optimal order preconditioners for the morse ingard equations abstract the morse ingard equations of thermoacoustics morse and ingard 1986 are a system of coupled time harmonic equations for the temperature and pressure of an excited gas they form a critical aspect of modeling trace gas sensors in this paper we analyze a reformulation of the system that has a weaker coupling between the equations than the original form we give a garding type inequality for the system that leads to optimal order asymptotic finite element error estimates we also develop preconditioners for the coupled system these are derived by writing the system as a 2 2 block system with pressure and temperature unknowns segregated into separate blocks and then using either the block diagonal or block lower triangular part of this matrix as a preconditioner consequently the preconditioner requires inverting smaller helmholtz like systems individually for the pressure and temperature rigorous eigenvalue bounds are given for the preconditioned system and these are supported by numerical experiments

exactly soluble random field ising models in one dimension the authors solve exactly the one dimensional random field ising model for two classes of magnetic field distributions symmetric exponential model i and non symmetric exponential model ii for both models expressions for the free energy at all finite temperatures are presented the low temperature region is examined in more detail they obtain the zero temperature energy and entropy in closed form it is shown that the free energy of both models has an expansion in integer powers of temperature model i has a non vanishing zero point entropy for all values of the parameters as soon as randomness is diluted in model ii the zero point entropy is zero except for a discrete sequence of values of one parameter in some cases the zero temperature magnetisation is positive whereas the average magnetic field is negative the magnetisation may also change sign as a function of temperature

allison mixture and the two envelope problem in the present study we have investigated the allison mixture a variant of the parrondo s games where random mixing of two random sequences creates autocorrelation we have obtained the autocorrelation function and mutual entropy of two elements our analysis shows that the mutual information is nonzero even if two distributions have identical average values we have also considered the two envelope problem and solved for its exact probability distribution

applying gmres to the helmholtz equation with shifted laplacian preconditioning what is the largest shift for which wavenumber independent convergence is guaranteed there has been much recent research on preconditioning discretisations of the helmholtz operator delta k 2 k2 subject to suitable boundary conditions using a discrete version of the so called shifted laplacian delta k 2 mathrm i varepsilon k2 i for some varepsilon 0 0 this is motivated by the fact that as varepsilon increases the shifted problem becomes easier to solve iteratively despite many numerical investigations there has been no rigorous analysis of how to chose the shift in this paper we focus on the question of how large varepsilon can be so that the shifted problem provides a preconditioner that leads to k k independent convergence of gmres and our main result is a sufficient condition on varepsilon for this property to hold this result holds for finite element discretisations of both the interior impedance problem and the sound soft scattering problem with the radiation condition in the latter problem imposed as a far field impedance boundary condition note that we do not address the important question of how large varepsilon should be so that the preconditioner can easily be inverted by standard iterative methods

truncation and reset process on the dynamics of parrondo s games the counter intuitive feature of parrondo s games is illustrated on various dynamical systems combined from different deterministic and stochastic subsystems the concept of truncation and reset process is introduced which provides a transparent perspective to understand the underlying mechanism of this class of dynamics including the transport of flashing ratchets and clarifies the puzzlement why random switching between two games can generate reversal dynamics as periodical switching does

on implementing a primal dual interior point method for conic quadratic optimization based on the work of the nesterov and todd on self scaled cones an implementation of a primal dual interior point method for solving large scale sparse conic quadratic optimization problems is presented the main features of the implementation are it is based on a homogeneous and self dual model it handles rotated quadratic cones directly it employs a mehrotra type predictor corrector extension and sparse linear algebra to improve the computational efficiency finally the implementation exploits fixed variables which naturally occurs in many conic quadratic optimization problems this is a novel feature for our implementation computational results are also presented to document that the implementation can solve very large problems robustly and efficiently

finite element approximation and preconditioners for a coupled thermal acoustic model we consider a time harmonic mathematical model for a coupled thermal acoustic model we demonstrate coercivity of the pde system and hence well posedness and optimal error estimates for standard galerkin methods the large scale and ill conditioning of the discrete system motivates the study of preconditioners three block preconditioners are studied the first two applying block jacobi and block gauss seidel approaches to our problem give provably mesh independent spectral bounds the third preconditioner based on problem specific physical reasoning does not have this property however on moderate sized meshes it considerably outperforms the existing mesh techniques numerical experiments in two and three dimensions confirm the theoretical results

