the poisson embedding approach to the calderon problem we introduce a new approach to the anisotropic calderon problem based on a map called poisson embedding that identifies the points of a riemannian manifold with distributions on its boundary we give a new uniqueness result for a large class of calderon type inverse problems for quasilinear equations in the real analytic case the approach also leads to a new proof of the result of lassas et al annales de l ens 34 5 771 787 2001 solving the calderon problem on real analytic riemannian manifolds the proof uses the poisson embedding to determine the harmonic functions in the manifold up to a harmonic morphism the method also involves various runge approximation results for linear elliptic equations

determining the first order perturbation of a polyharmonic operator on admissible manifolds abstract we consider the inverse boundary value problem for the first order perturbation of the polyharmonic operator l g x q with x being a w 1 vector field and q being an l function on compact riemannian manifolds with boundary which are conformally embedded in a product of the euclidean line and a simple manifold we show that the knowledge of the dirichlet to neumann map determines x and q uniquely the method is based on the construction of complex geometrical optics solutions using the carleman estimate for the laplace beltrami operator due to dos santos ferreira kenig salo and uhlmann notice that the corresponding uniqueness result does not hold for the first order perturbation of the laplace beltrami operator

an inverse problem for a semi linear elliptic equation in riemannian geometries abstract we study the inverse problem of unique recovery of a complex valued scalar function v m c c defined over a smooth compact riemannian manifold m g with smooth boundary given the dirichlet to neumann map in a suitable sense for the elliptic semi linear equation g u v x u 0 we show that uniqueness holds for a large class of non linearities when the manifold is conformally transversally anisotropic the proof is constructive and is based on a multiple fold linearization of the semi linear equation near complex geometric optic solutions for the linearized operator and the resulting non linear interactions these interactions result in the study of a weighted integral transform along geodesics that we call the jacobi weighted ray transform

a new algebraic geometry algorithm for integer programming we propose a new algorithm for solving integer programming ip problems that is based on ideas from algebraic geometry the method provides a natural generalization of the farkas lemma for ip leads to a way of performing sensitivity analysis offers a systematic enumeration of all feasible solutions and gives structural information of the feasible set of a given ip we provide several examples that offer insights on the algorithm and its properties

a finite element method for the simulation of strong and weak discontinuities in solid mechanics in this paper we introduce and analyze a finite element method for elasticity problems with interfaces the method allows for discontinuities internal to the elements in the approximation across the interface we propose a general approach that can handle both perfectly and imperfectly bonded interfaces without modifications of the code for the case of linear elasticity we show that optimal order of convergence holds without restrictions on the location of the interface relative to the mesh we present numerical examples for the linear case as well as for contact and crack propagation model problems

an inverse boundary value problem for schrodinger operators with vector potentials we consider the schrodinger operator for a magnetic potential a and an electric potential q which are supported in a bounded domain in r n with n 3 we prove that knowledge of the dirichlet to neumann map associated to the schrodinger operator determines the magnetic field rot a and the electric potential 4 simultaneously provided rot a is small in the l topology

a variational multiscale discontinuous galerkin formulation for both implicit and explicit dynamic modeling of interfacial fracture abstract a stabilized discontinuous galerkin method is presented for modeling interfacial debonding under dynamic conditions the method s distinctive feature is its treatment of the inelastic gap at the interface as an internal variable that is evolved through a traction separation constitutive model enabling initially perfect adhesion to be captured numerical stability is derived using variational multiscale ideas and comparisons are drawn with both the intrinsic cohesive zone method and hybrid discontinuous galerkin cohesive zone method to expose subtle differences the proposed formulation is applied to model the nonlinear response of a composite unit cell under impact loading both explicit and implicit time integration schemes provide similar accuracy and stability and the critical time step for explicit analyses is only slightly reduced below the value for the continuous galerkin mesh without an interface further studies of mesh refinement and adjustments to the initial elastic interface stiffness in the reference cohesive zone model reveal the improved accuracy of the variational multiscale discontinuous galerkin method on coarser grids

