preconditioned formulation of fe bi equations with domain decomposition method for calculation of electromagnetic scattering from cavities a new formulation of finite element boundary integral fe bi equations with non overlapping and non conforming domain decomposition method ddm is proposed to calculate electromagnetic scattering from cavities the computational domain is divided into two parts cavity and non cavity domains tetrahedral elements with higher order and lower order vector basis functions are used in the cavity and non cavity domains respectively and they are not conformal on the interface between two sub domains the application of robin transmission condition at the aperture of the cavity relates the fields in the interior and exterior regions of the cavity in addition an effective preconditioner is designed to speed up the solution process of iterative solvers numerical results obtained show that the proposed method is suitable for this class of problems and the preconditioner is highly effective to reduce the number of iterations for the solution

the velocity tracking problem for navier stokes flows with bounded distributed controls we present some systematic approaches to the mathematical analysis and numerical approximation of the time dependent optimal control problem of tracking the velocity for navier stokes flows in bounded two dimensional domains with bounded distributed controls we study the existence of optimal solutions and derive an optimality system from which optimal solutions may be determined we also define and analyze semidiscrete in time and fully space time discrete approximations of the optimality system and a gradient method for the solution of the fully discrete system the results of some computational experiments are provided

an efficient high order nystrom scheme for acoustic scattering by inhomogeneous penetrable media with discontinuous material interface this text proposes a fast rapidly convergent nystrom method for the solution of the lippmann schwinger integral equation that mathematically models the scattering of time harmonic acoustic waves by inhomogeneous obstacles while allowing the material properties to jump across the interface the method works with overlapping coordinate charts as a description of the given scatterer in particular it employs partitions of unity to simplify the implementation of high order quadratures along with suitable changes of parametric variables to analytically resolve the singularities present in the integral operator to achieve desired accuracies in approximations to deal with the discontinuous material interface in a high order manner a specialized quadrature is used in the boundary region the approach further utilizes an fft based strategy that uses equivalent source approximations to accelerate the evaluation of large number of interactions that arise in the approximation of the volumetric integral operator and thus achieves a reduced computational complexity of o n log n for an n point discretization a detailed discussion on the solution methodology along with a variety of numerical experiments to exemplify its performance are presented in this paper

a monte carlo method for solving unsteady adjoint equations traditionally solving the adjoint equation for unsteady problems involves solving a large structured linear system this paper presents a variation on this technique and uses a monte carlo linear solver the monte carlo solver yields a forward time algorithm for solving unsteady adjoint equations when applied to computing the adjoint associated with burgers equation the monte carlo approach is faster for a large class of problems while preserving sufficient accuracy

analysis and approximation of linear feedback control problems for the boussinesq equations the mathematical formulation and numerical solution of the linear feedback control problem associated with the boussinesq equations are presented we show that the unsteady solutions to the boussinesq equations are stabilizable by internal controllers with exponential decaying property semidiscrete in time and full space time discrete approximations are also studied some computational results are presented

the bymoment method for two dimensional electromagnetic scattering the bymoment method is presented for analyzing two dimensional electromagnetic wave scattering in an unbounded region the method introduces a conforming surface to geometrically decouple the interior region containing the scatterer from the exterior region extending to infinity the solution in the interior is generated using the standard finite element solution of an interior dirichlet boundary value problem the interior solution is then coupled to the exterior using green s theorem in the unbounded exterior region the validity of the method and the associated computer program is demonstrated by comparing the results to those of other methods for scattering by various cylindrical geometries

domain decomposition method for harmonic wave propagation a general presentation in this paper we give a general presentation of non overlapping domain decomposition methods for harmonic wave propagation models our abstract framework leads to concise convergence proofs and contains some recent developments about the use of non local transmission conditions it also includes applications to acoustic electromagnetic or elastic waves as well as the treatment of space discretization