evolution of a fluctuating population in a randomly switching environment environment plays a fundamental role in the competition for resources and hence in the evolution of populations here we study a well mixed finite population consisting of two strains competing for the limited resources provided by an environment that randomly switches between states of abundance and scarcity assuming that one strain grows slightly faster than the other we consider two scenarios one of pure resource competition and one in which one strain provides a public good and investigate how environmental randomness external noise coupled to demographic internal noise determines the population s fixation properties and size distribution by analytical means and simulations we show that these coupled sources of noise can significantly enhance the fixation probability of the slower growing species we also show that the population size distribution can be unimodal bimodal or multimodal and undergoes noise induced transitions between these regimes when the rate of switching matches the population s growth rate

an upper bound limit analysis of mindlin plates using cs dsg3 method and second order cone programming the paper presents a numerical procedure for kinematic limit analysis of mindlin plate governed by von mises criterion the cell based smoothed discrete shear gap method cs dsg3 is combined with a second order cone optimization programming socp for determining the upper bound limit load of the mindlin plates the limit analysis problem of mindlin plates is formulated by minimizing the dissipation power subjected to a set of constraints of boundary conditions and unitary external work this minimization problem is then transformed into an explicit form suitable for the solution using the socp the numerical results of some benchmark problems show that the proposal procedure can provide the reliable upper bound collapse multipliers for the mindlin plates cs dsg3 is combined with socp for determining upper bound limit load of mindlin plates limit analysis problem is transformed into an explicit form suitable for solution using socp and cs dsg3 numerical results show that cs dsg3 is free of shear locking and can provide reliable upper bound collapse multipliers for mindlin plates

computation of collapse states with von mises type yield condition a new computational approach to the problem of limit analysis with quadratic yield condition is developed and tested the problem is solved with the exact convex yield condition and the general case of unbounded yield set corresponding to unrestricted hydrostatic pressure is treated the solution method simultaneously approximates the collapse fields for stresses and flow the approach consists of two separate steps first the continuous problem is discretized by the finite element method into a finite dimensional optimization problem which turns out to be of a very specific form then this problem is solved by a suitable optimization method this way it is not necessary to be an expert in optimization in order to solve collapse problems and we can take advantage of the rapid development in optimization methods for large sparse problems without changing the discretization program the efficiency and accuracy of the method for large problems is demonstrated by solving a classical problem in the plane strain model approximately 90000 finite element nodes with 3 stress components and 2 velocity components at each node in two space dimensions this may be overkill but it shows that we are able to solve problems in three space dimensions

lyapunov exponents one dimensional anderson localization and products of random matrices the concept of lyapunov exponent has long occupied a central place in the theory of anderson localisation its interest in this particular context is that it provides a reasonable measure of the localisation length the lyapunov exponent also features prominently in the theory of products of random matrices pioneered by furstenberg after a brief historical survey we describe some recent work that exploits the close connections between these topics we review the known solvable cases of disordered quantum mechanics involving random point scatterers and discuss a new solvable case finally we point out some limitations of the lyapunov exponent as a means of studying localisation properties

intrinsic noise in systems with switching environments we study individual based dynamics in finite populations subject to randomly switching environmental conditions these are inspired by models in which genes transition between on and off states regulating underlying protein dynamics similarly switches between environmental states are relevant in bacterial populations and in models of epidemic spread existing piecewise deterministic markov process approaches focus on the deterministic limit of the population dynamics while retaining the randomness of the switching here we go beyond this approximation and explicitly include effects of intrinsic stochasticity at the level of the linear noise approximation specifically we derive the stationary distributions of a number of model systems in good agreement with simulations this improves existing approaches which are limited to the regimes of fast and slow switching

the lyapunov exponent of products of random 2 2 matrices close to the identity we study products of arbitrary random real 2 2 matrices that are close to the identity matrix using the iwasawa decomposition of sl 2 we identify a continuum regime where the mean values and the covariances of the three iwasawa parameters are simultaneously small in this regime the lyapunov exponent of the product is shown to assume a scaling form in the general case the corresponding scaling function is expressed in terms of gauss hypergeometric function a number of particular cases are also considered where the scaling function of the lyapunov exponent involves other special functions airy bessel whittaker elliptic the general solution thus obtained allows us among other things to recover in a unified framework many results known previously from exactly solvable models of one dimensional disordered systems

