stefan problems with nonlinear diffusion and convection abstract we consider a class of stefan type problems having a convection term and a pseudomonotone nonlinear diffusion operator assuming data in l 1 we prove existence uniqueness and stability in the framework of renormalized solutions existence is established from compactness and monotonicity arguments which yield stability of solutions with respect to l 1 convergence of the data uniqueness is proved through a classical l 1 contraction principle obtained by a refinement of the doubling variable technique which allows us to extend previous results to a more general class of nonlinear possibly degenerate operators

existence and uniqueness of solutions for a class of doubly degenerate parabolic equations abstract in this paper we study the dirichlet problem for degenerate parabolic equations of the form u t div a x t u u div u f div g where the main operator a x t u u is allowed to degenerate with respect to the unknown u under suitable conditions on a and we prove that there exists an unique solution u of this problem

on the existence of weak solutions for quasilinear parabolic initial boundary value problems structure conditions on a strongly nonlinear operator a u are given under whichthe initial dirichlet boundary value problem for has weak solutions

a novel technique for inverse identification of distributed stiffness factor in structures abstract a computational inverse technique for identifying stiffness distribution in structures is proposed in this paper using structural dynamics response in the frequency domain in the present technique element stiffness factors of the finite element model of a structure are taken to be the parameters and explicitly expressed in a linear form in the system equation for forward analysis of the harmonic response of the structure this offers great convenience in applying newton s method to search for the parameters of stiffness factor inversely as the jacobian matrix can be obtained simply by solving sets of linear algebraic equation derived from the system equation examples of identifying stiffness factor distribution which is often related to damage in the elements of the structure are presented to demonstrate the present technique the advantages of the present technique for inverse parameter identification problem are 1 the number of the parameters can be very large 2 the identification process is very fast and 3 the accuracy is very high the efficiency of the proposed technique is compared with genetic algorithms

nondestructive identification of multiple flaws using xfem and a topologically adapting artificial bee colony algorithm summary we present a novel algorithm based on the extended finite element method xfem and an enhanced artificial bee colony eabc algorithm to detect and quantify multiple flaws in structures the concept is based on recent work that have shown the excellent synergy between xfem used to model the forward problem and a genetic type algorithm to solve an inverse identification problem and converge to the best flaw parameters in this paper an adaptive algorithm that can detect multiple flaws without any knowledge on the number of flaws beforehand is proposed the algorithm is based on the introduction of topological variables into the search space used to adaptively activate deactivate flaws during run time until convergence is reached the identification is based on a limited number of strain sensors assumed to be attached to the structure surface boundaries each flaw is approximated by a circular void with the following three variables center coordinates xc yc and radius rc within the xfem framework in addition the proposed eabc scheme is improved by a guided to best solution updating strategy and a local search ls operator of the nelder mead simplex type that show fast convergence and superior global ls abilities compared with the standard abc or classic genetic algorithms several numerical examples with increasing level of difficulty are studied in order to evaluate the proposed algorithm in particular we consider identification of multiple flaws with unknown a priori information on the number of flaws which makes the inverse problem harder the proximity of flaws flaws having irregular shapes similar to artificial noise and the effect of structured unstructured meshes the results show that the proposed xfem eabc algorithm is able to converge on all test problems and accurately identify flaws hence this methodology is found to be robust and efficient for nondestructive detection and quantification of multiple flaws in structures copyright 2013 john wiley sons ltd

existence of solutions for a class of porous medium type equations with l1 data in this paper we study a class of degenerate parabolic equations of porous medium type with a lower order term and l1 data i e u t div a x t u u f x t u u f where the principal part of the operator is degenerate in u 0 under some hypothesis on a and f we prove that the problem admits at least a renormalized solution

quasi linear degenerate elliptic problems with l1 data abstract we prove existence and uniqueness of a solution for a class of quasi linear problems with l 1 data the diffusion matrix a x u is allowed to degenerate with respect to the unknown u we obtain uniqueness of the solution under a weak assumption on a x u that permits to consider highly oscillating or and increasing coefficients with respect to u

