a divergence free reconstruction of the nonconforming virtual element method for the stokes problem abstract in this paper we propose and investigate a divergence free reconstruction of the nonconforming virtual element for the stokes problem by constructing the computable raviart thomas like interpolation operator we guarantee the independence between the velocity error estimation u u h 1 h and the continuous pressure p as it happens for the divergence free flow solver moreover this modified scheme can also inherit the advantages of the classical nonconforming virtual element method such as very general meshes including non convex and degenerate elements a unified scheme for an arbitrary order approximation accuracy k etc then we provide the optimal l 2 error estimates for the velocity gradient and the pressure by taking advantage of the raviart thomas like interpolation operator and avoiding the use of a trace inequality finally three numerical experiments are presented to conform the theoretical analysis

application of the karhunen loeve procedure for the characterization of human faces the use of natural symmetries mirror images in a well defined family of patterns human faces is discussed within the framework of the karhunen loeve expansion this results in an extension of the data and imposes even and odd symmetry on the eigenfunctions of the covariance matrix without increasing the complexity of the calculation the resulting approximation of faces projected from outside of the data set onto this optimal basis is improved on average

the virtual element method for discrete fracture network simulations abstract in this work an optimization based approach presented in berrone et al 2013 2014 10 12 for discrete fracture network simulations is coupled with the virtual element method vem for the space discretization of the underlying darcy law the great flexibility of the vem in handling rather general polygonal elements allows in a natural way for an effective description of irregular solutions starting from an arbitrary triangulation which is built independently of the mesh on other fractures only partial conformity is in fact obtained with this approach numerical results performed on several dfn configurations confirm the viability and efficiency of the resulting method

percolation parameter and percolation threshold estimates for three dimensional random ellipses with widely scattered distributions of eccentricity and size in fractured materials of very low matrix permeability fracture connectivity is the first order determinant of the occurrence of flow for systems having a narrow distribution of object sizes short range percolation a first order percolation criterion is given by the total excluded volume which is almost constant at threshold in the case of fractured media recent observations have demonstrated that the fracture length distribution is extremely large because of this widely scattered fracture length distribution the classical expression of the total excluded volume is no longer scale invariant at the percolation threshold and has no finite limit for infinitely large systems thus the classical estimation method of the percolation threshold established in short range percolation becomes useless for the connectivity determination of fractured media in this study we derive an expression for the total excluded volume that remains scale invariant at the percolation threshold and that can thus be used as the proper control parameter called the parameter of percolation in percolation theory we show that the scale invariant expression of the total excluded volume is the geometrical union normalized by the system volume rather than the summation of the mutual excluded volumes normalized by the system volume the summation of the mutual excluded volume classical expression remains linked to the number of intersections between fractures whereas the normalized geometrical union of the mutual excluded volume our expression can be essentially identified with the percolation parameter moreover fluctuations of this percolation parameter at threshold with length and eccentricity distributions remain limited within a range of less than one order of magnitude giving in turn a rough percolation criterion we finally show that the scale dependence of the percolation parameter causes the connectivity of fractured media to increase with scale meaning especially that the hydraulic properties of fractured media can dramatically change with scale

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

two algorithms for weighted matroid intersection consider a finite sete a weight functionw e r and two matroidsm1 andm2 defined one the weighted matroid intersection problem consists of finding a seti e independent in both matroids that maximizes w e e ini we present an algorithm of complexity o nr r c logn for this problem wheren e r min rank m1 rank m2 c max c1 c2 and fori 1 2 ci is the complexity of finding the circuit ofi e inmi or show that none exists wheree is ine andi e is independent inm1 andm2 a related problem is to find a maximum weight set independent in both matroids and of given cardinalityk if one exists our algorithm also solves this problem in addition we present a second algorithm that given a feasible solution of cardinalityk finds an optimal one of the same cardinality a sensitivity analysis on the weights is easy to perform using this approach our two algorithms are related to existing algorithms in fact our framework provides new simple proofs of their validity other contributions of this paper are the existence of nonnegative reduced weights theorem 6 allowing the improved complexity bound and the introduction of artificial elements allowing an improved start and flexibility in the implementation of the algorithms

