models for disc infiltrometers disc infiltrometers are popular devices for determining in situ hydraulic properties of unsaturated soils this paper compares alternative solutions of richards equation for both steady state and time dependent cases the steady state solutions were in general agreement using alternative hydraulic conductivity functions of the same capillary length scale small time solutions for the nonlinear cases were consistent with linear diffusion from a disc source using an average diffusivity value which is simply related to the capillary length this offers a refinement over the one dimensional solution for short times in that the geometric effect of the circular source is included simulations for two examples indicate that the approach to the steady state solution may take considerably longer than what is commonly reported in the literature for field applications

linear maps preserving idempotents of tensor products of matrices abstract let f be a field of characteristic not 2 and m n the algebra of all n n matrices over f the aim of this paper is to characterize linear maps m m 1 m l m m 1 m l such that a 1 a l is an idempotent whenever a 1 a l is an idempotent

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

estimating unsaturated soil hydraulic properties from tension disc infiltrometer data by numerical inversion tension disc infiltrometers are becoming increasingly popular devices for in situ measurement of the unsaturated hydraulic properties of soil tension infiltration data are generally used to evaluate the parametersks and ain gardner s exponential model of the unsaturated hydraulic conductivity either two measurements using different disc diameters or measurements with a single disc but using multiple pressure heads are then used in this paper we describe a parameter estimation procedure which combines the levenberg marquardt nonlinear parameter optimization method involving weighted least squares with a quasi three dimensional numerical model which solves the variably saturatedflow equation by numerical inversion of richards equation the unknown parameters in van genuchten s model of the unsaturated soil hydraulic properties are estimated from observed cumulative infiltration data during transient waterflow additional measurements of the pressure head or water content as well as a penalty function for constraining the unknown parameters to remain in some feasible region bayesian estimation can be optionally included into the parameter estimation procedure the problem of optimal sampling design that is selecting the best points in space and time for making measurements is addressed by studying the sensitivity of the objective function to changes in the optimized hydraulic parameters we calculate objective functions based on available cumulative infiltration pressure head and water content measurements and also on several combinations of these data the behavior of the objective function in three dimensional parameter space is evaluated by means of a series of two dimensional response surfaces the utility of the parameter estimation procedure is demonstrated using numerically generated data the sensitivity of the procedure to different initial estimates of the model parameters is also discussed

boundary layer techniques for solving the helmholtz equation in the presence of small inhomogeneities we consider solutions to the helmholtz equation in two and three dimensions based on layer potential techniques we provide for such solutions a rigorous systematic derivation of complete asymptotic expansions of perturbations resulting from the presence of diametrically small inhomogeneities with constitutive parameters different from those of the background medium it is expected that our results will find important applications for developing effective algorithms for reconstructing small dielectric inhomogeneities from boundary measurements

estimation of root water uptake parameters by inverse modeling with soil water content data 1 in this paper we have tested the feasibility of the inverse modeling approach to derive root water uptake parameters rwup from soil water content data using numerical experiments for three differently textured soils and for an optimal drying period the rwup of interest are the rooting depth and the bottom root length density in a first step a thorough sensitivity analysis was performed this showed that soil water content dynamics is relatively insensitive to rwup and that the sensitivity depends on the texture of the considered soil for medium fine textured soil the sensitivity is particularly low due to relatively high unsaturated hydraulic conductivity values these ones allow a compensating effect to occur i e vertical unsaturated water fluxes overshadowing in some way the root water uptake in a second step we analyzed the well posedness of the solution stability and nonuniqueness when only rwup are optimized for this case the inverse problem is clearly ill posed except for the estimation of the rooting depth parameter for coarse and the very fine textured soils in a third step we addressed the case where rwup are estimated simultaneously with additional parameters of the system i e with soil hydraulic parameters for this case our study showed that the inverse problem is well posed for the coarse and very fine textured soils allowing for the estimation of both rwup of interest provided that a powerful global optimization algorithm is used on the contrary the estimation of rwup is unfeasible for medium fine textured soil due to the compensating effect of the vertical unsaturated water flows in conclusion we can state that the inverse modeling approach can be applied to derive rwup for some soils coarse and very fine textured and that the feasibility is strongly improved if the rwup are simultaneously optimized with additional parameters nevertheless more detailed research is needed to apply the inverse modeling approach to real cases for which additional issues are likely to be encountered such as soil heterogeneity and root dynamics

topology optimization with closed b splines and boolean operations abstract in this work free form curves of closed b splines cbs are introduced as basic design primitives to realize structural topology optimization in the way of shape optimization unlike the existing density and level set methods the cbs takes full advantage of its parametric form for the design deformability and flexibility with a few number of design variables and its implicit form for boolean operations of the structural topology accounting for any overlapping merging and separation of different cbs no matter how geometric complexities of the cbs and the design domain are the cbs is implemented within the computing framework of finite cell method fcm so that structural analysis and topology optimization can efficiently be carried out using the fixed mesh typical examples are tested to demonstrate the effectiveness and generality of the proposed method in dealing with engineering design problems

on convergence in elliptic shape optimization the present paper aims at analyzing the existence and convergence of approximate solutions in shape optimization motivated by illustrative examples an abstract setting of the underlying shape optimization problem is suggested taking into account the so called two norm discrepancy a ritz galerkin type method is applied to solve the associated necessary condition existence and convergence of approximate solutions are proved provided that the infinite dimensional shape problem admits a stable second order optimizer the rate of convergence is confirmed by numerical results

