a two step approach to measurement error in time dependent covariates in nonlinear mixed effects models with application to igf i pharmacokinetics abstract the usual approach to the analysis of population pharmacokinetic studies is to represent the concentration time data by a nonlinear mixed effects model primary objectives are to characterize the pattern of drug disposition in the population and to identify individual specific covariates associated with pharmacokinetic behavior we consider data from a study of insulin like growth factor i igf i administered by intravenous infusion to patients with severe head trauma failure to maintain steady state levels of igf i was thought to be related to the temporal pattern of several covariates measured in the study and an analysis investigating this issue was of interest observations on these potentially relevant covariates for each subject were made at time points different from those at which igf i concentrations were determined moreover the covariates themselves were likely subject to measurement error the usual approach to time dependent covariates in population analysis is to invoke a simple

boundary integral equations for the scattering of electromagnetic waves by a homogeneous chiral obstacle the time harmonic scattering of electromagnetic waves by a homogeneous chiral media are considered herein the scattering problem is reduced using bohren s decomposition to an equivalent boundary integral equation which is shown to be uniquely solvable except for a discrete set of values of electromagnetic parameters of the scatterer it should be noted that the boundary integral operators appearing in this equation are the same as for a dielectric scatterer and hence their mapping properties are well known

absolute conductivity reconstruction in magnetic induction tomography using a nonlinear method magnetic induction tomography mit attempts to image the electrical and magnetic characteristics of a target using impedance measurement data from pairs of excitation and detection coils this inverse eddy current problem is nonlinear and also severely ill posed so regularization is required for a stable solution a regularized gauss newton algorithm has been implemented as a nonlinear iterative inverse solver in this algorithm one needs to solve the forward problem and recalculate the jacobian matrix for each iteration the forward problem has been solved using an edge based finite element method for magnetic vector potential a and electrical scalar potential v a so called a a v formulation a theoretical study of the general inverse eddy current problem and a derivation paying special attention to the boundary conditions of an adjoint field formula for the jacobian is given this efficient formula calculates the change in measured induced voltage due to a small perturbation of the conductivity in a region this has the advantage that it involves only the inner product of the electric fields when two different coils are excited and these are convenient computationally this paper also shows that the sensitivity maps change significantly when the conductivity distribution changes demonstrating the necessity for a nonlinear reconstruction algorithm the performance of the inverse solver has been examined and results presented from simulated data with added noise

distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution summary a fairly general procedure is studied to perturb a multivariate density satisfying a weak form of multivariate symmetry and to generate a whole set of non symmetric densities the approach is sufficiently general to encompass some recent proposals in the literature variously related to the skew normal distribution the special case of skew elliptical densities is examined in detail establishing connections with existing similar work the final part of the paper specializes further to a form of multivariate skew t density likelihood inference for this distribution is examined and it is illustrated with numerical examples

an electromagnetic inverse problem in chiral media we consider the inverse boundary value problem for maxwell s equations that takes into account the chirality of a body in r3 more precisely we show that knowledge of a boundary map for the electromagnetic fields determines the electromagnetic parameters namely the conductivity electric permittivity magnetic permeability and chirality in the interior we rewrite maxwell s equations as a first order perturbation of the laplacian and construct exponentially growing solutions and obtain the result in the spirit of complex geometrical optics

simultaneous inference for semiparametric nonlinear mixed effects models with covariate measurement errors and missing responses semiparametric nonlinear mixed effects nlme models are flexible for modeling complex longitudinal data covariates are usually introduced in the models to partially explain interindividual variations some covariates however may be measured with substantial errors moreover the responses may be missing and the missingness may be nonignorable we propose two approximate likelihood methods for semiparametric nlme models with covariate measurement errors and nonignorable missing responses the methods are illustrated in a real data example simulation results show that both methods perform well and are much better than the commonly used naive method

the condition number of the schur complement in domain decomposition it is shown that for elliptic boundary value problems of order 2m the condition number of the schur complement matrix that appears in nonoverlapping domain decomposition methods is of order d 1 h 2m 1 where d measures the diameters of the subdomains and h is the mesh size of the triangulation the result holds for both conforming and nonconforming finite elements

the static condensation reduced basis element method for a mixed mean conjugate heat exchanger model we propose a new approach for the simulation of conjugate heat exchangers first we introduce a dimensionality reduced mathematical model for conjugate fluid solid heat transfer in the fluid channels we consider a mixed mean temperature defined on one dimensional filaments in the solid we consider a detailed partial differential equation conduction representation we then propose a petrov galerkin finite element fe numerical approximation which provides suitable stability and accuracy for our mathematical model we next apply the static condensation reduced basis element scrbe method a domain synthesis approach with parametric model order reduction at the intradomain level to populate a schur complement at the interdomain level we first build a library of components each corresponding to a subdomain with a simple fluid channel geometry for each component we prepare petrov galerkin reduced basis bubble approximations and error bounds we then assemble the system equations by static con