absorbing boundary conditions on arbitrary boundaries for the scalar and vector wave equations the solution of open region scattering problems involving inhomogeneous arbitrarily shaped objects may be performed through the use of partial differential equation techniques which require enclosing the scatterer by an outer boundary on which an absorbing boundary condition abc is applied in order to minimize the size of the domain to be meshed and consequently the number of unknowns if may be advisable to implement abc s devised for outer boundaries of arbitrary shapes such abc s are obtained for the 3d scalar and vector wave equations they incorporate most of existing boundary conditions when used in conjunction with a finite element technique the numerical results derived by using a simplified form of these abc s compare favourably to those obtained by using a rigorous hybrid finite element integral equation formulation these boundary conditions have been obtained in the frequency domain framework they may however be used in time domain calculations

non overlapping domain decomposition algorithm based on modified transmission conditions for the helmholtz equation abstract a square root based transmission conditions domain decomposition method was recently introduced for the helmholtz equation it produces an effective algorithm where the convergence is independent of the wavenumber and the mesh discretization we modify here these conditions in order to guarantee well posedness of local problems and further improve the efficiency of the whole method numerical results in particular in the three dimensional case show significant reduction of the computational time needed in the iterative procedure while preserving the iteration number when compared with the original algorithm

performance analysis of derivative constraint adaptive arrays with pointing errors the performance of adaptive arrays with arbitrary order derivative constraints to avoid the signal nulling caused by the error in the steering angle is investigated the generalized sidelobe canceller gsc is used to evaluate the bearing responses of adaptive arrays with pointing errors under the assumption of equispaced linear arrays the legendre polynomial is used to derive a closed form formula for the sidelobe leakage factor the ratio in which the signal leaks into the gsc sidelobe cancelling branch moreover the effective beamwidth the maximum range of pointing inaccuracy allowable to keep the signal loss in array output less than a given value is derived for the gsc with a delay and sum quiescent beamformer such adaptive arrays can achieve the maximum output signal to noise ratio when the presteering is perfect and the performance is independent of the location of the phase origin numerical results are presented to confirm the analysis

plane wave scattering from three dimensional multiple objects using the iterative multiregion technique based on the fdfd method an iterative approach using the finite difference frequency domain method is presented in this paper in order to solve the problem of scattering from large three dimensional electromagnetic scatterers the idea of iterative multiregion technique is introduced to divide one computational domain into smaller subregions and solve each subregion separately then the subregion solutions are combined iteratively to obtain a solution for the complete domain as a result a considerable reduction in the computation time and memory has been achieved

a partitioning technique for the finite element solution of electromagnetic scattering from electrically large dielectric cylinders a finite element partitioning scheme has been developed to reduce the computational costs of modeling electrically large geometries in the partitioning scheme the cylinder is divided into many sections the finite element method is applied to each section independent of the other sections and then the solutions in each section are coupled through the use of the tangential field continuity conditions between adjacent sections since the coupling matrix is significantly smaller than the original finite element matrix it is expected that both the cpu time and memory costs can be significantly reduced the partitioning scheme is coupled to the bymoment method to account for the boundary truncation numerical results are presented to demonstrate the efficiency and accuracy of the method

a domain decomposition method for the vector wave equation a nonoverlapping domain decomposition method ddm is presented for the finite element fe solution of electromagnetic scattering problems by inhomogeneous three dimensional 3 d bodies the computational domain is partitioned into concentric subdomains on the interfaces of which conformal vector transmission conditions are prescribed and that can be implemented in the inhomogeneous part the ddm is numerically implemented when a conformal vector absorbing boundary condition abc is utilized on the outer boundary terminating the fe mesh while employing the standard edge based fe formulation then numerical experiments are performed on a sphere and a cone sphere that emphasize the advantages of this technique in terms of memory storage and computing times especially when the total number of unknowns is very large also these numerical experiments serve as a severe test for the performances of the abc

