revisiting iterative time reversal processing application to detection of multiple targets the iterative time reversal processing represents a high speed and easy way to self focus on the strongest scatterer in a multitarget medium however finding weaker scatterers is a more difficult task that can be solved by computing the eigenvalue and eigenvector decomposition of the time reversal operator the so called dort method nevertheless as it requires the measurement of the complete interelements response matrix and time consuming computation the separation of multiple targets may not be achieved in real time in this study a new real time technique is proposed for multitarget selective focusing that does not require the experimental acquisition of the time reversal operator this technique achieves the operator decomposition using a particular sequence of filtered waves propagation instead of computational power due to its simplicity of implementation this iterative process can be achieved in real time this high speed selective focusing is experimentally demonstrated by detecting targets through a heterogeneous medium and in a speckle environment a theoretical analysis compares this technique to the dort formalism

incorporation of exact boundary conditions into a discontinuous galerkin finite element method for accurately solving 2d time dependent maxwell equations a scheme that discretizes exact absorbing boundary conditions eacs to incorporate them into a time domain discontinuous galerkin finite element method td dg fem is described the proposed td dg fem with eacs is used for accurately characterizing transient electromagnetic wave interactions on two dimensional waveguides numerical results demonstrate the proposed method s superiority over the td dg fem that employs approximate boundary conditions and perfectly matched layers additionally it is shown that the proposed method can produce the solution with ten eleven digit accuracy when high order spatial basis functions are used to discretize the maxwell equations as well as the eacs

discontinuous galerkin finite element method for the wave equation the symmetric interior penalty discontinuous galerkin finite element method is presented for the numerical discretization of the second order wave equation the resulting stiffness matrix is symmetric positive definite and the mass matrix is essentially diagonal hence the method is inherently parallel and leads to fully explicit time integration when coupled with an explicit time stepping scheme optimal a priori error bounds are derived in the energy norm and the l 2 norm for the semidiscrete formulation in particular the error in the energy norm is shown to converge with the optimal order cal o h min s ell with respect to the mesh size h the polynomial degree ell and the regularity exponent s of the continuous solution under additional regularity assumptions the l 2 error is shown to converge with the optimal order cal o h min s ell numerical results confirm the expected convergence rates and illustrate the versatility of the method

marching on in time solution of the time domain magnetic field integral equation using a predictor corrector scheme an explicit marching on in time mot scheme for solving the time domain magnetic field integral equation td mfie is presented the proposed mot td mfie solver uses rao wilton glisson basis functions for spatial discretization and a pe ce m type linear multistep method for time marching unlike previous explicit mot td mfie solvers the time step size can be chosen as large as that of the implicit mot td mfie solvers without adversely affecting accuracy or stability an algebraic stability analysis demonstrates the stability of the proposed explicit solver its accuracy and efficiency are established via numerical examples

on the quasi analytic treatment of hysteretic nonlinear response in elastic wave propagation microscopic features and their hysteretic behavior can be used to predict the macroscopic response of materials in dynamic experiments preisach modeling of hysteresis provides a refined procedure to obtain the stress strain relation under arbitrary conditions depending on the pressure history of the material for hysteretic materials the modulus is discontinuous at each stress strain reversal which leads to difficulties in obtaining an analytic solution to the wave equation numerical implementation of the integral preisach formulation is complicated as well under certain conditions an analytic expression of the modulus can be deduced from the preisach model and an elementary description of elastic wave propagation in the presence of hysteresis can be obtained this approach results in a second order partial differential equation with discontinuous coefficients classical nonlinear representations used in acoustics can be found as limiting cases the differential equation is solved in the frequency do

