a mortar method based on nurbs for curved interfaces abstract to tackle general sub domain problems in geomechanics we present an mfem scheme on curved interfaces based on nurbs curves and surfaces the goal is to have a more robust geometrical representation for mortar spaces which allows gluing non conforming interfaces on realistic geometries the resulting mortar saddle point problem is decoupled using standard domain decomposition techniques such as dirichlet neumann to exploit current parallel machine architectures two and three dimensional examples ranging from near wellbore applications to field level subsidence computations show that the proposed scheme can handle problems of practical interest

relaxation oscillations in a class of predator prey systems abstract we consider a class of three dimensional singularly perturbed predator prey systems having two predators competing exploitatively for the same prey in a constant environment by using dynamical systems techniques and the geometric singular perturbation theory we give precise conditions which guarantee the existence of stable relaxation oscillations for systems within the class such result shows the coexistence of the predators and the prey with quite diversified time response which typically happens when the prey population grows much faster than those of predators as an application a well known model will be discussed in detail by showing the existence of stable relaxation oscillations for a wide range of parameters values of the model

the entry exit theorem and relaxation oscillations in slow fast planar systems abstract the entry exit theorem for the phenomenon of delay of stability loss for certain types of slow fast planar systems plays a key role in establishing existence of limit cycles that exhibit relaxation oscillations the general existing proofs of this theorem depend on fenichel s geometric singular perturbation theory and blow up techniques in this work we give a short and elementary proof of the entry exit theorem based on a direct study of asymptotic formulas of the underlying solutions we employ this theorem to a broad class of slow fast planar systems to obtain existence global uniqueness and asymptotic orbital stability of relaxation oscillations the results are then applied to a diffusive predator prey model with holling type ii functional response to establish periodic traveling wave solutions furthermore we extend our work to another class of slow fast systems that can have multiple orbits exhibiting relaxation oscillations and subsequently apply the results to a two time scale holling tanner predator prey model with holling type iv functional response it is generally assumed in the literature that the non trivial equilibrium points exist uniquely in the interior of the domains bounded by the relaxation oscillations we do not make this assumption in this paper

estimation of aquifer parameters under transient and steady state conditions 2 uniqueness stability and solution algorithms paper 2 of this three part series starts with a discussion of the question under what conditions is the aquifer inverse problem well posed after defining the terms uniqueness identifiability and stability theoretical considerations and synthetic examples are used to demonstrate that ill posedness can be mitigated by including prior information about the parameters in the estimation criterion to be minimized at the same time the inclusion of such information is shown to be insufficient to guarantee uniqueness and stability in all cases several test problems in the recent literature which have resulted in pessimistic conclusions about the solvability of the aquifer inverse problem are shown to be ill posed a question is thus raised about the validity of these conclusions in the general case various conjugate gradient algorithms coupled with the adjoint state finite element method for computing the gradient of the estimation criterion and with newton s method for determining the optimum step size downgradient are compared a marked improvement in the rate at which these algorithms converge is shown to be achieved by switching from one method to another when the former slows down or fails to converge

robust feti dp methods for heterogeneous three dimensional elasticity problems iterative substructuring methods with lagrange multipliers are considered for heterogeneous linear elasticity problems with large discontinuities in the material stiffnesses in particular results for algorithms belonging to the family of dual primal feti methods are presented the core issue of these algorithms is the construction of an appropriate global problem in order to obtain a robust method which converges independently of the material discontinuities in this article several necessary and sufficient conditions arising from the theory are numerically tested and confirmed furthermore results of numerical experiments are presented for situations which are not covered by the theory such as curved edges and material discontinuities not aligned with the interface and an attempt is made to develop rules for these cases

bddc and feti dp preconditioners for spectral element discretizations abstract two of the most recent and important nonoverlapping domain decomposition methods the bddc method balancing domain decomposition by constraints and the feti dp method dual primal finite element tearing and interconnecting are here extended to spectral element discretizations of second order elliptic problems in spite of the more severe ill conditioning of the spectral element discrete systems compared with low order finite elements and finite differences these methods retain their good properties of scalability quasi optimality and independence on the discontinuities of the elliptic operator coefficients across subdomain interfaces