a spectral viscosity method for correcting the long term behavior of pod models low dimensional flow dynamical systems may converge to erroneous states after long time integration even if they are initialized with the correct state in this paper we investigate the accuracy of such two dimensional models constructed from karhunen loeve expansions for flows past a circular cylinder we first demonstrate that although the short term dynamics may be predicted accurately with only a handful of modes retained drifting of the solution may arise after a few hundred vortex shedding cycles we then propose a dissipative model based on a spectral viscosity sv diffusion convolution operator the parameters of the sv model are selected rigorously based on bifurcation analysis our results show that this is an effective way of improving the accuracy of long term predictions of low dimensional galerkin systems

a generalized mixed hybrid mortar method for solving flow in stochastic discrete fracture networks the simulation of flow in fractured media requires handling both a large number of fractures and a complex interconnecting network of these fractures networks considered in this paper are three dimensional domains made up of two dimensional fractures intersecting each other and randomly generated due to the stochastic generation of fractures intersections can be highly intricate the numerical method must generate a mesh and define a discrete problem for any discrete fracture network dfn a first approach erhel de dreuzy and poirriez siam j sci comput 31 2009 pp 2688 2705 is to generate a conforming mesh and to apply a mixed hybrid finite element method however the resulting linear system becomes very large when the network contains many fractures hence a second approach pichot erhel and de dreuzy appl anal 89 2010 pp 1629 1643 is to generate a nonconforming mesh using an independent mesh generation for each fracture then a mortar technique applied to the mixed hybrid finite element method deals with the nonmatching grids when intersections do not cross or overlap pairwise mortar relations for each intersection are efficient pichot erhel and de dreuzy 2010 but for most random networks discretized intersections involve more than two fractures in this paper we design a new method generalizing the previous one and that is applicable for stochastic networks the main idea is to combine pairwise mortar relations with additional relations for the overlapping part this method still ensures the continuity of fluxes and heads and still yields a symmetric positive definite linear system numerical experiments show the efficiency of the method applied to complex stochastic fracture networks we also study numerical convergence when reducing the mesh step this method makes it easy to perform mesh optimization and appears to be a very promising tool to simulate flow in multiscale fracture networks

impact of velocity correlation and distribution on transport in fractured media field evidence and theoretical model flow and transport through fractured geologic media often leads to anomalous non fickian transport behavior the origin of which remains a matter of debate whether it arises from variability in fracture permeability velocity distribution connectedness in the flow paths through fractures velocity correlation or interaction between fractures and matrix here we show that this uncertainty of distribution versus correlation controlled transport can be resolved by combining convergent and push pull tracer tests because flow reversibility is strongly dependent on velocity correlation whereas late time scaling of breakthrough curves is mainly controlled by velocity distribution we build on this insight and propose a lagrangian statistical model that takes the form of a continuous time random walk ctrw with correlated particle velocities in this framework velocity distribution and velocity correlation are quantified by a markov process of particle transition times that is characterized by a distribution function and a transition probability our transport model accurately captures the anomalous behavior in the breakthrough curves for both push pull and convergent flow geometries with the same set of parameters thus the proposed correlated ctrw modeling approach provides a simple yet powerful framework for characterizing the impact of velocity distribution and correlation on transport in fractured media

a cut finite element method for a model of pressure in fractured media we develop a robust cut finite element method for a model of diffusion in fractured media consisting of a bulk domain with embedded cracks the crack has its own pressure field and can cut through

parallel solvers for virtual element discretizations of elliptic equations in mixed form abstract the aim of this paper is twofold on the one hand we numerically test the performance of mixed virtual elements in three dimensions to solve the mixed formulation of three dimensional elliptic equations on polyhedral meshes on the other hand we focus on the parallel solution of the linear system arising from such discretization considering both direct and iterative parallel solvers in the latter case we develop two block preconditioners one based on the approximate schur complement and one on a regularization technique both these topics are numerically validated by several parallel tests performed on a linux cluster more specifically we show that the proposed virtual element discretization recovers the expected theoretical convergence rates and we analyze the performance of the direct and iterative parallel solvers taken into account