on single integral equations for the transmission problem of acoustics the transmission problem namely scattering of time harmonic waves in a compressible fluid by a fluid inclusion with different material properties is usually formulated as a pair of coupled boundary integral equations over the interface s between the inclusion and the exterior fluid in this paper however we consider methods for solving the transmission problem using a single integral equation over s for a single unknown function in fact we derive four different integral equations using a hybrid of the direct green s theorem and indirect layer ansatz methods and give conditions for the unique solvability of each and for the subsequent construction of the solution to the transmission problem some of our single integral equations are fredholm integral equations of the second kind with weakly singular kernels thus these equations all of which appear to be new are attractive computationally

a new certification framework for the port reduced static condensation reduced basis element method abstract in this paper we introduce a new certification framework for the port reduced static condensation reduced basis element pr scrbe method which has been developed for the simulation of large component based applications such as bridges or acoustic waveguides in an offline computational stage we construct a library of interoperable parametrized reference components in the subsequent online stage we instantiate and connect the components at the interfaces ports to form a system of components to compute a truth finite element approximation of the say coercive elliptic partial differential equation on the component based system we use a domain decomposition approach for an efficient simulation we employ two different types of model reduction a reduced basis rb approximation within the interior of the component huynh et al 2013 and empirical port reduction eftang and patera 2013 on the ports where the components connect we demonstrate the well posedness of the pr scrbe approximation and introduce a new certification framework to assess the quality of the port reduction we use conservative fluxes we adapt the standard estimators from rb methods to the scrbe setting to derive an a posteriori error estimator for the rb error contribution in order to combine the a posteriori estimators for both error contributions and derive a rigorous a posteriori error estimator for pr scrbe we adapt techniques from multi scale methods and component mode synthesis finally we prove that the effectivity of the derived estimator can be bounded we provide numerical experiments for heat conduction and linear elasticity to show that the derived a posteriori error estimator provides an effective estimator moreover we demonstrate the applicability of the introduced certification framework by analyzing the computational online costs

proper generalized decomposition solutions within a domain decomposition strategy this is the peer reviewed version of the following article huerta antonio enrique nadal and francisco chinesta 2018 proper generalized decomposition solutions within a domain decomposition strategy international journal for numerical methods in engineering 113 13 wiley 1972 94 doi 10 1002 nme 5729 which has been published in final form at https doi org 10 1002 nme 5729 this article may be used for non commercial purposes in accordance with wiley terms and conditions for self archiving

adjoint recovery of superconvergent functionals from pde approximations motivated by applications in computational fluid dynamics a method is presented for obtaining estimates of integral functionals such as lift or drag that have twice the order of accuracy of the computed flow solution on which they are based this is achieved through error analysis that uses an adjoint pde to relate the local errors in approximating the flow solution to the corresponding global errors in the functional of interest numerical evaluation of the local residual error together with an approximate solution to the adjoint equations may thus be combined to produce a correction for the computed functional value that yields the desired improvement in accuracy numerical results are presented for the poisson equation in one and two dimensions and for the nonlinear quasi one dimensional euler equations the theory is equally applicable to nonlinear equations in complex multi dimensional domains and holds great promise for use in a range of engineering disciplines in which a few integral quantities are a key output of numerical approximations

generalized stokes eigenfunctions a new trial basis for the solution of incompressible navier stokes equations abstract the present study focuses on the solution of the incompressible navier stokes equations in general non separable domains and employs a galerkin projection of divergence free vector functions as a trial basis this basis is obtained from the solution of a generalized constrained stokes eigen problem in the domain of interest faster convergence can be achieved by constructing a singular stokes eigen problem in which the stokes operator is modified to include a variable coefficient which vanishes at the domain boundaries the convergence properties of such functions are advantageous in a least squares sense and are shown to produce significantly better approximations to the solution of the navier stokes equations in post critical states where unsteadiness characterizes the flowfield solutions for the eigen systems are efficiently accomplished using a combined laoczos uzawa algorithm and spectral element discretizations results are presented for different simulations using these global spectral trial basis on non separable and multiply connected domains it is confirmed that faster convergence is obtained using the singular eigen expansions in approximating stationary navier stokes solutions in general domains it is also shown that 100 mode expansions of time dependent solutions based on the singular stokes eigenfunctions are sufficient to accurately predict the dynamics of flows in such domains including hopf bifurcations intermittency and details of flow structures

galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics error estimates for galerkin proper orthogonal decomposition pod methods for nonlinear parabolic systems arising in fluid dynamics are proved for the time integration the backward euler scheme is considered the asymptotic estimates involve the singular values of the pod snapshot set and the grid structure of the time discretization as well as the snapshot locations