mathcal h matrices compressed multiplicative schwarz preconditioner for nonconformal fem bem ddm an mathcal h matrices compressed multiplicative schwarz ms preconditioner for the nonconformal finite element method fem boundary element method bem domain decomposition method ddm is proposed to analyze the electromagnetic radiation and scattering from periodic structures such as frequency selective surfaces fsss or antenna arrays to improve the overall convergence an ms preconditioner is proposed for the ddm matrix the hierarchical matrix mathcal h matrices technique is introduced into the preconditioned system to compress the dense matrices to further improve the efficiency moreover a finite element tearing and interconnecting like algorithm is adopted to eliminate the interior volumetric fem unknowns and the multilevel fast multipole algorithm is integrated to reduce the computational complexity of bem numerical examples are presented to validate the proposed method it is observed that this method exhibits superior performance and consumes far less memory and cpu time than the traditional implementation

analysis and approximation for linear feedback control for tracking the velocity in navier stokes flows abstract some systematic approaches to the mathematical formulation and numerical resolution of the linear feedback control problem for tracking the velocity in navier stokes flows in a bounded two dimensional domain with bounded distributed control are presented semidiscrete in time and full space time discrete approximations are also studied some computational results are presented and compared with analogous results from optimal control theory

electromagnetic scattering from 3 d targets in a random medium using finite difference frequency domain in this paper a three dimensional 3 d numerical technique based on the finite difference frequency domain fdfd is implemented to calculate the scattering from arbitrary shaped objects embedded in a continuous random medium the total field scattered field tf sf algorithm is integrated with the fdfd to minimize the memory consumption and speed up the calculations for validation purposes the radar cross section of a 2 d conducting cylinder in random medium is calculated using the fdfd technique and compared to previously published data based on the current generator method an upgrade to a 3 d solver was then inspired once the idea of using the multi grid technique was introduced to accelerate the convergence rate of the bicgstab iterative solver thus allowing the fdfd technique to become a robust method to solve the scattering problem from large targets embedded in random medium therefore using the introduced simulating scheme one can easily elucidate any scattering information out of real life targets surrounded by random environmental effects

on the formulation of hybrid finite element and boundary integral methods for 3 d scattering this paper studies in detail a variety of formulations for the hybrid finite element and boundary integral fe bi method for three dimensional 3 d electromagnetic scattering by inhomogeneous objects it is shown that the efficiency and accuracy of the fe bi method depends highly on the formulation and discretization of the boundary integral equation bie used a simple analysis of the matrix condition number identifies the efficiency of the different fe bi formulations and an analysis of weighting functions shows that the traditional fe bi formulations cannot produce accurate solutions a new formulation is then proposed and numerical results show that the resulting solution has a good efficiency and accuracy and is completely immune to the problem of interior resonance finally the multilevel fast multipole algorithm mlfma is employed to significantly reduce the memory requirement and computational complexity of the proposed fe bi method

existence of optimal controls for viscous flow problems a class of optimal control problems in viscous flow is studied main result is the existence theorem for optimal control three typical flow control problems are formulated within this general class

a quasi optimal non overlapping domain decomposition algorithm for the helmholtz equation this paper presents a new non overlapping domain decomposition method for the helmholtz equation whose effective convergence is quasi optimal these improved properties result from a combination of an appropriate choice of transmission conditions and a suitable approximation of the dirichlet to neumann operator a convergence theorem of the algorithm is established and numerical results validating the new approach are presented in both two and three dimensions

dynamics and approximations of a velocity tracking problem for the navier stokes flows with piecewise distributed controls we study the dynamics of a piecewise in time distributed optimal control problem for the navier stokes equations which models velocity tracking over time we also study the dynamics of semidiscrete and fully discrete approximations of this velocity tracking problem we prove that the rates of velocity tracking are exponential some computational results are presented which reinforces the theoretical results derived