inverse methods and data assimilation in nonlinear ocean models abstract an overview is given of the current status of inverse methods and data assimilation for nonlinear ocean models the inverse theory for time dependent dynamical models is formulated and the most promising solution methods like simulated annealing the representer method and sequential methods based on monte carlo simulations are discussed with special focus on applications with nonlinear dynamics a rather general model independent presentation has been used to make the methodology more accessible for different scientific areas dealing with dynamical models and data

lazy learning for local modelling and control design this paper presents local methods for modelling and control of discrete time unknown non linear dynamical systems when only input output data are available we propose the adoption of lazy learning a memory based technique for local modelling the modelling procedure uses a query based approach to select the best model configuration by assessing and comparing different alternatives a new recursive technique for local model identification and validation is presented together with an enhanced statistical method for model selection a lso three methods to design controllers based on the local linearization provided by the lazy learning algorithm are described in the first method the lazy technique returns the forward and inverse models of the system which are used to compute the control action to take the second is an indirect method inspired by self tuning regulators where recursive least squares estimation is replaced by a local approximator the third method combines the linearization provided by t

approximating capacitated routing and delivery problems we provide approximation algorithms for some capacitated vehicle routing and delivery problems these problems can all be viewed as instances of the following k delivery tsp given n source points and n sink points in a metric space with exactly one item at each source find a minimum length tour by a vehicle of finite capacity k to pick up and deliver exactly one item to each sink the only known approximation algorithm for this family of problems is the 2 5 approximation algorithm of anily and hassin networks 22 1992 pp 419 433 for the special case k 1 for this case we use matroid intersection to obtain a 2 approximation algorithm based on this algorithm and some additional lower bound arguments we devise a factor approximation for k delivery tsp with arbitrary finite k we also present a 2 approximation algorithm for the case k infty we then initiate the study of dynamic variants of k delivery tsp that model problems in industrial robotics and other applications specifically we consider the situation where a robot arm with finite or infinite capacity must collect n point objects moving in the euclidean plane and deliver them to the origin the point objects are moving in the plane with known identical velocities they might for instance be on a moving conveyor belt we derive several useful structural properties that lead to constant factor approximations for problems of this type that are relevant to the robotics application along the way we show that maximum latency tsp is implicit in the dynamic problems and that the natural farthest neighbor heuristic produces a good approximation for several notions of latency

upscaling discrete fracture network simulations an alternative to continuum transport models 1 particle tracking through stochastically generated networks of discrete fractures provides an alternative to the conventional advection dispersion description of transport in fractured rock however discrete fracture network simulations are computationally intensive and usually limited to small scales an approach for direct upscaling of discrete fracture simulations is described trajectories for nonreacting tracer particles are first extracted from relatively small discrete fracture network simulations tracer rock interaction is represented by also calculating a cumulative reactivity parameter along each trajectory the residence time reactivity information is then used in a monte carlo simulation to construct artificial particle trajectories of any length thereby achieving the upscaling objective in its simplest form the procedure has the form of a random walk evolving in a two dimensional space tests using site specific and generic networks show that it is necessary to modify the random walk to produce sequential correlation along the trajectories we achieve this by using a discrete state markov process to direct the random walk the procedure is computationally efficient easily implemented and compares well with the network simulations

spatiotemporal analysis of complex signals theory and applications we present a space time description of regular and complex phenomena which consists of a decomposition of a spatiotemporal signal into orthogonal temporal modes that we call chronos and orthogonal spatial modes that we call topos this permits the introduction of several characteristics of the signal three characteristic energies and entropies one temporal one spatial and one global and a characteristic dimension although the technique is general we concentrate on its applications to hydrodynamic problems specifically the transition to turbulence we consider two cases of application a coupled map lattice as a dynamical system model for spatiotemporal complexity and the open flow instability on a rotating disk in the latter we show a direct relation between the global entropy and the different instabilities that the flow undergoes as reynolds number increases

convergence analysis of multilevel monte carlo variance estimators and application for random obstacle problems we develop a novel convergence theory for the multilevel sample variance estimators in the framework of the multilevel monte carlo methods we prove that dependent on the regularity of the quantity of interest the multilevel sample variance estimator may achieve the same asymptotic cost error relation as the multilevel sample mean which is superior to the standard monte carlo method weaker regularity assumptions result in reduced convergence rates quantified in our analysis the general convergence theory is applied to a class of scalar elliptic obstacle problems with rough random obstacle profiles which is a simple model of contact between a deformable body with a rough uncertain substrate numerical experiments confirm theoretical convergence proofs