discriminating linear from nonlinear elastic damage using a nonlinear time reversal dort method the dort method is a selective detection and focusing technique originally developed to detect defects and damages which induce linear changes of the elastic moduli it is based on the time reversal tr where a signal collected from an array of transducers is time reversed and then back propagated into the medium to obtain focusing on selected targets tr is based on the principle of spatial reciprocity attenuation dispersion multiple scattering mode conversion etc do not break spatial reciprocity the presence of defects or damage may cause materials to show nonlinear elastic wave propagation behavior that will break spacial reciprocity therefore the dort method will not allow focusing on nonlinear elastic scatterers this paper presents a new method for the detection and identification of multiple linear and nonlinear scatterers by combining nonlinear elastic wave spectroscopy time reversal and dort method in the presence of nonlinear hysteretic elastic scatterers forcing the solid with a harmonic excitation the time reversal operator can be obtained not only at the fundamental frequency of excitation but also at the odd harmonics at the fundamental harmonic either inhomogeneities and linear damages can be individually selected but only at odd harmonics nonlinear hysteretic elastic damages exist a procedure was developed where by decomposing the operator at the odd harmonics it was possible to focus on nonlinear scatterers and to differentiate them from the linear inhomogeneities a complete mathematical nonlinear dort formulation for 1 and 2d structures is presented to model the presence of nonlinear elastic hysteretic scatterers a preisach mayergoyz pm material constitutive model was used results relative to 1 and 2 dimensional structures are reported showing the capability of the method to focus and discern selectively linear and nonlinear scatterers furthermore an analysis was conducted to study the influence of the number of sources and their location on the imaging process showing that using a higher numbers of sensors does not automatically bring to a minor uncoupled behaviour between the nonlinear targets

interior penalty discontinuous galerkin time domain method based on wave equation for 3 d electromagnetic modeling built on the vector wave equation an interior penalty discontinuous galerkin time domain ipdg we method is presented for 3 d real life electromagnetic modeling in this paper we develop the interior penalty fluxes corresponding to different types of boundary conditions which are commonly used in electromagnetic modeling to construct the ipdg we system in local elements in addition to model the incident wave excitation the total field scattered field approach is incorporated into the proposed method the stability of the ipdg we method is studied analytically and demonstrated numerically we also compare the performance between wave equation based finite element time domain method the maxwell s equation based discontinuous galerkin time domain method and the proposed method both in cpu time and memory usage which demonstrates that the ipdg we method is very competitive among time domain solvers besides the presented method shows good characteristics including the energy conservation and the optimal convergence rate of o h p 1 numerical examples are presented to illustrate the validity versatility and potential of the proposed method in 3 d electromagnetic problems modeling

efficient multiple time stepping algorithms of higher order multiple time stepping mts algorithms allow to efficiently integrate large systems of ordinary differential equations where a few stiff terms restrict the timestep of an otherwise non stiff system in this work we discuss a flexible class of mts techniques based on multistep methods our approach contains several popular methods as special cases and it allows for the easy construction of novel and efficient higher order mts schemes in addition we demonstrate how to adapt the stability contour of the non stiff time integration to the physical system at hand this allows significantly larger timesteps when compared to previously known multistep mts approaches as an example we derive novel predictor corrector pcmts schemes specifically optimized for the time integration of damped wave equations on locally refined meshes in a set of numerical experiments we demonstrate the performance of our scheme on discontinuous galerkin time domain dgtd simulations of maxwell s equations

a hybrid time domain discontinuous galerkin boundary integral method for electromagnetic scattering analysis a scheme hybridizing discontinuous galerkin time domain dgtd and time domain boundary integral tdbi methods for accurately analyzing transient electromagnetic scattering is proposed radiation condition is enforced using the numerical flux on the truncation boundary the fields required by the flux are computed using the tdbi from equivalent currents introduced on a huygens surface enclosing the scatterer the hybrid dgtdbi ensures that the radiation condition is mathematically exact and the resulting computation domain is as small as possible since the truncation boundary conforms to scatterer s shape and is located very close to its surface locally truncated domains can also be defined around each disconnected scatterer additionally reducing the size of the overall computation domain numerical examples demonstrating the accuracy and versatility of the proposed method are presented

an efficient discontinuous galerkin finite element method for highly accurate solution of maxwell equations a discontinuous galerkin finite element method dg fem with a highly accurate time integration scheme for solving maxwell equations is presented the new time integration scheme is in the form of traditional predictor corrector algorithms pe ce m but it uses coefficients that are obtained using a numerical scheme with fully controllable accuracy numerical results demonstrate that the proposed dg fem uses larger time steps than dg fem with classical pe ce m schemes when high accuracy which could be obtained using high order spatial discretization is required

sampling piecewise sinusoidal signals with finite rate of innovation methods we consider the problem of sampling piecewise sinusoidal signals classical sampling theory does not enable perfect reconstruction of such signals since they are not band limited however they can be characterized by a finite number of parameters namely the frequency amplitude and phase of the sinusoids and the location of the discontinuities in this paper we show that under certain hypotheses on the sampling kernel it is possible to perfectly recover the parameters that define the piecewise sinusoidal signal from its sampled version in particular we show that at least theoretically it is possible to recover piecewise sine waves with arbitrarily high frequencies and arbitrarily close switching points extensions of the method are also presented such as the recovery of combinations of piecewise sine waves and polynomials finally we study the effect of noise and present a robust reconstruction algorithm that is stable down to snr levels of 7 db