analysis of two dimensions sparse multicylinder scattering problem using dd fdtd method an algorithm of two dimensional 2 d domain decomposition finite difference time domain dd fdtd using in sparse multicylinders scattering problem is proposed in this paper the idea of domain decomposition is introduced to divide the sparse problem domain into several subdomains all of subdomains are connected by means of the 2 d time domain green s function as a result a great deal of meshes memory between cylinders is removed especially when the distances between cylinders become large furthermore the coupling between cylinders can be regarded as the equivalent cylindrical wave irradiations the incident signals of the equivalent cylindrical waves are expressed as cylindrical wave input field array cwifa according to huygens principle then the calculation time is significantly reduced the near field to far field transformation is used to obtain the equivalent cylindrical wave as a result the calculation time can be reduced further the new method has been demonstrated in 2 d multicylinders scattering problem numerical results are in good agreement with the results obtained using classical fdtd method and moment of methods mm

instantaneous closed loop control of the navier stokes system instantaneous control is applied to the control of the instationary navier stokes system this control technique is closely related to receding horizon control and allows for an interpretation as suboptimal closed loop controller whose parameters may be adjusted so as to stabilize the nonlinear equation under consideration besides stability analysis for the distributed control case numerical examples for the continuous and discrete in time control laws are presented

parallelized characteristic basis finite element method cbfem mpi a non iterative domain decomposition algorithm for electromagnetic scattering problems in this paper we introduce a parallelized version of a novel non iterative domain decomposition algorithm called characteristic basis finite element method cbfem mpi for efficient solution of large scale electromagnetic scattering problems by utilizing a set of specially defined characteristic basis functions cbfs this approach is based on the decomposition of the computational domain into a number of non overlapping subdomains wherein the cbfs are generated by employing a novel procedure which differs from all those that have been used in the past clearly the cbfs are obtained by calculating the fields radiated by a finite number of dipole type sources which are placed hypothetically along the boundary of the conducting object the major advantages of the proposed technique are twofold i it provides a substantial reduction in the matrix size and thus makes use of direct solvers efficiently and ii it enables the utilization of parallel processing techniques that considerably decrease the overall computation time we illustrate the application of the proposed approach via several 3d electromagnetic scattering problems

a fast domain decomposition method for the solution of electromagnetic scattering by large objects a nonoverlapping domain decomposition method is proposed for the finite element solution of the scattering problem by electrically large inhomogeneous infinite cylinders of arbitrary cross section to minimize the size of the total computational domain a second order absorbing boundary condition abc is applied upon an outer boundary of arbitrary shape which may be conformal to the surface of the scatterer this domain is then partitioned into concentric subdomains circumscribing the object a second order transmission condition derived from the abc is prescribed upon the interfaces between two adjacent subdomains this particular configuration is responsible for the fast convergence of the domain decomposition iterative algorithm which is parallelizable numerical results obtained with a nonparallelized computer code are presented which emphasize the superiority of this technique in terms of memory storage requirements and computing times over the standard finite element approach as well as over the rigorous hybrid finite element integral equation formulation

necessary and sufficient conditions for optimal controls in viscous flow problems a class of optimal control problems in viscous flow is studied main results are the pontryagin maximum principle and the verification theorem for the hamilton jacobi bellman equation characterising the feedback problem the maximum principle is established by two quite different methods

numerical absorbing boundary conditions for the scalar and vector wave equations electromagnetic field computation may be carried out conveniently by using the finite element method fem when solving open region problems using this technique it becomes necessary to enclose the scatterer with an outer boundary upon which an absorbing boundary condition abc is applied analytically derived abcs have been used extensively for this purpose numerical absorbing boundary conditions nabcs have been proposed as alternatives to analytical abcs for the two dimensional 2 d helmholtz equation it has been demonstrated analytically that these nabcs become equivalent to many of the existing analytical abs in the limit as the cell size tends to zero in addition the numerical efficiency of these nabcs has been evaluated by using as an indicator the reflection coefficient for plane and cylindrical waves incident upon an arbitrary boundary we have extended this procedure to the study of the nabcs derived for the three dimensional 3 d scalar and vector wave equations from the point of view of their numerical implementation in node and edge based fem formulations respectively

