adaptive grid generation from harmonic maps on reimannian manifolds abstract in this paper we describe a new method for generation of solution adaptive grids based on harmonic maps on riemannian manifolds the reliability of the method is assured by an existence and uniqueness theorem for one to one maps between multidimensional multiconnected domains we formulate an adaptive riemannian metric consistent with this theorem several examples demonstrating application of the developed procedure are provided

fast sweeping algorithms for a class of hamilton jacobi equations we derive a godunov type numerical flux for the class of strictly convex homogeneous hamiltonians that includes h p q sqrt ap 2 bq 2 2cpq c 2 ab we combine our godunov numerical fluxes with simple gauss seidel type iterations for solving the corresponding hamilton jacobi hj equations the resulting algorithm is fast since it does not require a sorting strategy as found e g in the fast marching method in addition it providesa way to compute solutions to a class of hj equations for which the conventional fast marching method is not applicable our experiments indicate convergence after a few iterations even in rather difficult cases

fast methods for the eikonal and related hamilton jacobi equations on unstructured meshes the fast marching method is a numerical algorithm for solving the eikonal equation on a rectangular orthogonal mesh in o m log m steps where m is the total number of grid points the scheme relies on an upwind finite difference approximation to the gradient and a resulting causality relationship that lends itself to a dijkstra like programming approach in this paper we discuss several extensions to this technique including higher order versions on unstructured meshes in rn and on manifolds and connections to more general static hamilton jacobi equations

finite size scaling properties of the damage distance and dynamical critical exponent for the ising model abstract with the damage spreading method scaling properties of the damage distance on the ising model with heat bath dynamics are studied numerically with the parallel flipping scheme the scaling curves fall on two curves which depend on the odd or even lattice sizes the both scaling curves give the consistent dynamical exponent as z 2 16 0 04 for d 2 and z 2 09 0 05 for d 3 respectively by shifting one of them two curves overlap each other perfectly meanwhile all the scaling curves obtained by single spin flipping processes with different odd or even lattice sizes fall on a single curve from which the consistent dynamical critical exponent with the parallel scheme is obtained z 2 18 0 02 for d 2 and z 2 08 0 04 for d 3

variational barrier method of adaptive grid generation in hyperbolic problems of gas dynamics application of the harmonic mapping using a variational approach to generate moving adaptive grids in the hyperbolic problems of gas dynamics is considered using the example of a three point model of adaptation the possibility to generate an unfolded mesh with strong grid lines condensing in the vicinity of discontinuities of the control monitor function is demonstrated the algorithm of redistributing the boundary nodes is suggested and consists of using constrained minimization of the discrete harmonic functional when constraints define the boundary of the domain in real computations due to mesh adaptation it is possible to reduce the errors caused by shock waves smearing over the cells by many factors of ten modeling of the two dimensional 2 d supersonic gas flow in the channel has shown that the same accuracy on the adaptive grid with the same structure as the quasi uniform mesh can be acheived while requiring less cpu memory by a factor of 25 and less running time by a factor of 50 to 60 computational tests of the steady transonic and supersonic flow over an airfoil demonstrate the ability of the method to control mesh sizes across shocks

a parallel two scale method for eikonal equations numerous applications of eikonal equations prompted the development of many efficient numerical algorithms the heap cell method hcm is a recent serial two scale technique that has been shown to have advantages over other serial state of the art solvers for a wide range of problems a chacon and a vladimirsky siam j sci comput 34 2012 pp a547 a578 this paper presents a parallelization of hcm for a shared memory architecture the numerical experiments in r 3 show that the parallel hcm exhibits good algorithmic behavior and scales well resulting in a very fast and practical solver

a viscosity solutions approach to shape from shading the problem of recovering a lambertian surface from a single two dimensional image may be written as a first order nonlinear equation which presents the disadvantage of having several continuous and even smooth solutions a new approach based on hamilton jacobi bellman equations and viscosity solutions theories enables one to study non uniqueness phenomenon and thus to characterize the surface among the various solutions a consistent and monotone scheme approximating the surface is constructed thanks to the dynamic programming principle and numerical results are presented

fast marching methods for stationary hamilton jacobi equations with axis aligned anisotropy the fast marching method fmm has proved to be a very efficient algorithm for solving the isotropic eikonal equation because it is a minor modification of dijkstra s algorithm for finding the shortest path through a discrete graph fmm is also easy to implement in this paper we describe a new class of hamilton jacobi hj pdes with axis aligned anisotropy which satisfy a causality condition for standard finite difference schemes on orthogonal grids and can hence be solved using the fmm the only modification required to the algorithm is in the local update equation for a node this class of hj pdes has applications in anelliptic wave propagation and robotic path planning and brief examples are included since our class of hj pdes and grids permit asymmetries we also examine some methods of improving the efficiency of the local update that do not require symmetric grids and pdes finally we include explicit update formulas for variations of the eikonal equation that use the manhattan euclidean and infinity norms on orthogonal grids of arbitrary dimension and with variable node spacing

modeling uncertainty in steady state diffusion problems via generalized polynomial chaos abstract we present a generalized polynomial chaos algorithm for the solution of stochastic elliptic partial differential equations subject to uncertain inputs in particular we focus on the solution of the poisson equation with random diffusivity forcing and boundary conditions the stochastic input and solution are represented spectrally by employing the orthogonal polynomial functionals from the askey scheme as a generalization of the original polynomial chaos idea of wiener amer j math 60 1938 897 a galerkin projection in random space is applied to derive the equations in the weak form the resulting set of deterministic equations for each random mode is solved iteratively by a block gauss seidel iteration technique both discrete and continuous random distributions are considered and convergence is verified in model problems and against monte carlo simulations

