numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media a numerical procedure for the determination of equivalent grid block permeability tensors for heterogeneous porous media is presented the method entails solution of the fine scale pressure equation subject to periodic boundary conditions to yield upon appropriate averaging of the fine scale velocity field the coarse scale or equivalent grid block permeability when the region over which this coarse scale permeability is computed constitutes a representative elementary volume rev the resulting equivalent permeability may be interpreted as the effective permeability of the region solution of the pressure equation on the fine scale is accomplished through the application of an accurate triangle based finite element numerical procedure which allows for the modeling of geometrically complex features the specification of periodic boundary conditions is shown to yield symmetric positive definite equivalent permeability tensors in all cases the method is verified through application to a periodic model problem and is then applied to the scale up of areal and cross sections with fractally generated permeability fields the applicability and limitations of the method for these more general heterogeneity fields are discussed

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

generalized multiscale finite element method for a strain limiting nonlinear elasticity model abstract in this paper we consider multiscale methods for nonlinear elasticity in particular we investigate the generalized multiscale finite element method gmsfem for a strain limiting elasticity problem being a special case of the naturally implicit constitutive theory of nonlinear elasticity strain limiting relation has presented an interesting class of material bodies for which strains remain bounded even infinitesimal while stresses can become arbitrarily large the nonlinearity and material heterogeneities can create multiscale features in the solution and multiscale methods are therefore necessary to handle the resulting nonlinear monotone quasilinear elliptic equation we use linearization based on the picard iteration we consider two types of basis functions offline and online basis functions following the general framework of gmsfem the offline basis functions depend nonlinearly on the solution thus we design an indicator function and we will recompute the offline basis functions when the indicator function predicts that the material property has significant change during the iterations on the other hand we will use the residual based online basis functions to reduce the error substantially when updating basis functions is necessary our numerical results show that the above combination of offline and online basis functions is able to give accurate solutions with only a few basis functions per each coarse region and adaptive updating basis functions in selected iterations

crack tip enrichment in the xfem using a cutoff function we consider a variant of the extended finite element method xfem in which a cutoff function is used to localize the singular enrichment surface the goal of this variant is to obtain numerically an optimal convergence rate while reducing the computational cost of the classical xfem with a fixed enrichment area we give a mathematical result of quasi optimal error estimate one of the key points of this paper is to prove the optimality of the coupling between the singular and the discontinuous enrichments finally we present some numerical computations validating the theoretical result these computations are compared with those of the classical xfem and a non enriched method copyright 2008 john wiley sons ltd

approximate controllability of impulsive differential equations with state dependent delay in order to describe various real world problems in physical and engineering sciences subject to abrupt changes at certain instants during the evolution process impulsive differential equations have been used to describe the system model in this article the problem of approximate controllability for nonlinear impulsive differential equations with state dependent delay is investigated we study the approximate controllability for nonlinear impulsive differential system under the assumption that the corresponding linear control system is approximately controllable using methods of functional analysis and semigroup theory sufficient conditions are formulated and proved finally an example is provided to illustrate the proposed theory

multigrid with rough coefficients and multiresolution operator decomposition from hierarchical information games we introduce a near linear complexity geometric and meshless algebraic multigrid multiresolution method for pdes with rough l infty coefficients with rigorous a priori accuracy and performance estimates the method is discovered through a decision game theory formulation of the problems of 1 identifying restriction and interpolation operators 2 recovering a signal from incomplete measurements based on norm constraints on its image under a linear operator and 3 gambling on the value of the solution of the pde based on a hierarchy of nested measurements of its solution or source term the resulting elementary gambles form a hierarchy of deterministic basis functions of h 1 0 omega gamblets that 1 are orthogonal across subscales subbands with respect to the scalar product induced by the energy norm of the pde 2 enable sparse compression of the solution space in h 1 0 omega and 3 induce an orthogonal multiresolution operator decomposition the operating diagram of the multig