a fully coupled dynamic model for two phase fluid flow in deformable porous media abstract a fully coupled dynamic model is presented for the analysis of water and air flow in deforming porous media in fully or partially saturated conditions the solid displacements and the pressures of fluids are taken as primary unknowns of the model the finite element method is used for the discrete approximation of the partial differential equations governing the problem the mathematical framework and the numerical implementation of the model are given in detail and the adopted approximations are put into evidence first the model is validated with respect to documented experiments on partially saturated soil behaviour in quasi static condition then the results of a full dynamic analysis are shown and discussed in this paper merits and drawbacks of the proposed model are highlighted

stability loss delay in harvesting competing populations abstract when populations are in competition it often happens that one of them disappears harvesting may be used for the control and management of competing species to stabilize the populations at a persistent equilibrium a three dimensional model where the harvesting effort is a dynamic variable is studied in the case where the growth rate of the harvesting effort is very slow the analysis shows that the system can have relaxation oscillations dynamic bifurcation theory is used to determine the maximal and minimal values of harvesting effort along this cycle of oscillations

persistent unstable periodic motions i we study the initial value problems of the two dimensional system formula wherei t ii tis a slowly varying parameter f u t i is analytic on all variables and periodic ontwith period 2 andu0 t i are periodic solutions of the system formula whereiis a constant parameter we assume that the variational equations of 0 2 wt fv u0 t i t i w have the corresponding characteristic exponents 1 i 2 i 1 i which move across the imaginary axis from the left half complex plane to the right half complex plane asiincreases pasti we show that under the nonresonant conditions h4 and h5 that 2 n im 1 i forn n in section 4 along with other generic conditions such as h1 h3 below the separations ofu i t fromu0 t1 t i t do not occur at the critical point wherei t i rather the bifurcations are substantially delayed untili t ii treachesiq i which is independent of as 0 in other words u t u0 t1 t i t 0 fort t ii i t iq for someiq iq ii i independent of when 0 an exact formula foriqis given for general situations in near resonance cases a sharp estimate ofiqis also derived

the entry exit function and geometric singular perturbation theory this work was partly supported by fwo project g093910 de maesschalck and nsf grant dms 1211707 schecter we thank the referee for a careful reading of the paper which led to a number of clarifications and corrections

the representer method for state and parameter estimation in single phase darcy flow the objective of this paper is to study the representer method for the inverse problem of combined parameter and state estimation in single phase darcy flow in porous media a variational formulation is posed for the generalized inverse problem in the sense of weighted least squares an iterative representer based algorithm is derived to approximate the euler lagrange equations it is proved that the linearized problem can be solved exactly by an extension of the representer method which inherits the same well known properties of this technique implementation of the numerical algorithm for synthetic numerical experiments shows improved estimates of the poorly known prior guess 2007 elsevier b v all rights reserved

three dimensional stochastic analysis of macrodispersion in aquifers the dispersive mixing resulting from complex flow in three dimensionally heterogeneous porous media is analyzed using stochastic continuum theory stochastic solutions of the perturbed steady flow and solute transport equations are used to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of a three dimensional statistically anisotropic input covariance describing the hydraulic conductivity with a statistically isotropic input covariance the longitudinal macrodispersivity is convectively controlled but the transverse macrodispersivity is proportional to the local dispersivity and is several orders of magnitude smaller than the longitudinal term with an arbitrarily oriented anisotropic conductivity covariance all components of the macrodispersivity tensor are convectively controlled and the ratio of transverse to longitudinal dispersivity is of the order of 10 1 in this case the off diagonal components of the dispersivity tensor are significant being numerically larger than the diagonal transverse terms and the transverse dispersion process can be highly anisotropic dispersivities predicted by the stochastic theory are shown to be consistent with controlled field experiments and monte carlo simulations the theory which treats the asymptotic condition of large displacement indicates that a classical gradient transport fickian relationship is valid for large scale displacements

