an efficient jacobi like algorithm for parallel eigenvalue computation a very fast jacobi like algorithm for the parallel solution of symmetric eigenvalue problems is proposed it becomes possible by not focusing on the realization of the jacobi rotation with a cordic processor but by applying approximate rotations and adjusting them to single steps of the cordic algorithm i e only one angle of the cordic angle sequence defines the jacobi rotation in each step this angle can be determined by some shift add and compare operations although only linear convergence is obtained for the most simple version of the new algorithm the overall operation count shifts and adds decreases dramatically a slow increase of the number of involved cordic angles during the runtime retains quadratic convergence

redundant cordic methods with a constant scale factor for sine and cosine computation proposes two redundant cordic coordinate rotation digital computer methods with a constant scale factor for sine and cosine computation called the double rotation method and the correcting rotation method in both methods the cordic is accelerated by the use of a redundant binary number representation as in the previously proposed redundant cordic in the proposed methods since the number of rotation extensions performed for each angle is a constant the scale factor is a constant independent of the operand hence one does not need to calculate the scale factor during the computation and can make a more efficient sine and cosine generator than that based on the previous redundant cordic

spatial spectral filtering with linearly constrained minimum variance beamformers in this paper orthogonal low dimension models for broad band sources as observed by an array delay line structure are developed the models are termed broad band source representation spaces and are subspaces of the observation space they are generated from eigenstructures of source sample covariance matrices and represent sources efficiently in the 2nd order statistical sense for a single broad band source propagating in a pure delay environment and observed with an isotropic array an accurate indication of the model dimension is derived which is independent on the array configuration being a function of the observed source time bandwidth product only using these representations procedures are described for controlling the spatial and spectral response of linearly constrained minimum variance broad band array beamformers the procedures employ linear constraints to control complex gain characteristics over selected bands of frequency for multiple points of 3 d regions of source locations and do not require the use of steering delays the constraints are derived from source representation spaces and are termed eigenvector constraints simulations are presented which illustrate the effectiveness of the new linear constraints

tetrahedral mesh adaptation for lagrangian shock hydrodynamics abstract lagrangian shock hydrodynamics simulations will fail to proceed past a certain time if the mesh is approaching tangling a common solution is an arbitrary lagrangian eulerian ale form in which the mesh is improved remeshing and the solution is remapped onto the improved mesh the simplest remeshing techniques involve moving only the nodes of the mesh more advanced remeshing techniques involve altering the mesh connectivity in portions of the domain in order to prevent tangling work has been done using voronoi based polygonal mesh generators and 2d quad triangle mesh adaptation this paper presents the use of tetrahedral mesh adaptation methods as the remeshing step in an otherwise lagrangian finite element shock hydrodynamics code called alexa

pattern optimization of a reflector antenna with planar array feeds and cluster feeds we study pattern optimization of a parabolic reflector with planar array feeds and cluster feeds the optimization is carried out within the conjugate gradient method cgm in which the optimum weight vector of a linearly constrained minimum variance lcmv beam former is used as the initial condition optimization with the cgm to determine element weights is found to yield better sidelobe suppression and true settlement of desired scan direction compared to the lcmv beam former and conjugate field matching cfm techniques for the continuous beam scanning case the proposed method is also applied to multibeam reflector antenna design

on sampling continuous aperture distributions for discrete planar arrays the theory of sampling continuous distributions for the purpose of determining planar array excitation coefficients is examined the cause of pattern degradation associated with conventional sampling is identified and a new method called integrated sampling is introduced which provides superior results implementation details are given for the specific case of a rectangular grid planar array with a roughly circular boundary numerical examples are provided for both uniform and taylor distributions in order to perform comparative studies and to demonstrate the advantages of the new technique

iterative reweighted least squares design of fir filters develops a new iterative reweighted least squares algorithm for the design of optimal l sub p approximation fir filters the algorithm combines a variable p technique with a newton s method to give excellent robust initial convergence and quadratic final convergence details of the convergence properties when applied to the l sub p optimization problem are given the primary purpose of l sub p approximation for filter design is to allow design with different error criteria in pass and stopband and to design constrained l sub 2 approximation filters the new method can also be applied to the complex chebyshev approximation problem and to the design of 2d fir filters