modeling and identification of an arbitrarily shaped scatterer using dynamic xfem with cubic splines abstract localization and shape identification of an arbitrarily shaped scatterer embedded in elastic heterogeneous media is investigated using the dynamic extended finite element method xfem the scatterer s geometry is represented using cubic splines whose parameters are adaptively updated in a gradient based minimization framework that is used to solve the inverse identification problem the dynamic xfem is employed to solve the forward wave propagation problem because it enables direct parametric modeling of the moving boundary of the scatterer over a stationary background mesh the use of open close cubic splines combined with xfem enables the effective construction of the complicated scatterer geometry by minimizing the number of unknown shape parameters a two phase divide and conquer approach is adopted to alleviate complications due to the potential manifestation of multiple solutions to the inverse problem and for increased computational efficiency in first phase the scatterer is localized using a simple geometric representation and the search is carried out using multiple independent inversions starting from different initial estimates incidentally this strategy is perfectly scalable in parallel computation in the second phase the geometric representation is adaptively refined using cubic splines to obtain an accurate estimate of the scatterer s shape several numerical experiments are provided which clearly show that the proposed approach is robust and can yield highly accurate results

the validity of modulation equations for extended systems with cubic nonlinearities modulation equations play an essential role in the understanding of complicated systems near the threshold of instability here we show that the modulation equation dominates the dynamics of the full problem locally at least over a long time scale for systems with no quadratic interaction term we develop a method which is much simpler than previous ones it involves a careful bookkeeping of errors and an estimate of gronwall type as an example for the dissipative case we find that the ginzburg landau equation is the modulation equation for the swift hohenberg problem moreover the method also enables us to handle hyperbolic problems the nonlinear schrodinger equation is shown to describe the modulation of wave packets in the sine gordon equation

elastodynamic green s functions for a smoothly heterogeneous half space in this paper the response of a vertically heterogeneous elastic half space with a smooth modulus variation under a set of time harmonic ring and point sources is derived analytically a method of evaluation via asymptotic decomposition for the singular green s functions is presented in the technique the green s functions are decomposed into an analytical part and a residual component capturing the corresponding singular behavior the analytical parts of the ring and point load green s functions are expressible in terms of the elliptic integrals and algebraic functions respectively the residual integrals which are regular can be evaluated by numerical contour integration to obtain correct results one must note and take into account the existence of multiple poles along the formal path of the inversion integrals the details of which are discussed in the paper to highlight the various aspects of the physical problem a set of illustrative numerical results is included

rapid inverse parameter estimation using reduced basis approximation with asymptotic error estimation this paper presents a rapid and reliable approach to solve inverse problems of parameter estimation for structural systems using reduced basis method rbm a reduced basis model is first developed with asymptotic error estimation and is used for fast computation of solving forward mechanics problems of solids and structures a genetic algorithm ga is then used in the inverse search procedure for parameter estimation the approach is applied to a typical inverse problem of estimating the crack location length and orientation inside a cantilever beam the displacements measured at five points on the lower surface of the beam which can also be evaluated by our fast rbm solver are used as inputs for constructing objective functions of error the genetic algorithm is used to search these parameters of the crack inside cantilever beam that minimize the objective function an example has been presented it is found that the estimated results are very accurate and reliable due to the use of rbm forward model with an effective and robust error estimation and detailed sensitivity analysis the present procedure is 460 times faster than the full fem model used inverse procedure

modeling holes and inclusions by level sets in the extended finite element method a methodology to model arbitrary holes and material interfaces inclusions without meshing the internal boundaries is proposed the numerical method couples the level set method s osher j a sethian j comput phys 79 1 1988 12 to the extended finite element method x fem n moes j dolbow t belytschko int j numer methods engrg 46 1 1999 131 in the x fem the finite element approximation is enriched by additional functions through the notion of partition of unity the level set method is used for representing the location of holes and material interfaces and in addition the level set function is used to develop the local enrichment for material interfaces numerical examples in two dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique

existence of solutions for degenerate quasilinear elliptic equations abstract this paper deals with a class of degenerate quasilinear elliptic equations of the form div a x u u g div f where a x u u is allowed to be degenerate with the unknown u we prove existence of bounded solutions under some hypothesis on f and g moreover we prove that there exists a renormalized solution in the case where g l 1 and f l p n