invariance of the reachable set under nonlinear perturbations for the abstract controlled volterra equation qquad x t bar x t int 0 t boldsymbol psi t s phi s x s bf b s v s ds on 0 t we consider the reachable set mathcal k phi x t text for some v in mathfrak b viewing phi cdot cdot as a nonlinear perturbation of an otherwise linear control problem conditions are obtained under which mathcal k phi mathcal k 0 for a suitable class mathfrak f of such nonlinear perturbations phi whenever the linear problem is known to have a reachable set invariant under affine perturbations phi cdot cdot g in mathfrak z the results generalize those obtained by naito 7 for control of the heat equation

adaptive generalized multiscale finite element methods for h curl elliptic problems with heterogeneous coefficients abstract in this paper we construct an adaptive multiscale method for solving h curl elliptic problems in highly heterogeneous media our method is based on the generalized multiscale finite element method we will first construct a suitable snapshot space and a dimensional reduction procedure to identify important modes of the solution we next develop and analyze an a posteriori error indicator and the corresponding adaptive algorithm in addition we will construct a coupled offline online adaptive algorithm which provides an adaptive strategy to the selection of offline and online basis functions our theory shows that the convergence is robust with respect to the heterogeneities and contrast of the media we present several numerical results to illustrate the performance of our method

on concepts of controllability for deterministic and stochastic systems the new necessary and sufficient conditions which are formulated in terms of convergence of a certain sequence of operators involving the resolvent of the negative of the controllability operator are found for deterministic linear stationary control systems to be completely and approximately controllable respectively these conditions are applied to study the s controllability a property of attaining an arbitrarily small neighborhood of each point in the state space with a probability arbitrarily close to one and c controllability the s controllability fortified with some uniformity of stochastic systems it is shown that the s controllability the c controllability of a partially observable linear stationary control system with an additive gaussian white noise disturbance on all the intervals 0 t for t 0 is equivalent to the approximate complete controllability of its deterministic part on all the intervals 0 t for t 0

approximate controllability of second order distributed implicit functional systems abstract in this paper we study the approximate controllability of control systems with states and controls in hilbert spaces and described by a second order semilinear abstract functional differential equation with infinite delay initially we establish a characterization for the approximate controllability of a second order abstract linear system and in the last section we compare the approximate controllability of a semilinear abstract functional system with the approximate controllability of the associated linear system

convergence of a nonconforming multiscale finite element method the multiscale finite element method msfem t y hou x h wu and z cai math comp 1998 to appear t y hou and x h wu j comput phys 134 1997 pp 169 189 has been introduced to capture the large scale solutions of elliptic equations with highly oscillatory coefficients this is accomplished by constructing the multiscale base functions from the local solutions of the elliptic operator our previous study reveals that the leading order error in this approach is caused by the resonant sampling which leads to large error when the mesh size is close to the small scale of the continuous problem similar difficulty also arises in numerical upscaling methods an oversampling technique has been introduced to alleviate this difficulty t y hou and x h wu j comput phys 134 1997 pp 169 189 a consequence of the oversampling method is that the resulting finite element method is no longer conforming here we give a detailed analysis of the nonconforming error our analysis also reveals a new cell resonance error which is caused by the mismatch between the mesh size and the wavelength of the small scale we show that the cell resonance error is of lower order our numerical experiments demonstrate that the cell resonance error is generically small and is difficult to observe in practice

controllability of a backward fractional semilinear differential equation abstract in this paper we study the approximate controllability of a fractional semilinear differential equation involving the right fractional caputo derivative more precisely we construct by means of tikhonov type regularization method the controllability operator then under certain condition on this operator we obtain that the associate backward fractional linear system can be steered to an arbitrary small neighborhood of the state at initial time this allows us to prove the approximate controllability of the semilinear system

on the approximate controllability of fractional evolution equations with compact analytic semigroup in this paper we discuss the approximate controllability of fractional evolution equations involving caputo fractional derivative the results are obtained with the help of the theory of fractional calculus semigroup theory and the schauder s fixed point theorem under the assumption that the corresponding linear system is approximately controllable finally an example is provided to illustrate the obtained results