gradient constitutive relations numerical aspects and application to gradient damage abstract the description of localisation and structural failure through local strain softening constitutive laws leads to ill posed problems to retrieve a well posed problem the material state is described through the gradients of internal variables in addition to the strain and the internal variables themselves under some assumptions it is shown that these gradient laws can be cast into a variational formulation after time discretisation the evolution of the internal variable field is characterised by a minimum principle a specific algorithm is proposed to perform the minimisation in the context of finite elements finally it is applied to a gradient brittle damage model

inverse problems for lorentzian manifolds and non linear hyperbolic equations we study two inverse problems on a globally hyperbolic lorentzian manifold m g the problems are 1 passive observations in spacetime consider observations in an open set v subset m the light observation set corresponding to a point source at q in m is the intersection of v and the light cone emanating from the point q let w subset m be an unknown open relatively compact set we show that under natural causality conditions the family of light observation sets corresponding to point sources at points q in w determine uniquely the conformal type of w 2 active measurements in spacetime we develop a new method for inverse problems for non linear hyperbolic equations that utilizes the non linearity as a tool this enables us to solve inverse problems for non linear equations for which the corresponding problems for linear equations are still unsolved to illustrate this method we solve an inverse problem for semilinear wave equations with quadratic non linearities we assume that we are given the neighborhood v of the time like path mu and the source to solution operator that maps the source supported on v to the restriction of the solution of the wave equation to v when m is 4 dimensional we show that these data determine the topological differentiable and conformal structures of the spacetime in the maximal set where waves can propagate from mu and return back to mu

inverse boundary value problem for the stokes and the navier stokes equations in the plane in this paper we prove in two dimensions the global identifiability of the viscosity in an incompressible fluid by making boundary measurements the main contribution of this work is to use more natural boundary measurements the cauchy forces than the dirichlet to neumann map previously considered in imanuvilov and yamamoto global uniqueness in inverse boundary value problems for navier stokes equations and lame ststem in two dimensions arxiv 1309 1694 2013 to prove the uniqueness of the viscosity for the stokes equations and for the navier stokes equations

on uniqueness for an inverse boundary value problem in electrical prospection1this work was completed at wichita state university 1 in this paper we consider the problem of determining the discontinuous conductivity l in the equation div l grad u 0 in w when for any dirchlet data g we are given the neumann data h in other words results of all possible boundary measurements are known we derive a uniqueness proof of inclusions of different analytic conductivities under the minimal assumptions i the boundaries of inclusions are only lipschitz ii no topological assumptions after some modification of alessandrini s construction j diff eq 84 1990 252 272 we gave an existence proof of singular solution for lipschitz piecewise analytic coefficients and used it for our purpose

a new path following constraint for strain softening finite element simulations the application of strain softening constitutive relations to model the failure modes of real life structures is faced to numerical difficulties related to instabilities that appear as sharp snap backs of the structural response a path following method has to complement the solution algorithm to achieve convergence despite these critical points because of the sharpness of the snap backs it is believed essential that the path following constraint distinguish between a purely elastic unloading and a dissipative path for that purpose a new constraint based on the maximal value of the elastic predictor for the yield function is proposed as it is highly non linear a specific solution algorithm is required the robustness of this constraint is illustrated by three applications the study of crack propagations by means of a cohesive zone model the failure of a structure submitted to nonlocal damage and the simulation of a nonlocal strain softening plastic specimen copyright 2004 john wiley sons ltd

theoretical and computational issues in modelling material failure in strong discontinuity scenarios the paper deals with several aspects related to numerical modelling of material failure in strong discontinuity settings a the onset and development of local material failure in terms of continuum constitutive models equipped with strain softening closed forms formulas for the solutions of the discontinuous material bifurcation problem are given for a class of those models b finite elements with embedded discontinuities nodal and elemental enrichments families are formulated in the continuum strong discontinuity approach csda c instability treatment a discrete viscous perturbation method at the failure surfaces is presented as a way to substantially improve the robustness of the numerical simulations

stable recovery of time dependent coefficient from arbitrary measurements for wave equation abstract this paper concerns the stability in the inverse problem of determining the time dependent coefficient in the wave equation from partial knowledge of the dirichlet to neumann map at the boundary of a bounded domain of interest we first establish a stability estimate in the determination of the time dependent coefficient from partial boundary observations then we prove that by enlarging the set of data the unknown coefficient can be stably determined in larger regions