parameter equivalence for the brooks corey and van genuchten soil characteristics preserving the effective capillary drive this paper provides a simple way to convert brooks corey bc parameters to van genuchten vg parameters and vice versa for use primarily in situations where saturated conditions are likely to be encountered essential in this conversion is the preservation of the maximum value of a physical characteristic the effective capillary drive h morel seytoux and khanji 1974 defined with a good approximation for a soil water and air system as h jg k dh where k is relative permeability or conductivity to water and ii is capillary pressure head a positive quantity with this conversion infiltration calculations are essentially insensitive to the model used to represent the soil hydraulic properties it is strictly a matter of convenience for the user which expression is used on the other hand the paper shows that other equivalences may lead to great variations in predictions of infiltration capacity consequently the choice of the proper equivalence to use in calculations for rainfall runoff modeling or for low level radioactive waste disposal design is a serious matter

linear maps preserving idempotence on matrix modules over principal ideal domains abstract let r be a commutative principal ideal domain t m n r m m r an r linear map which preserves idempotence we determine the forms of t when n m and r f 2 and solve some of beasley s open problems as a consequence we prove that the set l r of all r linear maps on m n r which preserve both idempotence and nonidempotence is a proper subset of f r the set of all linear maps on m n r that preserve idempotence when the characteristic of r is 2

linear operators preserving idempotent matrices over fields abstract suppose f is a field we show that if the characteristic of the field is not 2 then the semigroup of linear operators on the n n matrices over f that preserve idempotence is the group g f generated by transposition and similarity chan lim and tan have previously established that theorem for the real and complex fields by other methods we also show that the semigroup l f of linear operators on the n n matrices over f that preserve both idempotence and nonidempotence is g f when the characteristic of f is not 2 we determine the structure of l f when the characteristic of f is 2 and present some open problems

linear maps preserving drazin inverses of matrices over fields abstract let f be a field with at least five elements m n f the n n full matrix algebra over f in this paper we determine the forms of linear maps from m n f to m m f preserving drazin inverses of matrices under ch f 2 and m n 1 and also determine the forms of linear bijections from m n f to itself preserving drazin inverses of matrices under ch f 2 and n 1

stochastic modeling of large scale transient unsaturated flow systems a new framework for modeling large scale transient unsaturated flow systems in spatially variable soils is proposed in order to overcome the problem of limited information about the local details of spatial soil variability a stochastic approach which assumes that local soil properties are realizations of three dimensional random fields is followed for derivation of a large scale model representation structure the three dimensionality of the local flow and the nonlinear dependence of the local flow output on the local soil properties are considered the large scale model structure is derived by averaging the local governing flow equation over the ensemble of realizations of the underlying soil property random fields the resulting mean model representation is in the form of a partial differential equation in which averaged or effective model parameters occur these effective model parameters i e effective hydraulic conductivity and effective specific moisture capacity are evaluated using a quasi linearized fluctuation equation and a spectral representation of stationary processes the large scale model representation considers the large scale effects of soil property variability and has relatively few parameters the general conclusions of this study are that soil property variability produces large scale hysteresis and anisotropy of the effective parameters the potential theoretical and practical ramifications of these results in the area of unsaturated flow modeling need to be investigated the general stochastic modeling framework developed here is applicable not only to unsaturated flow but also to other distributed parameter systems e g saturated flow and transport geothermal and oil reservoir modeling

determining soil hydraulic functions from evaporation experiments by a parameter estimation approach experimental verifications and numerical studies a parameter estimation method is developed for the determination of unsaturated soil hydraulic properties from evaporation experiments under laboratory conditions variables used in the inversion procedure are soil water pressure heads at various positions and total soil weights both measured as a function of time during the experiment unknown parameters of different analytical expressions used to describe the soil hydraulic properties are estimated by coupling a finite difference solution of the richards equation with a nonlinear optimization problem this problem is formulated by minimizing the deviations between the numerical solution of the transient flow process and the real system response measured during the experiment minimization of the objective function is performed using a version of the levenberg marquardt s method the procedure also provides information about the uncertainty in parameter estimates the performance of the selected parametric relationships is evaluated and the applicability and accuracy of the proposed inverse method are shown by comparing estimated water retention and hydraulic conductivity functions with experimental results obtained via the instantaneous profile method parameter sensitivity analyses and stability of the inverse solutions are discussed with reference to the originally designed evaporation experiment and to an evaporation method that is developed with a view to reducing experimental efforts further insights into the properties of existence and uniqueness of inverse solutions are gained by examining contour plots of the objective functions under varying experimental conditions the results confirm the reliability and flexibility of the proposed method and suggest that the evaporation flux imposed at the upper soil surface may determine the well posedness of the optimization problem

an efficient method for simulating steady unsaturated flow in random porous media using an analytical perturbation solution as initial guess to a numerical model numerical simulation of flow through multidimensional heterogeneous soils under unsaturated conditions is a computationally intensive task the governing unsaturated flow equation is nonlinear the degree of nonlinearity depends on the unsaturated hydraulic properties of the soil and the degree of heterogeneity in this paper we present a highly efficient method to simulate unsaturated steady state flow through random porous media our method utilizes the analytical approximate solution derived by a perturbation spectral method as an initial guess solution for a numerical model to simulate two dimensional vertical infiltration problems it is found that this approach which we call asigning reduces the required cpu time by one to two orders of magnitude asigning is demonstrated to operate successfully under a wide variety of boundary conditions which may substantially deviate from those imposed on the initial guess solution a large range of mean and variances in the independent variables ln ks and or alternatively in has been tested and it is shown that the method works well for variances of the unsaturated hydraulic conductivity ln2k 5 and average 0 1 cm 1