synthesis of modular contiguously clustered linear arrays through a sparseness regularized solver an innovative methodology for the design of modular and contiguously clustered linear arrays is proposed the approach formulates the subarraying problem as a pattern matching one in which elementary modules taken from a user defined dictionary are combined to synthesize the final antenna layout by recasting such a synthesis problem within the compressive sensing framework an efficient solver is used to determine the array architecture starting from the a priori specification of the features e g the length of the admissible subarrays a set of representative numerical experiments is discussed to assess the advantages and drawbacks of the proposed algorithm also in comparison with some state of the art methods

compatible fluxes for van leer advection application of the standard second order upstream centered advection method of van leer to a coupled transport equation system of the form t a a u 0 can produce artificial extrema in the ratiot a even thoughtsatisfies a simple advection equation and is expected to preserve monotonicity hereuis velocity is mass density andais a conserved quantity such as momentum density energy density or chemical species density thustis a mass specific transport quantity such as velocity energy per unit mass temperature or species mass fraction a new flux formulation and gradient limiting procedure is presented here which eliminates these artificial extrema preserves the second order accuracy and preserves the monotone character of the van leer method even in the limit of vanishing mass density such a formulation is calledcompatible the method is noniterative i e explicit and can be employed in a general finite volume framework sample results for the transport of a square wave in one and two dimensions are provided

a simple algorithm to achieve desired patterns for arbitrary arrays a simple iterative algorithm which can be used to find array weights that produce array patterns with a given look direction and an arbitrary sidelobe specification is presented the method can be applied to nonuniform array geometries in which the individual elements have arbitrary and differing radiation patterns the method is iterative and uses sequential updating to ensure that peak sidelobe levels in the array meet the specification computation of each successive pattern is based on the solution of a linearly constrained least squares problem the constraints ensure that the magnitude of the sidelobes at the locations of the previous peaks takes on the prespecified values phase values for the sidelobes do not change during this process and problems associated with choosing a specific phase value are therefore avoided experimental evidence suggests that the procedure terminates in remarkably few iterations even for arrays with significant numbers of elements

optimum weighted smoothing in finite data the authors consider a generalized smoothing problem and develop a procedure to obtain a set of optimum weights which gives minimum mean squared error in the estimates of directions of arrival doas of signals in finite data when the signals are arbitrarily correlated using the optimum weights they study the optimum tradeoff between the number of subarrays and the subarray size for a fixed total size of the array the computation of optimum weights however requires full knowledge of the scenario since exact doas powers and correlations of signals are unknown a priori a method for estimating these weights from the observed finite data is given it is shown through empirical studies that the optimum weights can be approximated by taylor weights which serve as near optimum weights simulation results are included to support the theoretical assertions

computing functions cos sup 1 and sin sup 1 using cordic an extension of the cordic coordinate rotation digital computer algorithm that makes it possible to compute the functions cos sup 1 sin sup 1 square root 1 t sup 2 sinh sup 1 cosh sup 1 and square root 1 t sup 2 is presented the algorithms are suitable for vlsi implementation and require only a slight modification of the original cordic algorithm

metric based mesh adaptation for 2d lagrangian compressible flows in this paper we present a method to compute compressible flows in 2d it uses two steps a lagrangian step and a metric based triangular mesh adaptation step computational mesh is locally adapted according to some metric field that depends on physical or geometrical data this mesh adaptation step embeds a conservative remapping procedure to satisfy consistency with euler equations the whole method is no more lagrangian after describing mesh adaptation patterns we recall the metric formalism then we detail an appropriate remapping procedure which is first order and relies on exact intersections we give some hints about the parallel implementation finally we present various numerical experiments which demonstrate the good properties of the algorithm

a cell by cell anisotropic adaptive mesh ale scheme for the numerical solution of the euler equations in this paper a cell by cell anisotropic adaptive mesh technique is added to an existing staggered mesh lagrange plus remap finite element ale code for the solution of the euler equations the quadrilateral finite elements may be subdivided isotropically or anisotropically and a hierarchical data structure is employed an efficient computational method is proposed which only solves on the finest level of resolution that exists for each part of the domain with disjoint or hanging nodes being used at resolution transitions the lagrangian equipotential mesh relaxation and advection solution remapping steps are generalised so that they may be applied on the dynamic mesh it is shown that for a radial sod problem and a two dimensional riemann problem the anisotropic adaptive mesh method runs over eight times faster