strongly elliptic boundary integral equations for electromagnetic transmission problems we study a boundary integral equation method for transmission problems for strongly elliptic differential operators which yields a strongly elliptic system of pseudodifferential operators and which therefore can be used for numerical computations with galerkin s procedure the method is shown to work for the vector helmholtz equation in 3 with electromagnetic transmission conditions we propose a slightly modified system of boundary values in order for the corresponding bilinear form to be coercive over h 1 we analyse the boundary integral equations using the calculus of pseudodifferential operators here the concept of the principal symbol is used to derive existence and regularity results for the solution

nearly cloaking the electromagnetic fields the approximate cloaking is investigated for time harmonic maxwell s equations via the approach of transformation optics the problem is reduced to certain boundary effect estimates due to an inhomogeneous electromagnetic inclusion with an asymptotically small support but an arbitrary content enclosed by a thin high conducting layer sharp estimates are established in terms of the asymptotic parameter which are independent of the material tensors of the small electromagnetic inclusion the result implies that the blow up a small region construction via the transformation optics approach yields a near cloak for the electromagnetic waves a novelty lies in the fact that the geometry of the cloaking construction of this work can be very general moreover by incorporating the conducting layer developed in the present paper right between the cloaked region and the cloaking region arbitrary electromagnetic contents can be nearly cloaked our mathematical technique extends the general one developed in h y

numerical resolution of an electromagnetic inverse medium problem at fixed frequency the aim of this paper is to solve numerically the inverse problem of determining the complex refractive index of an electromagnetic medium from partial boundary field measurements at a fixed frequency the governing equations are the time harmonic maxwell equations formulated in electric field in a two dimensional bounded domain we express the inverse problem as the minimization of a cost function representing the difference between the measured and predicted fields our numerical reconstruction algorithm combines the bfgs method and an iterative process called the adaptive eigenspace inversion the unknown complex coefficient is expanded in terms of eigenfunctions of an elliptic operator both the eigenspace and the mesh are iteratively adapted during the minimization procedure numerical experiments illustrate the performance of the reconstruction for various configurations

on approximate electromagnetic cloaking by transformation media we give a comprehensive study on regularized approximate electromagnetic cloaking in the spherical geometry via the transformation optics approach the following aspects are investigated i near invisibility cloaking of passive media as well as active radiating sources ii the existence of cloak busting inclusions without lossy medium lining iii overcoming the cloaking busts by employing a lossy layer outside the cloaked region and iv the frequency dependence of the cloaking performances we address these issues and connect the obtained asymptotic results to singular ideal cloaking numerical verifications and demonstrations are provided to show the sharpness of our analytical study

inverse problem for schrodinger equations with yang mills potentials in a slab abstract in this work we consider the inverse boundary value problem for schrodinger equations with yang mills potentials in the domain of infinite slab type we prove that the potentials can be determined uniquely up to a gauge equivalent class assuming that only partial measurements are known on the boundary hyperplanes

global uniqueness in the inverse scattering problem for the schrodinger operator with external yang mills potentials we consider the schrodinger equation in r n n 3 with external yang mills potentials having compact supports we prove the uniqueness modulo a gauge transformation of the solution of the inverse boundary value problem in a bounded convex domain a similar uniqueness result holds for the inverse scattering problem at a fixed energy

on the low frequency asymptotics in electromagnetic theory on considere les equations de maxwell harmoniques par rapport au temps avec des conditions aux limites on etudie le comportement asymptotique a basse frequence

adaptive component mode synthesis in linear elasticity component mode synthesis cms is a classical method for the reduction of large scale finite element models in linear elasticity in this paper we develop a methodology for adaptive refinement of c

regularized integral equations and curvilinear boundary elements for electromagnetic wave scattering in three dimensions the boundary integral equations bies in their original forms which govern the electromagnetic em wave scattering in three dimensional space contain at least a hypersingularity 1 r sup 3 or a cauchy singularity 1 r sup 2 usually both thus obtaining reliable numerical solutions using such equations requires considerable care especially when developing systematic numerical integration procedures for realistic problems regularized bies for the numerical computation of time harmonic em scattering fields due to arbitrarily shaped scatterers are introduced two regularization approaches utilizing an isolation method plus a mapping are presented to remove all singularities prior to numerical integration both approaches differ from all existing approaches to em scattering problems both work for integral equations initially containing either hypersingularities or cauchy singularities without the need to introduce surface divergences or other derivatives of the em fields on the boundary also neither approach is limited to flat surfaces nor flat element models of curved surfaces the muller linear combination of the electric and magnetic field integral equations efie and mfie is used to avoid the resonance difficulty that is usually associated with integral equation based formulations some preliminary numerical results for em scattering due to single and multiple dielectric spheres are presented and compared with analytical solutions