inversion formulas for the linearized problem for an inverse boundary value problem in elastic prospection the problem of determining an unknown pair gamma lambda mu of lame parameters inside a body by its dirichlet to neumann data map lambda gamma is considered using explicit exact solutions for the case of constant gamma it is seen that the deflection h between gamma h and gamma is uniquely determined by the first order approximation of lambda gamma h at gamma

simultaneous reconstruction of the spatially distributed reaction coefficient initial temperature and heat source from temperature measurements at different times abstract in many practical situations concerned with high temperatures pressures loads and or hostile environments certain properties of the physical medium geometry boundary and or initial conditions are not known and their direct measurement can be very inaccurate or even inaccessible in such situations one can adopt an inverse approach and try to infer the unknowns from some extra accessible measurements of other quantities that may be available however the simultaneous identification of several non constant physical properties along with initial and or boundary conditions is very challenging especially when it cannot be decoupled as it combines both nonlinear as well as ill posedness features one such new inverse problem concerning the identification of the space dependent reaction coefficient the initial temperature and the source term from measured temperatures at two instants t 1 t 2 and at the final time t where 0 t 1 t 2 t is investigated in this paper insight into the uniqueness of solution is gained by considering various particular cases moreover as in practice the input temperature data are usually noise polluted due to the errors that are inherently present their influence on the solution of inversion has to be assessed as such the least squares objective functional modelling the gap between the measured and computed data is minimized to obtain the quasi solution to the inverse problem and the frechet gradients are obtained the conjugate gradient method cgm with the fletcher reeves formula is applied to estimate the three unknown coefficients numerically numerical examples are illustrated to show that accurate and stable numerical solutions are obtained using the cgm regularized by the discrepancy principle

stability in the determination of a time dependent coefficient for wave equations from partial data let be a c2 bounded domain of rn n 2 and fix q 0 t with t 0 we consider the stability in the inverse problem of determining a time dependent coefficient of order zero q appearing in a dirichlet initial boundary value problem for a wave equation t2u xu q t x u 0 in q from partial observations on q the observation is given by a boundary operator associated to the wave equation using suitable geometric optics solutions and carleman estimates we prove a stability estimate in the determination of q from the boundary operator

on uniqueness of recovery of a discontinuous conductivity coefficient on considere le probleme de retrouver le coefficient a de l equation elliptique div a u 0 dans un domaine avec la condition aux limites u sur quand u n est donnee pour tout regulier on demontre l unicite pour a a 0 b discontinu ou est la fonction indicateur d un ensemble ouvert a o est une fonction c 2 donnee et b est une fonction c 2 inconnue

completeness of products of solutions and some inverse problems for pde abstract in this paper we give conditions which guarantee that products of solutions of partial differential equations pu au 0 are complete in l 2 here p is a linear partial differential operator with constant coefficients and a is a function in l we check these conditions for elliptic parabolic and hyperbolic equations of second order and give applications to inverse problems for related equations where a is to be found

simultaneous reconstruction of space dependent heat transfer coefficients and initial temperature abstract many complex physical phenomena and engineering systems e g in heat exchanges reflux condensers combustion chambers nuclear vessels etc due to the high temperatures high pressures hostile environment involved possess certain properties which are inaccessible to measure and therefore their influence determination using inverse analysis is very important and desirable in this spirit the purpose of this paper is to mathematically formulate and analyse a new inverse problem in which given measurements of temperature at two different instants it is required to obtain the space dependent heat transfer coefficients htcs and the initial temperature this simultaneous identification is challenging since it is both nonlinear and ill posed the uniqueness of solution is established based on the max min principle for parabolic equations and the contraction mapping principle for the existence and uniqueness of a fixed point the novel inverse mathematical model that is proposed offers appropriate scientific guidance to the polymer heat transfer processing industry as to which data to measure provide in order to be able to reliably determine the desirable htcs along with the initial temperature which is in general unknown furthermore for the reconstruction the surface htc is determined separately whilst the variational formulation is introduced for the simultaneous determination of the domain htc and the initial temperature the frechet gradient of the minimizing objective functional is derived the numerical reconstruction process is based on the conjugate gradient method cgm regularized by the discrepancy principle accurate and stable numerical solutions are obtained even in the presence of noise in the input temperature data since noisy data are invented the study models realistic practical situations in which temperature measurements recorded using sensors or thermocouples are inherently contaminated with random noise