on the use of inexact subdomain solvers for bddc algorithms the standard bddc balancing domain decomposition by constraints preconditioner is shown to be equivalent to a preconditioner built from a partially subassembled finite element model this results in a system of linear algebraic equations which is much easier to solve in parallel than the fully assembled model the cost is then often dominated by that of the problems on the subdomains an important role is also played both in theory and practice by an averaging operator and in addition exact dirichlet solvers are used on the subdomains in order to eliminate the residual in the interior of the subdomains the use of inexact solvers for these problems and even the replacement of the dirichlet solvers by a trivial extension are considered it is established that one of the resulting algorithms has the same eigenvalues as the standard bddc algorithm and the connection of another with the feti dp algorithm with a lumped preconditioner is also considered multigrid methods are used in the experimental work and under certain assumptions it is established that the iteration count essentially remains the same as when exact solvers are used while considerable gains in the speed of the algorithm can be realized since the cost of the exact solvers grows superlinearly with the size of the subdomain problems while the multigrid methods are linear

dynamic hopf bifurcations generated by nonlinear terms abstract we consider the so called delayed loss of stability phenomenon for singularly perturbed systems of differential equations in case that the associated autonomous system with a scalar parameter undergoes the hopf bifurcation at the zero equilibrium point it is assumed that the linearization of the associated system is independent of the parameter and the next terms in the expansion of the right hand parts at zero are positive homogeneous of order 1 simple formulas are presented to estimate the asymptotic delay for the delayed loss of stability phenomenon more precisely we suggest sufficient conditions which ensure that zeros of a simple function defined by the positive homogeneous nonlinear terms are the hopf bifurcation points of the associated system the sign of at other points determines stability of the zero equilibrium and the asymptotic delay equals the distance between the bifurcation point and a zero of some primitive of

incorporation of prior information on parameters into nonlinear regression groundwater flow models 1 theory prior information on the parameters of a groundwater flow model can be used to improve parameter estimates obtained from nonlinear regression solution of a modeling problem two scales of prior information can be available 1 prior information having known reliability that is bias and random error structure and 2 prior information consisting of best available estimates of unknown reliability a regression method that incorporates the second scale of prior information assumes the prior information to be fixed for any particular analysis to produce improved although biased parameter estimates approximate optimization of two auxiliary parameters of the formulation is used to help minimize the bias which is almost always much smaller than that resulting from standard ridge regression it is shown that if both scales of prior information are available then a combined regression analysis may be made

inverse modeling of multimodal conductivity distributions 1 we present a method for the calibration of multimodal hydraulic conductivity distributions and apply this method to the particular case of confining layers with a complex geological architecture the basis of our technique is the transformation of the original multimodal conductivity distribution to the standard normal distribution thus fulfilling the condition of normality which is required by the used representer based inverse algorithm valstar et al 2004 using this transformation a calibration that starts from a homogeneous prior field is shown to radically improve the estimation of the protective properties of the confining layer compared to a unimodal approach to the calibration the method is also used for the calibration of multimodal heterogeneous prior fields the inevitable distortion of the original parameter covariances in the posterior fields that results from the transformation process is absorbed by an iterative postprocessing procedure in which lithologic information obtained from the distorted calibrated fields is used to condition the generation of a new multimodal field that complies again with the original geostatistics after transformation this new field can be calibrated again and this process is repeated until the newly generated field agrees with the measurement information sufficiently well then the lithologic distribution of this new field is fixed and the intrafacies conductivity distributions are calibrated this approach is shown to preserve the original geostatistics both of the lithology field and of the intralithology hydraulic conductivity distributions

multiscale finite element methods for stochastic porous media flow equations and application to uncertainty quantification in this paper we study multiscale finite element methods for stochastic porous media flow equations as well as applications to uncertainty quantification we assume that the permeability field the diffusion coefficient is stochastic and can be described in a finite dimensional stochastic space this is common in applications where the coefficients are expanded using chaos approximations the proposed multiscale method constructs multiscale basis functions corresponding to sparse realizations and these basis functions are used to approximate the solution on the coarse grid for any realization furthermore we apply our coarse scale model to uncertainty quantification problem where the goal is to sample the porous media properties given an integrated response such as production data our algorithm employs pre computed posterior response surface obtained via the proposed coarse scale model using fast analytical computations of the gradients of this posterior we propose approximate langevin samples these samples are further screened through the coarse scale simulation and finally used as a proposal in metropolis hasting markov chain monte carlo method numerical results are presented which demonstrate the efficiency of the proposed approach

