obtained for the scalar unknown and rate o h 3 2 for its gradient and flux in certain discrete norms moreover the full o h 2 is obtained in the strict interior of the domain computational results illustrate these theoretical results

characteristic block centered finite difference method for simulating incompressible wormhole propagation in this paper the characteristic block centered finite difference method is introduced and analyzed to solve the incompressible wormhole propagation error estimates for the pressure velocity porosity concentration and its flux in different discrete norms are established rigorously and carefully on non uniform grids finally some numerical experiments are presented to show that the convergence rates are in agreement with the theoretical analysis

shape optimization of thin walled structures governed by geometrically nonlinear mechanics this paper introduces a structural optimization strategy that combines fe based parametrization with nonlinear kinematics in order to optimize the shape of thin shell structures the optimization is based on gradient based strategies where the required derivatives are formulated by the adjoint approach the applied solution algorithm combines the well known nonlinear path following strategies with the design update procedure of the shape optimization this results in robust and flexible methods that require only a minimum of system evaluations the proposed optimization goals improve the load carrying behavior of the structure and minimize displacements and stresses it is shown that such efficient designs also exhibit an improved limit load this contribution illustrates the application of the proposed method by several shape optimization problems the presented results prove the exceptional performance of the optimized designs even if the optimal design is disturbed by unavoidable imperfections it is shown that the application of nonlinear kinematics in the shape optimization of thin shell structures allows for a much more realistic system response and gradient data the proposed approach is applicable to all kind of optimization strategies like topology sizing or material optimization respectively

minimum weight design of truss structures with geometric nonlinear behavior the paper presents an optimization method based on optimality criterion for minimum weight design of structures with geometric nonlinear behavior the nonlinear critical load is determined by finding the load level at which the hessian of the potential energy ceases to be positive definite a recurrence relation based on the criterion that at optimum the nonlinear strain energy density be equal in all the members is used to develop an algorithm sample problems are given to illustrate the application of the method to truss type structures with a large number of design variables number of algorithms based on the optimality criterion approach have been developed to design a minimum weight structure with specified constraints on nodal displacements element stresses system stability etc 1 2 the optimization algorithm consisted of analyzing the structure by the finite element method and using a recurrence relation derived from the appropriate optimality criterion to modify the design variables the optimality criterion was derived by differentiating the lagrangian with respect to the design variables the displacements were assumed to be small and in the finite element analysis linear equilibrium equations were solved to determine the response of the structure to the ap plied loads in the case of system stability the constraints were defined see refs 3 6 by the associated linear eigenvalue problem this definition of system stability for some structures may not be valid because of the nonlinear behavior of the structure which may be due to the geometry of the structure or the presence of geometric imperfections the correct procedure for these structures would be to analyze the structure by using nonlinear equilibrium equations this will be particularly true for large space structures lss in this paper an optimization method based on the optimality criterion approach is presented for structures with geometric nonlinear behavior in the case of a structure optimized with constraints on linear stability the optimum structure can have more than one critical buckling mode this design tends to become im perfection sensitive and a small deviation in the geometry of the structure can reduce its load carrying capacity sub stantially the imperfection sensitivity of the optimized structure can be reduced by designing the structure so that buckling loads associated with the critical buckling modes are not equal see ref 7 a real structure has geometric im perfections and these structures tend to have nonlinear

quantum transport on two dimensional regular graphs we study the quantum mechanical transport on two dimensional graphs by means of continuous time quantum walks and analyse the effect of different boundary conditions bcs for periodic bcs in both directions i e for tori the problem can be treated in a large measure analytically some of these results carry over to graphs which obey open boundary conditions obcs such as cylinders or rectangles under obcs the long time transition probabilities lps also display asymmetries for certain graphs as a function of their particular sizes interestingly these effects do not show up in the marginal distributions obtained by summing the lps along one direction