simple finite element based computation of distance functions in unstructured grids a distance field is a representation of the closest distance from a point to a given surface distance fields are widely used in applications ranging from computer vision physics and computer graphics and have been the subject of research of many authors in the last decade most of the methods for computing distance fields are devoted to cartesian grids while little attention has been paid to unstructured grids finite element methods are well known for their ability to deal with partial differential equations in unstructured grids therefore we propose an extension of the fast marching method for computing a distance field in a finite element context employing the element interpolation to hold the eikonal property 1 a simple algorithm to develop the computations is also presented and its efficiency demonstrated through various unstructured grid examples we observed that the presented algorithm has processing times proportional to the number of mesh nodes

vibrational analysis of structures with stochastic interfaces in the medium frequency range experimental validation on a touch screen abstract this paper proposes a dedicated approach and its experimental validation when dealing with structures including stochastic parameters such as interface parameters in medium frequency vibrations the first ingredient is the use of a dedicated approach the variational theory of complex rays vtcr to solve the medium frequency problem the vtcr which uses two scale shape functions verifying the dynamic equation and the constitutive relation can be viewed as a means of expressing the power balance at the different interfaces between substructures the second ingredient is the use of the polynomial chaos expansion pce to calculate the random response since the only uncertain parameters are those which appear in the interface equations which in this application are the complex connection stiffness parameters this approach leads to very low computation costs this method is validated on a new kind of touch screen the simulated mobilities are compared with experimental ones obtained with a laser vibrometer and a good agreement is founded on a large medium frequency bandwidth

a fast level set method for propagating interfaces a method is introduced to decrease the computational labor of the standard level set method for propagating interfaces the fast approach uses only points close to the curve at every time step we describe this new algorithm and compare its efficiency and accuracy with the standard level set approach

a gradient augmented level set method for unstructured grids we present and test a gradient augmented level set method for unstructured grids which has been designed to allow for easy integration in parallel flow solvers the means to this end is a hermite formulation where the gradient is stored and advected as an independent variable along with the level set function the method uses narrow band storage in conjunction with a fast marching method which is also designed to take advantage of the gradient augmentation we demonstrate through standard passive advection test cases that the proposed method is able to compute interface motion with performance comparable to popular high performing methods on structured grids

maximum entropy approach for modeling random uncertainties in transient elastodynamics a new approach is presented for analyzing random uncertainties in dynamical systems this approach consists of modeling random uncertainties by a nonparametric model allowing transient responses of mechanical systems submitted to impulsive loads to be predicted in the context of linear structural dynamics the information used does not require the description of the local parameters of the mechanical model the probability model is deduced from the use of the entropy optimization principle whose available information is constituted of the algebraic properties related to the generalized mass damping and stiffness matrices which have to be positive definite symmetric matrices and the knowledge of these matrices for the mean reduced matrix model an explicit construction and representation of the probability model have been obtained and are very well suited to algebraic calculus and to monte carlo numerical simulation in order to compute the transient responses of structures submitted to impulsive loads the fundamental properties related to the convergence of the stochastic solution with respect to the dimension of the random reduced matrix model are analyzed finally an example is presented

damage spreading and dynamic stability of kinetic ising models we investigate how the time evolution of different kinetic ising models depends on the initial conditions of the dynamics to this end we consider the simultaneous evolution of two identical systems subjected to the same thermal noise we derive a master equation for the time evolution of a joint probability distribution of the two systems this equation is then solved within an effective field approach by analysing the fixed points of the master equation and their stability we identify regular and chaotic phases

an efficient discontinuous galerkin method on triangular meshes for a pedestrian flow model in this paper we develop a discontinuous galerkin method on triangular meshes to solve the reactive dynamic user equilibrium model for pedestrian flows the pedestrian density in this model is governed by the conservation law in which the flow flux is implicitly dependent on the density through the eikonal equation to solve the eikonal equation efficiently at each time level we use the fast sweeping method two numerical examples are then used to demonstrate the effectiveness of the algorithm copyright 2008 john wiley sons ltd

level set based deformation methods for adaptive grids a new method for generating adaptive moving grids is formulated based on physical quantities level set functions are used to construct the adaptive grids which are solutions of the standard level set evolution equation with the cartesian coordinates as initial values the intersection points of the level sets of the evolving functions form a new grid at each time the velocity vector in the evolution equation is chosen according to a monitor function and is equal to the node velocity a uniform grid is then deformed to a moving grid with desired cell volume distribution at each time the method achieves precise control over the jacobian determinant of the grid mapping as the traditional deformation method does the new method is consistent with the level set approach to dynamic moving interface problems

a variational form of the winslow grid generator a structured grid generator based on a new approximation of dirichlet s functional is developed an unconstrained minimization process guarantees that all quadrilateral grid cells are convex at each iteration numerical results are presented in comparison with those for the original form of the winslow method a generalization to the case of adaptive grids based on harmonic maps between surfaces is considered

equidistribution schemes poisson generators and adaptive grids equidistribution of a weight function over a mesh is the main concept employed in the recent development of adaptive grid schemes this idea is reviewed in this paper and several examples of grids produced using equidistribution are presented the shortcomings of this approach are identified and its usefulness is evaluated next the traditional poisson grid generators are written as nonlinear equidistribution schemes in this form the relationship between the numerical solution of a physical problem the source terms in the grid generation equations and the weight functions in equidistribution schemes are identified examples are given illustrating the case of providing a useful adaptive grid with this approach

evolution implementation and application of level set and fast marching methods for advancing fronts abstract a variety of numerical techniques are available for tracking moving interfaces in this review we concentrate on techniques that result from the link between the partial differential equations that describe moving interfaces and numerical schemes designed for approximating the solutions to hyperbolic conservation laws this link gives rise to computational techniques for tracking moving interfaces in two and three space dimensions under complex speed laws we discuss the evolution of these techniques the fundamental numerical approximations involved implementation details and applications in particular we review some work on three aspects of materials sciences semiconductor process simulations seismic processing and optimal structural topology design