system identification using nonstationary signals the conventional method for identifying the transfer function of an unknown linear system consists of a least squares fit of its input to its output it is equivalent to identifying the frequency response of the system by calculating the empirical cross spectrum between the system s input and output divided by the empirical auto spectrum of the input process however if the additive noise at the system s output is correlated with the input process e g in case of environmental noise that affects both system s input and output the method may suffer from a severe bias effect we present a modification of the cross spectral method that exploits nonstationary features in the data in order to circumvent bias effects caused by correlated stationary noise the proposed method is particularly attractive to problems of multichannel signal enhancement and noise cancellation when the desired signal is nonstationary in nature e g speech or image

scattering from 3 d cavities with a plug and play numerical scheme combining ie pde and modal techniques in this paper we present a multidomain and multi method coupling scheme called factopo based on generalized scattering matrix computations on three dimensional 3 d subdomains the global target spl omega is split in n sub v subdomains v sub i i 1 n sub v separated by n sub i fictitious surfaces spl gamma sub j j 1 n sub i we use a modal representation of the tangent fields on the interfaces in each domain the generalized scattering matrix s sub i is computed with different methods such as the 3 d finite element method fem or the electric field integral equation efie this coupling scheme leads to an important reduction in computational resources especially for cavities with one dimension much larger than the other two the advantages of this formulation for parametric studies is illustrated by two cases computing the rcs of an air intake terminated with a flat pec or a fan channel and of an antenna structure coupled to an electronic feed with a varying parameter deneb numerical as well as experimental results are presented

analysis of the power spectral deviation of the general transfer function gsc in recent work we considered a microphone array located in a reverberated room where general transfer functions tfs relate the source signal and the microphones for enhancing a speech signal contaminated by interference it was shown that it is sufficient to use the ratio between the different tfs rather than the tfs themselves in order to implement the suggested algorithm an unbiased estimate of the tfs ratios was obtained by exploiting the nonstationarity of the speech signal in this correspondence we present an analysis of a distortion indicator namely power spectral density psd deviation imposed on the desired signal by our newly suggested transfer function generalized sidelobe canceller tf gsc algorithm it is well known that for speech signals psd deviation between the reconstructed signal and the original one is the main contribution for speech quality degradation as we are mainly dealing with speech signals we analyze the psd deviation rather than the regular waveform distortion the resulting expression depends on the tfs involved the noise field and the quality of estimation of the tf s ratios for the latter dependency we provide an approximated analysis of estimation procedure that is based on the signal s nanstationarity and explore its dependency on the actual speech signal and on the signal to noise ratio snr level the theoretical expression is then used to establish empirical evaluation of the psd deviation for several tfs of interest various noise fields and a wide range of snr levels it is shown that only a minor amount of psd deviation is imposed on the beamformer output the analysis presented in this correspondence is in good agreement with the actual performance presented in the former tf gsc paper

a hybrid finite element and integral equation domain decomposition method for the solution of the 3 d scattering problem abstract a domain decomposition method ddm is presented for the solution of the time harmonic electromagnetic scattering problem by inhomogeneous 3 d objects the computational domain is partitioned into concentric subdomains on the interfaces of which robin type transmission conditions are prescribed on the outer boundary terminating the computational domain the radiation condition is accounted for by employing an integral equation ie formulation the ddm decouples the interior problems that correspond to the solution of maxwell s equations inside each subdomain and are formulated by using a finite element method from the exterior problem solved by employing the ie it has been shown that the solutions of this ddm algorithm converge to those of the original problem a particular ie is used that allows the implementation of a very simple and fully iterative solver the main advantage offered by this technique is a reduction in memory requirements various numerical examples are presented that illustrate its potential