generalized multiscale finite element methods gmsfem in this paper we propose a general approach called generalized multiscale finite element method gmsfem for performing multiscale simulations for problems without scale separation over a complex input space as in multiscale finite element methods msfems the main idea of the proposed approach is to construct a small dimensional local solution space that can be used to generate an efficient and accurate approximation to the multiscale solution with a potentially high dimensional input parameter space in the proposed approach we present a general procedure to construct the offline space that is used for a systematic enrichment of the coarse solution space in the online stage the enrichment in the online stage is performed based on a spectral decomposition of the offline space in the online stage for any input parameter a multiscale space is constructed to solve the global problem on a coarse grid the online space is constructed via a spectral decomposition of the offline space and by choosing the eigenvectors corresponding to the largest eigenvalues the computational saving is due to the fact that the construction of the online multiscale space for any input parameter is fast and this space can be re used for solving the forward problem with any forcing and boundary condition compared with the other approaches where global snapshots are used the local approach that we present in this paper allows us to eliminate unnecessary degrees of freedom on a coarse grid level we present various examples in the paper and some numerical results to demonstrate the effectiveness of our method

approximate controllability of riemann liouville fractional differential inclusions in this paper by using fractional calculus multi valued analysis semigroup theory and the fixed point technique we study the approximate controllability for a class of riemann liouville fractional differential inclusions an example is given to illustrate the application of the abstract results

partial approximate controllability of nonlocal fractional evolution equations via approximating method abstract in this paper we study partial approximate controllability of semilinear nonlocal fractional evolution equations in hilbert spaces by using fractional calculus variational approach and approximating technique we give the approximate problem of the control system and get the compactness of approximate solution set then new sufficient conditions for the partial approximate controllability of the control system are obtained when the compactness conditions or lipschitz conditions for the nonlocal function are not required finally we apply our abstract results to the partial approximate controllability of the semilinear heat equation and delay equation

controllability results for a class of fractional semilinear integro differential inclusions via resolvent operators this paper deals with the controllability of fractional integro differential inclusions the results are obtained by using bohnenblust karlin s fixed point theorem further we extend the result to study the controllability concept with nonlocal conditions finally an example is also given to illustrate our main results in this paper we consider a class of fractional integro differential inclusions in banach spaces this paper deals with the controllability for fractional integro differential control systems first we establishes a set of sufficient conditions for the controllability of fractional semilinear integro differential inclusions in banach spaces via resolvent operators we use bohnenblust karlin s fixed point theorem to prove our main results further we extend the result to study the controllability concept with nonlocal conditions an example is also given to illustrate our main results

approximate controllability of semilinear functional equations in hilbert spaces in this paper approximate and complete controllability for semilinear functional differential systems is studied in hilbert spaces sufficient conditions are established for each of these types of controllability the results address the limitation that linear systems in infinite dimensional spaces with compact semigroup cannot be completely controllable the conditions are obtained by using the schauder fixed point theorem when the semigroup is compact and the banach fixed point theorem when the semigroup is not compact

controllability for a class of fractional neutral integro differential equations with unbounded delay abstract in this paper we consider a class of fractional neutral integro differential equations with unbounded delay in banach spaces this paper deals with the exact controllability for fractional integro differential neutral control systems first we establish a new set of sufficient conditions for the exact controllability of nonlinear fractional systems by using a fixed point analysis approach further we extend the result to study the exact controllability concept with nonlocal conditions examples are provided to illustrate our main results

approximate controllability of evolution systems with nonlocal conditions we study the approximate controllability for the abstract evolution equations with nonlocal conditions in hilbert spaces assuming the approximate controllability of the corresponding linearized equation we obtain sufficient conditions for the approximate controllability of the semilinear evolution equation the results we obtained are a generalization and continuation of the recent results on this issue at the end an example is given to show the application of our result

a geometric approach for reachability and observability of linear switched impulsive systems abstract this paper is concerned with the reachability and observability of linear switched impulsive systems with singular impulse matrices first some new concepts with respect to the reachability and unobservability are introduced especially span reachability is proposed because the reachable sets of switched impulsive systems do not always constitute subspaces then the geometric characterization of the span reachable and unobservable sets is presented moreover the relations between the span reachable set unobservable set and the invariant subspaces of such systems are discussed finally corresponding criteria applied to linear impulsive systems and linear switched systems are also discussed