the construction of compatible hydrodynamics algorithms utilizing conservation of total energy the principal goal of all numerical algorithms is to represent as faithfully and accurately as possible the underlying continuum equations to which a numerical solution is sought however in the transformation of the equations of fluid dynamics into discretized form important physical properties are either lost or obeyed only to an approximation that often becomes worse with time this is because the numerical methods used to form the discrete analog of these equations may only represent them to some order of local truncation error without explicit regard to global properties of the continuum system although a finite truncation error is inherent to all discretization methods it is possible to satisfy certain global properties such as conservation of mass momentum and total energy to numerical roundoff error the purpose of this work is to show how these equations can be differenced compatibly so that they obey the aforementioned properties in particular it is shown how conservation of total energy can be utilized as an intermediate device to achieve this goal for the equations of fluid dynamics written in lagrangian form and with a staggered spatial placement of variables for any number of dimensions and in any coordinate system for staggered spatial variables it is shown how the momentum equation and the specific internal energy equation can be derived from each other in a simple and generic manner by use of the conservation of total energy this allows for the specification of forces that can be of an arbitrary complexity such as those derived from an artificial viscosity or subzonal pressures these forces originate only in discrete form nonetheless the change in internal energy caused by them is still completely determined the procedure given here is compared to the method of support operators to which it is closely related difficulties with conservation of momentum volume and entropy are also discussed the proper treatment of boundary conditions and differencing with respect to time are detailed

lagrangian gas dynamics in two dimensions and lagrangian systems we propose a new and canonical way of writing the equations of gas dynamics in lagrangian coordinates in two dimensions as a weakly hyperbolic system of conservation laws one part of the system is called the physical part and contains physical variables the other part is the geometrical part we show that the physical part is symmetrizable we show that the weak hyperbolicity is due to shear contact discontinuities free divergence constraints play an important role in the system we prove the l2 stability of the physical part of the system based on this formulation we derive a new conservative and entropy consistent finite volume numerical scheme we prove the stability of the numerical scheme numerical results show the potential interest of this approach various examples born infeld mhd 3d lagrangian gas dynamics can be written using the same abstract formalism

approximate synthesis of nonseparable design responses for rectangular arrays a method is presented for the approximation of any real symmetrical nonseparable array design response polynomial of order m 1 by n 1 for rectangular arrays with m by n uniformly spaced elements m geq n previously a sampling method has been used to exactly synthesize response functions of a single variable by n element line arrays 1 and nonseparable functions of two variables by n times n square arrays the sampling method is extended herein to apply to rectangular arrays by deriving the element weights for an m by n rectangular array that exactly yield the values of any desired real symmetrical array response function on an m by n grid of the interelement phase shifts this would yield the designed array response exactly everywhere if the design equation were of order m 1 with respect to one dimension and of order n 1 with respect to the other dimension to approximate this condition the original design function of order n 1 in both dimensions is modified to make it of order m 1 in one dimension and of order n 1 along a single grid line in the other dimension a second function is derived with these roles reversed the resulting function has the form of the original design function exactly equaling it along the n grid lines of m points each and along the single perpendicular chosen grid line of n points and closely approximating it throughout the entire range of the variables this technique is illustrated for chebyshev response functions for which the two approximating functions are derived and evaluated for several combinations of m and n the responses are shown to have generally uniform sidelobe regions with all but a small percentage of the sidelobes within 1 db of the designed sidelobe value

bayesian compressive sampling for pattern synthesis with maximally sparse non uniform linear arrays a numerically efficient technique based on the bayesian compressive sampling bcs for the design of maximally sparse linear arrays is introduced the method is based on a probabilistic formulation of the array synthesis and it exploits a fast relevance vector machine rvm for the problem solution the proposed approach allows the design of linear arrangements fitting desired power patterns with a reduced number of non uniformly spaced active elements the numerical validation assesses the effectiveness and computational efficiency of the proposed approach as a suitable complement to existing state of the art techniques for the design of sparse arrays