a general non linear optimization algorithm for lower bound limit analysis the non linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided the algorithm is an interior point method and is completely general in the sense that no particular finite element discretization or yield criterion is required as with interior point methods for linear programming the number of iterations is affected only little by the problem size some practical implementation issues are discussed with reference to the special structure of the common lower bound load optimization problem and finally the efficiency and accuracy of the method is demonstrated by means of examples of plate and slab structures obeying different non linear yield criteria copyright 2002 john wiley sons ltd

parrondo effect in quantum coin toss simulations game a game b game c parrondo s games follow this basic structure where a and b are losing games and c is a winning game a phenomenon called parrondo s paradox these games can take on a wider class of definitions and exhibit these paradoxical results in this paper we show three paradoxical cases i the successive tossing of a single fair quantum coin gives a biased result a previously known result ii the random tossing of two quantum coins each with successive biased expectations gives an average random walk position of approximately zero iii the sequential periodic tossing of two quantum coins each with successive negative biased expectations gives an average random walk with positive expectation using these results we then propose a protocol for identifying and classifying quantum operations that span the same hilbert space for a two level quantum system

a projected newton algorithm for the dual convex program of elastoplasticity summary in this paper we study a dual optimization problem that arises when taking a mathematical programming approach to incremental state update in nonlinear problems the mathematical programming approach stems from energy based descriptions of constitutive models we describe a projected newton algorithm to solve the dual optimization problem this algorithm requires solution of an unconstrained optimization problem at the integration point level rather than a constrained one as carried out by classical return mapping schemes especially implementation of multi surface plasticity models is no more involved than that of single surface models we explore characteristics and performance of the projected newton algorithm through numerical examples insights gained from such a further exploration of mathematical programming algorithms are likely to aid in development of successive convex programming approaches to geometric nonlinear and other non convex problems such as non associated flow models copyright 2014 john wiley sons ltd

semianalytical solution of the random product problem of matrices and discrete time random evolution we consider the product of a large number of matrices chosen randomly with some correlation as a or b we introduce an exact functional equation whose solution gives the limiting distribution and the lyapunov exponent for the product of large number of matrices thus we suggest new semianalytical method to solve the random product problem of correlated matrices the method can be easily generalized to high order matrices as we deal with a larger systems of functional equations we have provided a known numerical algorithm for the solution of the matrix product problem we have also applied our method for a solution of discrete time random evolution our functional equation method provides exact transition point

a stopping criterion for the conjugate gradient algorithm in a finite element method framework the conjugate gradient method has always been successfully used in solving the symmetric and positive definite systems obtained by the finite element approximation of self adjoint elliptic partial differential equations taking into account recent results 13 19 20 22 which make it possible to approximate the energy norm of the error during the conjugate gradient iterative process we adapt the stopping criterion introduced in 3 moreover we show that the use of efficient preconditioners does not require to change the energy norm used by the stopping criterion finally we present the results of several numerical tests that experimentally validate the effectiveness of our stopping criterion

a weighted least squares finite element method for elliptic problems with degenerate and singular coefficients we consider second order elliptic partial differential equations with coefficients that are singular or degenerate at an interior point of the domain this paper presents formulation and analysis of a novel weighted norm least squares finite element method for this class of problems we propose a weighting scheme that eliminates the pollution effect and recovers optimal convergence rates theoretical results are carried out in appropriately weighted sobolev spaces and include ellipticity bounds on the weighted homogeneous least squares functional regularity bounds on the elliptic operator and error estimates numerical experiments confirm the predicted error bounds

limit analysis of plates and slabs using a meshless equilibrium formulation a meshless element free galerkin efg equilibrium formulation is proposed to compute the limit loads which can be sustained by plates and slabs in the formulation pure moment fields are approximated using a moving least squares technique which means that the resulting fields are smooth over the entire problem domain there is therefore no need to enforce continuity conditions at interfaces within the problem domain which would be a key part of a comparable finite element formulation the collocation method is used to enforce the strong form of the equilibrium equations and a stabilized conforming nodal integration scheme is introduced to eliminate numerical instability problems the combination of the collocation method and the smoothing technique means that equilibrium only needs to be enforced at the nodes and stable and accurate solutions can be obtained with minimal computational effort the von mises and nielsen yield criteria which are used in the analysis of plates and slabs respectively are enforced by introducing second order cone constraints ensuring that the resulting optimization problem can be solved using efficient interior point solvers finally the efficacy of the procedure is demonstrated by applying it to various benchmark plate and slab problems