mixed effects models with censored data with application to hiv rna levels summary mixed effects models are often used for estimating fixed effects and variance components in longitudinal studies of continuous data when the outcome being modelled is a laboratory measurement however it may be subject to lower and upper detection limits i e censoring in this paper the usual em estimation procedure for mixed effects models is modified to account for left and or right censoring

inverse problems for the anisotropic maxwell equations we prove that the electromagnetic material parameters are uniquely determined by boundary measurements for the time harmonic maxwell equations in certain anisotropic settings we give a uniqueness result in the inverse problem for maxwell equations on an admissible riemannian manifold and a uniqueness result for maxwell equations in euclidean space with admissible matrix coefficients the proofs are based on a new fourier analytic construction of complex geometrical optics solutions on admissible manifolds and involve a proper notion of uniqueness for such solutions

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

a domain decomposition approach for uncertainty analysis this paper proposes a decomposition approach for uncertainty analysis of systems governed by partial differential equations pdes the system is split into local components using domain decomposition our domain decomposed uncertainty quantification dduq approach performs uncertainty analysis independently on each local component in an offline phase and then assembles global uncertainty analysis results using precomputed local information in an online phase at the heart of the dduq approach is importance sampling which weights the precomputed local pde solutions appropriately so as to satisfy the domain decomposition coupling conditions to avoid global pde solves in the online phase a proper orthogonal decomposition reduced model provides an efficient approximate representation of the coupling functions

statistical applications of the multivariate skew normal distribution azzalini and dalla valle have recently discussed the multivariate skew normal distribution which extends the class of normal distributions by the addition of a shape parameter the first part of the present paper examines further probabilistic properties of the distribution with special emphasis on aspects of statistical relevance inferential and other statistical issues are discussed in the following part with applications to some multivariate statistics problems illustrated by numerical examples finally a further extension is described which introduces a skewing factor of an elliptical density

a linear mixed effects model with heterogeneity in the random effects population abstract this article investigates the impact of the normality assumption for random effects on their estimates in the linear mixed effects model it shows that if the distribution of random effects is a finite mixture of normal distributions then the random effects may be badly estimated if normality is assumed and the current methods for inspecting the appropriateness of the model assumptions are not sound further it is argued that a better way to detect the components of the mixture is to build this assumption in the model and then compare the fitted model with the gaussian model all of this is illustrated on two practical examples

electromagnetic scattering by a homogeneous chiral obstacle boundary integral equations and low chirality approximations time harmonic electromagnetic waves are scattered by a homogeneous chiral obstacle the corresponding transmission problem is reduced to a pair of coupled integral equations over s where s is the interface between the obstacle and the surrounding medium this is done using a generalization of the stratton chu representation that is valid for chiral media the integral equations obtained are a generalization of those obtained by muller for a homogeneous dielectric obstacle finally we develop approximations for low chirality obstacles these approximations can be computed using simple modifications to existing codes for solving muller s equations

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

galerkin lumped parameter methods for transient problems in this paper we propose a general methodology to obtain lumped parameter models for systems governed by parabolic partial differential equations which we call galerkin lumped parameter methods the idea consists of decomposing the computational domain into several subdomains connected through so called ports then a time independent adapted reduced basis is introduced by numerically solving several elliptic problems in each subdomain the proposed lumped parameter model is the galerkin approximation of the original problem in the space spanned by this basis the relationship of these methods with classical lumped parameter models is analyzed numerical results are shown as well as a comparison of the solution obtained with the lumped model and the exact one computed by standard finite element procedures copyright 2011 john wiley sons ltd

bayesian bent cable growth mixture tobit models for longitudinal data with skewness and detection limit application to aids studies this paper presents a new bayesian methodology for identifying a transition period for the development of drug resistance to antiretroviral drug or therapy in hiv aids studies or other related fields estimation of such a transition period requires an availability of longitudinal data where growth trajectories of a response variable tend to exhibit a gradual change from a declining trend to an increasing trend rather than an abrupt change we assess this clinically important feature of the longitudinal hiv aids data using the bent cable framework within a growth mixture tobit model to account for heterogeneity of drug resistance among subjects the parameters of the bent cable growth mixture tobit model are also allowed to differ by subgroups subpopulations of patients classified into latent classes on the basis of trajectories of observed viral load data with skewness and left censoring the proposed methods are illustrated using real data from an aids clinical study copyright 2016 john wiley sons ltd