minimum variance beamforming with phase independent derivative constraints a set of first and second order derivative constraints that can be used in minimum variance beamformers to achieve flat main beam response is presented efficient algorithms are derived for the implementation of these constraints in contrast to conventional derivative constraint methods which constrain both the magnitude power and phase responses of the beamformer the method only constrains the magnitude response the unnecessary constraint on the phase is a major drawback to the conventional methods since it causes the beamformer performance to vary with the particular spatial reference point used to define the array element positions this phenomenon is clearly undesirable because the choice of a reference point is generally made for notational convenience as a direct sequence of the phase constraint an inappropriately chosen reference point can easily result in a beamformer response which has undesirably high sidelobes the problem is avoided through the use of phase independent derivative constraints

pattern synthesis with multipoint accurate array response control in this paper the problem of pattern synthesis with antenna arrays is addressed and new approaches based on the recently developed accurate array response control textrm a 2 textrm rc algorithm are presented it is shown that the array weight vector obtained by the textrm a 2 textrm rc algorithm to control the normalized response at a single direction in each step belongs to a specific set thus an appropriate weight vector chosen from the intersection of weight vector sets corresponding to the desired responses at multiple directions is capable of simultaneously controlling those responses this results in the so called multipoint accurate array response control textrm ma 2 textrm rc algorithm moreover in order to avoid possible beam axis shift in pattern synthesis a modified textrm ma 2 textrm rc textrm m 2 textrm a 2 textrm rc algorithm is proposed by imposing a derivative constraint on the direction of beam axis representative numerical examples are provided to demonstrate the effectiveness of the proposed textrm ma 2 textrm rc and textrm m 2 textrm a 2 textrm rc algorithms for multipoint responses control and pattern synthesis

redundant and on line cordic for unitary transformations two sided unitary transformations of arbitrary 2 spl times 2 matrices are needed in parallel algorithms based on jacobi like methods for eigenvalue and singular value decompositions of complex matrices this paper presents a two sided unitary transformation structured to facilitate the integrated evaluation of parameters and application of the typically required transformations using only the primitives afforded by cordic thus enabling significant speedup in the computation of these transformations on special purpose processor array architectures implementing jacobi like algorithms we discuss implementation in nonredundant cordic to motivate and lead up to implementation in the redundant and on line enhancements to cordic both variable and constant scale factor redundant cfr cordic approaches are detailed and it is shown that the transformations may be computed in 10n spl delta time where n is the data precision in bits and spl delta is a constant accounting for accumulated on line delays a more area intensive approach using a novel on line cordic encoded angle summation difference scheme reduces computation time to 6n spl delta the area time complexities involved in the various approaches are detailed

a flexible array synthesis method using quadratic programming a highly flexible synthesis method for an arbitrary array is proposed to best approximate a desired array pattern in a minimum mean square error sense the basic idea of the technique is to form a quadratic program with its cost function given by the mean square error between the array response and a properly selected pattern described by a known mathematical function this quadratic program can be a constrained or unconstrained optimization problem depending on the requirements of the desired array pattern in formulating the quadratic program no assumption has been made on the gain phase response or characteristics of the individual array elements therefore one can synthesize an array of arbitrary shape to any appropriate pattern with the characteristic of the array elements taken into consideration as long as one is able to model the array accurately the proposed method is used to synthesize arrays of different shapes linear as well as planar arrays including rectangular and circular planar arrays using a chebyshev polynomial or zero function as a design template to illustrate the feasibility of the proposed method

a hybrid approach to the synthesis of subarrayed monopulse linear arrays in this paper a hybrid approach for the synthesis of the ldquooptimalrdquo compromise between sum and difference patterns for subarrayed monopulse antennas is presented first the subarray configuration is determined by exploiting the knowledge of the optimum difference mode coefficients to reduce the dimension of the searching space in the second step the subarray weights are computed by means of a convex programming procedure which takes advantages from the convexity for a fixed clustering of the problem at hand a set of representative results is reported to assess the effectiveness of the proposed approach comparisons with state of the art techniques are also presented