application of a gpu accelerated hybrid preconditioned conjugate gradient approach for large 3d problems in computational geomechanics this paper presents a hybrid preconditioning technique for conjugate gradient method and discusses its parallel implementation on graphic processing unit gpu for solving large sparse linear systems arising from application of interior point methods to conic optimization problems in the context of nonlinear finite element limit analysis fela for computational geomechanics for large 3d problems the use of direct solvers in general becomes prohibitively expensive due to exponentially growing memory requirements and computational time besides the so called saddle point systems resulting from use of optimization framework is not an exemption on the other hand although preconditioned iterative methods have moderate storage requirements and therefore can be applied to much larger problems than direct methods they usually exhibit high number of iterations to reach convergence in present paper we show that this problem can be effectively tackled using the proposed hybrid preconditioner along with an elaborate implementation on gpu furthermore numerical results verify the robustness and efficiency of the proposed technique

cooperative quantum parrondo s games abstract coordination and cooperation are among the most important issues of game theory recently the attention turned to game theory on graphs and social networks encouraged by interesting results obtained in quantum evolutionary game analysis we study cooperative parrondo s games in a quantum setup the game is modeled using multidimensional quantum random walks with biased coins we use the ghz and w entangled states as the initial state of the coins our analysis shows that an apparent paradox in cooperative quantum games and some interesting phenomena can be observed

occurrence of complementary processes in parrondo s paradox abstract parrondo s paradox involves two losing processes producing a winning outcome we analyze the paradox with an original and novel method in which we start with one process and seek to construct a complementary process to achieve the paradox we then derive a general condition for the classical parrondo game to have a complementary process numerical simulation predicts that approximately two thirds of such losing games satisfy the required condition this suggests the common occurrence of the paradox indicative of many potentially undiscovered applications in real life scenarios involving stochastic processes

the influence of the linearisation of the yield surface on the load bearing capacity of reinforced concrete slabs this paper will demonstrate that the degree of linearisation of the yield surface has a major impact on the bearing capacity when the lower bound theorem of ideal plasticity for reinforced concrete slabs combined with linear mathematical programming methods are applied the finite element descretization is applied and it is shown that the influence of a refinement of the yield surface linearisation may be more important than the refinement of the geometrical mesh

ellipsoidal load domain shakedown analysis with von mises yield criterion a robust optimization approach summary the static formulation of elastic shakedown analysis based upon melan s lower bound theorem can essentially be viewed as a robust optimization problem this paper discusses an advantage that is enjoyed by taking this perspective specifically we assume the von mises yield criterion and an ellipsoidal load domain in this setting the shakedown analysis problem which is viewed as robust second order cone programming can be recast as semidefinite programming copyright 2016 john wiley sons ltd

limit analysis of plates using the efg method and second order cone programming the meshless element free galerkin efg method is extended to allow computation of the limit load of plates a kinematic formulation that involves approximating the displacement field using the moving least squares technique is developed only one displacement variable is required for each efg node ensuring that the total number of variables in the resulting optimization problem is kept to a minimum with far fewer variables being required compared with finite element formulations using compatible elements a stabilized conforming nodal integration scheme is extended to plastic plate bending problems the evaluation of integrals at nodal points using curvature smoothing stabilization both keeps the size of the optimization problem small and also results in stable and accurate solutions difficulties imposing essential boundary conditions are overcome by enforcing displacements at the nodes directly the formulation can be expressed as the problem of minimizing a sum of euclidean norms subject to a set of equality constraints this non smooth minimization problem can be transformed into a form suitable for solution using second order cone programming the procedure is applied to several benchmark beam and plate problems and is found in practice to generate good upper bound solutions for benchmark problems

from potential theory to matrix iterations in six steps the theory of the convergence of krylov subspace iterations for linear systems of equations conjugate gradients biconjugate gradients gmres qmr bi cgstab and so on is reviewed for a computation of this kind an estimated asymptotic convergence factor rho le 1 can be derived by solving a problem of potential theory or conformal mapping six approximations are involved in relating the actual computation to this scalar estimate these six approximations are discussed in a systematic way and illustrated by a sequence of examples computed with tools of numerical conformal mapping and semidefinite programming