optimization of large scale truss structures using sparse sand formulations sparsity features of simultaneous analysis and design sand formulations are studied and exploited for optimization of large scale truss structures three formulations are described and implemented with an existing analysis code sand formulations have large number of variables however gradients of the functions and hessian of the lagrangian are quite sparsely populated therefore this structure of the problem is exploited and an optimization algorithm with sparse matrix capability is used to solve large scale problems an existing analysis software is integrated with an optimizer based on a sparse sequential quadratic programming sqp algorithm to solve sample problems the formulations and algorithms work quite well for the sample problems and their performances are compared and discussed for all the cases considered the sand formulations out perform the conventional formulation except one case further research is suggested to fully study and utilize sparse features of the alternative sand formulations and to develop more efficient sparse solvers for large scale and more complex applications

an algorithm for optimization of non linear shell structures an algorithm for optimal design of non linear shell structures is presented the algorithm uses numerical optimization techniques and nonlinear finite element analysis to find a minimum weight structure subject to equilibrium conditions stability constraints and displacement constraints a barrier transformation is used to treat an apparent non smoothness arising from posing the stability constraints in terms of the eigenvalues of the hessian of the potential energy of the structure a sequential quadratic programming strategy is used to solve the resulting non linear optimization problem matrix sparsity in the constraint jacobian is exploited because of the large number of variables the usefulness of the proposed algorithm is demonstrated by minimizing the weight of a number of stiffened thin shell structures

an integrated approach to the synthesis of geometrically non linear structures an integrated approach to the minimum weight design of geometrically non linear three dimensional truss structures with geometric imperfections subject to inequality constraints on static displacements stresses local buckling and cross sectional areas is investigated the integrated structural synthesis problem involves design and response quantities as independent variables and equilibrium equations describing the finite element model as equality constraints the non linear structural analysis and the optimization are thus merged together into a single process a computer program developed to compute the contraint values and analytical gradients is coupled with a generalized reduced gradient algorithm to solve the integrated problem numerical results for a geometrically non linear shallow dome example problem are presented for various types of imperfections furthermore it is found that the algorithm is capable of detecting and guarding against system as well as element elastic instability using equilibrium information only that is without imposing system and local buckling inequality constraints

large scale optimization of eigenvalues optimization problems involving eigenvalues arise in many applications let x be a vector of real parameters and let a x be a continuously differentiable symmetric matrix function of x we consi

quantum walks and trapping on regular hyperbranched fractals the present work studies the behaviour of continuous time quantum walks on regular hyperbranched fractals whose centre is a trap we focus on the variations of the eigenvalue spectrum of the transfer operator by tuning the trap strength from zero to infinity we show that the degenerate eigenvalues are independent from the trap strength and can be obtained analytically due to this the mean survival probability is just in the intermediate range affected by the trap strength moreover because of the presence of real eigenvalues the asymptotical probability of being outside the trap is not zero

an interior point method for minimizing the maximum eigenvalue of a linear combination of matrices we consider the problem of finding lambda opt mathop inf limits x in r m lambda max a 0 sum limits i 1 m x i a i 1 and an optimal solution xopt if it exists here the a i are given symmetric matrices in ir n n for 0 i m and max a is the largest eigenvalue of a matrix a problem 1 can be rewritten as a convex differentiable problem with a positive definite constraint positive definiteness can easily be verified numerically via cholesky decomposition moreover the cone of positive definite matrices a is characterized by the domain of the smooth convex barrier function log det a

alternative formulations for structural optimization an evaluation by using trusses the concept of simultaneous analysis and design sand is revisited with two objectives in mind 1 to study and evaluate three alternative formulations for structural optimization using trusses as examples and 2 to implement the formulations with a structural analysis program and study their implementation aspects the idea is to gain insights for use of the alternative formulations for structural optimization three alternative formulations are defined using displacements and forces or stresses as optimization variables all of the problem functions in the formulations become explicit in terms of the variables gradients of the functions can be evaluated more easily compared to the conventional approach where special design sensitivity analysis methods are needed existing analysis software is integrated with an optimizer based on a sparse sequential quadratic programming method to solve examples with known solutions with the sand type formulations only the pre and postprocessing capabilities of the analysis software are used to evaluate the problem functions however the conventional formulation also needs the equation solving capabilities for analysis as well as design sensitivity analysis performance of the formulations is evaluated with extensive numerical experiments and their advantages and disadvantages are discussed based on the present research it is concluded that the alternative sand formulations are more efficient compared to the conventional approach and have potential for further development for practical applications particularly the formulations that do not require calculation of the global stiffness matrix