an explicit dynamics extended finite element method part 1 mass lumping for arbitrary enrichment functions this paper presents a general mass lumping technique for explicit dynamics simulations using the extended finite element method with arbitrary enrichment functions the proposed mass lumping technique is a generalization of previously published results for cracks and holes time step estimates are studied for crack singular enrichment functions and for hole enrichment in both cases we show that the critical time step does not tend to zero and is of the same order as that of the same unenriched element the performance of the method is demonstrated on several numerical examples that compare well with classical finite elements and previously published x fem results

regularity in sobolev spaces for doubly nonlinear parabolic equations abstract the doubly nonlinear parabolic equation u t div u m 1 u p 2 u m 1 u m 1 m p 1 1 is considered in several dimensions and regularity results in fractional order sobolev spaces are obtained the main tools in the proof are a difference quotient technique and the imbedding theorem of nikolskii spaces into sobolev spaces

continuity estimates for porous medium type equations with measure data abstract we consider parabolic equations of porous medium type of the form u t div a x t u d u in e t in some space time cylinder e t the most prominent example covered by our assumptions is the classical porous medium equation u t u m in e t with m 1 we establish a sufficient condition for the continuity of u in terms of a natural riesz potential of the right hand side measure as an application we come up with a borderline condition ensuring the continuity of u more precisely if l n 2 2 1 then u is continuous in e t

global existence via ginzburg landau formalism and pseudo orbits of ginzburg landau approximations the so called ginzburg landau formalism applies for parabolic systems which are defined on cylindrical domains which are close to the threshold of instability and for which the unstable fourier modes belong to non zero wave numbers this formalism allows to describe an attracting set of solutions by a modulation equation here the ginzburg landau equation if the coefficient in front of the cubic term of the formally derived ginzburg landau equation has negative real part the method allows to show global existence in time in the original system of all solutions belonging to small initial conditions inl another aim of this paper is to construct a pseudo orbit of ginzburg landau approximations which is close to a solution of the original system up tot we consider here as an example the socalled kuramoto shivashinsky equation to explain the methods but it applies also to a wide class of other problems like e g hydrodynamical problems or reaction diffusion equations too

renormalization group theory for global asymptotic analysis we show with several examples that renormalization group rg theory can be used to understand singular and reductive perturbation methods in a unified fashion amplitude equations describing slow motion dynamics in nonequilibrium phenomena are rg equations the renormalized perturbation approach may be simpler to use than other approaches because it does not require the use of asymptotic matching and yields practically superior approximations

amplitude equation for lattice maps a renormalization group approach we consider the development of instabilities of homogeneous stationary solutions of discrete time lattice maps under some generic hypotheses we derive an amplitude equation which is the space time continuous ginzburg landau equation using dynamical renormalization group methods we control the accuracy of this approximation in a large ball of its basin of attraction

the time dependent amplitude equation for the swift hohenberg problem precise estimates for the validity of the amplitude approximation for the swift hohenberg equation are given in a fully time dependent framework it is shown that small solutions of ordero which are modulated like stationary solutions have an evolution which is well described in the amplitude approximation for a time of ordero 2 for the proofs we use techniques for nonlinear semigroups and oscillatory integrals

inverse identification of thermal parameters using reduced basis method a novel computational method is presented to inversely identify heat convection constants for complex engineering systems a reduced basis approach is developed as a forward solver for heat transfer analysis in order to significantly reduce the computational complexity in each forward analysis which is crucial for the inverse analysis of complex systems an intergeneration projection genetic algorithm ip ga is introduced as the inverse procedure to speed up the process of finding the desired global minimum of the fitness function of error that leads to the parameters to be identified as an example identification of the heat convection constants of a typical microelectronic package are performed using the present method and the performance is examined comparing with other inverse identification methods it is found that the reduced basis method combined with the ip ga significantly outperforms the conventional methods the proposed inverse identification method is efficient enough even for online analysis of inverse problems due to both the use of the reduced basis approach and the present inverse procedure

existence of solutions for some doubly degenerate parabolic equations with natural growth terms abstract this paper deals with a class of doubly degenerate parabolic equations of the type b u t div a x t u u f x t u u f where b is a strictly increasing c 1 function under some suitable hypothesis we prove that there exists at least a bounded solution to this problem in standard weak sense