a quasi steady state method for solving transient darcy flow in complex 3d fractured networks accounting for matrix to fracture flow modeling natural discrete fracture networks dfn receives more and more attention in applied geosciences from oil and gas industry to geothermal recovery and aquifer management the fractures may be either natural or artificial in case of well stimulation accounting for the flow inside the fracture network and accounting for the transfers between the matrix and the fractures with the same level of accuracy is an important issue for calibrating the well architecture and for setting up optimal resources recovery strategies recently we proposed an original method allowing to model transient pressure diffusion in the fracture network only 1 the matrix was assumed to be impervious a systematic approximation scheme was built allowing to model the initial dfn by a set of n unknowns located at each identified intersection between fractures the higher n the higher the accuracy of the model the main assumption was using a quasi steady state hypothesis that states that the characteristic diffusion time over one single fracture is negligible compared with the characteristic time of the macroscopic problem e g change of boundary conditions in that context the lowest order approximation n 1 has the form of solving a transient problem in a resistor capacitor network a so called pipe network its topology is the same as the network of geometrical intersections between fractures in this paper we generalize this approach in order to account for fluxes from matrix to fractures the quasi steady state hypothesis at the fracture level is still kept then we show that in the case of well separated time scales between matrix and fractures the preceding model needs only to be slightly modified in order to incorporate these fluxes the additional knowledge of the so called matrix to fracture transfer function allows to modify the mass matrix that becomes a time convolution operator this is reminiscent of existing space averaged transient dual porosity models

uncertainty quantification in discrete fracture network models we consider flows in fractured media described by discrete fracture network dfn models we perform an uncertainty quantification analysis assuming the fractures transmissivity coefficients to be random variables two probability distributions log uniform and log normal are used within different laws that express the coefficients in terms of a family of independent stochastic variables truncated karhunenlove expansions provide instances of such laws the approximate computation of quantities of interest such as mean value and variance for outgoing fluxes is based on a stochastic collocation approach that uses suitable sparse grids in the range of the stochastic variables whose number defines the stochastic dimension of the problem this produces a non intrusive computational method in which the dfn flow solver is applied as a black box a very fast error decay related to the analytical dependence of the observed quantities upon the stochastic variables is obtained in the low dimensional cases using isotropic sparse grids comparisons with monte carlo results show a clear gain in efficiency for the proposed method for increasing dimensions attained via successive truncations of karhunenlove expansions results are still good although the rates of convergence are progressively reduced resorting to suitably tuned anisotropic grids is an effective way to contrast such curse of dimensionality in the explored range of dimensions the resulting convergence histories are nearly independent of the dimension

dual virtual element method for discrete fractures networks discrete fracture networks is a key ingredient in the simulation of physical processes which involve fluid flow in the underground when the surrounding rock matrix is considered impervious in this paper we present two different models to compute the pressure field and darcy velocity in the system the first allows a normal flow out of a fracture at the intersections while the second grants also a tangential flow along the intersections for the numerical discretization we use the mixed virtual element method as it is known to handle grid elements of almost any arbitrary shape the flexibility of the discretization allows us to loosen the requirements on grid construction and thus significantly simplify the flow discretization compared to traditional discrete fracture network models a coarsening algorithm from the algebraic multigrid literature is also considered to further speed up the computation the performance of the method is validated by numerical experiments

constrained spanning trees and the traveling salesman problem abstract minimum weight 1 trees provide a well known lower bound for the symmetric traveling salesman problem we propose to strengthen this bound by imposing degree constraints upon the 1 trees the vertices for the constraints are chosen to form a stable set s we propose an o m log log n s n s m m n algorithm for this problem and report on its use in a lagrangian approach to the traveling salesman problem