optimal control of two and three dimensional incompressible navier stokes flows the focus of this work is on the development of large scale numerical optimization methods for optimal control of steady incompressible navier stokes flows the control is affected by the suction or injection of fluid on portions of the boundary and the objective function represents the rate at which energy is dissipated in the fluid we develop reduced hessian sequential quadratic programming methods that avoid converging the flow equations at each iteration both quasi newton and newton variants are developed and compared to the approach of eliminating the flow equations and variables which is effectively the generalized reduced gradient method optimal control problems are solved for two dimensional flow around a cylinder and three dimensional flow around a sphere the examples demonstrate at least an order of magnitude reduction in time taken allowing the optimal solution of flow control problems in as little as half an hour on a desktop workstation

coherent dynamics on hierarchical systems abstract we study the coherent transport modeled by continuous time quantum walks focussing on hierarchical structures for these we use husimi cacti lattices dual to the dendrimers we find that the transport depends strongly on the initial site of the excitation for systems of sizes n 21 we find that processes which start at central sites are nearly recurrent furthermore we compare the classical limiting probability distribution to the long time average of the quantum mechanical transition probability which shows characteristic patterns we succeed in finding a good lower bound for the space average of the quantum mechanical probability to be still or again at the initial site

mixed finite element based fully conservative methods for simulating wormhole propagation abstract wormhole propagation during reactive dissolution of carbonates plays a very important role in the product enhancement of oil and gas reservoir because of high velocity and nonuniform porosity the darcy forchheimer model is applicable for this problem instead of conventional darcy framework we develop a mixed finite element scheme for numerical simulation of this problem in which mixed finite element methods are used not only for the darcy forchheimer flow equations but also for the solute transport equation by introducing an auxiliary flux variable to guarantee full mass conservation in theoretical analysis aspects based on the cut off operator of solute concentration we construct an analytical function to control and handle the change of porosity with time we treat the auxiliary flux variable as a function of velocity and establish its properties we employ the coupled analysis approach to deal with the fully coupling relation of multivariables from this the stability analysis and a priori error estimates for velocity pressure concentration and porosity are established in different norms numerical results are also given to verify theoretical analysis and effectiveness of the proposed scheme

continuous time quantum walks on nonorientable surfaces analytical solutions for mobius strips and klein bottles in this paper we present an extensive analytical study of continuous time quantum walks ctqws occurring on two dimensional lattices under various boundary conditions focusing on the m n lattice wrapped on mobius strips and klein bottles which are featured by the twisted boundary conditions we find that the eigenvalue spectra and transport efficiency both quantum mechanical and classical for the two structures show comparable results with those for other well known two dimensional lattices including rectangles cylinders and tori we also demonstrate that the behaviors of ctqws depend on the initial node of the excitation and the network size both on short and long timescales in addition we discover the asymmetric behaviors of limiting probabilities for mobius strips and klein bottles which are quite different from each other and are also compared to those discovered in other two dimensional networks our work provides a comprehensive understanding of recent results about ctqws on two dimensional lattices and sheds light on quantum dynamics on lattices especially those with different boundary conditions

sparse approach to simultaneous analysis and design of geometricallynonlinear structures this method to increase the efficiency of the opimization process for nonlinear structures considers the equilibrium equations as equality constraints of the nonlinear mathematical programming problem

integrated nonlinear structural analysis and design proposition d une approche integree de l optimisation de structures mecaniques necessitant une analyse non lineaire le processus d optimisation part d une reponse linearisee de la structure les non linearites etant introduites au fur et a mesure de la convergence verification de la reduction du cout de l analyse par cette methode traitement de deux exemples de structure en treillis