uniqueness of renormalized solutions of degenerate elliptic parabolic problems we consider a general class of degenerate elliptic paraboic problems associated with the equation b v t div a v dv f using kruzhkov s method of doubling variables both in space and time we prove uniqueness and a comparison principle in l 1 for renormalized solutions

xfem based crack detection scheme using a genetic algorithm a new computational tool is developed for the accurate detection and identification of cracks in structures to be used in conjunction with non destructive testing of specimens it is based on the solution of an inverse problem based on some measurements typically along part of the boundary of the structure that describe the response of the structure to vibration in a chosen frequency or a combination of frequencies the goal is to estimate whether the structure contains a crack and if so to find the parameters location size orientation and shape of the crack that produces a response closest to the given measurement data in some chosen norm the inverse problem is solved using a genetic algorithm ga the ga optimization process requires the solution of a very large amount of forward problems the latter are solved via the extended finite element method xfem this enables one to employ the same regular mesh for all the forward problems performance of the method is demonstrated via a number of numerical examples involving a cracked flat membrane various computational aspects of the method are discussed including the a priori estimation of the ill posedness of the crack identification problem copyright 2007 john wiley sons ltd

identification of a scatterer embedded in elastic heterogeneous media using dynamic xfem abstract a numerical approach for identifying a scatterer embedded in elastic heterogeneous media is described this scatterer may be a crack a void or an inclusion with properties that have detectable contrasts from those of the host medium the forward wave propagation problem is solved using the dynamic extended finite element method xfem which allows the boundary of the scatterer to be easily relocated over a stationary background mesh the inverse problem is cast as a minimization problem whereby the unknown shape parameters of the scatterer e g a line crack s center coordinates size and orientation are the updating parameters a gradient based method is utilized to solve the minimization problem in order to alleviate the potential manifestation of multiple solutions to the inverse problem various deployment patterns for multiple sensors are investigated and also a divide and conquer approach is adopted wherein a set of independent inversions using multiple initial guesses are carried out

flaw detection in sandwich plates based on time harmonic response using genetic algorithm an inverse identification technique is proposed to assess the presence location size and degree of flaw in the core layer of sandwich plates the time harmonic response of the sandwich plates is used as the input for inverse analysis the responses of the plates in forward analysis are predicted using finite element method fem based on mindlin plate theory the flaw is characterized by a set of parameters the genetic algorithm ga is applied to search the parameters to improve the efficiency of ga in searching for the true solution a two stage searching method is proposed numerical examples are given to illustrate the proposed technique

elastic wave scattering around cavities in inhomogeneous continua by the bem this work examines elastic wave scattering around cavities embedded in a continuum with depth dependent shear modulus and under conditions of plane strain a restricted case of inhomogeneity is considered where the poisson ratio is fixed at 0 25 and where the density profile also varies but proportionally to the shear modulus for this specific case the wave speeds remain macroscopically constant and it becomes possible to recover the exact green functions by using an algebraic transformation method these functions are subsequently used as kernels in a standard 2d boundary element formulation defined in the laplace transform domain the final step involves an inverse laplace transformation whereby the transient behavior of cavities in the aforementioned inhomogeneous continuum can be recovered two basic examples are solved namely the circular cylindrical cavity under sudden internal explosion and under a pressure wave sweep in the latter case it is possible to investigate the effect that the angle of wave incidence has on the displacement and stress that develop along the cavity s perimeter given the fact that the shear modulus is changing along the vertical direction these examples serve to illustrate the present approach and to reveal some interesting differences that are observed in transient wave scattering phenomena between homogeneous and continuously inhomogeneous models where the latter models yield a more realistic representation of geological formations

analyticity of ginzburg landau modes ginzburg landau formalism applies for dissipative systems defined on cylindrical domains which are close to the threshold of instability and for which the unstable fourier modes belong to non zero wave numbers in these situations the real part of the curve of critical eigenvalues as function drawn over the wave numbers k is positive of height o 2 and of width o here it is shown that the set of solutions which can be described by the ginzburg landau formalism is attractive to do this we demonstrate that in fourier space peaks appear at integer multiples of the critical wave number kc these peaks called ginzburg landau modes concentrate in time like e k mkc t for 0 t o 1 2 and m z the inverse fourier transform of such a ginzburg landau mode is an analytic function in a strip of width t this result extends a former work of w eckhaus