progressive minimal path method for segmentation of 2d and 3d line structures we propose a novel minimal path method for the segmentation of 2d and 3d line structures minimal path methods perform propagation of a wavefront emanating from a start point at a speed derived from image features followed by path extraction using backtracing usually the computation of the speed and the propagation of the wave are two separate steps and point features are used to compute a static speed we introduce a new continuous minimal path method which steers the wave propagation progressively using dynamic speed based on path features we present three instances of our method using an appearance feature of the path a geometric feature based on the curvature of the path and a joint appearance and geometric feature based on the tangent of the wavefront these features have not been used in previous continuous minimal path methods we compute the features dynamically during the wave propagation and also efficiently using a fast numerical scheme and a low dimensional parameter space our method does not suffer from discretization or metrication errors we performed qualitative and quantitative evaluations using 2d and 3d images from different application areas

the two dimensional site diluted ising ferromagnet a damage spreading analysis abstract the quenched site diluted ising ferromagnet on a square lattice for which each site is occupied or empty with probabilities p and 1 p respectively is studied numerically through damage spreading procedures by making use of the glauber dynamics the percolation threshold pc is estimated within the heat bath dynamics the damage spreading temperatures td p for several values of p pc are computed indicating a strong correlation with the corresponding critical temperatures tc p a procedure for estimating the fractal dimensions of clusters of damaged sites at low temperatures is presented as p pc our estimate is very close to 91 48 which is the fractal dimension of the infinite cluster at p pc in two dimensional site percolation whenever possible to compare our results are in good agreement with the best estimates available from other techniques in spite of a modest computational effort

hybrid deterministic statistical analysis of vibro acoustic systems with domain couplings on statistical components abstract recently a hybrid analysis method has been developed in which the various components of a complex vibro acoustic system can be modeled either deterministically or statistically the coupling between these two types of component is effected by using a diffuse field reciprocity relation which relates the cross spectrum of the forces at the boundary of a statistical component to the vibrational energy level of the component in practical applications components may be coupled over a domain rather than just at the component boundaries for example the coupling between a plate and an acoustic volume involves the surface of the plate it is shown in the present work that the reciprocity relation and the hybrid method can be extended to this situation so that for example it is possible to couple a statistical model of a plate to a finite element model of an acoustical cavity or to a statistical acoustical cavity the coupling of statistical acoustical and structural components is not new but rather is done routinely within statistical energy analysis sea this part of the present work demonstrates that the relevant coupling loss factors can be found by using the hybrid method the analysis is illustrated by various numerical examples

dynamical critical exponent for the majority vote model we investigate the dynamical behavior of the isotropic majority vote model on a square lattice using a combination of damage spreading and finite size scaling methods for initial damage d 0 1 2 the dynamical phase diagram exhibits a chaotic frozen phase transition at a critical noise parameter qc 0 0818 0 0002 while for d 0 1 2 the damage does not propagate for any value of the model s parameter 0 q 1 2 from simulations at qc we find that the dynamical critical exponent is z 0 65 0 05

damage spreading in a two dimensional potts ferromagnet in an external field we study using the damage spreading method and within the heat bath dynamics the dynamical behaviour of the square lattice three state potts ferromagnet subjected to an external field in the zero field case we verify that this very simple model presents besides the transition consistent with the equilibrium one a new dynamical chaotic phase with unusual features although the unexpected transition occurs within the error bars at the static ising critical temperature it is in the directed percolation universality class we observe that the application of a uniform magnetic field does not destroy any of the two transitions while the unexpected one is annihilated by a new kind of field which plays the role of a conjugate field to the hamming distance

definition of a high frequency threshold for plates and acoustical spaces an extension of the modal overlap factor is introduced that includes ensemble variations and frequency averaging of plates and acoustic spaces uniformly and normally distributed variations of geometric and material parameters are considered using this modal overlap factor approximate formulas are derived to identify the limit of predictability for the combined case of damping ensemble variation and frequency averaging the extended modal overlap factor is used to define a high frequency threshold for plates and acoustical spaces that depends on system parameters and their variations as well as on damping and the bandwidth of frequency averaging monte carlo simulations are shown to illustrate and validate the results

extended space time finite elements for landslide dynamics summary the paper introduces a methodology for numerical simulation of landslides experiencing considerable deformations and topological changes within an interface capturing approach all interfaces are implicitly described by specifically defined level set functions allowing arbitrarily evolving complex topologies the transient interface evolution is obtained by solving the level set equation driven by the physical velocity field for all three level set functions in a block jacobi approach the three boundary coupled fluid like continua involved are modeled as incompressible governed by a generalized non newtonian material law taking into account capillary pressure at moving fluid fluid interfaces the weighted residual formulation of the level set equations and the fluid equations is discretized with finite elements in space and time using velocity and pressure as unknown variables non smooth solution characteristics are represented by enriched approximations to fluid velocity weak discontinuity and fluid pressure strong discontinuity special attention is given to the construction of enriched approximations for elements containing evolving triple junctions numerical examples of three fluid tank sloshing and air water liquefied soil landslides demonstrate the potential and applicability of the method in geotechnical investigations copyright 2012 john wiley sons ltd