determining conductivity by boundary measurements a p calderon pose la question est il possible de determiner la conductivite thermique d un objet a partir de mesures statiques de la temperature et du flux de chaleur a la limite on demontre que ces mesures determinent de facon unique la conductivite thermique et toutes ses derivees a la limite

an algebraic approach to integer portfolio problems abstract integer variables allow the treatment of some portfolio optimization problems in a more realistic way and introduce the possibility of adding some natural features to the model we propose an algebraic approach to maximize the expected return under a given admissible level of risk measured by the covariance matrix to reach an optimal portfolio it is an essential ingredient the computation of different test sets via grobner basis of linear subproblems that are used in a dual search strategy

path following and augmented lagrangian methods for contact problems in linear elasticity a certain regularization technique for contact problems leads to a family of problems that can be solved efficiently using infinite dimensional semismooth newton methods or in this case equivalently primal dual active set strategies we present two procedures that use a sequence of regularized problems to obtain the solution of the original contact problem first order augmented lagrangian and path following methods the first strategy is based on a multiplier update while path following with respect to the regularization parameter uses theoretical results about the path value function to increase the regularization parameter appropriately comprehensive numerical tests investigate the performance of the proposed strategies for both a 2d as well as a 3d contact problem

an inverse radiative coefficient problem arising in a two dimensional heat conduction equation with a homogeneous dirichlet boundary condition in a circular section abstract in this study we investigate the well posedness of the solution of an optimal control problem related to a nonlinear inverse coefficient problem problems of this type have important applications in several fields of applied science unlike other terminal control problems the observation data are only given for a fixed direction rather than for the whole domain which may make the conjugate theory for parabolic equations ineffective moreover the coefficients in our model are singular so we propose some weighted sobolev spaces based on the optimal control framework the problem is transformed into an optimization problem and the existence of the minimizer is established after deducing the necessary conditions that must be satisfied by the minimizer we prove the uniqueness and stability of the minimizer following a minor modification of the cost functional and imposing some a priori regularity conditions on the forward operator we obtain the convergence of the minimizer for the noisy input data considered in this study the results obtained in this study are interesting and useful and they can be extended to more general parabolic equations with singular coefficients

a geometric buchberger algorithm for integer programming let ip a c denote the family of integer programs of the form min cx ax b x nn obtained by varying the right hand side vector b but keeping a and c fixed a test set for ipa c is a set of vectors in zn such that for each nonoptimal solution to a program in this family there is at least one element g in this set such that g has an improved cost value as compared to we describe a unique minimal test set for this family called the reduced grobner basis of ip a c an algorithm for its construction is presented which we call a geometric buchberger algorithm for integer programming and we show how an integer program may be solved using this test set the reduced grobner basis is then compared with some other known test sets from the literature we also indicate an easy procedure to construct test sets with respect to all cost functions for a matrix a zn 2 n of full row rank

an incremental minimization principle suitable for the analysis of low cycle fatigue in metals a coupled ductile brittle damage model abstract the present paper is concerned with a novel variational constitutive update suitable for the analysis of low cycle fatigue in metals the underlying constitutive model originally advocated in 1 accounts for plastic deformation as well as for damage accumulation the latter is captured by a combination of two constitutive models while the first of those is associated with ductile damage the second material law is related to a quasi brittle response the complex overall model falls into the range of so called generalized standard materials and thus it is thermodynamically consistent however since the evolution equations are non associative it does not show an obvious variational structure by enforcing the flow rule as well as the evolution equations through a suitable parameterization a minimization principle can be derived nevertheless discretized in time this principle is employed for developing an effective numerical implementation since the mechanical subproblems corresponding to ductile damage and that of quasi brittle damage are uncoupled an efficient staggered scheme can be elaborated within both steps newton s method is applied while the evolution of the quasi brittle damage requires only the computation of a one dimensional optimization problem the ductile damage model is defined by a numerically more expensive tensor valued variable for further increasing the numerical performance of the respective minimization principle a closed form solution for the inverse of the hessian matrix is derived by numerically analyzing the prediction of mesocrack initiation in low cycle fatigue simulations the performance of the resulting algorithm is demonstrated