a level set based topology optimization method targeting metallic waveguide design problems in this paper we propose a level set based topology optimization method targeting metallic waveguide design problems where the skin effect must be taken into account since the metallic waveguides are generally used in the high frequency range where this effect critically affects performance one of the most reasonable approaches to represent the skin effect is to impose an electric field constraint condition on the surface of the metal to implement this approach we develop a boundary tracking scheme for the arbitrary lagrangian eulerian ale mesh pertaining to the zero iso contour of the level set function that is given in an eulerian mesh and impose dirichlet boundary conditions at the nodes on the zero iso contour in the ale mesh to compute the electric field since the ale mesh accurately tracks the zero iso contour at every optimization iteration the electric field is always appropriately computed during optimization for the sensitivity analysis we compute the nodal coordinate sensitivities in the ale mesh and smooth them by solving a helmholtz type partial differential equation the obtained smoothed sensitivities are used to compute the normal velocity in the level set equation that is solved using the eulerian mesh and the level set function is updated based on the computed normal velocity finally the utility of the proposed method is discussed through several numerical examples copyright 2011 john wiley sons ltd

the topological asymptotic for pde systems the elasticity case the aim of the topological sensitivity analysis is to obtain an asymptotic expansion of a design functional with respect to the creation of a small hole in this paper such an expansion is obtained and analyzed in the context of linear elasticity for general functionals and arbitrary shaped holes by using an adaptation of the adjoint method and a domain truncation technique the method is general and can be easily adapted to other linear pdes and other types of boundary conditions

parameter estimation in flow through partially saturated porous materials a class of numerical simulators were developed and critically evaluated to be incorporated as the solver of a forward problem in the framework of an inverse modeling strategy the strategy couples a mass lumped galerkin linear finite element solution of the mixed form richards equation with an experimental time space series and the osborne more revised form of the levenberg marquardt algorithm to retrieve hydraulic parameters of a partially saturated porous medium the numerical simulator shows excellent agreement with a reference solution obtained on a dense grid and infinitesimal time step in terms of fluid pressure head fluid content and fluid volumetric flux density and perfectly conserves the global mass an adaptive algorithm was implemented to estimate sensitivity matrix in the inverse algorithm a multi criterion stopping rule was developed and successfully implemented to end the inverse code at the solution the result of the optimization was compared with a large scale in situ soil moisture space time series measured during the course of a drainage experiment and excellent agreements were found analysis of the parameter response surfaces and hyper space plots closeness of the gradient of the penalty function at minimum to zero and positive definiteness of the approximation for the hessian at the solution eigs h 0 indicate that the obtained solution is a strong local minimum a state of the art sensitivity analysis carried out to quantify sensitivity of the state variable with respect to uncertainty and changes in different model parameters

the topological asymptotic for the helmholtz equation with dirichlet condition on the boundary of an arbitrarily shaped hole the aim of the topological sensitivity analysis is to obtain an asymptotic expansion of a design functional with respect to the creation of a small hole in the domain in this paper such an expansion is obtained for the helmholtz equation in two and three space dimensions with a dirichlet condition on the boundary of an arbitrarily shaped hole in this case the main difficulty is related to the nonhomogeneous symbol of the helmholtz operator in the numerical part of this work we will show that the topological sensitivity method is very promising for solving shape inverse problems in electromagnetic applications

stochastic analysis of unsaturated flow in heterogeneous soils 1 statistically isotropic media steady unsaturated flow with vertical mean infiltration through unbounded heterogeneous porous media is analyzed using a perturbation approximation of the stochastic flow equation which is solved by spectral representation techniques the hydraulic conductivity k is related to the capillary pressure head by k ks exp where ks is the saturated conductivity and is a soil parameter a general formulation is presented for the case with ks and represented as statistically homogeneous spatial random fields in part 1 solutions are developed assuming is constant and representing ks variability by one dimensional and three dimensional isotropic random fields results are obtained for head variances and covariance functions effective hydraulic conductivities variances of the unsaturated hydraulic conductivity flux variances and variance of pressure gradient when the parameter is relatively large corresponding to coarse textured soils the head variance decreases and all of the results demonstrate a trend toward gravitationally dominated one dimensional vertical flow the effective conductivity is dependent on the correlation scale of ln ks and the mean hydraulic gradient

topology optimization of steady navier stokes flow with body force abstract this paper presents the topology optimization of steady navier stokes flows with body forces that influence the optimal shape and topology of fluid flows based on the implicit expression of the fluid flow with the level set method an optimization problem is formulated and analyzed using the continuous adjoint method the shape and topological sensitivities are computed based on the adjoint and asymptotic analysis of the optimization problem in the optimization procedure the level set surface is evolved based on the shape sensitivity and nucleated based on the topological sensitivity simultaneously three kinds of body forces that are commonly used in the design of fluid devices i e constant nonuniform and solution dependent body forces are considered in the two dimensional and three dimensional numerical examples numerical results demonstrate that this method can effectively achieve the topology optimization of the navier stokes flows with body forces

incorporating topological derivatives into shape derivatives based level set methods shape derivatives and topological derivatives have been incorporated into level set methods to investigate shape optimization problems the shape derivative measures the sensitivity of boundary perturbations while the topological derivative measures the sensitivity of creating a small hole in the interior domain the combination of these two derivatives yields an efficient algorithm which has more flexibility in shape changing and may escape from a local optimal examples on finding the optimal shapes for maximal band gaps in photonic crystal and acoustic drum problems are demonstrated