fractional factorial split plot designs for robust parameter experiments for robust parameter designs it has been noted that performing the experiment as a split plot often provides cost savings and increased efficiency thus experiments are often performed using fractional factorial split plot designs we consider how one should best choose such designs for robust parameter experiments and what is meant by maximum resolution and by minimum aberration in this context under various experimental settings

d optimal split plot designs with given numbers and sizes of whole plots the design of split plot experiments has received considerable attention during the last few years the goal of this article is to provide an efficient algorithm to compute d optimal split plot designs with given numbers of whole plots and given whole plot sizes the algorithm is evaluated and applied to a protein extraction experiment in addition it is shown that two level factorial and fractional factorial designs are d optimal for estimating first order response surface models for specific numbers and sizes of whole plots

a feti method with a mesh independent condition number for the iteration matrix abstract we introduce a framework for feti methods using ideas from the decomposition via lagrange multipliers of h 0 1 derived by raviart thomas p a raviart j m thomas primal hybrid finite element methods for second order elliptic equations math comput 31 138 1977 391 413 and complemented with the detailed work on polygonal domains developed by grisvard p grisvard singularities in boundary value problems rech math appl 22 1992 we compute the action of the lagrange multipliers using the natural h 00 1 2 scalar product therefore no consistency error appears our analysis allows to deal with cross points and floating subdomains in a natural manner as a byproduct we obtain that the condition number for the iteration matrix is independent of the mesh size and there is no need for preconditioning this result improves the standard asymptotic bound for this condition number given by 1 log h h 2 where h and h are the characteristic subdomain size and element size respectively shown by mandel tezaur in j mandel r tezaur convergence of a substructuring method with lagrange multipliers numer math 73 1996 473 487 numerical results that confirm our theoretical analysis are presented

adaptive selection of face coarse degrees of freedom in the bddc and the feti dp iterative substructuring methods we propose a class of method for the adaptive selection of the coarse space of the bddc and feti dp iterative substructuring methods the methods work by adding coarse degrees of freedom constructed from eigenvectors associated with intersections of selected pairs of adjacent substructures it is assumed that the starting coarse degrees of freedom are already sufficientto prevent relative rigid body motions in any selected pair of adjacent substructures a heuristic indicator of the the condition number is developed and a minimal number of coarse degrees of freedom is added to decrease the indicator under a given threshold it is shown numerically on 2d elasticity problems that the indicator based on pairs of substructures with common edges predicts the actual condition number reasonably well and that the method can select adaptively the hard part of the problem and concentrate computational work there to achieve good convergence of the iterations at a modest cost

uncertainty transformation via hopf bifurcation in fast slow systems propagation of uncertainty in dynamical systems is a significant challenge here we focus on random multiscale ordinary differential equation models in particular we study hopf bifurcation in the fast subsystem for random initial conditions we show that a random initial condition distribution can be transformed during the passage near a delayed dynamic hopf bifurcation i to certain classes of symmetric copies ii to an almost deterministic output iii to a mixture distribution with differing moments and iv to a very restricted class of general distributions we prove under which conditions the cases i iv occur in certain classes vector fields