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

stable determination of a semilinear term in a parabolic equation in 5 the flrst and third authors establish holder type stability estimates for the inverse problem consisting in the determination of a semilinear term of a parabolic equation from a single boundary measurement when the domain is a rectangle in the present paper we extend the results in 5 for a general smooth domain

stability estimates for the inverse boundary value problem for the biharmonic operator with bounded potentials abstract in this article stability estimates are given for the determination of the zeroth order bounded perturbations of the biharmonic operator when the boundary neumann measurements are made on the whole boundary and on slightly more than half the boundary respectively for the case of measurements on the whole boundary the stability estimates are of ln type and for the case of measurements on slightly more than half of the boundary we derive estimates that are of ln ln type

a comparative study on finite elements for capturing strong discontinuities e fem vs x fem a comparative study on finite elements for capturing strong discontinuities by means of elemental e fem or nodal enrichments x fem is presented based on the same constitutive model continuum damage and linear elements triangles and tetrahedra optimized implementations of both types of enrichments in the same non linear code are tested for a representative set of 2d and 3d crack propagation examples it is shown that both methods provide the same qualitative and quantitative results for enough refined meshes for the performed tests e fem exhibited in general a higher accuracy mostly for coarse meshes whereas convergence rate with mesh refinement which is super linear showed slightly higher for x fem as for the computational costs for single crack modelling x fem showed depending on the case from 1 1 to about 2 5 times more expensive than e fem for multiple cracks the computational cost of e fem keeps constant whereas the cost associated to x fem increases linearly with the number of modelled cracks

inverse boundary value problems at the boundary continuous dependence we use the methods of microlocal analysis to give a new proof of a theorem of kohn and vogelius showing that the boundary values of a continuous isotropic conductivity can be recovered from voltage and current measurements at the boundary moreover we prove sharp estimates to establish the continuous dependence of the boundary values of the conductivity on the voltage to current maps

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

determination of viscosity in the stationary navier stokes equations abstract in this paper we consider the stationary navier stokes equations in a bounded domain with a variable viscosity we prove that one can uniquely determine the viscosity function from the knowledge of boundary data

global uniqueness for an inverse boundary value problem arising in elasticity we prove that we can determine the lame parameters of an elastic isotropic inhomogeneous medium in dimensionsn 3 by making measurements of the displacements and corresponding stresses at the boundary of the medium

inverse boundary value problems for the perturbed polyharmonic operator author s krupchyk k lassas m uhlmann g abstract we show that a first order perturbation a x d q x of the polyharmonic operator m m 2 can be determined uniquely from the set of the cauchy data for the perturbed polyharmonic operator on a bounded domain in n n 3 notice that the corresponding result does not hold in general when m 1 2013 american mathematical society

a special green s function for the biharmonic operator and its application to an inverse boundary value problem abstract a construction of the special green s function for the biharmonic operator is given this result is used to recover the operator a2 v x from its diricldet to neumann map 1 introduction let n 2 and put az e ix a z z ei z for z e c r with z z o since the inverse of the symbol of az is locally absolutely integrable and decays algebraically at infinity its inverse fourier transform defines a tempered distribution which is a fundamental solution of az and called a green faddeev function at z z for the laplace operator this terminology is seen in 1 this function plays an important role in studying several inverse problems for example inverse scattering problems see 1 2 inverse boundary value problems see 3 in short those problems are to determine the coefficients of an elliptic partial differential operator l in r n or a bounded domain f by the scattering datum at izl oo or the cauchy datum on a of the solutions of