a mass conservative switching algorithm for modeling fluid flow in variably saturated porous media numerical solutions of flow equation in fluid content based form or in fluid pressure head based form are often tradeoffs between speed accuracy and convenience the fluid content based form can be solved quite rapidly with low cpu time and perfect mass balance however it cannot be used in saturated regions as diffusivity function becomes infinite and strictly becomes invalid in composite layered and real heterogeneous porous materials due to singularity and discontinuity in fluid content profile this formulation also gives misleading impression that gradient in fluid content causes the flow of fluid in porous materials where in reality gravity and fluid pressure potential gradient produce the motion the pressure head based form on the other hand is more flexible but due to its highly nonlinear nature is much more time consuming and produces poor global mass balance for dry initial conditions very fine spatial and temporal discretizations are needed to maintain mass balance property for these scenarios the mixed form of the flow equation partially solves these issues as it maintains acceptable mass balance and is applicable to layered heterogeneous and composite fractured foundations however it is only applicable in unsaturated zones in this study a switching algorithm was proposed and implemented in which the mass conservative mixed form and the pressure head based form were respectively used in the unsaturated and saturated zones of an initial boundary value flow problem involving a variably saturated porous medium the algorithm showed excellent agreement with a reference solution obtained on a very fine spatiotemporal mesh the simulator was then calibrated with several real world large scale experimental datasets in all cases the proposed algorithm exhibited close agreements with the experimental time space series the algorithm poses excellent mass balance property and can easily be used in both saturated and unsaturated regions without special treatment of fluid content discontinuities in heterogeneous and layered porous media the proposed algorithm can also be extended to simulate multiphase and multidimensional flow problems

a binary level set model and some applications to mumford shah image segmentation in this paper we propose a pde based level set method traditionally interfaces are represented by the zero level set of continuous level set functions instead we let the interfaces be represented by discontinuities of piecewise constant level set functions each level set function can at convergence only take two values i e it can only be 1 or 1 thus our method is related to phase field methods some of the properties of standard level set methods are preserved in the proposed method while others are not using this new method for interface problems we need to minimize a smooth convex functional under a quadratic constraint the level set functions are discontinuous at convergence but the minimization functional is smooth we show numerical results using the method for segmentation of digital images

an iterative geostatistical inverse method for steady flow in the vadose zone an iterative geostatistical inverse approach is developed to estimate conditional effective unsaturated hydraulic conductivity parameters soil water pressure head and degree of saturation in heterogeneous vadose zones this approach is similar to the classical cokriging technique and it uses a linear estimator that depends on covariances and cross covariances of unsaturated hydraulic parameters soil water pressure head and degree of saturation the linear estimator is however improved successively by solving the governing flow equation and by updating the residual covariance and cross covariance functions in an iterative manner as a result the nonlinear relationship between unsaturated hydraulic conductivity parameters and head is incorporated in the estimation and the estimated fields are approximate conditional means the ability of the iterative approach is demonstrated through some numerical examples

a level set method for shape and topology optimization of both structure and support of continuum structures abstract we present a level set method for the shape and topology optimization of both structure and support two level set functions are used to implicitly represent a structure the traction free boundary and the dirichlet boundary are represented separately and are allowed to be continuously changed during the optimization the optimization problem of minimum compliance is considered the shape derivatives of both boundaries are derived by using a lagrangian function and the adjoint method the finite element analysis is done by modifying a fixed background mesh and we do not use the artificial weak material numerical examples in two dimensions are investigated

on the identification of macroscopic root water uptake parameters from soil water content observations 1 in this paper we analyze the identification problem of macroscopic root water uptake parameters from soil water content observations for this study the macroscopic root water uptake is considered to be linearly decreasing with depth with a and b parameters conditioning respectively the maximum root water uptake at the surface and the decreasing rate with depth for identification of parameter a and b two different identification approaches are tested using a detailed soil moisture data set consisting of vertical profiles measured with time domain reflectometry tdr and neutron probe on 28 locations within a small maize cropped field during a dry period of 26 days the first approach is based on a simplified water balance while the second one uses an integrated soil vegetation atmosphere transfer svat model in an inverse mode results of the simplified water balance show first that the root water uptake measured within the field is quite variable with cv ranging from 22 to 34 for the root uptake parameters a and b respectively furthermore positive correlation between a and b suggests that low superficial root water uptake could be compensated by high deep root water uptake second numerical simulations used to test the validity of this simplified approach show that the method is quite robust at least for a certain range of a parameter values 0 008 a 0 013 for b and for all investigated differently textured soils except the coarse sand to investigate the feasibility and the robustness of the second approach we address the problems of insensitivity instability and nonuniqueness by means of numerical simulations results show for soils with different textures that the soil water content and to a lesser extent the time derivative of soil water content are quite insensitive to root water uptake parameters at least compared to soil hydraulic parameters furthermore instability analysis clearly illustrates that root water uptake parameters are quite and even very instable with respect to small uncertainties on the apparently known parameters e g soil parameters finally results show that if root water uptake plus additional other parameters e g soil parameters are simultaneously optimized nonuniqueness of parameter sets must be expected therefore a robust identification of root water uptake parameters by means of a full svat inversion is unlikely to be achieved during a dry period with soil water content observations at least when some other parameters driving the system like soil hydraulic properties are not error free in this context further in depth research is needed to investigate if the use of longer periods characterized by both drying and redistribution events may increase the success of a full svat inversion finally to extend the results of this study we recommend applying a similar analysis to other macroscopic conceptual root water uptake models