stochastic free vibration of orthotropic plates using generalized polynomial chaos expansion this paper presents the theory and application of the generalized polynomial chaos expansion for the stochastic free vibration of orthotropic plates specifically the stochastic analysis of orthotropic plates under the uncertainties in elasticity moduli is investigated the uncertain moduli eigen frequencies and eigen modes of the plates are represented by truncated polynomial chaos expansions with arbitrary random basis the expansions are substituted in the governing differential equations to calculating the polynomial chaos coefficients of the eigen frequencies and the eigen modes distribution functions of the uncertain moduli are derived from experimental data where the pearson model is used to identify the type of density functions this realization then is employed to construct random orthogonal basis for each uncertain parameter because of available experimental modal analysis data this paper provides a useful practical example on the efficacy of polynomial chaos where the statistical moments and the probability distributions of modal responses are compared with experimental results

adaptive zoning for singular problems in two dimensions abstract winslow s method for the automatic generation of computation meshes is extended to adaptively vary the zone sizes and orthogonality of grid lines in the resulting mesh through simple analysis and numerical examples the adaptive mesh is shown to give significant increases in accuracy in the computation of singular problems

adaptive mesh methods for one and two dimensional hyperbolic conservation laws we develop efficient moving mesh algorithms for one and two dimensional hyperbolic systems of conservation laws the algorithms are formed by two independent parts pde evolution and mesh redistribution the first part can be any appropriate high resolution scheme and the second part is based on an iterative procedure in each iteration meshes are first redistributed by an equidistribution principle and then on the resulting new grids the underlying numerical solutions are updated by a conservative interpolation formula proposed in this work the iteration for the mesh redistribution at a given time step is complete when the meshes governed by a nonlinear equation reach the equilibrium state the main idea of the proposed method is to keep the mass conservation of the underlying numerical solution at each redistribution step in one dimension we can show that the underlying numerical approximation obtained in the mesh redistribution part satisfies the desired tvd property which guarantees that the numerical solution at any time level is tvd provided that the pde solver in the first part satisfies such a property several test problems in one and two dimensions are computed using the proposed moving mesh algorithm the computations demonstrate that our methods are efficient for solving problems with shock discontinuities obtaining the same resolution with a much smaller number of grid points than the uniform mesh approach

conditions of nondegeneracy of three dimensional cells a formula of a volume of cells numerical solutions of partial differential equations in three dimensions often use hexahedral cells composing a computational grid after the grid is constructed it is first of all verified whether the grid is unfolded or not for such a test in this paper conditions of nondegeneracy are found for hexahedral cells which are given by eight corner points and generated by the trilinear map from a unit cube to a region defined by these points the conditions include necessary conditions and two sets of sufficient conditions they are found as conditions of positivity of the jacobian of the trilinear map thus the conditions which guarantee the invertibility of the trilinear map from a unit cube to a hexahedron are given how general the nondegeneracy conditions are is shown by a numerical experiment formulas of the jacobian of the trilinear map are obtained and following from them as a separate result a formula of a volume of a cell is obtained

ordered upwind methods for static hamilton jacobi equations abstract we introduce a family of fast ordered upwind methods for approximating solutions to a wide class of static hamilton jacobi equations with dirichlet boundary conditions standard techniques often rely on iteration to converge to the solution of a discretized version of the partial differential equation our fast methods avoid iteration through a careful use of information about the characteristic directions of the underlying partial differential equation these techniques are of complexity o m log m where m is the total number of points in the domain we consider anisotropic test problems in optimal control seismology and paths on surfaces

identification and prediction of stochastic dynamical systems in a polynomial chaos basis non parametric system identification techniques have been proposed for constructing predictive models of dynamical systems without detailed knowledge of the mechanisms of energy transfer and dissipation in a class of such models multi dimensional chebychev polynomials in the state variables are fitted to the observed dynamical state of the system due to the approximative nature of this non parametric model as well as to various other sources of uncertainty such as measurement errors and non anticipative excitations the parameters of the model exhibit a scatter that is treated here in a probabilistic context the statistics of these coefficients are related to the physical properties of the model being analyzed and are used to endow the model predictions with a probabilistic structure they are also used to obtain a parsimonious characterization of the predictive model while maintaining a desirable level of accuracy the proposed methodology is quite simple and robust

three dimensional elliptic grid generation with fully automatic boundary constraints a new procedure for generating smooth uniformly clustered three dimensional structured elliptic grids is presented here which formulates three dimensional boundary constraints by extending the two dimensional counterpart presented by the author earlier this fully automatic procedure obviates the need for manual specification of decay parameters over the six bounding surfaces of a given volume grid the procedure has been demonstrated here for the mars science laboratory msl geometries such as aeroshell and canopy as well as the inflatable aerodynamic decelerator iad geometry and a 3d analytically defined geometry the new procedure also enables generation of single block grids for such geometries because the automatic boundary constraints permit the decay parameters to evolve as part of the solution to the elliptic grid system of equations these decay parameters are no longer just constants as specified in the conventional approach but functions of generalized coordinate variables over a given bounding surface since these decay functions vary over a given boundary orthogonal grids around any arbitrary simply connected boundary can be clustered automatically without having to break up the boundaries and the corresponding interior or exterior domains into various blocks for grid generation the new boundary constraints are not limited to the simply connected regions only but can also be formulated around multiply connected and isolated regions in the interior the proposed method is superior to other methods of grid generation such as algebraic and hyperbolic techniques in that the grids obtained here are c 2 continuous whereas simple elliptic smoothing of algebraic or hyperbolic grids to enforce c 2 continuity destroys the grid clustering near the boundaries