a low latency pipelined 2d and 3d cordic processors the unfolded and pipelined cordic is a high performance hardware element that produces a wide variety of one and two argument functions with high throughput the reduction in delay power and area cost are of significant interest regarding this module due to its high demand for resources the linear approximation to rotation has been proposed to achieve such reductions however the schemes for rotation multiplication and vectoring division complicate the implementation in a single unit in this work we improve the linear approximation scheme leading to a unified implementation for rotation and vectoring where fully parallel tree multipliers are used instead of the second half of cordic iterations we also combine the linear approximation to rotation with the scale factor compensation so that the compensation is concurrently performed with the rotation process we then extend the method to 3d cordic such an extension is not straightforward due to the lack of existing analytical expressions for the convergence of the algorithm a comparison using a rough area time model and synthesis results shows that our proposals may achieve significant reductions in delay with no increase in area in actual implementations

a multi objective approach to subarrayed linear antenna arrays design based on memetic differential evolution in this paper we present a multi objective optimization approach to subarrayed linear antenna arrays design we define this problem as a bi objective one we consider two objective functions for directivity maximization and sidelobe level minimization memetic algorithms mas are hybrid algorithms that combine the benefits of a global search evolutionary algorithm ea with a local search method in this paper we introduce a new memetic multi objective evolutionary algorithm namely the memetic generalized differential evolution mgde3 this algorithm is a memetic extension of the popular generalized differential evolution gde3 algorithm another popular moea is the nondominated sorting genetic algorithm ii nsga ii mgde3 gde3 and nsga ii are applied to the synthesis of uniform and nonuniform subarrayed linear arrays providing an extensive set of solutions for each design case depending on the desired array characteristics the designer can select the most suitable solution the results of the proposed method are compared with those reported in the literature indicating the advantages and applicability of the multi objective approach

pattern characteristics of linear arrays using the constrained least squares distribution the constrained least squares cls distribution is a method for obtaining distribution functions that yield low sidelobe patterns with specified constraints on the aperture efficiency and are especially useful for the transmit patterns of active array antennas the widely used taylor distribution optimizes only pattern performance while the cls distribution optimizes pattern performance while taking into account the constraints on both the peak element amplitude and the total effective radiated voltage erv of the aperture distribution the paper compares the pattern characteristics of linear arrays with cls and taylor distributions the results help to establish guidelines on when a cls distribution would be preferable over a taylor distribution when a specified aperture efficiency is important

a numerical pattern synthesis algorithm for arrays a numerical technique for pattern synthesis in arrays is presented for a given set of elements the technique allows one to find a set of array coefficients that steer the main beam in a given direction and yield sidelobes meeting a specified criterion if such a set of array coefficients exists if the pattern specifications cannot be met with the given elements the algorithm finds the best attainable pattern the advantage of this technique is that it can be used with an arbitrary set of array elements different elements in the array can have different element patterns and the array can have arbitrary nonuniform spacing between elements the synthesis technique is based on adaptive array theory the given array elements are assumed to be used as the elements of an adaptive array the main beam is pointed in the proper direction by choosing the steering vector for that direction and the sidelobes are controlled by introducing a large number of interfering signals at many angles throughout the sidelobe region the algorithm iterates on the interference powers until a suitable pattern is obtained

redundant and on line cordic application to matrix triangularization and svd several modifications to the cordic method of computing angles and performing rotations are presented 1 the use of redundant carry free addition instead of a conventional carry propagate one 2 a representation of angles in a decomposed form to reduce area and communication bandwidth 3 the use of on line addition left to right digit serial addition to replace shifters by delays and 4 the use of online multiplication square root and division to compute scaling factors and perform the scaling operations the modifications improve the speed and the area of cordic implementations the proposed scheme uses efficiently floating point representations the application of the modified cordic method to matrix triangularization by givens rotations and to the computation of the singular value decomposition svd are discussed

a lagrangian finite element method for the 2 d euler equations a grid free lagrangian finite element method is introduced for the 2 d incompressible euler equations the method is derived based on the observation that the product of the biot savart kernel and a polynomial can be integrated analytically over any triangle this enables us to obtain a numerically stable lagrangian method without using numerical smoothing moreover we show that the method converges uniformly with second order accuracy actually we establish a l stability result which applies to kernels that are more singular than the biot savart kernel as long as the kernel is l integrable another useful result is that we prove convergence of our method when using local regridding which allows the method to run for longer time even with a fixed mesh the second order convergence is also illustrated by our numerical experiments