extended finite element method for three dimensional crack modelling an extended finite element method x fem for three dimensional crack modelling is described a discontinuous function and the two dimensional asymptotic crack tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity this enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed stress intensity factors sifs for planar three dimensional cracks are presented which are found to be in good agreement with benchmark solutions copyright 2000 john wiley sons ltd

fast online generalized multiscale finite element method using constraint energy minimization abstract local multiscale methods often construct multiscale basis functions in the offline stage without taking into account input parameters such as source terms boundary conditions and so on these basis functions are then used in the online stage with a specific input parameter to solve the global problem at a reduced computational cost recently online approaches have been introduced where multiscale basis functions are adaptively constructed in some regions to reduce the error significantly in multiscale methods it is desired to have only 1 2 iterations to reduce the error to a desired threshold using generalized multiscale finite element framework 10 it was shown that by choosing sufficient number of offline basis functions the error reduction can be made independent of physical parameters such as scales and contrast in this paper our goal is to improve this using our recently proposed approach 4 and special online basis construction in oversampled regions we show that the error reduction can be made sufficiently large by appropriately selecting oversampling regions our numerical results show that one can achieve a three order of magnitude error reduction which is better than our previous methods we also develop an adaptive algorithm and enrich in selected regions with large residuals in our adaptive method we show that the convergence rate can be determined by a user defined parameter and we confirm this by numerical simulations the analysis of the method is presented

on the approximate controllability of semilinear fractional differential systems fractional differential equations have wide applications in science and engineering in this paper we consider a class of control systems governed by the semilinear fractional differential equations in hilbert spaces by using the semigroup theory the fractional power theory and fixed point strategy a new set of sufficient conditions are formulated which guarantees the approximate controllability of semilinear fractional differential systems the results are established under the assumption that the associated linear system is approximately controllable further we extend the result to study the approximate controllability of fractional systems with nonlocal conditions an example is provided to illustrate the application of the obtained theory

approximate controllability for stochastic evolution inclusions of clarke s subdifferential type in this paper we deal with the approximate controllability of stochastic evolution inclusions of clarke s subdifferential type firstly by using stochastic analysis nonsmooth analysis theory of operator semigroups and fixed point theorems of multivalued maps we show the existence of mild solutions for the stochastic evolution inclusions then we provide a sufficient condition to guarantee the approximate controllability of the stochastic evolution inclusions actually our results cover a broader class of inclusion problems involving time depending operators finally an example is included to illustrate the applicability of the main results

approximate controllability of stochastic differential systems driven by a levy process in this paper we are concerned with the approximate controllability of stochastic differential systems driven by teugels martingales associated with a levy process we derive the approximate controllability with the coefficients in the system satisfying some non lipschitz conditions which include classic lipschitz conditions as special cases the desired result is established by means of standard picard s iteration

multiscale simulations for upscaled multi continuum flows abstract we consider in this paper a challenging problem of simulating fluid flows in complex multiscale media possessing multi continuum background as an effort to handle this obstacle model reduction is employed in a recent work by park and ha homogenization was nicely applied to find effective coefficients and homogenized equations for fluid flow pressures of a dual continuum system with new convection terms and negative interaction coefficients however some degree of multiscale still remains this motivates us to propose a numerical strategy based on the generalized multiscale finite element method gmsfem coupled with the dual continuum homogenized equations toward speeding up the simulation improving the accuracy as well as clearly representing the interactions between the dual continua in our paper globally each continuum is viewed as a system and connected to the other throughout the domain we take into consideration the flow transfers between the dual continua and within each continuum itself such multiscale flow dynamics are modeled by the gmsfem which systematically generates either uncoupled or coupled multiscale basis to carry the local characteristics to the global ones via establishing local snapshots and spectral decomposition in the snapshot space as a result we will work with a system of two equations coupled with some interaction terms and each equation describes one of the dual continua on the fine grid convergence analysis of the proposed scheme is accompanied with the numerical results which support the favorable outcomes