flexible longitudinal linear mixed models for multiple censored responses data in biomedical studies and clinical trials repeated measures are often subject to some upper and or lower limits of detection hence the responses are either left or right censored a complication arises when more than one series of responses is repeatedly collected on each subject at irregular intervals over a period of time and the data exhibit tails heavier than the normal distribution the multivariate censored linear mixed effect mlmec model is a frequently used tool for a joint analysis of more than one series of longitudinal data in this context we develop a robust generalization of the mlmec based on the scale mixtures of normal distributions to take into account the autocorrelation existing among irregularly observed measures a damped exponential correlation structure is considered for this complex longitudinal structure we propose an exact estimation procedure to obtain the maximum likelihood estimates of the fixed effects and variance components using a stochastic approximation of the em algorithm this approach allows us to estimate the parameters of interest easily and quickly as well as to obtain the standard errors of the fixed effects the predictions of unobservable values of the responses and the log likelihood function as a byproduct the proposed method is applied to analyze a set of aids data and is examined via a simulation study

an inverse source problem for maxwell s equations in magnetoencephalography consider an inverse source problem for maxwell s equations which arises in determining locations of epileptic foci in the living human brain the human brain is modeled as a heterogeneous medium where the electric permittivity magnetic permeability and conductivity may all be functions a current dipole is used to model the epilepsy the inverse source problem in this context is to determine the current dipole from boundary measurements of the fields in this paper a new computational method is introduced for solving the inverse problem the method is based on a low frequency asymptotic analysis of maxwell s equations our method is constructive and has good convergence properties a crucial step of the method is to construct special test functions uniqueness and stability results for the inverse problem are also established the method and results are expected to find applications particularly in magnetoencephalography

fluid solid interaction acoustic scattering by a smooth elastic obstacle a bounded three dimensional elastic obstacle is surrounded by an unbounded inviscid compressible fluid acoustic waves are scattered by the obstacle the problem is to find the scattered waves and the response of the obstacle this problem is formulated mathematically existence and uniqueness theorems are proved various systems of boundary integral equations over the interface between the fluid and the solid are derived and analysed these systems include a system obtained by a straightforward direct method and a smaller system for a single vector field

fast numerical solution for scattering from rough surfaces with small slopes the rigorous solution of the scattering by two dimensional rough surfaces can be numerically performed thanks to the sparse matrix flat surface iterative approach smfsia however this kind of computation still requires both large cpu time and memory consequently a lot of work has been dedicated at extending the domain of validity of approximate methods beyond that of standard high and low frequency approximations in this paper it is shown that smsfia can be simplified in order to get a fast approximate method with low memory requirements this approximation is valid for surfaces with small slopes and covers the domain of validity of both the kirchhoff tangent plane approximation and the first order small slope approximation

boundary integral equations for magnetic screens in ℝ 3 on developpe une methode d integrale limite pour la diffusion d ondes electromagnetiques sur des objets minces le probleme aux limites exterieur pour l equation de helmholtz vectorielle avec donnees de neumann sur un morceau de surface ouvert est converti en un systeme d equations integrales pour les sauts de la composante tangentielle du champ et sa divergence a travers l ecran une legere modification des donnees de cauchy donne un systeme fortement elliptique d equations pseudodifferentielles sur s

port reduction in parametrized component static condensation approximation and a posteriori error estimation summary we introduce a port interface approximation and a posteriori error bound framework for a general component based static condensation method in the context of parameter dependent linear elliptic partial differential equations the key ingredients are as follows i efficient empirical port approximation spaces the dimensions of these spaces may be chosen small to reduce the computational cost associated with formation and solution of the static condensation system and ii a computationally tractable a posteriori error bound realized through a non conforming approximation and associated conditioner the error in the global system approximation or in a scalar output quantity may be bounded relatively sharply with respect to the underlying finite element discretization our approximation and a posteriori error bound framework is of particular computational relevance for the static condensation reduced basis element scrbe method we provide several numerical examples within the scrbe context which serve to demonstrate the convergence rate of our port approximation procedure as well as the efficacy of our port reduction error bounds copyright 2013 john wiley sons ltd

the linear sampling method for solving the electromagnetic inverse scattering problem we consider the inverse scattering problem of determining the shape of an obstacle in mathbb r from knowledge of the time harmonic incident electromagnetic wave and the far field pattern of the scattered wave with frequency in the resonance region the approach used is the linear sampling method which does not require a priori knowledge of either the boundary condition or the connectivity of the scattering obstacle numerical examples are given for the case of both a simply connected perfect conductor and multiply connected obstacles satisfying an impedance boundary condition on the boundary of one component and satisfying a perfect conducting boundary condition on the boundary of another component

the reduced basis element method application to a thermal fin problem the reduced basis element method is a new approach for the approximation of partial differential equations that takes its roots in the domain decomposition method and in the reduced basis discretization the basic idea is to decompose the domain of computation into a series of subdomains the elements that are similar to a few reference domains these reference domains are actually filled with reduced basis functional spaces that are mapped to each subdomain together with the geometry the discrete approximation space is then composed of functions with the property that a function restricted to a subdomain belongs to the mapped reduced spaces finally a mortar type method is applied to glue the various local functions in this paper we focus on the definition of the reference shapes and together with theoretical and numerical justifications of the method we provide a posteriori error analysis tools that allow us to certify the computational results