the topological asymptotic expansion for the dirichlet problem the topological sensitivity analysis provides an asymptotic expansion of a shape function when creating a small hole inside a domain this expansion yields a descent direction which can be used for shape optimization if one wishes to keep a classical domain throughout the optimization process in this paper such an expansion is obtained for the poisson equation for a large class of cost functions and arbitrarily shaped holes in the three dimensional case this expansion depends on the shape of the hole but not on its orientation if the cost function involves only the solution u to the underlying partial differential equation whereas it may also depend on its orientation if the cost function involves the gradient nabla u in contrast the asymptotic expansion is independent of the shape in the two dimensional case a numerical example illustrates the use of the asymptotic expansion which yields a minimizing sequence of classical domains in a case where no classical solution exists

a global multilevel coordinate search procedure for estimating the unsaturated soil hydraulic properties we present a new inverse modeling procedure to characterize the hydraulic properties of partially saturated soils from soil moisture measurements during a natural transient flow experiment the inversion of the governing one dimensional richards equation is carried out using the global multilevel coordinate search optimization algorithm in sequential combination with the local nelder mead simplex algorithm gmcs nms we introduce this optimization method in the area of unsaturated zone hydrology since it is adapted for solving accurately and efficiently complex nonlinear problems several numerical experiments have been conducted to evaluate the proposed inversion method using synthetic error free and error contaminated data for different textured soils inversion of the simulated error free data and examination of the related response surfaces demonstrated the uniqueness of the inverse solution and the suitability of the gmcs nms strategy when identifying four key parameters of the hydraulic functions described by the mualem van genuchten model inversion of the error contaminated data proved further the good stability of the inverse solution that is consistent with the needs required by real experiments

shape and topology optimization of compliant mechanisms using a parameterization level set method in this paper a parameterization level set method is presented to simultaneously perform shape and topology optimization of compliant mechanisms the structural shape boundary is implicitly embedded into a higher dimensional scalar function as its zero level set resultantly establishing the level set model by applying the compactly supported radial basis function with favorable smoothness and accuracy to interpolate the level set function the temporal and spatial hamilton jacobi equation from the conventional level set method is then discretized into a series of algebraic equations accordingly the original shape and topology optimization is now fully transformed into a parameterization problem namely size optimization with the expansion coefficients of interpolants as a limited number of design variables design of compliant mechanisms is mathematically formulated as a general optimization problem with a nonconvex objective function and two additionally specified constraints the structural shape boundary is then advanced as a process of renewing the level set function by iteratively finding the expansion coefficients of the size optimization with a sequential convex programming method it is highlighted that the present method can not only inherit the merits of the implicit boundary representation but also avoid some unfavorable features of the conventional discrete level set method such as the cfl condition restriction the re initialization procedure and the velocity extension algorithm finally an extensively investigated example is presented to demonstrate the benefits and advantages of the present method especially its capability of creating new holes inside the design domain

the computational modeling of problems on domains with small holes abstract the modeling challenges arising when the problem domain has small supported holes in it are considered through a representative membrane problem such problems are sometimes modeled intuitively in engineering practice by taking the limiting case of holes with zero radius this intuitive model is incorrect since it has no mathematical solution it is demonstrated however that finite element approximations based on it can still satisfy verification tests and appear to converge leading to erroneous recovery of quantities of interest this points to the need for an alternate approach where the holes of finite radius are properly incorporated in the modeling and robustness with respect to the radius is maintained to this end a computational method is presented which combines analytic knowledge of the solution singularities with finite element approximation of its smooth components theoretical and numerical results are provided establishing the efficacy and robustness of the method in extracting quantities of interest the method converges both with respect to the size of the holes and the mesh discretization parameter and provides a more accurate alternative to using the asymptotic limit

a hybrid global optimization method for inverse estimation of hydraulic parameters annealing simplex method inverse estimation of unsaturated hydraulic parameters is often a highly nonlinear optimization problem with multiple parameters the objective functions involved are often topographically complex and may contain many local minima because of these reasons the inverse solutions are commonly very sensitive to the initial guess of the parameters when conventional optimizers are used this paper presents an annealing simplex method that incorporates simulated annealing strategies into a classical downhill simplex method an upward infiltration experiment was used as an example of inverse estimation to test the method numerical experiments of both minimizing an algebraic function and inversion of upward infiltration data showed that the new method successfully converged to the global minimum in all cases irrespective of the initial hydraulic parameter estimates while the classical downhill method often converged to unfavorable local minima the cpu times needed for the annealing simplex method to estimate 5 and 7 hydraulic parameters simultaneously are about a half hour and 1 hour on a pc respectively additionally no special requirements are imposed on the objective function and the method is independent of the details of the simulation submodel therefore the proposed method should be applicable to other optimization problems in water resources when it is important to have a robust global search capability

topological sensitivity analysis the so called topological derivative concept has been seen as a powerful framework to obtain the optimal topology for several engineering problems this derivative characterizes the sensitivity of the problem when a small hole is created at each point of the domain however the greatest limitation of this methodology is that when a hole is created it is impossible to build a homeomorphic map between the domains in study because they have not the same topology therefore some specific mathematical framework should be developed in order to obtain the derivatives this work proposes an alternative way to compute the topological derivative based on the shape sensitivity analysis concepts the main feature of this methodology is that all the mathematical procedure already developed in the context of shape sensitivity analysis may be used in the calculus of the topological derivative this idea leads to a more simple and constructive formulation than the ones found in the literature further to point out the straightforward use of the proposed methodology it is applied for solving some design problems in steady state heat conduction