stochastic reduced order computational model of structures having numerous local elastic modes in low frequency dynamics this paper is devoted to the construction of a stochastic reduced order computational model of structures having numerous local elastic modes in low frequency dynamics the considered structure is characterized by the fact that it exhibits in the low frequency range not only the classical global elastic modes but also numerous local elastic modes which cannot easily be separated from the global elastic modes a new adapted generalized eigenvalue problem is introduced and allows a global vector basis to be constructed for the global displacements space this method requires to decompose the domain of the structure into sub domains such a decomposition is carried out using the fast marching method this global vector basis is then used to construct the reduced order computational model since there are model uncertainties induced by modeling errors in the computational model the nonparametric probabilistic approach of uncertainties is used and implemented in the reduced order computational model the methodology is applied to an automotive vehicle

fast and accurate redistancing by directional optimization a fast and accurate algorithm for the reinitialization of the signed distance function in two and three spatial dimensions is presented the algorithm has computational complexity o n log n for the reinitialization of n grid points the order of accuracy of the reinitialization is demonstrated to depend primarily on the interpolation algorithm used bicubic interpolation is demonstrated to result in fourth order accuracy for smooth interfaces simple numerical examples demonstrating the convergence and computational complexity of the reinitialization algorithm in two and three dimensions are presented as verification of the algorithm

ingredients for a general purpose stochastic finite elements implementation abstract the stochastic finite element method has seen a number of incarnations over the past few years ranging from perturbation based methods and neumann expansion based methods to methods for evaluating bounds on the response variability and more recent functional expansions combined with error minimization techniques of these only the last class of methods provides an explicit expression to the solution of the problem as opposed to evaluating a global norm of this solution and can thus be viewed as a rational extension of concepts developed for the deterministic finite element method the main obstacle in developing a substantial user community of various stochastic finite element methods has been the lack of a general purpose formalism for addressing issues of general engineering interest this paper presents the main ingredients for developing a general purpose version of the spectral stochastic finite element method

damage spreading in random field systems we investigate how a quenched random field influences the damage spreading transition in kinetic ising models to this end we generalize a recent master equation approach and derive an effective field theory for damage spreading in random field systems this theory is applied to the glauber ising model with a bimodal random field distribution we find that the random field influences the spreading transition by two different mechanisms with opposite effects first the random field favours the same particular direction of the spin variable at each site in both systems which reduces the damage second the random field suppresses the magnetization which in turn tends to increase the damage the competition between these two effects leads to a rich behaviour

computational study of fast methods for the eikonal equation a computational study of the fast marching and the fast sweeping methods for the eikonal equation is given it is stressed that both algorithms should be considered as direct as opposed to iterative methods on realistic grids fast sweeping is faster than fast marching for problems with simple geometry for strongly nonuniform problems and or complex geometry the situation may be reversed finally fully second order generalizations of methods of this type for problems with obstacles are proposed and implemented

time evolution of damage in the ising model the time evolution of the damage in the ising model with the heat bath and glauber dynamics has been investigated with the damage spreading method the damage density d t and the average distance r t of damaged sites from the origin have been measured numerically from the simulational data the scaling forms have been established as d t tx r t t1z and d t r t df and the corresponding exponents x z and df have been estimated

a new multi frequency approach based on pade approximants for the treatment of transient dynamics problems with the variational theory of complex rays abstract frequency based methods were set up in order to circumvent the limits of classical finite element methods in fast dynamic simulations due to discretizations in this approach the dynamic loading was shifted in the frequency domain by fft then treated by the variational theory of complex rays and then the time response was reconstructed through an ifft this strategy proved to be very efficient due to the cpu vtcr very low cost however in the case of a large loading spectrum this frequency by frequency approach could seriously degrade the computational performances of the strategy this paper addresses this point by proposing the use of pade approximants in order to limit the number of frequencies at which the response should be calculated pade approximation is applied to the overall vtcr system based on its frequency dependency finally as simulations on a simple academic case and on a civil engineering structure show this method is found to be very efficient for interpolating the frequency response functions of a complex structure this is a key point to preserve the efficiency of the complete vtcr strategy for transient dynamic problems

non equilibrium critical relaxation of the three dimensional ising model abstract the non equilibrium relaxation process at the critical point is studied using monte carlo simulation for the ferromagnetic ising model on a cubic lattice it was observed that the time dependent magnetization decayed following a power law t from the all up initial condition three kinds of single spin flip dynamics were studied for several lattices up to 1536 3 the system size dependences are also studied the value of was estimated to be 0 250 2 this value of leads to the estimation of the dynamical exponent z to be 2 06 2 if we assume z where and denote the critical exponents for spontaneous magnetization and correlation length in equilibrium state respectively and 0 515 the result of the non equilibrium relaxation in the ordered phase is also given

derivatives with respect to metrics and applications subgradient marching algorithm this paper introduces a subgradient descent algorithm to compute a riemannian metric that minimizes an energy involving geodesic distances the heart of the method is the subgradient marching algorithm to compute the derivative of the geodesic distance with respect to the metric the geodesic distance being a concave function of the metric this algorithm computes an element of the subgradient in o n 2 log n operations on a discrete grid of n points it performs a front propagation that computes a subgradient of a discrete geodesic distance we show applications to landscape modeling and to traffic congestion both applications require the maximization of geodesic distances under convex constraints and are solved by subgradient descent computed with our subgradient marching we also show application to the inversion of travel time tomography where the recovered metric is the local minimum of a non convex variational problem involving geodesic distances

a global local probabilistic approach for reduced order modeling adapted to the low and mid frequency structural dynamics abstract the research presented here is devoted to the construction of a probabilistic reduced order computational model adapted to the low and mid frequency structural dynamics the methodology presented here is based on a global local separation of the space of admissible displacements by solving two separated eigenvalue problems in which the kinetic energy is modified this paper presents a general framework for constructing the modified kinetic energy by introducing classes of kinematic reductions the global local separation allows the construction of a probabilistic model of uncertainties for which the fluctuations of the global displacements and the fluctuations of the local displacements can be controlled separately