performance limits of the broadband generalized sidelobe cancelling structure in an isotropic noise field in acoustic applications the signal source of interest is generally broadband and the background noise field is predominantly isotropic in this letter the performance of the broadband generalized sidelobe canceller optimized with respect to an isotropic noise field is analyzed and compared against the performance of the conventional summing beamformer the comparison is based on an ideal continuous time infinite length generalized sidelobe canceller with the aim of determining the performance limits of this beamforming structure

a new hybrid method for analysis of scattering from arbitrary configuration of cylindrical objects a new hybrid method for analysis of scattering on configuration of cylindrical objects with arbitrary geometries is presented in this approach each scatterer is treated as an effective circular cylinder represented by its impedance matrix to obtain the impedance matrix representation of the arbitrary geometry post the combination of finite difference frequency domain fdfd and mode matching mm technique is applied in the analysis of an arbitrary configuration of objects the iterative scattering procedure isp is used the error estimation of the method and numerical results are presented and discussed a good agreement of the presented results with analytical approach and commercial finite difference time domain fdtd software is obtained

parallel domain decomposition based algorithm of hybrid fe bi mlfma method for 3 d scattering by large inhomogeneous objects the hybrid method of the finite element boundary integral multilevel fast multipole algorithm fe bi mlfma has been recognized as one of the most powerful numerical methods for analyzing large inhomogeneous radiation scattering problems a domain decomposition algorithm dda of fe bi mlfma is presented in this paper by using the finite element tearing and interconnecting method feti the formulation of dda fe bi mlfma is presented and analyzed in detail the numerical performance of dda fe bi mlfma is investigated by numerical experiments from many aspects it includes the convergence speed versus types of domain decomposition number of subdomains types and inhomogeneity of dielectrics involving in solved problems and the scalability of dda fe bi mlfma the comparison of dda and previous algorithms of fe bi mlmfma is also carried out finally the capability of dda fe bi mlfma is shown for large inhomogeneous problems

improved transmission conditions for a one dimensional domain decomposition method applied to the solution of the helmholtz equation the scattering problem of a time harmonic electromagnetic wave from a perfect electric conductor pec coated with materials is considered and solved by coupling a finite element method with an integral equation prescribed on the outer boundary of the computational domain to reduce the numerical complexity a one dimensional domain decomposition method ddm is employed the computational domain is partitioned into concentric subdomains sds and robin transmission conditions tcs are prescribed on the interfaces for some configurations and or materials the convergence of the corresponding ddm algorithm happens to be slow a possible remedy is to enhance the efficiency of the tcs by approximating the exact ones more accurately to this end we first consider the simplified 2d problem of a circular pec cylinder with an homogeneous coating and up to four sds with circular interfaces thus allowing to obtain the exact tcs in closed form approximate local or non local tcs are derived from these exact ones and numerical examples demonstrate their superiority over the standard robin tcs then the case of an elliptical pec cylinder with one interface in free space is investigated also the issues pertaining to the uniqueness of the solutions and convergence of the algorithm are addressed

a self contained automated methodology for optimal flow control this paper describes a self contained automated methodology for active flow control which couples the time dependent navier stokes system with an adjoint navier stokes system and optimality conditions from which optimal states i e unsteady flow fields and controls e g actuators may be determined the problem of boundary layer instability suppression through wave cancellation is used as the intital validation case to test the methodology here the objective of control is to match the stress vector along a portion of the boundary to a steady base flow control is effected through the injection or suction of fluid through a single orifice on the boundary the results demonstrate that instability suppression can be achieved without any a priori knowledge of the flow unsteadiness such as frequencies instability type etc the present methodology has been extended to three dimensions and may potentially be applied to separation control relaminarization and turbulence control applications using one to many sensors and actuators