topological derivative based topology optimization of structures subject to drucker prager stress constraints abstract an algorithm for topology optimization of elastic structures under plane stress subject to the drucker prager stress constraint is presented the algorithm is based on the use of the topological derivative of the associated objective functional in conjunction with a level set representation of the structure domain in this context a penalty functional is proposed to enforce the point wise stress constraint and a closed formula for its topological derivative is derived the resulting algorithm is of remarkably simple computational implementation it does not require post processing procedures of any kind and features only a minimal number of user defined algorithmic parameters this is in sharp contrast with current procedures for topological structural optimization with local stress constraints the effectiveness and efficiency of the algorithm presented here are demonstrated by means of numerical examples the examples show in particular that it can easily handle structural optimization problems with underlying materials featuring strong asymmetry in their tensile and compressive yield strengths

asymptotic analysis polarization matrices and topological derivatives for piezoelectric materials with small voids asymptotic formulae for the mechanical and electric fields in a piezoelectric body with a small void are derived and justified such results are new and useful for applications in the field of design of smart materials in this way the topological derivatives of shape functionals are obtained for piezoelectricity the asymptotic formulae are given in terms of the so called polarization tensors matrices which are determined by the integral characteristics of voids the distinguishing feature of the piezoelectricity boundary value problems under consideration is the absence of positive definiteness of a differential operator which is non self adjoint two specific gibbs functionals of the problem are defined by the energy and the electric enthalpy the topological derivatives are defined in different manners for each of the governing functionals actually the topological derivative of the enthalpy functional is local i e defined by the pointwise values of the mechanical and electric fields which is contrary to the energy functional and some other suitable shape functionals which admit nonlocal topological derivatives i e depending on the whole problem data an example with weak interaction between mechanical and electric fields provides the analytic asymptotic expansions and can be used in numerical procedures of optimal design for smart materials

sounding of finite solid bodies by way of topological derivative this paper is concerned with an application of the concept of topological derivative to elastic wave imaging of finite solid bodies containing cavities building on the approach originally proposed in the elastostatic theory of shape optimization the topological derivative which quantifies the sensitivity of a featured cost functional due to the creation of an infinitesimal hole in the cavity free reference body is used as a void indicator through an assembly of sampling points where it attains negative values the computation of topological derivative is shown to involve an elastodynamic solution to a set of supplementary boundary value problems for the reference body which are here formulated as boundary integral equations for a comprehensive treatment of the subject formulas for topological sensitivity are obtained using three alternative methodologies namely i direct differentiation approach ii adjoint field method and iii limiting form of the shape sensitivity analysis the competing techniques are further shown to lead to distinct computational procedures methodologies i and ii are implemented within a bem based platform and validated against an analytical solution a set of numerical results is included to illustrate the utility of topological derivative for 3d elastic wave sounding of solid bodies an approach that may perform best when used as a pre conditioning tool for more accurate gradient based imaging algorithms despite the fact that the formulation and results presented in this investigation are established on the basis of a boundary integral solution the proposed methodology is readily applicable to other computational platforms such as the finite element and finite difference techniques

on the topological derivative in shape optimization in this paper the topological derivative for an arbitrary shape functional is defined examples are provided for elliptic equations and the elasticity system in the plane the topological derivative can be used for solving shape optimization problems in structural mechanics

review of parameter identification procedures in groundwater hydrology the inverse problem the purpose of this survey is to review parameter identification procedures in groundwater hydrology and to examine computational techniques which have been developed to solve the inverse problem parameter identification methods are classified under the error criterion used in the formulation of the inverse problem the problem of ill posedness in connection with the inverse problem is addressed typical inverse solution techniques are highlighted the review also includes the evaluation of methods used for computing the sensitivity matrix statistics which can be used to estimate the parameter uncertainty are outlined attempts have been made to compare and contrast representative inverse procedures and direction for future research is suggested

qualitative identification of cracks using 3d transient elastodynamic topological derivative formulation and fe implementation a time domain topological derivative td approach is developed for transient elastic wave imaging of buried cracks the td which quantifies the sensitivity of the misfit cost functional to the creation at a specified location of an infinitesimal trial crack is expressed in terms of the time convolution of the free field and an adjoint field as a function of that specified location and of the trial crack shape following previous studies on cavity identification in similar conditions the td field is here considered as a natural and computationally efficient approach for defining a crack location indicator function this study emphasizes the implementation and exploitation of td fields using the standard displacement based fem a straightforward exploitation of the relevant sensitivity formulation established here results on several numerical experiments on 3d elastodynamic and acoustic configurations are reported and discussed allowing to assess and highlight many features of the proposed td based fast qualitative crack identification including its ability to identify multiple cracks and its robustness against data noise

analyses of infiltration events in relation to determining soil hydraulic properties by inverse problem methodology at the field scale because of the relatively large number of observation points required to estimate the spatial distributions of hydraulic properties application of inversion procedures must be based on a characteristic of the flow that for a given point in the field can be measured with relative ease and can be used as input for the inversion procedure suggesting the use of infiltration data for this purpose and recognizing the fact that a basic requirement for the design of a transient flow experiment is that the resulting inverse problem be sufficiently well posed to allow solution this paper addresses the question under which circumstances the resulting inverse problem is well posed utilizing the concepts of identifiability uniqueness and stability for this purpose three different models of the soil hydraulic properties were analyzed the main conclusion of this study is that when infiltration data measured at the darcy scale are used as input for the inversion procedure the inclusion of prior information on a single measurable parameter the saturated conductivity ks in the estimation criterion will enhance the likelihood of uniqueness and stability of the inverse solution provided that the structure of the hydraulic model is sufficiently simple however since for a particular situation it is impossible to determine a priori whether the resultant inverse problem is well posed or not this must be carried out only a posteriori by solving the problem several times with different initial parameter estimates accompanied by an analysis of the associated estimation errors