global 2d digital image correlation for motion estimation in a finite element framework a variational formulation and a regularized pyramidal multi grid implementation in this study the inverse problem of reconstructing the in plane 2d displacements of a monitored surface through a sequence of two dimensional digital images severely ill posed in hadamard s sense is deeply investigated a novel variational formulation is presented for the continuum 2d digital image correlation problem and critical issues such as semi coercivity and solution multiplicity are discussed by functional analysis tools in the framework of a galerkin finite element discretization of the displacement field a robust implementation for 2d digital image correlation is outlined aiming to attenuate the spurious oscillations which corrupt the deformation scenario especially when very fine meshes are adopted recourse is made to a hierarchical family of grids linked by suitable restriction and prolongation operators and defined over an image pyramid multi grid cycles are performed ascending and descending along the pyramid with only one newton iteration per level irrespective of the tolerance satisfaction as if the problem were linear at each level the conventional least square matching functional is herein enriched by a tychonoff regularization provision preserving the solution against an unstable response the algorithm is assessed on the basis of both synthetic and truly experimental image pairs copyright 2013 john wiley sons ltd

convergence analysis of a multigrid method for convection diffusion equations this paper is concerned with the convergence analysis of robust multigrid methods for convection diffusion problems we consider a finite difference discretization of a 2d model convection diffusion problem with constant coefficients and dirichlet boundary conditions for the approximate solution of this discrete problem a multigrid method based on semicoarsening matrix dependent prolongation and restriction and line smoothers is applied for a multigrid w cycle we prove an upper bound for the contraction number in the euclidean norm which is smaller than one and independent of the mesh size and the diffusion convection ratio for the contraction number of a multigrid v cycle a bound is proved which is uniform for a class of convection dominated problems the analysis is based on linear algebra arguments only

quantum parrondo s games parrondo s paradox arises when two losing games are combined to produce a winning one a history dependent quantum parrondo game is studied where the rotation operators that represent the toss of a classical biased coin are replaced by general su 2 operators to transform the game into the quantum domain in the initial state a superposition of qubits can be used to couple the games and produce interference leading to quite different payoffs to those in the classical case

exact probability distribution functions for parrondo s games we study the discrete time dynamics of brownian ratchet models and parrondo s games using the fourier transform we calculate the exact probability distribution functions for both the capital dependent and history dependent parrondo s games in certain cases we find strong oscillations near the maximum of the probability distribution with two limiting distributions for odd and even number of rounds of the game indications of such oscillations first appeared in the analysis of real financial data but now we have found this phenomenon in model systems and a theoretical understanding of the phenomenon the method of our work can be applied to brownian ratchets molecular motors and portfolio optimization

an algebraic multigrid method for linear elasticity we present an algebraic multigrid amg method for the efficient solution of linear block systems stemming from a discretization of a system of partial differential equations pdes it generalizes the classical amg approach for scalar problems to systems of pdes in a natural blockwise fashion we apply this approach to linear elasticity and show that the block interpolation described in this paper reproduces the rigid body modes i e the kernel elements of the discrete linear elasticity operator it is well known from geometric multigrid methods that this reproduction of the kernel elements is an essential property to obtain convergence rates which are independent of the problem size we furthermore present results of various numerical experiments in two and three dimensions they confirm that the method is robust with respect to variations of the poisson ratio nu we obtain rates rho 0 4 for nu 0 4 these measured rates clearly show that the method provides fast convergence for a large variety of discretized elasticity problems

quantum models of parrondo s games abstract a parrondo s paradox is an effect where two losing games when combined can produce a net winning result we provide a short introduction to quantum versions of parrondo s games and review the current status of the work

parrondo games as lattice gas automata parrondo games are coin flipping games with the surprising property that alternating plays of two losing games can produce a winning game we show that this phenomenon can be modelled by probabilistic lattice gas automata furthermore motivated by the recent introduction of quantum coin flipping games we show that quantum lattice gas automata provide an interesting definition for quantum parrondo games