towards effective flow simulations in realistic discrete fracture networks we focus on the simulation of underground flow in fractured media modeled by means of discrete fracture networks focusing on a new recent numerical approach proposed by the authors for tackling the problem avoiding mesh generation problems we further improve the new family of methods making a step further towards effective simulations of large multi scale heterogeneous networks namely we tackle the imposition of dirichlet boundary conditions in weak form in such a way that geometrical complexity of the dfn is not an issue we effectively solve dfn problems with fracture transmissivities spanning many orders of magnitude and approaching zero furthermore we address several numerical issues for improving the numerical solution also in quite challenging networks

gradient radial basis function networks for nonlinear and nonstationary time series prediction we present a method of modifying the structure of radial basis function rbf network to work with nonstationary series that exhibit homogeneous nonstationary behavior in the original rbf network the hidden node s function is to sense the trajectory of the time series and to respond when there is a strong correlation between the input pattern and the hidden node s center this type of response however is highly sensitive to changes in the level and trend of the time series to counter these effects the hidden node s function is modified to one which detects and reacts to the gradient of the series we call this new network the gradient rbf grbf model single and multistep predictive performance for the mackey glass chaotic time series were evaluated using the classical rbf and grbf models the simulation results for the series without and with a tine varying mean confirm the superior performance of the grbf predictor over the rbf predictor

an efficient polynomial time approximation scheme for the constrained minimum spanning tree problem using matroid intersection given an undirected graph g v e with v n and e m nonnegative integers ce and de for each edge e in e and a bound d the constrained minimum spanning tree problem cst is to find a spanning tree t v et such that sum e in e t d e leq d and sum e in e t c e is minimized we present an efficient polynomial time approximation scheme eptas for this problem specifically for every epsilon 0 we present a 1 epsilon approximation algorithm with time complexity o frac 1 epsilon o frac 1 epsilon n 4 our method is based on lagrangian relaxation and matroid intersection

a new approach to simulating flow in discrete fracture networks with an optimized mesh natural fractured media are highly unpredictable because of existing complex structures at the fracture and at the network levels fractures are by themselves heterogeneous objects of broadly distributed sizes shapes and orientations that are interconnected in large correlated networks with little field data and evidence numerical modeling can provide important information on the underground hydraulic phenomena however it must overcome several barriers first the complex network structure produces a structure difficult to mesh second the absence of a priori homogenization scale along with the double fracture and network heterogeneity levels requires the calculation of large but finely resolved fracture networks resulting in very large simulation domains to tackle these two related issues we reduce the highly complex geometry of the fractures by applying a local transformation that suppresses the cumbersome meshing configurations while keeping the networks fundamental geological and geometrical characteristics we show that the flow properties are marginally affected while the problem complexity i e memory capacity and resolution time can be divided by orders of magnitude the goal of this article is to propose a method of resolution which takes into account the geometrical complexity met in the networks and which makes it possible to treat a few thousand fractures the principal aim of this article is to present a tool to slowly modify the structures of the fracture networks to have a good quality mesh with a marginal loss in precision

regression by local fitting methods properties and computational algorithms abstract local regression is a procedure for estimating regression surfaces by the local fitting of linear or quadratic functions of the independent variables in a moving fashion that is analogous to how a moving average is computed for a time series the advantage of the methodology over the global fitting of parametric functions of the independent variables by least squares the current paradigm in regression studies is that a much wider class of regression functions can be estimated without distortion in this paper we discuss the methods their statistical properties and computational algorithms

crashing a maximum weight complementary basis we consider the problem of finding a maximum weight complementary basis of anm 2m matrix the problem arises naturally for example when a complementary set of columns is proposed as an initial basis for a warm start of lemke s algorithm but the set of columns is rank deficient we show that the problem is a special case of the problem of finding a maximum weight common base of two matroids furthermore we show how to efficiently implement an algorithm for the general problem in the present context finally we give computational results demonstrating the practicality of our algorithm in a typical application

emergence of stable laws for first passage times in three dimensional random fracture networks we study first passage behaviors in the flow through three dimensional random fracture networks network and flow heterogeneity lead to the emergence of heavy tailed first passage time distributions that evolve with increasing distance between the start and target planes and transition toward stable laws analysis of the spatial memory of the first passage process shows that particle motion can be quantified stochastically by a time domain random walk conditioned on the initial velocity data this approach identifies advective tortuosity the velocity point distribution and the average fracture link length as key quantities for the prediction of first passage times using this approach we develop a theory for the evolution of first passage times with increasing distance between the start and target planes and the convergence towards stable laws