determining soil hydraulic properties by parameter estimation on the selection of a model for the hydraulic properties parameter estimation procedures involving solution of the inverse flow problem pertinent to a transient experiment constitute a powerful method of determining the soil hydraulic properties one of the problems associated with these procedures is the selection of an appropriate model to describe the soil hydraulic properties three different models were considered those of van genuchten vg and brooks and corey bc model and the exponential model of gardner for the hydraulic conductivity soil water pressure relationships coupled with a new expression for the soil water content soil water pressure relationship gr model for a given model the soil hydraulic properties were determined from simulated and measured outflow experiments supplemented with water content at a soil water pressure head of 15 000 cm h2o using the parameter estimation procedure of kool et al 1985a and data from two soils a hypothetical sandy loam soil assumed to be described by the vg model and a silt loam soil model validation tests were performed and the most appropriate model was selected from the candidate models by discrimination tests using the akaike information criterion aic in the case of the hypothetical sandy loam the vg model was found to be the most accurate and most consistent with the data the performance of both the bc and the gr models in terms of the aic was less good but very similar to each other in the case of the silt loam soil the vg model with additional parameter m which accounts for the correlation between pores and for the flow path tortuosity m 2 02 rather than a constant m 0 5 was found to be most accurate and most consistent with the data the performance of the bc and the gr models was similar when m was considered as an unknown parameter instead of a constant

lognormal distribution model for unsaturated soil hydraulic properties the soil water retention model developed by kosugi was modified to be compatible with mualem s model in order to derive an analytical expression for the relative hydraulic conductivity kr the modified water retention model is to be derived by applying a lognormal distribution law to the soil pore radius distribution function parameters of this retention model have physical significance on the water content capillary pressure curve and are related directly to the statistics of the pore radius distribution the accuracy of the resulting combined water retention hydraulic conductivity model is verified for observed data sets for six soils results showed that the proposed model produces acceptable matches with observed water retention curves and adequate predictions of hydraulic conductivities in five out of six cases the and kr or kr curves generated by this model are generally similar to those generated by van genuchten s model

statistical analysis of spatial variability in unsaturated flow parameters core scale estimates of soil parameters of the gardner russo and van gemachten models of the hydraulic conductivity and water retention functions were obtained for 417 undisturbed soil cores taken from a wall of a trench 20 m long 2 5 m deep using a procedure based on inverse problem methodology these estimates were used to evaluate the first two statistical moments of the underlying random space functions rsfs using the restricted maximum likelihood estimation procedure coupled with the weighted least squares procedure to estimate parameters of models of the covariance and the drift functions of the pertinent rsfs the fitted models were used to evaluate the mean and covariance functions of the hydraulic conductivity and water rentention functions for given water saturations covariance functions of log saturated conductivity log ks and the shape parameters of the gardner russo and van genuchten models exhibited statistical anisotropy characterized by aspect ratios that vary between 3 to 4 correlation scales of log ks were larger than those of the shape parameters consequently the product of the variance of log unsaturated conductivity and its correlation scale remained essentially invariant for a considerable range of water saturation the implications of these results regarding stochastic modeling of transport in heterogeneous porous formations and possible applications of the results of this study are discussed briefly

modular automorphisms preserving idempotence and jordan isomorphisms of triangular matrices over commutative rings abstract suppose r is a commutative ring with 1 and 2 being the units of r let t n r be the n n upper triangular matrix modular over r and let l r be the set of all r module automorphisms on t n r that preserve idempotence the main result in this paper is that f l r if and only if there exist an invertible matrix u t n r and an idempotence e r such that f x u ex 1 e x u 1 for any x x ij t n r where x x n 1 j n 1 i as applications we determine all jordan isomomorphisms of t n r over the ring r

damage and fracture evolution in brittle materials by shape optimization methods this paper is devoted to a numerical implementation of the francfort marigo model of damage evolution in brittle materials this quasi static model is based at each time step on the minimization of a total energy which is the sum of an elastic energy and a griffith type dissipated energy such a minimization is carried over all geometric mixtures of the two healthy and damaged elastic phases respecting an irreversibility constraint numerically we consider a situation where two well separated phases coexist and model their interface by a level set function that is transported according to the shape derivative of the minimized total energy in the context of interface variations hadamard method and using a steepest descent algorithm we compute local minimizers of this quasi static damage model initially the damaged zone is nucleated by using the so called topological derivative we show that when the damaged phase is very weak our numerical method is able to predict crack propagation including kinking and branching several numerical examples in 2d and 3d are discussed

the shape and topological optimizations connection abstract in 1973 jean cea introduced a topological shape optimization algorithm based on a fixed point method the recent topological gradient concept provides a mathematical justification of cea s powerful method the aim of the topological gradient is to compute the sensitivity of a cost function when we drill a little hole in the domain some optimality conditions are derived when classical shape gradient and topological gradient are used simultaneously and numerical results are shown both in mechanics and electromagnetics