optimal local approximation spaces for component based static condensation procedures in this paper we introduce local approximation spaces for component based static condensation sc procedures that are optimal in the sense of kolmogorov to facilitate simulations for large structures such as aircraft or ships it is crucial to decrease the number of degrees of freedom on the interfaces or ports in order to reduce the size of the statically condensed system to derive optimal port spaces we consider a compact transfer operator that acts on the space of harmonic extensions on a two component system and maps the traces on the ports that lie on the boundary of these components to the trace of the shared port solving the eigenproblem for the composition of the transfer operator and its adjoint yields the optimal space for a related work in the context of the generalized finite element method we refer the reader to i babuska and r lipton multiscale model simul 9 2011 pp 373 406 we further introduce a spectral greedy algorithm to generalize the procedure to the parameter

recovery of an embedded obstacle and the surrounding medium for maxwell s system abstract in this paper we are concerned with the inverse electromagnetic scattering problem of recovering a complex scatterer by the corresponding electric far field data the complex scatterer consists of an inhomogeneous medium and a possibly embedded perfectly electric conducting pec obstacle the far field data are collected corresponding to incident plane waves with a fixed incident direction and a fixed polarisation but frequencies from an open interval it is shown that the embedded obstacle can be uniquely recovered by the aforementioned far field data independent of the surrounding medium furthermore if the surrounding medium is piecewise homogeneous then the medium can be recovered as well those unique recovery results are new to the literature our argument is based on low frequency expansions of the electromagnetic fields and certain harmonic analysis techniques

a static condensation reduced basis element method complex problems abstract we extend the static condensation reduced basis element scrbe method to treat the class of parametrized complex helmholtz partial differential equations the main ingredients are i static condensation at the interdomain level ii a conforming eigenfunction port representation at the interface level iii the reduced basis rb approximation of finite element fe bubble functions at the intradomain level and iv rigorous system level error bounds which reflect rb perturbation of the fe schur complement we then incorporate these ingredients in an offline online computational strategy to achieve rapid and accurate prediction of parametric systems formed from instantiations of interoperable parametrized archetype components from a library we introduce a number of extensions with respect to the original scrbe framework first primal dual rb methods for general non symmetric complex problems second stability constant procedures for weakly coercive problems at both the interdomain level and intradomain level third treatment of non port linear functional outputs as well as functions of outputs fourth consideration of particular components and outputs relevant to acoustic applications we consider several numerical examples in acoustics in particular focused on mufflers and horns to demonstrate that the approach can handle models with many parameters and or topology variations with particular reference to waveguide like applications

an exterior boundary value problem for the maxwell equations with boundary data in a sobolev space we treat the time harmonic maxwell equations in an exterior domain with prescribed boundary data n e in the sobolev space of square integrable tangential fields with square integrable surface divergence by using boundary integral equation methods existence and uniqueness results are established furthermore we investigate the completeness of electric and magnetic dipoles distributed on an inner surface in this sobolev space

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

identification of small amplitude perturbations in the electromagnetic parameters from partial dynamic boundary measurements we consider the inverse problem of reconstructing small amplitude perturbations in the conductivity for the wave equation from partial on part of the boundary dynamic boundary measurements through construction of appropriate test functions by a geometrical control method we provide a rigorous derivation of the inverse fourier transform of the perturbations in the conductivity as the leading order of an appropriate averaging of the partial dynamic boundary perturbations this asymptotic formula is generalized to the full time dependent maxwell s equations our formulae may be expected to lead to very effective computational identification algorithms aimed at determining electromagnetic parameters of an object based on partial dynamic boundary measurements

reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries the aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques the main idea behind this approach is to compute once locally and for few reference shapes some representative finite element solutions for different values of the parameters and with a set of different suitable boundary conditions on the boundaries these functions will represent the basis of a reduced space where the global solution is sought for the continuity of the latter is assured by a classical domain decomposition approach test results on poisson problem show the flexibility of the proposed method in which accuracy and computational time may be tuned by varying the number of reduced basis functions employed or the set of boundary conditions used for defining locally the basis functions the proposed approach simplifies the pre computation of the reduced basis space by splitting the global problem into smaller local subproblems thanks to this feature it allows dealing with arbitrarily complex network and features more flexibility than a classical global reduced basis approximation where the topology of the geometry is fixed c 2015 elsevier ltd all rights reserved