reconstructing polygons from moments with connections to array processing we establish a set of results showing that the vertices of any simply connected planar polygonal region can be reconstructed from a finite number of its complex moments these results find applications in a variety of apparently disparate areas such as computerized tomography and inverse potential theory where in the former it is of interest to estimate the shape of an object from a finite number of its projections whereas in the latter the objective is to extract the shape of a gravitating body from measurements of its exterior logarithmic potentials at a finite number of points we show that the problem of polygonal vertex reconstruction from moments can in fact be posed as an array processing problem and taking advantage of this relationship we derive and illustrate several new algorithms for the reconstruction of the vertices of simply connected polygons from moments

nonlinear wave propagation in damaged hysteretic materials using a frequency domain based pm space formulation abstract in this work a new and simple numerical approach to simulate nonlinear wave propagation in purely hysteretic elastic solids is presented conversely to classical time discretization method which fully integrates the nonlinear equation of motion this method utilizes a first order approximation of the nonlinear strain in order to separate linear and nonlinear contributions the problem for the nonlinear displacements is then posed as a linear one in which the solid is enforced with nonlinear forces derived from the linear strain in this manner a frequency analysis can be easily conducted leading directly to a well known frequency spectrum for the nonlinear strain a mesoscale approach known as preisach mayergoyz space pm space is used for the chacterization of the nonlinear elastic region of the solid a meshless element free galerkin method is implemented for the discretized equations of motion nevertheless a mesh based method can be still used as well without loss of generality results are presented for bidimensional isotropic plates both in plane stress and in plane strain subjected to harmonic monotone excitation

the iterative time reversal process analysis of the convergence the efficiency of a time reversal acoustic mirror to focus on a reflective target through an inhomogeneous media has been demonstrated in a multitarget media the ability of such a mirror to work in an iterative mode in order to focus selectively on the strongest target was shown c prada f wu and m fink j acoust soc am 90 1119 1991 the theory of how the iterative time reversal process is built is based on a matrix formalism and treats the array of l transducers in a given medium as a linear system of l inputs l outputs the system is characterized at each frequency by its transfer matrix k and the time reversal iterative process is then described by a time reversal operator k k because of the reciprocity principle this operator is hermitian the following result is shown if the scattering medium is a set of well resolved targets of different reflectivities then each eigenvector of the operator k k with nonzero eigenvalue corresponds to one of the targets in the set and provides the opt

interior penalty discontinuous galerkin finite element method for the time dependent first order maxwell s equations an interior penalty discontinuous galerkin method is described with a conformal perfectly matched layer pml for solving the two first order maxwell s equations in the time domain both central and upwind fluxes are studied in this work in both cases the proposed method is explicit and conditionally stable additionally a local time stepping strategy is applied to increase efficiency and reduce the computational time finally numerical examples are presented to validate the method

explicit time marching schemes for solving the magnetic field volume integral equation a method for constructing explicit marching on in time mot schemes to solve the time domain magnetic field volume integral equation td mfvie on inhomogeneous dielectric scatterers is proposed the td mfvie is cast in the form of an ordinary differential equation ode and the unknown magnetic field is expanded using curl conforming spatial basis functions inserting this expansion into the td mfvie and spatially testing the resulting equation yield an ode system with a gram matrix this system is integrated in time for the unknown time dependent expansion coefficients using a linear multistep method the gram matrix is sparse and well conditioned for galerkin testing and consists of only four diagonal blocks for point testing the resulting explicit mot schemes which call for the solution of this matrix system at every time step are more efficient than their implicit counterparts which call for inversion of a fuller matrix system at lower frequencies numerical results compare the efficiency accuracy and stability of the explicit mot schemes and their implicit counterparts for low frequency excitations the results show that the explicit mot scheme with point testing is significantly faster than the other three solvers without sacrificing from accuracy

analysis of transient em scattering from penetrable objects by time domain nonconformal vie a marching on in time mot based nonconformal volume integral equation vie is proposed to analyze the transient electromagnetic scattering from the inhomogeneous penetrable objects the gradient gradient operator is acted on the green s function to realize the nonconformal tetrahedral meshes discretization half schaubert wilton glisson swg basis functions are chosen for the trail and test spatial functions meanwhile the piecewise polynomial lagrange interpolation functions are applied for temporal expansion in addition the quasi explicit scheme is introduced to accelerate the calculation of conventional implicit mot system numerical results are given to demonstrate the flexibility and validity of the proposed scheme

