cloaking via change of variables for the helmholtz equation the transformation optics approach to cloaking uses a singular change of coordinates which blows up a point to the region being cloaked this paper examines a natural regularization obtained by 1 blowing up a ball of radius rather than a point and 2 including a well chosen lossy layer at the inner edge of the cloak we assess the performance of the resulting near cloak as the regularization parameter tends to 0 in the context of dirichlet and neumann boundary measurements for the time harmonic helmholtz equation since the goal is to achieve cloaking regardless of the content of the cloaked region we focus on estimates that are uniform with respect to the physical properties of this region in three space dimensions our regularized construction performs relatively well the deviation from perfect cloaking is of order in two space dimensions it does much worse the deviation is of order 1 log in addition to proving these estimates we give numerical examples demonstrating their sharpness some authors have argued that perfect cloaking can be achieved without losses by using the singular change of variable based construction in our regularized setting the analogous statement is false without the lossy layer there are certain resonant inclusions depending in general on that have a huge effect on the boundary measurements 2010 wiley periodicals inc

a new mesh generation scheme for arbitrary planar domains this paper describes a new algorithm to generate interior nodes within any arbitrary multi connected regions the boundary nodes and the interior nodes are then linked up to form the best possible triangular elements by a completely revised technique in an efficient and stable manner owing to the generality of the central generation program the global domain is allowed to be divided into as many irregular subdomains as desired in order to model closely the actual physical situation moreover the boundaries of the sub domains are updated from time to time when necessary to include the possibilities of progressive refinement around a sharp corner generating radiating mesh from a prescribed node generating mesh between two circular arcs etc despite its flexibility and capabilities data for triangulation have been kept to a minimum by a logical input module no connectivity information between subregions is needed and common boundaries are defined once only all these features have contributed to a powerful method to generate 3 node or 6 node triangular element meshes of great variety within the most irregular heterogeneous regions

a hierarchical domain decomposition preconditioner for h p finite element approximation on locally refined meshes a domain decomposition preconditioner suitable for h p finite element approximation on locally refined meshes with nonuniform polynomial degree is proposed and analysed the preconditioner is highly suited for parallel computation the algorithm generalizes methods proposed by smith domain decomposition algorithms for the partial differential equations of linear elasticity ph d thesis mathematics department new york university new york 1991 for the h version finite element method with piecewise linear basis functions and by mandel comput methods appl mech engrg 80 1990 pp 117 128 for the p version finite element method the analysis shows that the condition number of the preconditioned system grows at most as min h h 1 log 2p 1 log 2 hp h this result generalizes the known estimates in each of the special cases mentioned above numerical examples are given confirming the theoretical analysis

recovering dielectric constants of explosives via a globally strictly convex cost functional the inverse problem of estimating dielectric constants of explosives using boundary measurements of one component of the scattered electric field is addressed it is formulated as a coefficient inverse problem for a hyperbolic differential equation after applying the laplace transform a new cost functional is constructed and a variational problem is formulated the key feature of this functional is the presence of the carleman weight function for the laplacian the strict convexity of this functional on a bounded set in a hilbert space of an arbitrary size is proven this allows for establishing the global convergence of the gradient descent method some results of numerical experiments are presented

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

non locality of experimental qutrit pairs the insight due to john bell that the joint behavior of individually measured entangled quantum systems cannot be explained by shared information remains a mystery to this day we describe an experiment and its analysis displaying non locality of entangled qutrit pairs the non locality of such systems as compared to qubit pairs is of particular interest since it potentially opens the door for tests of bipartite non local behavior independent of probabilistic bell inequalities but of deterministic nature this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

integration of hp adaptivity and a two grid solver for elliptic problems we present implementation details and analyze convergence of a two grid solver forming the core of the fully automatic hp adaptive strategy for elliptic problems the solver delivers a solution for a fine grid obtained from an arbitrary coarse hp grid by a global hp refinement the classical v cycle algorithm combines an overlapping block jacobi smoother with optimal relaxation and a direct solve on the coarse grid a simple theoretical analysis is illustrated with extensive numerical experimentation

numerical solution of the quasilinear poisson equation in a nonuniform triangle mesh a finite difference method using a nonuniform triangle mesh is described for the numerical solution of the nonlinear two dimensional poisson equation s 0 where is a function of or its derivatives sis a function of position and or its normal derivative is specified on the boundary the finite difference equations are solved by successive overrelaxation the triangle mesh which is constructed numerically by solving laplace s equation is easily adapted to nonrectangular boundaries and interfaces examples of numerical results are given for the magnetostatic problem with iron and other possible applications are mentioned