from functional analysis to iterative methods we examine condition numbers preconditioners and iterative methods for finite element discretizations of coercive pdes in the context of the fundamental solvability result the lax milgram lemma working in this hilbert space context is justified because finite element operators are restrictions of infinite dimensional hilbert space operators to finite dimensional subspaces moreover useful insight is gained as to the relationship between hilbert space and matrix condition numbers and translating hilbert space fixed point iterations into matrix computations provides new ways of motivating and explaining some classic iteration schemes in this framework the simplest preconditioner for an operator from a hilbert space into its dual is the riesz isomorphism simple analysis gives spectral bounds and iteration counts bounded independent of the finite element subspaces chosen moreover the abstraction allows us to consider not only riesz map preconditioning for convection diffusion equations in h 1 but also operators on other hilbert spaces such as planar elasticity in left h 1 right 2

robust preconditioning estimates for convection dominated elliptic problems via a streamline poincare friedrichs inequality this paper is devoted to the streamline diffusion finite element method combined with equivalent preconditioning for solving convection dominated elliptic problems the preconditioner is obtained from the streamline diffusion inner product it is proved that the obtained convergence is robust i e bounded independently of the perturbation parameter varepsilon for proper convection vector fields the key to the estimates is an improved streamline poincare friedrichs inequality

a note on upper bound formulations in limit analysis summary in this paper we study some recent formulations for the computation of upper bounds in limit analysis we show that a previous formulation presented by the authors does not guarantee the strictness of the upper bound nor does it provide a velocity field that satisfies the normality rule everywhere we show that these deficiencies are related to the quadrature employed for the evaluation of the dissipation power we derive a formulation that furnishes a strict upper bound of the load factor which in fact coincides with a formulation reported in the literature from the analysis of these formulations we propose a post process which consists in computing exactly the dissipation power for the optimum upper bound velocity field this post process may further reduce the strict upper bound of the load factor in particular situations finally we also determine the quadratures that must be used in the elemental and edge gap contributions so that they are always positive and their addition equals the global bound gap copyright 2012 john wiley sons ltd

an interior point algorithm for elastoplasticity the problem of small deformation rate independent elastoplasticity is treated using convex programming theory and algorithms a finite step variational formulation is first derived after which the relevant potential is discretized in space and subsequently viewed as the lagrangian associated with a convex mathematical program next an algorithm based on the classical primal dual interior point method is developed several key modifications to the conventional implementation of this algorithm are made to fully exploit the nature of the common elastoplastic boundary value problem the resulting method is compared to state of the art elastoplastic procedures for which both similarities and differences are found finally a number of examples are solved demonstrating the capabilities of the algorithm when applied to standard perfect plasticity hardening multisurface plasticity and problems involving softening copyright 2006 john wiley sons ltd

discrete time ratchets the fokker planck equation and parrondo s paradox parrondo s games manifest the apparent paradox where losing strategies can be combined to win and have generated significant multidisciplinary interest in the literature here we review two recent approaches based on the fokker planck equation that rigorously establish the connection between parrondo s games and a physical model known as the flashing brownian ratchet this gives rise to a new set of parrondo s games of which the original games are a special case for the first time we perform a complete analysis of the new games via a discrete time markov chain analysis producing winning rate equations and an exploration of the parameter space where the paradoxical behaviour occurs

solving semidefinite quadratic linear programs using sdpt3 this paper discusses computational experiments with linear optimization problems involving semidefinite quadratic and linear cone constraints sqlps many test problems of this type are solved using a new release of sdpt3 a matlab implementation of infeasible primal dual path following algorithms the software developed by the authors uses mehrotra type predictor corrector variants of interior point methods and two types of search directions the hkm and nt directions a discussion of implementation details is provided and computational results on problems from the sdplib and dimacs challenge collections are reported

numerical solution of a functional equation on a circle in this article two numerical methods are analyzed and applied to compute an invariant closed curve for a particular class of maps a second order scheme based on linear interpolation and a scheme based on interpolation by cubic splines in suitable coordinates the invariant curve is determined by the solution of a functional equation on a circle a linearized version of this functional equation is studied in detail stability of the schemes is discussed and error estimates are derived depending on the smoothness of the solution roughly speaking the analysis predicts superior behavior of the spline scheme when the solution is sufficiently smooth but a more reliable behavior of the lower order scheme in situations when a smooth solution cannot be expected this is confirmed in numerical examples the analysis of the linear functional equation does not readily generalize to nonlinear equations but the algorithms for the linear equation can be used as a building block for a treatment of nonlinear equati

stopping criteria for iterations in finite element methods this work extends the results of arioli 1 2 on stopping criteria for iterative solution methods for linear finite element problems to the case of nonsymmetric positive definite problems we show that the residual measured in the norm induced by the symmetric part of the inverse of the system matrix is relevant to convergence in a finite element context we then use krylov solvers to provide alternative ways of calculating or estimating this quantity and present numerical experiments which validate our criteria