a mixed interface finite element for cohesive zone models abstract the phenomena of crack initiation propagation and ultimate fracture are studied here under the following assumptions i the crack law is modelled by means of a cohesive zone model and ii the crack paths are postulated a priori in this context a variational formulation is proposed which relies on an augmented lagrangian a mixed interface finite element is introduced to discretise the crack paths the degrees of freedom of which consist in the displacement on both crack lips and the density of cohesive forces this enables an exact treatment of multi valued cohesive laws e g initial adhesion contact conditions possible rigid unloading etc without penalty regularisation a special attention is paid to the convergence with mesh refinement i e the well posedness of the problem on the basis of theoretical results of contact mechanics and some complementary numerical investigations fulfilment of the lbb condition is the key factor to gain the desired properties moreover it is shown that the integration of the constitutive law admits a unique solution as soon as some condition on the augmented lagrangian is enforced finally a 3d simulation shows the applicability to practical engineer problems including in particular the robustness of the formulation and its compatibility with classical solution algorithms newton method line search path following techniques

direct reconstructions of conductivities from boundary measurements the problem of reconstructing an unknown electric conductivity from boundary measurements has applications in medical imaging geophysics and nondestructive testing a nachman ann of math 2 143 1996 pp 71 96 proved global uniqueness for the two dimensional inverse conductivity problem using a constructive method of proof based on this proof siltanen mueller and isaacson inverse problems 16 2000 pp 681 699 presented a new numerical reconstruction method that solves the nonlinear problem directly without iteration the method was verified with nonnoisy rotationally symmetric examples in this paper the method is extended by introducing a new regularization scheme which is analyzed theoretically and tested on symmetric and nonsymmetric numerical examples containing computer simulated noise

simultaneous determination of source terms in a linear parabolic problem from the final overdetermination weak solution approach the problem of determining the pair w f x t t0 t of source terms in the parabolic equation ut k x ux x f x t and robin boundary condition k l ux l t v u l t t0 t from the measured final data t x u x t is formulated it is proved that both components of the frechet gradient of the cost functional j w t x u x t w 02 can be found via the same solution of the adjoint parabolic problem lipschitz continuity of the gradient is derived the obtained results permit one to prove existence of a quasi solution of the considered inverse problem as well as to construct a monotone iteration scheme based on a gradient method

global uniqueness for a two dimensional inverse boundary value problem we show that the coefficient y x of the elliptic equation vie qyvu 0 in a two dimensional domain is uniquely determined by the corresponding dirichlet to neumann map on the boundary and give a reconstruction pro

an algebraic geometry algorithm for scheduling in presence of setups and correlated demands we study here a problem of schedulingn job types onm parallel machines when setups are required and the demands for the products are correlated random variables we model this problem as a chance constrained integer program

global uniqueness for a two dimensional semilinear elliptic inverse problem for a general class of nonlinear schrodinger equations au a x u 0 in a bounded planar domain 2 we show that the function a x u can be recovered from knowledge of the corresponding dirichlet to neumann map on the boundary dq

interfacial coupling across incompatible meshes in a monolithic finite strain thermomechanical formulation abstract a stabilized interface method is presented for monolithic coupling of thermomechanical fields across incompatible internal interfaces embedding discontinuous galerkin dg ideas in the variational multiscale vms framework yields interface coupling terms that accommodate nonmatching discretizations across glued meshes a unique feature of the method that emanates from fine scale modeling facilitated by vms is the derivation of analytical expressions for the lagrange multipliers that enforce continuity of the fields across nonmatching meshes this stabilized form is free of any user defined parameters and renders itself to consistent linearization that leads to quadratic convergence of the method the coupling terms at the interface also provide an avenue to employ various kinematic models for interfacial response in multi constituent materials an interfacial gap crack function is introduced together with the conjugate traction vector to model discrete interfacial failure in multi material applications an algorithm for consistent implementation of interfacial models for tension compression and sliding friction across non conforming meshes is presented test cases that employ 8 node hexahedra and 4 node tetrahedra are presented that highlight the generality of the method and validate its robustness for mathematically nonsmooth thermomechanical problems

stable determination outside a cloaking region of two time dependent coefficients in an hyperbolic equation from dirichlet to neumann map abstract in this paper we treat the inverse problem of determining two time dependent coefficients appearing in a dissipative wave equation from measured neumann boundary observations we establish in dimension n 2 stability estimates with respect to the dirichlet to neumann map of these coefficients provided that they are known outside cloaking regions moreover we prove that they can be stably recovered in larger subsets of the domain by enlarging the set of data