one way domain decomposition method with adaptive absorbing boundary condition for the solution of maxwell s equations for the solution of the time harmonic electromagnetic scattering problem by inhomogeneous 3 d objects a previously published one way domain decomposition method ddm is considered the computational domain is partitioned into concentric subdomains on the interfaces of which robin type transmission conditions tcs are prescribed with an integral equation ie on the outer boundary of the computational domain ddm ie on account of the large computing time required by the solution of the isolated ie system in this paper the ie is replaced by the integral representations irs of the fields that requires only a few matrix vector products adaptive absorbing boundary condition aabc the irs necessitate the calculation of the electric and magnetic currents on some inner surface s that is chosen to be the interface between the last two subdomains taking advantage of the tcs the unknown current on s here the magnetic current is obtained via a change of bases h rot to h div that allows the accurate computation of the ir integrals involving the surface divergence terms and permits the separate solution of the fe systems in the last two subdomains the matrix vector products in the aabc are performed only once per ddm iteration numerical results are presented that illustrate the accuracy of the ddm aabc and its superiority in terms of computing time over the ddm ie also some indications are given on how to estimate numerically the convergence rate of the ddm aabc

the broad band wiener solution for griffiths jim beamformers the authors treat the problem of finding the wiener filters for a wideband adaptive beamformer explicit expressions are given for the filters and error power spectrum in the frequency domain the expressions are simple to program and give the possibility of investigating superresolution for wideband signals and of determining sufficient lengths of the finite impulse response filters in adaptive arrays the major results are an analytical expression for the broadband array wiener solution given for an arbitrary spectrum for target interference and noise and an approximate analytic expression for the angular 3 db beamwidth for broadband signals

dynamic programming of the navier stokes equations a class of optimal control problems in viscous flow is studied main results are the pontryagin maximum principle and the verification theorem for the hamilton jacobi bellman equation

dynamics for controlled navier stokes systems with distributed controls the long time behavior of solutions for an optimal distributed control problem associated with the navier stokes equations is studied first a linear feedback solution for the navier stokes equations is constructed this feedback solution possesses decay in time properties then some preliminary estimates for the long time behavior of all solutions of the navier stokes equations are derived next the existence of a solution for the optimal control problem is proved finally the long time decay properties for the optimal solutions are established

time domain iterative multiregion technique for 3 d scattering and radiation problems integration of the finite difference time domain fdtd method into the iterative multiregion imr technique an iterative approach used to solve large scale electromagnetic scattering and radiation problems is presented in this paper the idea of the imr technique is to divide a large problem domain into smaller subregions solve each subregion separately and combine the solutions of subregions after introducing the effect of interaction to obtain solutions at multiple frequencies for the large domain solutions of the subregions using frequency domain solvers has been the preferred approach as such solutions using time domain solvers require computationally expensive bookkeeping of time signals in this paper we present an algorithm that makes it feasible to use the fdtd method a time domain numerical technique in the imr technique to obtain solutions at a prespecified number of frequencies in a single simulation a hybrid method integrated into the imr technique is also presented in this paper this hybrid method combines the desirable features of the fdtd method and the method of moments mom to solve radiation problems more efficiently as a result a considerable reduction in memory storage requirements and computation time is achieved

one way domain decomposition method with exact radiation condition and fast gmres solver for the solution of maxwell s equations for the solution of the time harmonic electromagnetic scattering problem by inhomogeneous 3 d objects a one way domain decomposition method ddm is considered the computational domain is partitioned into concentric subdomains on the interfaces of which robin type transmission conditions tcs are prescribed an integral representation of the electromagnetic fields on the outer boundary constitutes an exact radiation condition the global system obtained after discretization of the finite element fe formulations is solved via a krylov subspace iterative method gmres it is preconditioned in such a way that essentially only the solution of the fe subsystems in each subdomain is required this is made possible by a computationally cheap h curl h div transformation performed on the interfaces that separate the two outermost subdomains the eigenvalues of the preconditioned matrix of the system are bounded by two and optimized values of the coefficients involved in the local tcs on the interfaces are determined so as to maximize the minimum eigenvalue numerical experiments are presented that illustrate the numerical accuracy of this technique its fast convergence and legitimate the choices made for the optimized coefficients