numerical synthesis of arbitrary discrete arrays a numerical algorithm for the synthesis of arbitrary discrete arrays is given the technique is based on the algorithm of c a olen and r t compton 1990 but employs a different iterative recursive algorithm yielding an optimum convergence rate it is shown that the new algorithm converges to the optimum solution in a significantly reduced number of iterations compared with the technique of olen and compton use of the technique is illustrated by applying the synthesis procedure to a ten element linear array and to a conformal array consisting of ten dipoles located on a parabolic curve

parallel singular value decomposition of complex matrices using multidimensional cordic algorithms the singular value decomposition svd of complex matrices is computed in a highly parallel fashion on a square array of processors using kogbetliantz s analog of jacobi s eigenvalue decomposition method to gain further speed new algorithms for the basic svd operations are proposed and their implementation as specialized processors is presented the algorithms are 3 d and 4 d extensions of the cordic algorithm for plane rotations when these extensions are used in concert with an additive decomposition of 2 spl times 2 complex matrices which enhances parallelism and with low resolution rotations early on in the svd process which reduce operation count a fivefold speedup can be achieved over the fastest alternative approach

a subcell remapping method on staggered polygonal grids for arbitrary lagrangian eulerian methods we describe a new remapping algorithm for use in arbitrary lagrangian eulerian ale simulations the new features of this remapper are designed to complement a staggered mesh lagrangian phase in which the cells may be general polygons in two dimensions and which uses subcell discretizations to control unphysical mesh distortion and hourglassing our new remapping algorithm consists of three stages a gathering stage in which we interpolate momentum internal energy and kinetic energy to the subcells in a conservative way a subcell remapping stage in which we conservatively remap mass momentum internal and kinetic energy from the subcells of the lagrangian mesh to the subcells of the new rezoned mesh a scattering stage in which we conservatively recover the primary variables subcell density nodal velocity and cell centered specific internal energy on the new rezoned mesh we prove that our new remapping algorithm is conservative reversible and satisfies the debar consistency condition we also demonstrate computationally that our new remapping method is robust and accurate for a series of test problems in one and two dimensions

synthesis of minimax sidelobes for arbitrary arrays this paper presents a synthesis algorithm to minimize the maximum sidelobe level for an arbitrary array similar to dolph chebyshev patterns the minimax array patterns for arbitrary arrays have uniform sidelobes

taylor patterns for discrete arrays the equivalent of a taylor pattern for continuous apertures is developed for discrete arrays this array factor can be realized exactly since it belongs to the appropriate class of patterns a method for determining the element excitations is also presented as an example the pattern and excitations are calculated for a 41 element array with bar n 6 and a 25 db design sidelobe level comparison is made with the patterns obtained by applying root matching and sampling of a continuous taylor aperture

optimized weighting of uniform subarrays of unequal sizes amplitude weighting at the subarray outputs alone causes grating lobes in array factors an approach that disrupts the periodic quantization by dividing the array into subarrays of unequal sizes and amplitude weighting at the subarray ports is presented a hybrid genetic algorithm optimizes the subarray size and subarray weights to minimize the maximum sidelobe level

adaptive reconnection based arbitrary lagrangian eulerian method ew present a new adaptive arbitrary lagrangian eulerian ale method this method is based on the reconnection based ale reale methodology of refs 35 34 6 the main elements in a standard reale method are an explicit lagrangian phase on an arbitrary polygonal in 2d mesh in which the solution and positions of grid nodes are updated a rezoning phase in which a new grid is defined by changing the connectivity using voronoi tessellation but not the number of cells and a remapping phase in which the lagrangian solution is transferred onto the new grid in the standard reale method the rezoned mesh is smoothed by using one or several steps toward centroidal voronoi tessellation but it is not adapted to the solution in any way in the current paper we present a new adaptive reale method a reale that is based on the following design principles first a monitor function or error indicator based on the hessian of some flow parameter s is utilized second an equi distribution principle for the monitor function is used as a criterion for adapting the mesh third a centroidal voronoi tessellation is used to adapt the mesh fourth we scale the monitor function to avoid very small and large cells and then smooth it to permit the use of theoretical results related to weighted centroidal voronoi tessellation in the a reale method both number of cells and their locations are allowed to change at the rezone stage on each time step the number of generators at each time step is chosen to guarantee the required spatial resolution in regions where monitor function reaches its maximum value we present all details required for implementation of new adaptive a reale method and demonstrate its performance in comparison with standard reale method on series of numerical examples