approximate controllability of the semilinear heat equation this article is concerned with the study of approximate controllability for the semilinear heat equation in a bounded domain when the control acts on any open and nonempty subset of or on a part of the boundary in the case of both an internal and a boundary control the approximate controllability in l p for 1 p l in the case of the interior control we also prove approximate controllability in c 0 the proof combines a variational approach to the controllability problem for linear equations and a fixed point method we also prove that the control can be taken to be of quasi bang bang form

existence and controllability results for stochastic fractional evolution hemivariational inequalities in this paper we study a class of stochastic evolution hemivariational inequalities with fractional derivative the existence of mild solutions and controllability results are obtained by applying fractional calculation stochastic analysis techniques a fixed point theorem of multivalued maps and properties of generalized clarke subdifferential an example is included to show the applicability of our results

3d crack propagation in unreinforced concrete a two step algorithm for tracking 3d crack paths tensile failure of unreinforced concrete involves progressive micro cracking and the related strain softening can coalesce into geometrical discontinuities which separate the material advanced mechanical theories and numerical schemes are required to efficiently and adequately represent crack propagation in 3d in this paper we use the concept of strong discontinuities to model concrete failure we introduce a cohesive fracture process zone which is characterized by a transversely isotropic traction separation law we combine the cohesive crack concept with the partition of unity finite element method where the finite element space is enhanced by the heaviside function the concept is implemented for tetrahedral elements and the failure initialization is based on the simple non local rankine criterion for each element we assume the embedded discontinuity to be flat in the reference configuration which leads to a non smooth crack surfaces approximation in 3d in general different concepts for tracking non planar cracks in 3d are reviewed in addition we propose a two step algorithm for tracking the crack path where a predictor step defines discontinuities according to the non local failure criterion and a corrector step draws in non local information of the existing discontinuities in order to predict a closed 3d crack surface implementation details are provided the proposed framework is used to analyze the predictability of concrete failure by two benchmark examples i e the nooru moharned test and the brokenshire test we compare our numerical results which are mesh independent with experimental data and numerical results adopted from the literature

approximate controllability for a class of semilinear abstract equations in this paper a class of control systems governed by the semilinear abstract equation dot y ay f y bv is considered a sufficient condition for the approximate controllability is obtained which improves j henry s results on a nonlinear parabolic control systems with some more serious restrictions it is suitable not only to the infinite dimensional case but also to the finite dimensional case two examples are given to explain the applications of the theory

approximate controllability of the nonlinear third order dispersion equation abstract in this paper we consider the approximate controllability of nonlinear third order dispersion equation of the form w t x t 3 w x 3 x t gu x t f t w x t on the interval 0 x 2 t 0 with initial and periodic boundary conditions w x 0 0 k w x k 0 t k w x k 2 t k 0 1 2 we study the approximate controllability for nonlinear dispersion system under the assumption that the corresponding linear control system is approximately controllable the solutions are given by a variation of constants formula which allows us to study the approximate controllability for nonlinear dispersion systems based on the semigroup theory and fixed point approach sufficient conditions are formulated and proved

controllability of integrodifferential systems in banach spaces sufficient conditions for controllability of integrodifferential systems in a banach space are established the results are obtained by using the schaefer fixed point theorem an example is provided to illustrate the theory

approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces various sufficient conditions for approximate controllability of linear evolution systems in abstract spaces have been obtained but approximate controllability of semilinear control systems usually requires some complicated and limited assumptions in this paper we show the approximate controllability of the abstract semilinear deterministic and stochastic control systems under the natural assumption that the associated linear control system is approximately controllable the results are obtained using new properties of symmetric operators which are proved in this paper compact semigroups the schauder fixed point theorem and or the contraction mapping principle

localization of elliptic multiscale problems this paper constructs a local generalized finite element basis for elliptic problems with heterogeneous and highly varying coefficients the basis functions are solutions of local problems on vertex patches the error of the corresponding generalized finite element method decays exponentially with respect to the number of layers of elements in the patches hence on a uniform mesh of size h patches of diameter h log 1 h are sufficient to preserve a linear rate of convergence in h without pre asymptotic or resonance effects the analysis does not rely on regularity of the solution or scale separation in the coefficient this result motivates new and justifies old classes of variational multiscale methods see more at http www ams org journals mcom 2014 83 290 s0025 5718 2014 02868 8 sthash z2ccfxig dpuf