on an inverse boundary problem arising in brain imaging abstract we consider the inverse problem of recovering both an unknown electric current and the surrounding electromagnetic parameters of a medium from boundary measurements this inverse problem arises in brain imaging we show that under generic conditions one can recover both the source and the electromagnetic parameters if these are piecewise constant and the source current is invariant in a fixed direction or a harmonic function respectively

a recursive single source surface integral equation analysis for wave scattering by heterogeneous dielectric bodies the problem of electromagnetic wave scattering by heterogeneous dielectric bodies is formulated in a recursive manner by organizing their homogeneous subregions into hierarchical multiply nested structures the inner details of each multiply nested body are completely accounted for by an equivalent surface representation that yields the electric and magnetic fields tangent to the body only in terms of a single unknown electric surface current density distributed on its outer surface in this manner the problem of wave scattering by heterogeneous dielectric bodies is reduced to a scattering problem over their outermost surfaces in terms of only a single unknown current density for a large number n of different homogeneous dielectric subregions within such a heterogeneous body the proposed method has a computational complexity of o n sup 1 5 and storage requirements that increase in proportion to o n furthermore the equivalent surface representation derived for a particular subregion is invariant under rotation and translation and may therefore be applied to identical subregions without repeating the computation the fields at any interior points are calculated by a fast backward recursion

electromagnetic inverse problems and generalized sommerfeld potentials in this article we study the inverse boundary value problem for maxwell s equation that is we determine the scalar permeability permissibility and conductivity of a body from electromagnetic field measurements outside the body in this paper the problem is approached by using certain generalized sommerfeld potentials that are shown to satisfy a vector valued schrodinger equation by using these potentials the inverse boundary value problem is reduced to the problem of determining the potential of this second order operator further it is shown that the electromagnetic material parameters can be determined by using electric or magnetic dipole point sources only

approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations summary structured additive regression models are perhaps the most commonly used class of models in statistical applications it includes among others generalized linear models generalized additive models smoothing spline models state space models semiparametric regression spatial and spatiotemporal models log gaussian cox processes and geostatistical and geoadditive models we consider approximate bayesian inference in a popular subset of structured additive regression models latent gaussian models where the latent field is gaussian controlled by a few hyperparameters and with non gaussian response variables the posterior marginals are not available in closed form owing to the non gaussian response variables for such models markov chain monte carlo methods can be implemented but they are not without problems in terms of both convergence and computational time in some practical applications the extent of these problems is such that markov chain monte carlo sampling is simply not an appropriate tool for routine analysis we show that by using an integrated nested laplace approximation and its simplified version we can directly compute very accurate approximations to the posterior marginals the main benefit of these approximations is computational where markov chain monte carlo algorithms need hours or days to run our approximations provide more precise estimates in seconds or minutes another advantage with our approach is its generality which makes it possible to perform bayesian analysis in an automatic streamlined way and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged

scattering of electromagnetic waves from rough surfaces a boundary integral method for low grazing angles we present a boundary integral method for the numerical solution of the rigorous problem of wave scattering from rough surfaces under grazing illumination the model of a locally perturbated plane is adopted a finite patch of rough surface has its roughness flattened at the edges the boundary formulation unknowns are the tangential components of the scattered field defined as the contribution from the rough area this way the numerical domain of study is correctly bounded even with a plane wave as incident field and the sampled area is made independent of the incidence this rigorous approach called the grazing method of moments is implemented on two dimensional perfectly conducting surfaces and validated by comparison with a reference numerical solution for surfaces with gaussian correlation functions now the validity of approximate models at low grazing angles can be investigated the small perturbation method and the small slope approximation are addressed in this paper scattering diagrams show how the performances of these methods deteriorate drastically at backward scattering angles as the incidence goes to grazing

boundary integral equations for the scattering of electromagnetic waves by a homogeneous dielectric obstacle time harmonic electromagnetic waves are scattered by a homogeneous dielectric obstacle the corresponding electromagnetic transmission problem is reduced to a single integral equation over s for a single unknown tangential vector field where s is the interface between the obstacle and the surrounding medium in fact several different integral equations are derived and analysed including two previously known equations due to e marx and j r mautz and two new singular integral equations mautz s equation is shown to be uniquely solvable at all frequencies a new uniquely solvable singular integral equation is also found the paper also includes a review of methods using pairs of coupled integral equations over s it is these methods that are usually used in practice although single integral equations seem to offer some computational advantages

bayesian semiparametric mixture tobit models with left censoring skewness and covariate measurement errors common problems to many longitudinal hiv aids cancer vaccine and environmental exposure studies are the presence of a lower limit of quantification of an outcome with skewness and time varying covariates with measurement errors there has been relatively little work published simultaneously dealing with these features of longitudinal data in particular left censored data falling below a limit of detection lod may sometimes have a proportion larger than expected under a usually assumed log normal distribution in such cases alternative models which can account for a high proportion of censored data should be considered in this article we present an extension of the tobit model that incorporates a mixture of true undetectable observations and those values from a skew normal distribution for an outcome with possible left censoring and skewness and covariates with substantial measurement error to quantify the covariate process we offer a flexible nonparametric mixed effects model within the tobit framework a bayesian modeling approach is used to assess the simultaneous impact of left censoring skewness and measurement error in covariates on inference the proposed methods are illustrated using real data from an aids clinical study