an adaptive generalized sidelobe canceller with derivative constraints an adaptive broad band beamforming structure is presented which employs a gradient based weight adjustment algorithm to minimize output variance subject to a set of j linear constraints on broadband directional derivatives in the desired look direction a generalized sidelobe cancelling structure is employed in which a nonadaptive conventional beamformer operates in parallel with an adaptive beamformer the conventional portion has a broad band beampattern which adheres to the specified constraints while the adaptive path is a cascade of a fixed signal blocking matrix and a set of tapped delay line filters blocking is employed to ensure that all incident waveforms which meet the specified constraints do not reach the tapped delay lines as a result an unconstrained least mean square lms power minimization algorithm is employed to adapt the delay line weights it is shown that with the addition of the directional derivative constraints the beamformer quiescent bcampattern becomes a function of the location of the phase center used to specify the constraints a design criterion for choosing this location is suggested and simulation experiments which illustrate the performance of this new adaptive beamformer are presented

on the generalization of taylor and bayliss n bar array distributions taylor s asymptotic analysis theory is used to design the generalized taylor and bayliss patterns such a design technique allows generating array factors with arbitrary sidelobe level and envelope taper for both the taylor and bayliss patterns array excitation is obtained by the elliott s pattern zero matching technique a few examples are provided to validate the presented theory also variation of different array characteristics with respect to the sidelobe tapering is explained through graphical data

a new low side lobe pattern synthesis technique for conformal arrays the application of the new nonlinear optimization algorithms to array design is demonstrated by the low side lobe pattern synthesis of conformal arrays by adopting the information of array element realized gain patterns the authors formulate synthesis problems as nonlinearly constrained optimization problems and propose a direct method to solve them the technique allows them to find a set of array coefficients that yield a pattern meeting a specified side lobe level and achieving the maximum directivity if such a set of array coefficients exists if the side lobe specifications cannot be met with the given array the technique will result in a set of coefficients that yield a pattern meeting the best attainable side lobe level and having directivity as high as possible simplified synthesis problems for an axial dipole array in an infinite perfectly conducting cylinder are discussed and numerical results are given the synthesis technique works for general array patterns

sparse iteration 4d cordic algorithms for multiplying quaternions novel 4d cordic algorithms and hardware architecture for multiplying quaternions are presented aimed at constant coefficient multipliers in our solution microrotations are multiplications by hypercomplex numbers with only one non zero imaginary part such transformations can be described using sparse matrices and implemented using less hardware resources than the iteration of the known quaternion cordic algorithm chip area can be saved because sparse microrotations can be computed using a permutation network and two operand adders without four operand additions which are necessary in the known solution the obtainable area savings depend on the implementation technology and the architectures of adders and bit shifters but can be as large as 45 and 25 percent for asic and fpga circuits respectively the circuitry simplifications come at the cost of slowing down computations our approach improves the area delay product and a single sparse iteration can be executed up to 15 percent faster than the conventional one but more microrotations are usually necessary to achieve the required accuracy on the other hand a sparse 4d iteration can be identified with microrotations of two 2d cordics which work in parallel this makes convergence analysis easier than in the previous 4d solution as it is sufficient to consider only two dimensions

on the degrees of freedom of scattered fields starting from the observation that fields differing less than a prescribed error cannot be resolved as distinct entities the degrees of freedom of the scattered field are introduced and then computed the degrees of freedom are shown to be practically equal to the nyquist number appropriate to the effective spatial bandwidth of the scattered field and to the extension of the observation domain accordingly a finite number of elements of information can be used to determine the scattered field to a prescribed approximation error it is also shown that the field representation can be made in terms of field values and simple sampling functions provided that a marginal increase in the approximation error is tolerated the results not only completely justify the use of sampling interpolation for representing scattering fields but also demonstrate that such representation is practically an optimal one an algorithm for the reconstruction of scattered fields given the maximum allowed error is then produced