a model and numerical method in the medium frequency range for vibroacoustic predictions using the theory of structural fuzzy in linear dynamical analysis of complex mechanical systems the structural fuzzy is defined as the set of minor subsystems that are connected to the master structure but are not accessible by classical modeling the notion of master structure is presently extended to others elements such as an external dense compressible fluid strongly coupled with the primary structure for the low frequency lf dynamical analysis the modeling of the structural fuzzy is commonly made with a system of masses if the lf modeling of the structural fuzzy is applied in the medium frequency mf domain there are some large differences between calculations and experiment it is therefore necessary to take into account internal degrees of freedom of the structural fuzzy a global probabilistic modeling of the structural fuzzy is proposed to improve the calculated estimates of the mf vibrations into the master structure and of the far field radiated by itself in or out of context of the acoustic scattering this paper reviews the author s previous work and introduces the type ii probabilistic constitutive law in this paper 1 a probabilistic modeling of the structural fuzzy is presented 2 two probabilistic constitutive laws of the structural fuzzy are constructed 3 the modeling in the mf range for vibroacoustic predictions using theory of structural fuzzy is developed 4 the fuzzy solution in the mf range is studied and 5 numerical simulations on standard structures and on a submerged complex industrial structure are shown

numerical solution of spectral stochastic finite element systems abstract this paper addresses the issues involved in solving systems of linear equations which arise in the context of the spectral stochastic finite element ssfem formulation two efficient solution procedures are presented that dramatically reduce the amount of computations involved in numerically solving these problems a brief review is first provided of the underlying spectral approach which highlights the peculiar structure of the matrices generated and how their properties are related to both the level of approximation involved as well as to the convergence behavior of the proposed solution procedure the differences between these matrices from their deterministic finite element counterparts are illustrated an iterative solution scheme is proposed which utilizes their specific properties for efficient memory management and enhanced convergence behavior results from numerical tests are presented comparisons with standard algorithms illustrate the efficiency of the proposed algorithm the second solution procedure presented in this paper is based on hierarchical basis concepts results from numerical tests are again provided and the limitations of this approach are assessed the performance of both proposed algorithms indicates that the linear algebraic systems from the underlying ssfem formulation can be solved with considerably less effort in memory and computation time than their size suggests furthermore the data structures and the hierarchical concept introduced in this study are found to have great potential for the future development of adaptive procedures in stochastic fem

mid frequency structural dynamics with parameter uncertainty abstract in this paper a number of frequency domain dynamic analysis procedures of randomly disordered structural systems in the medium frequency range are integrated into the stochastic finite element method in all cases frequency domain model reduction strategies are used to minimize the computational effort in the mid frequency range firstly an energy operator approach eoa is investigated in this procedure an energy operator adapted to a fixed medium frequency band is defined whose dominant eigensubspace is used to construct a reduced model using a ritz galerkin method secondly the proper orthogonal decomposition method is used to extract the spatial dominant coherent structures in the vibration wave field in the mid frequency band the coherent structures are the eigenvectors corresponding to the dominant eigenvalues of the spatial autocorrelation function of the system response consequently a close relationship between the energy operator approach and the proper orthogonal decomposition method is identified although these two approaches are not mathematically identical the proper orthogonal decomposition method appears to be more straightforward compared to the energy operator method from the viewpoint of numerical implementation thirdly another approach namely the dynamic element method based on frequency dependent finite element shape functions is considered a stochastic reduction method is then utilized to represent the uncertain parameters modelled as stochastic processes in terms of their dominant scales of fluctuation the karhunen loeve and the polynomial chaos decompositions are used to that effect in the context of a stochastic finite element formalism the methodology adopted in the paper thus integrates efficient dynamical reduction techniques with a reduction scheme of stochastic processes for the mid frequency vibration of linear random systems the formulation is exemplified by its application to the analysis of the dynamics of a coupled uncertain rod assembly subjected to an external excitation the example is also used to highlight some of the relative features of the three dynamic reduction strategies

parallel re initialization of level set functions on distributed unstructured tetrahedral grids level set functions are employed to track interfaces in various application areas including simulation of two phase flows and image segmentation often a re initializing algorithm is incorporated to transform a numerically instable level set function to a signed distance function in this note we present a parallel algorithm for re initializing level set functions on unstructured three dimensional tetrahedral grids the main idea behind this new domain decomposition approach is to combine a parallel brute force re initializing algorithm with an efficient way to compute distances between the interface and grid points time complexity and error analysis of the algorithm are investigated detailed numerical experiments demonstrate the accuracy and scalability on up to 128 processes

non equilibrium relaxation and interface energy of the ising model abstract from the non equilibrium critical relaxation study of the two dimensional ising model the dynamical critical exponent z is estimated to be 2 165 0 010 for this model the relaxation in the ordered phase of this model is consistent with exp t behavior the interface energy of the three dimensional ising model is studied and the critical exponent of the correlation length and the critical amplitude of the surface tension 0 are estimated to be 0 6250 0 0025 and 1 42 0 04 respectively a dynamic monte carlo renormalization group method is successfully applied to the equilibrium properties of the three dimensional ising model

computer simulation studies of critical phenomena abstract the recent strides which have been made in the use of computer simulations to study phase transitions and critical phenomena are reviewed we describe how the use of a combination of recently developed histogram techniques and sophisticated monte carlo simulation algorithms have allowed the determination of the static critical behavior of the d 3 ising and heisenberg models with unprecedented precision we also discuss the study of dynamic critical behavior in simple spin models by both monte carlo and spin dynamics methods recent estimates for dynamic critical exponents are reviewed including the first high precision estimate for true dynamics