estimation of aquifer parameters under transient and steady state conditions 1 maximum likelihood method incorporating prior information in this series of three papers a method is presented to estimate the parameters of groundwater flow models under steady and nonsteady state conditions the parameters include values and directions of principal hydraulic conductivities or transmissivities in anisotropic media specific storage or storativity interior and boundary recharge or leakage rates coefficients of head dependent interior and boundary sources and boundary heads in transient situations the initial head distribution can also be estimated if the system is originally at a steady state paper 1 of the series discusses some of the advantage in treating the inverse problem statistically and in regularizing its solution by means of penalty criteria based on prior estimates of the parameters the inverse problem is posed in the framework of maximum likelihood theory cast in a manner that accounts for prior information about the parameters since not all the factors which contribute to the prior errors can be quantified statistically at the outset the covariance matrices of these errors are expressed in terms of several parameters which if unknown can be estimated jointly with the hydraulic parameters by a stagewise optimization process when transient head data are separated by a fixed time interval the temporal structure of these data is approximated by a lag one autoregressive model with a correlation coefficient that can be treated as another unknown parameter estimation errors are analyzed by examining the lower bound of their covariance matrix in the eigenspace paper 1 concludes by suggesting that certain model identification criteria developed in the time series literature all of which are based on the maximum likelihood concept might be useful for selecting the best groundwater model or the best method of parameterizing a particular model among a number of given alternatives

on bifurcation delay an alternative approach using geometric singular perturbation theory abstract to explain the phenomenon of bifurcation delay which occurs in planar systems of the form x f x z z g x z z where f x 0 0 0 and g x 0 0 changes sign at least once on the x axis we use the exchange lemma in geometric singular perturbation theory to track the limiting behavior of the solutions using the trick of extending dimension to overcome the degeneracy at the turning point we show that the limiting attracting and repulsion points are given by the well known entry exit function and the minimum of z on the trajectory is of order exp 1 also we prove smoothness of the return map up to arbitrary finite order in

low and high frequency oscillations in three dimensional food chain systems the dynamic behavior of a three trophic level food chain prey predator superpredator is analyzed in this paper prey is logistic while predator and superpredator have functional response of the holling type moreover the trophic levels are assumed to be characterized by increasing and quite diversified time responses using a singular perturbation approach explicit conditions for the persistence of the three populations are derived and the structure of the corresponding attractors is noted as well as the nature of transients the analysis shows that the system can have low frequency cycles due to the interactions between predator and superpredator nevertheless the interactions between prey and predator can give rise to high frequency oscillations which can arise during the transients toward the attractor or during the low frequency cycle this periodic burst of high frequency oscillations develops in particular when the two predators are fairly efficient these results note in a very concise w

a representer based inverse method for groundwater flow and transport applications groundwater inverse problems are concerned with the estimation of uncertain model parameters such as hydraulic conductivity from field or laboratory measurements in practice model and measurement errors compromise the ability of inverse procedures to provide accurate results it is important to account for such errors in order to determine the proper weight to give to each source of information probabilistic descriptions of model and measurement errors can be incorporated into classical variational inverse procedures but the computational demands are excessive if the model errors vary over time an alternative approach based on representer expansions is able to efficiently accommodate time dependent errors for large problems in the representer approach unknown variables are expanded in finite series which depend on unknown fonctions called representers each representer quantifies the influence of a given measurement on the estimate of a particular variable this procedure replaces the original inverse problem by an equivalent problem where the number of independent unknowns is proportional to the number of measurements the representer approach is especially advantageous in groundwater problems where the total number of measurements is often small this approach is illustrated with a synthetic flow and transport example that includes time dependent model errors the representer algorithm is able to provide good estimates of a spatially variable hydraulic conductivity field and good predictions of solute concentration its computational demands are reasonable and it is relatively easy to implement the example reveals that it is beneficial to account for model errors even when they are difficult to estimate

on convergence conditions of partitioned solution procedures for consolidation problems abstract a systematic approach to determine conditions for convergence of partitioned staggered procedures for consolidation problems is presented consistency convergence and stability is investigated for linear and nonlinear problems and a comparison of the partitioned and direct method is made conclusions based also on numerical evidence are drawn the significance of the ratio of the time step length to the square of the finite element mesh length is shown

an integrated geometric algebraic method for solving semi definite problems in structural mechanics a method for the general solution of structural semi definite problems in the presence of zero energy modes is described in this paper semi definite problems are usually associated in structural mechanics with floating structures namely totally unconstrained or partially constrained structures a general solution of these problems is obtained by the computation of a particular displacement field which ensures the equilibrium of the structure and of the zero energy modes of the structure the proposed method combines geometric and algebraic concepts and goes beyond the restrictions of existing methods in this field in particular it is robust cost effective and accounts for all rigid body and mechanism modes in either floating structures or semi definite subdomain problems encountered in domain decomposition methods furthermore it can be combined with any open or closed serial or parallel solver for symmetric positive definite spd problems at a very low cost