a c1 virtual element method on polyhedral meshes abstract the purpose of the present paper is to develop c 1 virtual elements in three dimensions for linear elliptic fourth order problems motivated by the difficulties that standard conforming finite elements encounter in this framework we focus the presentation on the lowest order case the generalization to higher orders being briefly provided in the appendix the degrees of freedom of the proposed scheme are only 4 per mesh vertex representing function values and gradient values interpolation error estimates for the proposed space are provided together with a set of numerical tests to validate the method at the practical level

conforming delaunay triangulation of stochastically generated three dimensional discrete fracture networks a feature rejection algorithm for meshing strategy we introduce the feature rejection algorithm for meshing fram to generate a high quality conforming delaunay triangulation of a three dimensional discrete fracture network dfn the geometric features fractures fracture intersections spaces between fracture intersections etc that must be resolved in a stochastically generated dfn typically span a wide range of spatial scales and make the efficient automated generation of high quality meshes a challenge to deal with these challenges many previous approaches often deformed the dfn to align its features with a mesh through various techniques including redefining lines of intersection as stair step functions and distorting the fracture edges in contrast fram generates networks on which high quality meshes occur automatically by constraining the generation of the network the cornerstone of fram is prescribing a minimum length scale and then restricting the generation of the network to only create features of that size and larger the process is f

a matroid algorithm and its application to the efficient solution of two optimization problems on graphs we address the problem of finding a minimum weight baseb of a matroid when in addition each element of the matroid is colored with one ofm colors and there are upper and lower bound restrictions on the number of elements ofb with colori fori 1 2 m this problem is a special case of matroid intersection we present an algorithm that exploits the special structure and we apply it to two optimization problems on graphs when applied to the weighted bipartite matching problem our algorithm has complexity o e v v 2log v herev denotes the node set of the underlying bipartite graph ande denotes its edge set the second application is defined on a general connected graphg v e whose edges have a weight and a color one seeks a minimum weight spanning tree with upper and lower bound restrictions on the number of edges with colori in the tree for eachi our algorithm for this problem has complexity o e v m 2 v m v 2 a special case of this constrained spanning tree problem occurs whenv is a set of pairwise nonadjacent nodes ofg one must find a minimum weight spanning tree with upper and lower bound restrictions on the degree of each node ofv then the complexity of our algorithm is o v e v v 2 finally we discuss a new relaxation of the traveling salesman problem

kernel partial least squares regression in reproducing kernel hilbert space a family of regularized least squares regression models in a reproducing kernel hilbert space is extended by the kernel partial least squares pls regression model similar to principal components regression pcr pls is a method based on the projection of input explanatory variables to the latent variables components however in contrast to pcr pls creates the components by modeling the relationship between input and output variables while maintaining most of the information in the input variables pls is useful in situations where the number of explanatory variables exceeds the number of observations and or a high level of multicollinearity among those variables is assumed motivated by this fact we will provide a kernel pls algorithm for construction of nonlinear regression models in possibly high dimensional feature spaces we give the theoretical description of the kernel pls algorithm and we experimentally compare the algorithm with the existing kernel pcr and kernel ridge regression techniques we will demonstrate that on the data sets employed kernel pls achieves the same results as kernel pcr but uses significantly fewer qualitatively different components

gappy data to krig or not to krig data recovery and reconstruction methods for unsteady flow fields with spatio temporal missing data are studied based on proper orthogonal decomposition pod and on kriging interpolation it is found that for sufficient temporal resolution pod based methods outperform kriging interpolation however for insufficient temporal resolution large spatial gappiness or for flow fields with black zones kriging interpolation is more effective the comparison is performed based on randomly generated laminar and turbulent flow fields obtained from simulations of uniform flow past a circular cylinder

calibrated reduced order pod galerkin system for fluid flow modelling to improve the behaviour of reduced order proper orthogonal decomposition pod galerkin systems two numerical methods are proposed these methods determine free parameters in the pod galerkin system from flow simulations via a minimization problem they give rise to linear systems and their computational costs are reasonable both methods are assessed for two flow configurations a two dimensional flow around a square cylinder for a reynolds number of 100 and a three dimensional flow past a backward facing step for a reynolds number of 7432 based on the step height and the streamwise velocity at the middle of the inlet for both configurations the methods are effective since accurate calibrated reduced order pod galerkin systems are obtained