efficient algorithms for computing a strong rank revealing qr factorization given anm n matrixm withm n it is shown that there exists a permutation fi and an integer k such that the qr factorization myi q ak ckbk reveals the numerical rank of m the k k upper triangular matrix ak is well conditioned ilckll2 is small and bk is linearly dependent on ak with coefficients bounded by a low degree polynomial in n existing rank revealing qr rrqr algorithms are related to such factorizations and two algorithms are presented for computing them the new algorithms are nearly as efficient as qr with column pivoting for most problems and take o ran2 floating point operations in the worst case

b spline signal processing i theory the use of continuous b spline representations for signal processing applications such as interpolation differentiation filtering noise reduction and data compressions is considered the b spline coefficients are obtained through a linear transformation which unlike other commonly used transforms is space invariant and can be implemented efficiently by linear filtering the same property also applies for the indirect b spline transform as well as for the evaluation of approximating representations using smoothing or least squares splines the filters associated with these operations are fully characterized by explicitly evaluating their transfer functions for b splines of any order applications to differentiation filtering smoothing and least squares approximation are examined the extension of such operators for higher dimensional signals such as digital images is considered

on the compression of low rank matrices a procedure is reported for the compression of rank deficient matrices a matrix a of rank k is represented in the form a u circ b circ v where b is a k times k submatrix of a and u v are well conditioned matrices that each contain a k times k identity submatrix this property enables such compression schemes to be used in certain situations where the singular value decomposition svd cannot be used efficiently numerical examples are presented

penalty factor threshold and time step bound estimations for discontinuous galerkin time domain method based on helmholtz equation in this article penalty factor threshold and time step bound in discontinuous galerkin time method based on vector wave equation dgtd we method are well estimated based on the semidiscrete form of the dgtd we method properties of the system matrices are studied and the stability condition related to the penalty factor is derived by decomposing the global system matrices of the dgtd we method into the local ones and developing an efficient iteration procedure the lower bound threshold of the penalty factor is well estimated to guarantee the positive semidefinite property of the global system matrices with the calculated penalty factor the maximum time step is analytically determined by approximating spectral radius of the local system matrix both the penalty factor bound and the maximal time step are computed element wise instead of a global system matrix operation and thus the proposed method can be efficiently applied into the large scale meshes with different types of the basis functions and boundary conditions numerical examples are presented to demonstrate the validity and good performance of the proposed methods

time reversal and the inverse filter to focus ultrasonic waves in an unknown inhomogeneous medium using a phased array one has to calculate the optimal set of signals to be applied on the transducers of the array in the case of time reversal mirrors one assumes that a source is available at the focus providing the green s function of this point in this paper the robustness of this time reversal method is investigated when loss of information breaks the time reversal invariance it arises in dissipative media or when the field radiated by the source is not entirely measured by the limited aperture of a time reversal mirror however in both cases linearity and reciprocity relations ensure time reversal to achieve a spatiotemporal matched filtering nevertheless though it provides robustness to this method no constraints are imposed on the field out of the focus and sidelobes may appear another approach consists of measuring the green s functions associated to the focus but also to neighboring points thus the whole information characterizing the medium is known and the inverse source problem can be solved a matrix formalism of the propagation operator is introduced to compare the time reversal and inverse filter techniques moreover experiments investigated in various media are presented to illustrate this comparison

decomposition of the time reversal operator detection and selective focusing on two scatterers the decomposition of the time reversal operator dort method is a selective detection and focusing technique using an array of transmit receive transducers it relies on the theory of iterative time reversal mirrors which was presented by prada et al c prada j l thomas and m fink j acoust soc am 97 62 71 1995 the time reversal operator was defined as k k where is the frequency means complex conjugate and k is the transfer matrix of the array of l transducers insonifying a time invariant scattering medium it was shown that this time reversal operator can be diagonalized and that for ideally resolved scatterers of different reflectivities each of its eigenvectors of nonzero eigenvalue provides the phase law to be applied to the transducers in order to focus on one of the scatterers the dort method consists in determining these eigenvectors and using them for the selective focusing this paper presents a complete analysis of this method in the case of two scatterers the