residual driven online generalized multiscale finite element methods the construction of local reduced order models via multiscale basis functions has been an area of active research in this paper we propose online multiscale basis functions which are constructed using the offline space and the current residual online multiscale basis functions are constructed adaptively in some selected regions based on our error indicators we derive an error estimator which shows that one needs to have an offline space with certain properties to guarantee that additional online multiscale basis function will decrease the error this error decrease is independent of physical parameters such as the contrast and multiple scales in the problem the offline spaces are constructed using generalized multiscale finite element methods gmsfem we show that if one chooses a sufficient number of offline basis functions one can guarantee that additional online multiscale basis functions will reduce the error independent of contrast we note that the construction of online basis functions is motivated by the fact that the offline space construction does not take into account distant effects using the residual information we can incorporate the distant information provided the offline approximation satisfies certain properties in the paper theoretical and numerical results are presented our numerical results show that if the offline space is sufficiently large in terms of the dimension such that the coarse space contains all multiscale spectral basis functions that correspond to small eigenvalues then the error reduction by adding online multiscale basis function is independent of the contrast we discuss various ways computing online multiscale basis functions which include a use of small dimensional offline spaces

non planar 3d crack growth by the extended finite element and level sets part ii level set update we present a level set method for treating the growth of non planar three dimensional cracks the crack is defined by two almost orthogonal level sets signed distance functions one of them describes the crack as a two dimensional surface in a three dimensional space and the second is used to describe the one dimensional crack front which is the intersection of the two level sets a hamilton jacobi equation is used to update the level sets a velocity extension is developed that preserves the old crack surface and can accurately generate the growing surface the technique is coupled with the extended finite element method which approximates the displacement field with a discontinuous partition of unity this displacement field is constructed directly in terms of the level sets so the discretization by finite elements requires no explicit representation of the crack surface numerical experiments show the robustness of the method both in accuracy and in treating cracks with significant changes in topology copyright 2002 john wiley sons ltd

the generalized finite element method an example of its implementation and illustration of its performance the generalized finite element method gfem was introduced in reference 1 as a combination of the standard fem and the partition of unity method the standard mapped polynomial finite element spaces are augmented by adding special functions which reflect the known information about the boundary value problem and the input data the geometry of the domain the loads and the boundary conditions the special functions are multiplied with the partition of unity corresponding to the standard linear vertex shape functions and are pasted to the existing finite element basis to construct a conforming approximation the essential boundary conditions can be imposed exactly as in the standard fem adaptive numerical quadrature is used to ensure that the errors in integration do not affect the accuracy of the approximation this paper gives an example of how the gfem can be developed for the laplacian in domains with multiple elliptical voids and illustrates implementation issues and the superior accuracy of the gfem versus the standard fem copyright 2000 john wiley sons ltd

approximate controllability of differential inclusions in hilbert spaces abstract in this paper controllability for the system originating from semilinear functional differential equations in hilbert spaces is studied we consider the problem of approximate controllability of semilinear differential inclusion assuming that semigroup generated by the linear part of the inclusion is compact and under the assumption that the corresponding linear system is approximately controllable by using resolvent of controllability gramian operator and fixed point theorem sufficient conditions have been formulated and proved an example is presented to illustrate the utility and applicability of the proposed method

approximate controllability results for analytic resolvent integro differential inclusions in hilbert spaces abstractin this work we consider a nonlinear resolvent integro differential evolution inclusions in hilbert spaces this paper deals with the approximate controllability for nonlinear resolvent integro differential inclusions in hilbert spaces we use bohnenblust karlin s fixed point theorem to establish a set of sufficient conditions for the approximate controllability for nonlinear resolvent integro differential inclusions in hilbert spaces further we extend the result to study the approximate controllability concept with non local conditions an example is presented to demonstrate the obtained theory