a domain decomposition method with nonconformal meshes for finite periodic and semi periodic structures we present a domain decomposition method as a preconditioner for krylov type solvers to model complex electromagnetic problems containing periodicities the method reduces memory requirements by decomposing the original problem into several nonoverlapping sub domains the 1st order transmission condition is employed on interfaces between adjacent sub domains to enforce continuity of electromagnetic fields and to ensure the sub domain problems are well posed by following the spirit of duality paring a symmetric system is obtained to reduce the computational burdens of the present method the finite element tearing and interconnecting like algorithm is adopted this algorithm results in the computation of the so called numerical green s function which can be compressed efficiently via a rank revealing matrix factorization algorithm the final system matrix is solved by krylov solvers instead of classical stationary solvers to improve the convergence of iterative solvers several robust implementation details are discussed and the choice of some popular krylov subspace solvers is studied through numerical examples

analysis and approximation of the velocity tracking problem for navier stokes flows with distributed control we consider the mathematical formulation analysis and the numerical solution of a time dependent optimal control problem associated with the tracking of the velocity of a navier stokes flow in a bounded two dimensional domain through the adjustment of a distributed control the existence of optimal solutions is proved and the first order necessary conditions for optimality are used to derive an optimality system of partial differential equations whose solutions provide optimal states and controls semidiscrete in time and fully discrete space time approximations are defined and their convergence to the exact optimal solutions is shown a gradient method for the solution of the fully discrete equations is examined as are its convergence properties finally the results of some illustrative computational experiments are presented

coupling of fast multipole method and microlocal discretization for the 3 d helmholtz equation we are concerned with an integral method applied to the solution of the helmholtz equation where the linear system is solved using an iterative method we need to perform matrix vector products whose time and memory requirements increase as a function of the wavenumber k many methods have been developed to speed up the matrix vector product calculation or to reduce the size of the system microlocal discretization methods enable one to consider new systems with reduced size another method the fast multipole method is one of the most efficient and robust methods used to speed up the calculation of matrix vector products in this paper a coupling of these two recently developed methods is presented this coupling enables one to reduce cpu time very efficiently for large wavenumbers satisfactory numerical tests are also presented to confirm the theoretical study within a new integral formulation results are obtained for a sphere with a size of 26 using a resolution based on a mesh with an average edge length of about 2 where is the wavelength results are also given for an industrial test case from dassault aviation the cetaf

frequency interpolation of the electromagnetic surface currents via singular value decomposition application to high frequency analysis the time harmonic electromagnetic scattering from conducting surfaces is considered in this context a recently published model order reduction for frequency interpolation of the surface current via singular value decomposition svd is analyzed and evaluated the exact currents computed at q frequencies are arranged columnwise in a matrix the svd of which provides an orthonormal basis on account of the observed exponential decrease of the singular values of this matrix it is assumed that the dimension of the basis required for an accurate interpolation is much smaller than the number of unknowns in the original formulation we propose in this paper a formal framework that justifies this decrease of the singular values as well as the corresponding behavior of the interpolation error made on the current from considerations based on high frequency electromagnetics it is shown that this method can be interpreted in terms of sampling criteria for the current that yield an a priori estimate for the minimum value of q numerical examples illustrate the capacities of this technique for frequency interpolation and for high frequency analysis of the currents

a parallel finite element tearing and interconnecting algorithm for solution of the vector wave equation with pml absorbing medium a domain decomposition method based on the finite element tearing and interconnecting feti algorithm is presented for the solution of the large sparse matrices associated with the finite element method fem solution of the vector wave equation the feti algorithm is based on the method of lagrange multipliers and leads to a reduced order system which is solved using the biconjugate gradient method bicgm it is shown that this method is highly scalable and is more efficient on parallel platforms when solving large matrices than traditional iterative methods such as a preconditioned conjugate gradient algorithm this is especially true when a perfectly matched layer pml absorbing medium is used to terminate the problem domain