fully automatic hp adaptivity in three dimensions the paper presents a three dimensional implementation of the fully automatic hp adaptive mesh refinement strategy proposed in l demkowicz w rachowicz ph devloo a fully automatic hp adaptivity j sci comput 17 1 3 2002 127 155 the methodology is based on a minimization of the projection based interpolation error with a fixed number of degrees of freedom a coarse grid is first uniformly refined in both h and p to yield a corresponding fine grid a two grid solver is used to solve the problem on the fine grid or iterate towards the fine grid solution the fine grid solution possibly partially converged serves then as a reference solution to be interpolated on the original coarse mesh and the next optimal coarse grid to be determined the difference between the coarse and fine grid solutions provides an excellent error estimate for the coarse grid error the procedure is repeated with the coarse and fine meshes generated during the adaptive process simultaneously until a prescribed error tolerance for the coarse grid error is met the solution obtained on the last fine grid is considered to be the final product delivered by the adaptive procedure

two single shot methods for locating multiple electromagnetic scatterers we develop two inverse scattering schemes for locating multiple electromagnetic em scatterers by the electric far field measurement corresponding to a single incident detecting plane wave the first scheme is for locating scatterers of small size compared to the wavelength of the detecting plane wave the multiple scatterers could be extremely general with an unknown number of components and each scatterer component could be either an impenetrable perfectly conducting obstacle or a penetrable inhomogeneous medium with an unknown content the second scheme is for locating multiple perfectly conducting obstacles of regular size compared to the detecting em wavelength the number of the obstacle components is not required to be known in advance but the shape of each component must be from a certain known admissible class the admissible class may consist of multiple different reference obstacles the second scheme could also be extended to include the medium components if a certain generic condition is s

maximal violation of the collins gisin linden massar popescu inequality for infinite dimensional states we present a much simplified version of the collins gisin linden massar popescu inequality for the 2 ifmmode times else texttimes fi 2 ifmmode times else texttimes fi d bell scenario numerical maximization of the violation of this inequality over all states and measurements suggests that the optimal state is far from maximally entangled while the best measurements are the same as conjectured best measurements for the maximally entangled state for very large values of d the inequality seems to reach its minimal value given by the probability constraints this gives numerical evidence for a tight quantum bell inequality or generalized csirelson inequality for the 2 ifmmode times else texttimes fi 2 ifmmode times else texttimes fi ensuremath infty scenario

domain decomposition preconditioners for p and hp finite element approximation of stokes equations abstract domain decomposition preconditioning techniques are developed in the context of hp finite element approximation of the stokes problem two basic types of preconditioner are considered a block diagonal scheme based on decoupling the velocity and pressure components and a scheme based on an indefinite system similar to the original stokes system for each type of scheme theoretical estimates are obtained for the location of the eigenvalues of the preconditioned operators in terms of the polynomial degree the mesh sizes on the coarse and fine grids and the inf sup constant for the method theoretical estimates show that the growth of the bounds is modest as the mesh is refined and the polynomial order is increased the preconditioners are shown to be applicable to various iterative schemes for the stokes systems the theoretical bounds are compared with actual quantities obtained in practical computations for several representative problems

computing the entropy of a large matrix given a large real symmetric positive semidefinite matrix the goal of this paper is to show how a numerical approximation of the von neumann entropy of the matrix can be computed in an efficient way without relying on matrix diagonalization an application from quantum optics dealing with the entanglement between photons illustrates the new algorithm

multilevel preconditioned qmr methods for unstructured mesh computation we present a variant of the quasi minimal residual qmr algorithm of freund and nachtigal with a preconditioner based on the algebraic multilevel amli algorithm of axelsson and vassilevski this combination provides an effective solution method for indefinite algebraic systems and is tested by application to finite element discretizations of the helmholtz equation the implementation is applicable with both h and p refinements and easily extends to a parallel environment

numerical design of fshl based approximate cloaks with arbitrary shapes this paper considers numerical design of finite sound hard lining fshl based approximate cloaks with arbitrary shapes regarding the complexity of the shape two new approaches are proposed to design the transformation map from the virtual space to the physical space via transformation optics for star shaped geometry we propose an explicit global transformation map which can be easily differentiated and inverted for more general shapes an initialize untangle extend iue approach is initiated to build locally piecewise differentiable deformations which can be locally inverted with the help of an approximate triangulation with the locally piecewise constructed transformation the parameters of acoustic scattering models in physical space can be determined in both approaches based on the transformation invariance of the helmholtz system then the cloaking effects for an arbitrary shape fshl based cloak can be realized following li et al 2012 5 extensive numerical experiments are presented to illustrate both the effectiveness of cloak design and the efficiency of the proposed fshl based cloaks with arbitrary shapes

achieving finite element mesh quality via optimization of the jacobian matrix norm and associated quantities part i a framework for surface mesh optimization structured mesh quality optimization methods are extended to optimization of unstructured triangular quadrilateral and mixed finite element meshes n ew interpretations of well known nodally bssed objective functions are made possible using matrices and matrix norms the matrix perspective also suggests several new objective functions particularly significant is the interpretation of the oddy metric and the smoothness objective functions in terms of the condition number of the metric tensor and jacobian matrix respectively objective functions are grouped according to dimensionality to form weighted combinations a simple unconstrained local optimum is computed using a modiiied n ewton iteration the optimization approach was implemented in the cubit mesh generation code and tested on several problems results were compared against several standard element based quaiity measures to demonstrate that good mesh quality can be achieved with nodally based objective functions