aperiodic electromagnetic waves in exterior domains on considere les problemes aux valeurs limites et initiales pour l equation d onde vectorielle dans des domaines exterieurs par rapport aux conditions limites electriques n e 0 e 0 sur et des conditions aux limites magnetiques n h 0 n h 0 sur on etudie le comportement asymptotique des solutions e x t et h x t quand

a spectral element method for fluid dynamics laminar flow in a channel expansion a spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible navier stokes equations in the spectral element discretization the computational domain is broken into a series of elements and the velocity in each element is represented as a high order lagrangian interpolant through chebyshev collocation points the hyperbolic piece of the governing equations is then treated with an explicit collocation scheme while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle the implementation of the technique is demonstrated on a one dimensional inflow outflow advection diffusion equation and the method is then applied to laminar two dimensional separated flow in a channel expansion comparisons are made with experiment and previous numerical work

scattering with critically singular and delta shell potentials we consider a scattering problem for electric potentials that have a component which is critically singular in the sense of lebesgue spaces and a component given by a measure supported on a compact lipschitz hypersurface we study direct and inverse point source scattering under the assumptions that the potentials are real valued and compactly supported to solve the direct scattering problem we introduce two functional spaces sort of bourgain type spaces that allow to refine the classical resolvent estimates of agmon and hormander and kenig ruiz and sogge these spaces seem to be very useful to deal with the critically singular and delta shell components of the potentials at the same time furthermore these spaces and their corresponding resolvent estimates turn out to have a strong connection with the estimates for the conjugated laplacian used in the context of the inverse calderon problem in fact we derive the classical estimates by sylvester and uhlmann and the more recent ones by haberman and tataru after some embedding properties of these new spaces regarding the inverse scattering problem we prove uniqueness for the potentials from point source scattering data at fix energy to address the question of uniqueness we combine some of the most advanced techniques in the construction of complex geometrical optics solutions

an initial boundary value problem for the maxwell equations abstract in this paper by using methods from complex analysis and quaternionic analysis we investigate an initial boundary value problem for the maxwell equations and obtain the general solutions and solvable conditions of the problem respectively in different cases in addition by using a similar method we also discuss an initial boundary value problem for a hyperbolic complex system of first order equations in r 3

the essential spectrum of the nonself adjoint maxwell operator in a bounded domain 1 introductionin this work we study the spectrum of the maxwell operator in theself adjoint case it is well known that the spectrum consists of oneeigenvalue with infinite multiplicity in zero and other eigenvalues havingfinite multiplicities however the spectrum of the nonself adjoint operatorwas not studied much though the nonself adjoint perturbation rises from avery common phenomena namely from the conductivity in this work weshow that the maxwell system with conductivity in a bounded domain hasquite a large essential spectrum the essential spectrum contains aninterval or another nondiscrete set let v be a

boundary integral method for multi layered electromagnetic scattering problems abstract in this paper we consider the scattering of time harmonic electromagnetic plane waves by an impenetrable obstacle which is embedded in a piecewise homogeneous medium applying potential theory the problem can be reformulated as a boundary integral system we obtain the existence and uniqueness of the solution to the system by using the generalized garding inequality and the fredholm theory

a linearized inverse boundary value problem for maxwell s equations abstract in this paper we consider the problem of determining the electromagnetic state of a body from measurements made on the surface of the body we study the full set of maxwell s equations that govern time harmonic electric and magnetic fields we seek to reconstruct the magnetic permeability the electric permitivity and the electric conductivity in the interior of the body from measurements made on the surface we exhibit appropriate boundary measurements in the form of a boundary mapping specifically the mapping from the tangential components of the electric field to the tangential components of the magnetic field this data can be used to reconstruct and approximately provided they deviate only slightly from known constants we also estimate the reconstruction errors

determination of small amplitude perturbations for the electric permittivity from partial dynamic boundary measurements the paper deals with reconstruction of small perturbation of the uniform isotropic complex electric permittivity from dynamic measurements of the tangential component of the magnetic field on the boundary or a part of the boundary of a domain the method is based on derived asymptotic inverse fourier transform of the perturbation in the complex permittivity through construction of appropriate test functions by a geometrical control method we provide a rigorous derivation of the inverse fourier transform of the perturbations in the electric permittivity as the leading order of an appropriate averaging of the partial dynamic boundary perturbations