ordered upwind methods for static hamilton jacobi equations theory and algorithms we develop a family of fast methods for approximating the solutions to a wide class of static hamilton jacobi pdes these fast methods include both semi lagrangian and fully eulerian versions numerical solutions to these problems are typically obtained by solving large systems of coupled nonlinear discretized equations our techniques which we refer to as ordered upwind methods oums use partial information about the characteristic directions to decouple these nonlinear systems greatly reducing the computational labor our techniques are considered in the context of control theoretic and front propagation problems we begin by discussing existing oums focusing on those designed for isotropic problems we then introduce a new class of oums which decouple systems for general anisotropic problems we prove convergence of one such scheme to the viscosity solution of the corresponding hamilton jacobi pde next we introduce a set of finite differences methods based on an analysis of the role played by anisotropy in the context of front propagation and optimal trajectory problems the performance of the methods is analyzed and computational experiments are performed using test problems from computational geometry and seismology

a method of constructing adaptive hexahedral moving grids a variational method of constructing an adaptive moving grid composed of hexahedral cells is considered the method is based on minimizing a functional defined on the riemannian manifold in space of variables including the physical space coordinates and components of a vector valued monitor function the mesh is generated in the manifold and then it is projected down to the physical region to provide the adaptive grid the integrand of the functional is the non dimensional ratio of the invariants of the metric the functional depends on metric elements of two metrics the curvilinear mesh generated in the manifold induces the monitor metric another control metric defined in a special way is responsible for additional cell shape control the issues of non degeneracy conditions for a hexahedral mesh are considered examples of adaptive grids are presented

evolution by damage spreading in kauffman model in kauffman s boolean automata model on the square lattice the darwinian fitness of survival can be defined as the fraction of elements which do not change from one iteration to the next biological mutations are simulated by filpping one bit in the rule of one site selection of the fitter mutant then optimizes the whole lattice completely this optimization is particularly effective near the critical point of the transition to chaos but is in itself not a critical phenomenon also a two dimensional spin glass can be optimized in this way

efficient algorithms for globally optimal trajectories we present serial and parallel algorithms for solving a system of equations that arises from the discretization of the hamilton jacobi equation associated to a trajectory optimization problem of the following type a vehicle starts at a prespecified point x sub o and follows a unit speed trajectory x t inside a region in spl rscr sup m until an unspecified time t that the region is exited a trajectory minimizing a cost function of the form spl int sub 0 sup t r x t dt q x t is sought the discretized hamilton jacobi equation corresponding to this problem is usually solved using iterative methods nevertheless assuming that the function r is positive we are able to exploit the problem structure and develop one pass algorithms for the discretized problem the first algorithm resembles dijkstra s shortest path algorithm and runs in time o n log n where n is the number of grid points the second algorithm uses a somewhat different discretization and borrows some ideas from a variation of dial s shortest path algorithm 1969 that we develop here it runs in time o n which is the best possible under some fairly mild assumptions finally we show that the latter algorithm can be efficiently parallelized for two dimensional problems and with p processors its running time becomes o n p provided that p o spl radic n log n

survivor statistics and damage spreading on social network with power law degree distributions abstract damage spreading ds of the random graph networks with power law degree distributions is investigated using glauber dynamics various subgraphs defined by the probability of acquaintance show distinct features in ds as measured by hamming distance a heuristic understanding of the long time value of damage is achieved through an analysis of the survivor statistics all survivors are dynamical flipping in unison for the controlled sample and the damaged sample verification of these dynamic survivors is achieved through the introduction of a new measure of self damage

second order godunov type scheme for reactive flow calculations on moving meshes the method of calculating the system of gas dynamics equations coupled with the chemical reaction equation is considered the flow parameters are updated in whole without splitting the system into a hydrodynamical part and an ode part the numerical algorithm is based on the godunov s scheme on deforming meshes with some modification to increase the scheme order in time and space the variational approach is applied to generate the moving adaptive mesh at every time step the functional of smoothness written on the graph of the control function is minimized the grid lines are condensed in the vicinity of the main solution singularities e g precursor shock fire zones intensive transverse shocks and slip lines which allows resolving a fine structure of the reaction domain the numerical examples relating to the chapman jouguet detonation and unstable overdriven detonation are considered in both one and two space dimensions

curvature and the evolution of fronts the evolution of a front propagating along its normal vector field with speedf dependent on curvaturek is considered the change in total variation of the propagating front is shown to depend only ondf dk only wherek changes sign analysis of the casef k 1 ek where e is a constant shows that curvature plays a role similar to that of viscosity in burgers equation for e 0 and non convex initial data the curvature blows up corners develop and an entropy condition can be formulated to provide an explicit construction for a weak solution beyond the singularity we then numerically show that the solution as e goes to zero converges to the constructed weak solution numerical methods based on finite difference schemes for marker particles along the front are shown to be unstable in regions where the curvature builds as a remedy we show that front tracking based on volume of fluid techniques can be used together with the entropy condition to provide transition from the classical to weak solution

a variational hexahedral grid generator with control metric a variational method of constructing a spatial structured grid composed of hexahedral cells is presented the method executes a minimization of the variational functional the integrand of the functional is a ratio of the orthogonal invariants the functional depends on two metrics one metric is induced by a curvilinear mesh generated in the physical domain and the other control metric given in the canonical domain is responsible for an additional cell shape control for instance for condensing the coordinate surfaces and orthogonalization of the grid lines towards the domain boundary generally defining the control metric allows to generate an arbitrary given non folded mesh in the physical domain for every cell the functional is discretized on ten tetrahedra forming two dodecahedrons with the same vertices which span the hexahedral cell the discrete functional possesses an infinite barrier on the boundary of the set of non folded dodecahedral cells that ensures the construction of the non folded grid composed of such cells in the most practical cases the hexahedral grid with the same nodes is non folded as well the method of boundary nodes redistribution is considered examples of the grid construction are reported