achieving finite element mesh quality via optimization of the jacobian matrix norm and associated quantities part ii a framework for volume mesh optimization and the condition number of the jacobian matrix three dimensional unstructured tetrahedral and hexahedral finite element mesh optimization is studied from a theoretical perspective and by computer experiments to determine what objective functions are most effective in attaining valid high quality meshes the approach uses matrices and matrix norms to extend the work in part i to build suitable 3d objective functions because certain matrix norm identities which hold for 2 x 2 matrices do not hold for 3 x 3 matrices significant differences arise between surface and volume mesh optimization objective functions it is shown for example that the equivalence in two dimensions of the smoothness and condition number of the jacobian matrix objective functions does not extend to three dimensions and further that the equivalence of the oddy and condition number of the metric tensor objective functions in two dimensions also fails to extend to three dimensions matrix norm identities are used to systematically construct dimensionally homogeneous groups of objective functions the concept of an ideal minimizing matrix is introduced for both hexahedral and tetrahedral elements non dimensional objective functions having barriers are emphasized as the most logical choice for mesh optimization the performance of a number of objective functions in improving mesh quality was assessed on a suite of realistic test problems focusing particularly on all hexahedral whisker weaved meshes performance is investigated on both structured and unstructured meshes and on both hexahedral and tetrahedral meshes although several objective functions are competitive the condition number objective function is particularly attractive the objective functions are closely related to mesh quality measures to illustrate it is shown that the condition number metric can be viewed as a new tetrahedral element quality measure

reconstruction procedures for two inverse scattering problems without the phase information this is a continuation of two recent publications of the authors j inverse ill posed probl 23 2015 pp 415 426 j inverse ill posed probl 23 2015 pp 187 193 about reconstruction pr

recovering a polyhedral obstacle by a few backscattering measurements abstract we propose an inverse scattering scheme of recovering a polyhedral obstacle in r n n 2 3 by only a few high frequency acoustic backscattering measurements the obstacle could be sound soft or sound hard it is shown that the modulus of the far field pattern in the backscattering aperture possesses a certain local maximum behavior from which one can determine the exterior normal directions of the front sides faces then by using the phaseless backscattering data corresponding to a few incident plane waves with suitably chosen incident directions one can determine the exterior unit normal vector of each side face of the obstacle after the determination of the exterior unit normals the recovery is reduced to a finite dimensional problem of determining a location point of the obstacle and the distance of each side face away from the location point for the latter reconstruction we need to make use of the far field data with phases numerical experiments are also presented to illustrate the effectiveness of the proposed scheme

bell inequalities for arbitrarily high dimensional systems we develop a novel approach to bell inequalities based on a constraint that the correlations exhibited by local variable theories must satisfy this is used to construct a family of bell inequalities for bipartite quantum systems of arbitrarily high dimensionality which are strongly resistant to noise in particular our work gives an analytic description of previous numerical results and generalizes them to arbitrarily high dimensionality

on the accuracy of p version elements for the reissner mindlin plate problem this paper addresses the question of accuracy of p version finite element formulations for reissner mindlin plate problems three model problems a circular arc a rhombic plate and a geometrically complex structure are investigated whereas displacements and bending moments turn out to be very accurate without any post processing even for very coarse meshes the quality of shear forces computed from constitutive equations is poor it is shown that significantly improved results can be obtained if shear forces are computed from equilibrium equations instead a consistent computation of second derivatives of the shape functions is derived 1998 john wiley sons ltd

aspects of an adaptive hp finite element method adaptive strategy conforming approximation and efficient solvers the main components needed for an adaptive hp version finite element algorithm are discussed an adaptive hp refinement strategy effective methods for constructing conforming hp approximations and efficient solvers for the large ill conditioned systems of linear equations together these provide the methodology for an effective adaptive hp version algorithm the presentation emphasizes the links between the differing components showing how the algorithms may be implemented efficiently in practice the main principles are illustrated by use of concrete examples so that a non expert may develop their own adaptive hp code the performance of the whole algorithm is illustrated for some representative problems taken from linear elasticity

cloaking via change of variables for the helmholtz equation in the whole space this paper is devoted to the study of a cloaking device that is composed of a standard near cloak based on a regularization of the transformation optics i e a change of variables that blows up a small ball to the cloaked region and a fixed lossy layer for the helmholtz equation in the whole space of dimension 2 or 3 with the outgoing condition at infinity we establish a degree of near invisibility which is independent of the content inside the cloaked region for this device we also show that the lossy layer is necessary to ensure the validity of the degree of near invisibility when no constraint on physical properties inside the cloaked region is imposed 2010 wiley periodicals inc