an optimization approach for large scale simulations of discrete fracture network flows in recent papers 1 2 the authors introduced a new method for simulating subsurface flow in a system of fractures based on a pde constrained optimization reformulation removing all difficulties related to mesh generation and providing an easily parallel approach to the problem in this paper we further improve the method removing the constraint of having on each fracture a non empty portion of the boundary with dirichlet boundary conditions this way dirichlet boundary conditions are prescribed only on a possibly small portion of dfn boundary the proposed generalization of the method in 1 2 relies on a modified definition of control variables ensuring the non singularity of the operator on each fracture a conjugate gradient method is also introduced in order to speed up the minimization process

the p and hp versions of the virtual element method for elliptic eigenvalue problems abstract we discuss the p and h p versions of the virtual element method for the approximation of eigenpairs of elliptic operators with a potential term on polygonal meshes an application of this model is provided by the schrodinger equation with a pseudo potential term as an interesting byproduct we present for the first time in literature an explicit construction of the stabilization of the mass matrix we present in detail the analysis of the p version of the method proving exponential convergence in the case of analytic eigenfunctions the theoretical results are supplied with a wide set of experiments we also show numerically that in the case of eigenfunctions with finite sobolev regularity an exponential approximation of the eigenvalues in terms of the cubic root of the number of degrees of freedom can be obtained by employing h p refinements importantly the geometric flexibility of polygonal meshes is exploited in the construction of the h p spaces

predictive flow field estimation abstract we are considering the problem of real time prediction of 3d turbulent velocity fields based on a small number of scalar measurements the method of proper orthogonal decomposition pod allows for the decomposition of an ensemble of velocity fields into a set of spatial basis functions and a set of temporal coefficients the computation of the temporal coefficients is by no means a trivial matter especially when one is faced with a large number of modes in this paper we discuss the use of radial basis function rbf models to capture the discrete time evolution and nonlinear dynamics of the pod coefficients further we propose the use of regularized regression techniques to generate models that provide mappings between the pod coefficients and scalar measurements as a final step towards real time prediction the state space rbf models and regression measurement models are combined using unscented kalman filters to produce optimal solutions such that a balance between the state models and measurement models is achieved the proposed methods are tested for two specific cases the classical lorenz model is chosen to demonstrate the use and effectiveness of rbf models as a potential candidate for state models flow around a wall mounted cube in a channel at r e 20 000 is considered as the second case the aim for the second case is to be able to accurately predict the pod coefficients outside the ensemble it is shown that a large number of pod coefficients is required to approximate the velocity fields with sufficient accuracy the rbf models are created based on only the temporal information available from the initial ensemble and it is shown that the rbf model is able to correctly approximate the high dimensional phase space combined with the unscented kalman filter it is indeed possible to track the evolution of the pod coefficients for a long time the robustness of the filter is demonstrated by considering the presence of noise in measurements and using measurement information at time steps greater than the evolution time step

virtual elements for linear elasticity problems we discuss the application of virtual elements to linear elasticity problems for both the compressible and the nearly incompressible case virtual elements are very close to mimetic finite differences see for linear elasticity l beirao da veiga m2an math model numer anal 44 2010 pp 231 250 and in particular to higher order mimetic finite differences as such they share the good features of being able to represent in an exact way certain physical properties conservation incompressibility etc and of being applicable in very general geometries the advantage of virtual elements is the ductility that easily allows high order accuracy and high order continuity

uncertainty quantification in discrete fracture network models stochastic geometry we consider the problem of uncertainty quantification analysis of the output of underground flow simulations we consider in particular fractured media described via the discrete fracture network model within this framework we address the relevant case of networks in which the geometry of the fractures is described by stochastic parameters in this context due to a possible lack of smoothness in the quantity of interest with respect to the stochastic parameters well assessed techniques such as stochastic collocation may fail in providing reliable estimates of first order moments of the quantity of interest in this paper we overcome this issue by applying the multilevel monte carlo method using as underlying solver an extremely robust method