mixed constraint preconditioning in computational contact mechanics contact mechanics can be addressed numerically by finite elements using either a penalty formulation or the lagrange multipliers the penalty approach leads to a linearized symmetric positive definite system which can prove severely ill conditioned with the iterative solution to large 3d problems requiring expensive preconditioners to accelerate or even to allow for convergence in the present paper a mixed constraint preconditioner mcp is developed and implemented for the iterative solution of contact problems based on the penalty approach a theoretical bound for the eigenspectrum of the preconditioned matrix is provided depending on the user specified parameters that control the preconditioner fill in the performance of mcp combined with the preconditioned conjugate gradient is studied in two real 3d test cases describing the geomechanics of faulted porous media and compared to a well established preconditioner such as the incomplete cholesky decomposition illt with optimal fill in numerical results show that typically mcp outperforms illt especially in the most challenging problems where very large penalty parameters must be used finally a modification aimed at simplifying the mcp implementation and increasing its robustness is developed and experimented with showing that the modified mcp can be viewed as an efficient and viable alternative to both mcp and illt especially in problems where the size of the contact surfaces is large with respect to the global domain

a simple and efficient extension of a class of substructure based preconditioners to heterogeneous structural mechanics problems several domain decomposition methods with lagrange multipliers have been recently designed for solving iteratively large scale systems of finite element equations while these methods differ typically by implementational details they share in most cases the same substructure based preconditioners that were originally developed for the feti method the success of these preconditioners is due to the fact that for homogeneous structural mechanics problems they ensure a computational performance that scales with the problem size in this paper we address the suboptimal behaviour of these preconditioners in the presence of material and or discretization heterogeneities we propose a simple and virtually no cost extension of these preconditioners that exhibits scalability even for highly heterogeneous systems of equations we consider several intricate structural analysis problems and demonstrate numerically the optimal performance delivered by the new preconditioners for problems with discontinuities copyright 1999 john wiley sons ltd

advances on the domain decomposition solution of large scale porous media problems abstract in this paper a family of state of the art parallel domain decomposition methods that combine the advantages of both direct and iterative solvers are investigated for the monolithic solution of the u p formulation of the porous media problem moreover a new family of parallel domain decomposition methods specifically tailored for the above problem formulation is presented which outperforms the current state of the art parallel domain decomposition solvers the power of this family of solvers is demonstrated in two large scale porous media problems

the mosaic of high performance domain decomposition methods for structural mechanics formulation interrelation and numerical efficiency of primal and dual methods a multitude of domain decomposition methods ddm for structural mechanics is available in the literature today a unified framework for formulating primal and dual ddm is thus presented in this paper aiming at providing a mathematical platform for a uniform treatment of high performance ddm in structural mechanics a novel approach for developing new ddm from existing methods is also proposed and is applied to dual and primal methods in the field of the feti methods this approach leads to a new category of methods derived from existing feti variants furthermore two alternative formulations of the balancing domain decomposition method are described while interrelations between the introduced and existing methods are established finally comparative numerical tests demonstrate the differences in the computational performance of the methods in question

the mosaic of high performance domain decomposition methods for structural mechanics part ii formulation enhancements multiple right hand sides and implicit dynamics domain decomposition methods ddm constitute a family of high performance solvers for large scale problems of computational mechanics and of structural mechanics in particular this paper compares popular ddm for structural analysis in both theory and computational performance while it investigates the impact of enhanced mapping operators in their convergence behavior multiple right hand side problems are considered while standard and new ddm solution techniques for implicit dynamics are tested the performed benchmark tests lead to useful conclusions regarding the comparative performance of the methods

an application of the separation principle for detecting slow fast limit cycles in a three dimensional system a geometric method called the separation principle is used in this paper for detecting limit cycles in a slow fast dynamical system describing a food chain with trophic levels with diversified time responses the analysis is very simple and based on singular perturbation arguments the limit cycle resulting from the method is composed of a concatenation of catastrophic transitions occuring at different speeds