damage spreading and critical exponents for model a ising dynamics using damage spreading and heat bath dynamics we study the ising model in 2 and 3 dimensions with non conservative dynamics our algorithm differs in some important points from previous ones which makes it rather efficient we give estimates for the exponent z which seem to be the most precise published so far 2 172 0 006 for d 2 2 032 0 004 for d 3 we also give precise estimates of the exponent introduced by janssen et al z phys b 73 1989 539 and of analogous but in principle independent exponents we find surprisingly that some of the latter agree with and give an explanation for this

response variance prediction for uncertain vibro acoustic systems using a hybrid deterministic statistical method imperfections during the manufacturing process can cause significant variations in the noise and vibration levels exhibited by nominally identical structures any response calculations employed during the design process should ideally take account of these uncertainties and predict the expected range in performance recently a hybrid method has been developed to predict the ensemble average response of a built up system by combining a deterministic model of parts of the system with a statistical model of other components shorter p j and langley r s 2005 j sound vib 288 669 700 in this paper the method is extended to predict the ensemble variance of the response expressions are derived for the variance of the vibrational energies in the statistical components and for the variance of the cross spectrum of the response of the deterministic components which augment the mean values of these quantities predicted by the original theory the method employs a nonparametric model of uncertainty in the sense that the statistical components are taken to carry diffuse wave fields and this obviates the requirement for a detailed description of the system uncertainties the method is validated by application to a range of coupled plate structures and good agreement with detailed monte carlo simulations is found

in an ising model with spin exchange dynamics damage always spreads we investigate the spreading of damage in ising models with kawasaki spin exchange dynamics which conserves the magnetization we first modify a recent master equation approach to account for dynamic rules involving more than a single site we then derive an effective field theory for damage spreading in ising models with kawasaki spin exchange dynamics and solve it for a two dimensional model on a honeycomb lattice in contrast to the cases of glauber or heat bath dynamics we find that the damage always spreads and never heals in the long time limit the average hamming distance approaches that of two uncorrelated systems these results are verified by monte carlo simulations

grid adaption based on modified anisotropic diffusion equations formulated in the parametric domain a new grid adaption algorithm for problems in computational fluid dynamics is presented the basic equations are derived from a variational problem formulated in the parametric domain of the mapping that defines the existing grid modification of the basic equations provides desirable properties in boundary layers the resulting modified anisotropic diffusion equations are solved for the computational coordinates as functions of the parametric coordinates and these functions are numerically inverted numerical examples show that the algorithm is robust that shocks and boundary layers are well resolved on the adapted grid and that the flow solution becomes a globally smooth function of the computational coordinates

the dynamic critical exponent of the three dimensional ising model we measure the dynamic exponent of the three dimensional ising model using a damage spreading monte carlo approach as described by macisaac and jan we simulate systems froml 5 tol 60 at the critical temperature tc 4 5115 we report a dynamic exponent z 2 35 0 05 a value much larger than the consensus value of 2 02 whereas if we assume logarithmic corrections we find thatz 2 05 0 05

damage spreading and critical exponents for model a ising dynamics abstract recent simulations by grassberger gave very precise estimates of the dynamical critical exponent z via damage spreading techniques we confirm these results using a slightly altered method and we examine larger systems up to 18161 2 and 695 2 giving z 2 18 0 02 and 2 04 0 01 respectively

dispersion and pollution of the fem solution for the helmholtz equation in one two and three dimensions for high wave numbers the helmholtz equation suffers the so called pollution effect this effect is directly related to the dispersion a method to measure the dispersion on any numerical method related to the classical galerkin fem is presented this method does not require to compute the numerical solution of the problem and is extremely fast numerical results on the classical galerkin fem p method is compared to modified methods presented in the literature a study of the influence of the topology triangles is also carried out the efficiency of the different methods is compared the numerical results in two of the mesh and for square elements show that the high order elements control the dispersion well the most effective modified method is the qsfem 1 2 but it is also very complicated in the general setting the residual free bubble 3 4 is effective in one dimension but not in higher dimensions the least square method 1 5 approach lowers the dispersion but relatively little the results for triangular meshes show that the best topology is the criss cross pattern copyright 1999 john wiley sons ltd

label setting methods for multimode stochastic shortest path problems on graphs stochastic shortest path ssp problems arise in a variety of discrete stochastic control contexts an optimal solution to such a problem is typically computed using the value function which can be found by solving the corresponding dynamic programming equations in the deterministic case these equations can be often solved by highly efficient label setting methods such as dijkstra s and dial s algorithms in this paper we define and study a class of multimode stochastic shortest path mssp problems and develop sufficient conditions for the applicability of label setting methods we illustrate our approach in a number of discrete stochastic control examples we also discuss the relationship of ssps with discretizations of static hamilton jacobi equations and provide an alternative derivation for several fast noniterative numerical methods for these partial differential equations pdes

time dependent thermodynamic properties of the ising model from damage spreading the relationship between damage spreading and static thermodynamic properties in the ising model developed by coniglioet al is here extended to include time dependent thermodynamic quantities we exploit this new result to measure the time dependent spin correlation function from damage spreading in the ising model with heat bath and glauber dynamics until now only static thermodynamic quantities have been correctly determined from damage spreading and even then only with heat bath dynamics we also show that there are significant differences between the kinetics of damage spreading as found in heat bath and glauber dynamics

fast numerical methods for bernoulli free boundary problems the numerical solution of the free boundary bernoulli problem is addressed an iterative method based on a level set formulation and boundary element method is proposed issues related to the implementation the accuracy and the generality of the method are discussed the efficiency of the approach is illustrated by numerical results