a robust solver for the finite element approximation of stationary incompressible mhd equations in 3d abstract in this paper we propose a newton krylov solver and a picard krylov solver for finite element discrete problem of stationary incompressible magnetohydrodynamic equations in three dimensions using a mixed finite element method we discretize the velocity and the pressure by h 1 conforming finite elements and discretize the magnetic field by h curl conforming edge elements an efficient preconditioner is proposed to accelerate the convergence of gmres method for solving linearized discrete problems by extensive numerical experiments we demonstrate the robustness of the newton krylov solver for relatively large physical parameters and the optimality with respect to the number of degrees of freedom moreover the numerical experiments show that the newton krylov solver is more robust than the picard krylov solver for large reynolds number

an iterative algorithm for limit analysis with nonlinear yield functions abstract a mathematical programming algorithm is proposed for the general limit analysis problem plastic behavior is described by a set of linear or nonlinear yield functions abstract formulations of limit analysis are first considered and a quasi newton strategy for solving the optimality conditions is then sketched the structure of the problem arising from a finite element discretization is taken into account in order that the algorithm should be able to solve large scale problems

superlinear convergence of krylov subspace methods for self adjoint problems in hilbert space the conjugate gradient and minimum residual methods for self adjoint problems in hilbert space are considered linear and superlinear convergence results with respect to both q and r rates are reviewed new results on ell step q superlinear and r superlinear convergence for the minimum residual method are provided and examples are considered to underscore the relevance of a hilbert space theory

formulation and solution of some plasticity problems as conic programs abstract the application of conic programming to some traditionally difficult plasticity problems is considered convenient standard forms for conic programming of both limit and incremental elastoplastic analysis are given the types of yield criteria that can be treated by conic programming is discussed and it is shown that the three dimensional mohr coulomb criterion can be cast as a set of conic constraints thus facilitating efficient treatment by dedicated algorithms finally the performance of a number of mixed finite elements is evaluated together with a state of the art second order cone programming algorithm

lyapunov exponents noise induced synchronization and parrondo s paradox we show that lyapunov exponents of a stochastic system when computed for a specific realization of the noise process are related to conditional lyapunov exponents in deterministic systems we propose to use the term stochastically induced regularity instead of noise induced synchronization and explain the reason why the nature of stochastically induced regularity is discussed in some instances it is a dynamical analog of parrondo s paradox

exact solution of the hidden markov processes we write a master equation for the distributions related to hidden markov processes hmps and solve it using a functional equation thus the solution of hmps is mapped exactly to the solution of the functional equation for a general case the latter can be solved only numerically we derive an exact expression for the entropy of hmps our expression for the entropy is an alternative to the ones given before by the solution of integral equations the exact solution is possible because actually the model can be considered as a generalized random walk on a one dimensional strip while we give the solution for the two second order matrices our solution can be easily generalized for the l values of the markov process and m values of observables we should be able to solve a system of l functional equations in the space of dimension m 1

field of values analysis of preconditioned iterative methods for nonsymmetric elliptic problems the convergence rate of krylov subspace methods for the solution of nonsymmetric systems of linear equations such as gmres or fom is studied bounds on the convergence rate are presented which are based on the smallest real part of the field of values of the coefficient matrix and of its inverse estimates for these quantities are available during the iteration from the underlying arnoldi process it is shown how these bounds can be used to study the convergence properties in particular the dependence on the mesh size and on the size of the skew symmetric part for preconditioners for finite element discretizations of nonsymmetric elliptic boundary value problems this is illustrated for the hierarchical basis and multilevel preconditioners which constitute popular preconditioning strategies for such problems

an optimal order process for solving finite element equations a k level iterative procedure for solving the algebraic equations which arise from the finite element approximation of elliptic boundary value problems is presented and analyzed the work estimate for this procedure is proportional to the number of unknowns an optimal order result general geometry is permitted for the underlying domain but the shape plays a role in the rate of convergence through elliptic regularity finally a short discussion of the use of this method for parabolic problems is presented