parameter estimation of hydraulic properties from one step outflow data the one step outflow method was presented by kool et al 1985a b as a fast procedure to estimate unsaturated soil hydraulic properties many investigators however encountered difficulties obtaining a unique solution to the problem the purpose of this paper is to evaluate some of the problems related to this method by looking at response surfaces and to make recommendations for improvements in the methodology the one step outflow procedure was investigated using synthetic data sets generated for 7 6 cm diameter by 7 6 cm high soil cores a finite difference solution of richards equation was used to generate the synthetic data sets response surfaces were calculated for the van genuchten parameters n and ks for various combinations of matric potential water content and outflow data from initially saturated soil cores subjected to a step change in pressure at one of its boundaries the results clearly show that with outflow data alone the parameter estimation procedure will have difficulty converging however if matric potential data are available for a point in the core at some distance from the outflow boundary parameter estimation sensitivity is greatly improved the procedure used was found to be most helpful for determining which auxiliary variables should be measured for parameter estimation from outflow experiments

regularized perimeter for topology optimization the perimeter functional is known to oppose serious difficulties when it has to be handled within a topology optimization procedure in this paper a regularized perimeter functional mbox per varepsilon defined for two and three dimensional domains is introduced on one hand the convergence of mbox per varepsilon to the exact perimeter when varepsilon tends to zero is proved on the other hand the topological differentiability of mbox per varepsilon for varepsilon 0 is analyzed these features lead to the design of a topology optimization algorithm suitable for perimeter dependent objective functionals several numerical results illustrate the method

linear k power k potent preservers between matrix spaces abstract suppose f is a field let mn f be the linear space of all n n matrices over f and let sn f be its subspace consisting of all symmetric matrices let m n k be positive integers with k 2 and let v m n f s n f and w m m f s m f a linear map f v w is called a k power preserver if f a k f ak for every a v and a k potent preserver if f a k f a for any a v with ak a we characterize i linear k power preservers from mn f to mm f when ch f k or ch f 0 ii linear k potent preservers from mn f to mm f when f is an algebraically closed field with ch f 0 iii linear k power preservers from sn f to mm f respectively sm f when ch f k 5 or ch f 0 and iv linear k potent preservers from sn f to mm f respectively sm f when f is an algebraically closed field with ch f 0

a topology optimization method based on the level set method incorporating a fictitious interface energy this paper proposes a new topology optimization method which can adjust the geometrical complexity of optimal configurations using the level set method and incorporating a fictitious interface energy derived from the phase field method first a topology optimization problem is formulated based on the level set method and the method of regularizing the optimization problem by introducing fictitious interface energy is explained next the reaction diffusion equation that updates the level set function is derived and an optimization algorithm is then constructed which uses the finite element method to solve the equilibrium equations and the reaction diffusion equation when updating the level set function finally several optimum design examples are shown to confirm the validity and utility of the proposed topology optimization method

estimation of brooks corey parameters from water retention data the parameters of the brooks corey soil moisture characteristic may be determined by either graphical or automatic numerical procedures a popular log log procedure for automatic estimation leads to a linear least squares optimization problem apparently it has been applied incorrectly in the past when all measurements were used for parameter estimation and this realization explains the inconsistencies in some published data its proper application generally requires the solution of more than one linear problem for each data set alternatively a nonlinear procedure will yield parameter estimates directly in either case there may exist multiple local minima in the sum of squared deviations between model and measurements and the parameter estimates so derived are demonstrably unreliable this appears to be a result of the distinct air entry suction implicit in the brooks corey model and usually absent in field measured characteristic curves a new procedure based on an integral objective function overcomes the problems cited

a semismooth newton method for topology optimization abstract this paper deals with elliptic optimal control problems for which the control function is constrained to assume values in 0 1 based on an appropriate formulation of the optimality system a semismooth newton method is proposed for the solution convergence results are proved and some numerical tests illustrate the efficiency of the method

idempotent elements determined matrix algebras abstract let m n r be the algebra of all n n matrices over a unital commutative ring r with 2 invertible v be an r module it is shown in this article that if a symmetric bilinear map from m n r m n r to v satisfies the condition that u u e u whenever u 2 u then there exists a linear map f from m n r to v such that x y f x y x y m n r applying the main result we prove that an invertible linear transformation on m n r preserves idempotent matrices if and only if it is a jordan automorphism and a linear transformation on m n r is a jordan derivation if and only if it is jordan derivable at all idempotent points

exploring dynamic effects in capillary pressure in multistep outflow experiments 1 traditional steady state experiments to measure constitutive relations governing two phase organic aqueous flow in the subsurface often extend over periods of weeks or months alternatively one step or multistep outflow mso experiments can be combined with application of a multiphase flow simulator and an optimization algorithm to achieve a more rapid technique for parameter estimation in this work mso experiments were conducted to produce a data set for the estimation of two phase constitutive parameters using this inverse modeling approach examination of experimental results reveals significant discrepancies between observed and simulated outflow data with simulated curves tending to approach equilibrium at a faster rate than the experimental observations similar behavior has been documented by other investigators application of alternative equilibrium constitutive models in the multiphase flow optimization simulator failed to improve model fits to observed data however when model governing equations were modified to incorporate a dynamic capillary pressure term there was significant improvement in the agreement between measured and simulated cumulative water outflow and outflow rates comparisons of simulated and measured data further suggest that the dynamic capillary pressure constitutive coefficient depends on saturation attribution of the observed experimental deviations to dynamic effects in capillarity is also supported by the consistency of the fit equilibrium retention function with an independently measured static retention relation