finite element analysis of poro elastic consolidation in porous media standard and mixed approaches abstract in this paper two different numerical approaches for consolidation in porous media are developed and thoroughly compared galerkin finite element method gfem and least squares mixed finite element methods ls mfem the primary variables of the gfem are fluid pressure and solid displacement fluid fluxes and stresses are derived quantities in the ls mfem method all four unknown functions are primary variables which results in more accurate approximations of fluid fluxes and stresses results of both numerical methods are compared for two examples the first example for which an analytical solution is known is used in order to verify the implementation of the numerical schemes in the second example for a footing problem which was proposed by murad et al m murad v thomee a loula asymptotic behavior of semidiscrete finite element approximations of biot s consolidation problem siam j numer anal 33 1996 1065 1083 a detailed numerical analysis and comparison of both schemes are presented

error propagation of staggered solution procedures for transient problems abstract closed formulas for the error of staggered and simultaneous procedures are derived and compared conditions of global convergence are determined it is shown that in some cases a complicated condition for stability of the staggered scheme can be replaced by a simpler one the simultaneous stability condition for one iteration step a counterexample for global convergence of the staggered method with a constant number of iterations is presented

mortar finite element discretization for the flow in a nonhomogeneous porous medium abstract darcy s equations model the flow of a viscous incompressible fluid in a rigid porous medium one of the parameters of the system depends on the permeability of the medium and when this medium is not homogeneous the variations of the parameter could be very high to handle this phenomenon we propose a discretization of the model that relies on the mortar finite element method indeed the idea is to construct a decomposition of the domain such that the permeability is constant on each element of the partition and to use independent meshes on the different subdomains we perform the a priori and a posteriori analysis of this discretization and present some numerical experiments which are in good coherency with the results of the analysis

inverse modeling of groundwater flow using model reduction numerical groundwater flow models often have a very high number of model cells greater than a million such models are computationally very demanding which is disadvantageous for inverse modeling this paper describes a low dimensional formulation for groundwater flow that reduces the computational burden necessary for inverse modeling the formulation is a projection of the original groundwater flow equation on a set of orthogonal patterns i e a galerkin projection the patterns empirical orthogonal functions are computed by a decomposition of the covariance matrix over an ensemble of model solutions those solutions represent the behavior of the model as a result of model impulses and the influence of a chosen set of parameter values for an interchangeable set of parameter values the patterns yield a low dimensional model as the number of patterns is often small an advantage of this model is that the adjoint is easily available and most accurate for inverse modeling for several synthetical cases the low dimensional model was able to find the global minimum efficiently and the result was comparable to that of the original model for several cases our model even converged where the original model failed our results demonstrate that the proposed procedure results in a 60 time reduction to solve the groundwater flow inverse problem greater efficiencies can be expected in practice for large scale models with a large number of grid cells that are used to compute transient simulations

a posteriori error estimation of the representer method for single phase darcy flow a framework for goal oriented a posteriori error estimation is developed for the representer method a data assimilation scheme due to bennett a f bennet inverse methods in physical oceanography cambridge university press new york ny 1992 this framework is used to derive an estimate in the case of a mixed finite element approximation of a linear parabolic equation modeling single phase darcy flow in porous media the representer method is computationally expensive as are most da schemes therefore the error estimates are used to increase computational efficiency by allowing a systematic coarsening of the grids used to calculate the representers numerical experiments illustrate the derived estimates and computational savings

the design of blocked fractional factorial split plot experiments in industrial screening experiments if some factors are hard to vary and others are easy to vary randomization restrictions may lead to the use of fractional factorial split plot ffsp designs blocked ffsp bffsp designs arise when all runs cannot be performed under homogeneous conditions this article introduces three approaches for blocking ffsp designs a catalog of designs is presented in which bffsp designs are ranked according to the minimum aberration criterion in addition additional optimality criteria are used to assist in the ranking procedure the case study that motivated this research is also discussed in detail