numerical assessment of the macroscopic strength criterion of reinforced soils using semidefinite programming summary the macroscopic strength properties of reinforced soils regarded as periodic composite materials are investigated by means of a fem based formulation of both static and kinematic approaches of yield design applied to the reinforced soil s unit cell because the reinforced soil s individual constituents obey a 3d mohr coulomb strength condition such a numerical problem can be treated through an optimization procedure using semidefinite programming the whole numerical procedure is applied to the derivation of both lower bound and upper bound estimates to the macroscopic yield surface of a soil reinforced either by columnar inclusions stone columns or a double array of trenches cross trench reinforcement the so obtained results highlight the efficiency of the proposed numerical method copyright 2014 john wiley sons ltd

convergence analysis of a multigrid method for a convection dominated model problem the paper presents a convergence analysis of a multigrid solver for a system of linear algebraic equations resulting from the discretization of a convection diffusion problem using a finite element method we consider piecewise linear finite elements in combination with a streamline diffusion stabilization we analyze a multigrid method that is based on canonical intergrid transfer operators a direct discretization approach for the coarse grid operators and a smoother of line jacobi type a robust diffusion and h independent bound for the contraction number of the two grid method and the multigrid w cycle are proved for a special class of convection diffusion problems namely with neumann conditions on the outflow boundary dirichlet conditions on the rest of the boundary and a flow direction that is constant and aligned with gridlines our convergence analysis is based on modified smoothing and approximation properties the arithmetic complexity of one multigrid iteration is optimal up to a logarithmic term

the cascadic multigrid method for elliptic problems the paper deals with certain adaptive multilevel methods at the confluence of nested multigrid methods and iterative methods based on the cascade principle of 10 from the multigrid point of view no correction cycles are needed from the cascade principle view a basic iteration method without any preconditioner is used at successive refinement levels for a prescribed error tolerance on the final level more iterations must be spent on coarser grids in order to allow for less iterations on finer grids a first candidate of such a cascadic multigrid method was the recently suggested cascadic conjugate gradient method of 9 in short ccg method whichused the cg method as basic iteration method on each level in 18 it has been proven that the ccg method is accurate with optimal complexity for elliptic problems in 2d and quasi uniform triangulations the present paper simplifies that theory and extends it to more general basic iteration methods like the traditional multigrid smoothers moreover an adaptive control strategy for the number of iterations on successive refinement levels for possibly highly non uniform grids is worked out on the basis of a posteriori estimates numerical tests confirm the efficiency and robustness of the cascadic multigrid method

a search for quantum coin flipping protocols using optimization techniques coin flipping is a cryptographic task in which two physically separated mistrustful parties wish to generate a fair coin flip by communicating with each other chailloux and kerenidis 2009 designed quantum protocols that guarantee coin flips with near optimal bias away from uniform even when one party deviates arbitrarily from the protocol the probability of any outcome in these protocols is provably at most tfrac 1 sqrt 2 delta 12 for any given delta 0 0 however no explicit description of these protocols is known in fact the smallest bias achieved by known explicit protocols is 1 4 1 4 ambainis 2001 we take a computational optimization approach based mostly on convex optimization to the search for simple and explicit quantum strong coin flipping protocols we present a search algorithm to identify protocols with low bias within a natural class protocols based on bit commitment nayak and shor in phys rev a 67 1 012304 2003 the techniques we develop enable a computational search for protocols given by a mesh over the corresponding parameter space we conduct searches for four round and six round protocols with bias below 0 2499 0 2499 each of varying dimension which include the best known explicit protocol with bias 1 4 1 4 after checking over 10 16 1016 protocols a task which would be infeasible using semidefinite programming alone we conjecture that the smallest achievable bias within the family of protocols we consider is 1 4 1 4

construction of novel stochastic matrices for analysis of parrondo s paradox abstract in parrondo s paradox a winning strategy is formed either by playing two losing games randomly or alternating them periodically the paradox is commonly analyzed using stochastic matrices in this paper we modify the stochastic matrices to allow a more systematic introduction of bias into fair processes while retaining the use of simple matrix operations throughout the analysis

parrondo s paradox and complementary parrondo processes abstract parrondo s paradox has gained a fair amount of attention due to it being counter intuitive given two stochastic processes both of which are losing in nature it is possible to have an overall net increase in capital by periodically or randomly alternating between the two processes in this paper we analyze the paradox with a different approach in which we start with one process and seek to derive its complementary process we will also state the conditions required for this to occur possible applications of our results include the development of future models based on the paradox