an effective approach for the optimal focusing of array fields subject to arbitrary upper bounds a new approach to the optimal focusing of array fields subject to arbitrary upper bounds is presented the approach formulates the problem as the minimization of a linear function in a convex set unlike other approaches this one guarantees the achievement of the global optimum by using local optimization techniques and can moreover deal with any convex constraint on the unknowns such as near field constraints optimization is performed by two ad hoc developed solution algorithms which exploit the geometrical characteristics of the problem at hand thus leading to extremely effective and computationally efficient numerical codes an extensive numerical analysis has been performed in all cases of linear planar and circular arc arrays the enhanced performance of the proposed technique with respect to the solution algorithms available in the literature fully confirms the effectiveness of the approach

sparsening conformal arrays through a versatile bcs based method sparsening conformal arrangements is carried out through a versatile multi task bayesian compressive sensing mt bcs strategy the problem formulated in a probabilistic fashion as a pattern matching synthesis is that of determining the sparsest excitation set locations and weights fitting a reference pattern subject to user defined geometrical constraints results from a set of representative numerical experiments are presented to illustrate the key features of the proposed approach as well as to assess also through comparisons its potentials in terms of matching accuracy element saving and computational costs

inverse scattering using a joint l1 l2 norm based regularization inverse scattering problems suffer from ill posedness and ill conditioning necessitating the use of regularization methods to get meaningful solutions commonly used regularizations are l2 norm based but these generate over smooth solutions we propose a regularization method using both the l1 and l2 norms to obtain sharp object boundaries while also achieving good interior reconstruction of the object permittivity knowledge about the permittivity can also be used as a priori information the applicability of the method is demonstrated on synthetically generated data for two dimensional 2 d microwave imaging using the born iterative method bim the optimization routine systematically estimates all parameters while minimizing the cost function different objects chosen to represent realistic features have been considered to evaluate the performance the reconstructed images indicate that the method can produce accurate object localization shape identification and good permittivity estimation

fast and accurate simulations of air cooled structures there are fields of engineering for which the cad based navier stokes solvers are too expensive architecture and medicine for blood flows are two such examples mesh generation and adaptation is also a bottleneck because the users are not expected to have the know how we report here on a navier stokes solver for incompressible temperature and time dependent flows dedicated to architectural applications the building blocks are not new a finite element method with time implicit pressure projection steps and mesh adaptativity but putting them together in an easy to use and efficient 3d code is the challenge which motivates this paper for non engineering applications the user interface is a big problem in an earlier attempt we designed freefem3d based on a fictitious domain discretization thus avoiding boundary fitted mesh however it turned out that the display of the solutions requires a boundary fitted mesh it is possible to generate a feasible surface mesh for graphics but it is much more difficult to generate a feasible surface mesh for fem in this project the user interface is taken from freefem3d then with a marching cube algorithm we produce a graphic only feasible mesh finally a surface mesh adapted to a fem computation is constructed with an adaptation module and the result is used as input to a delaunay volumic mesh generator the solver is optimized and parallelized all modules are the authors work three applications are presented for which the data preparation takes less than a day and results are obtained overnight on a pc cluster one of the application is presented in details it is an air cooling system for a canister containing radio nucleides

near field radar imaging via compressive sensing a novel two dimensional 2 d compressive sensing cs based method is presented for near field radar imaging first an accurate near field approximation is proposed based on which the circular wavefront curvature of spherical waves can be compensated by mapping the images to a rectified new grid more importantly the near field approximation makes the two dimensions of the scattered data separable for the range and cross range directions which makes it possible to solve the 2 d reflectivity matrix for the image reconstruction directly then a 2 d proximal subgradient algorithm for near field radar imaging based on a fast iterative shrinkage thresholding algorithm fista is introduced to resolve the memory usage and computation time issues simulation and experimental results are provided to demonstrate the performance of the proposed method with comparisons to the traditional fourier based method and to the conjugate gradient cg based method which proves that the proposed method is an effective way to solve the near field radar imaging problem

reduced dissipation remapping of velocity in staggered arbitrary lagrangian eulerian methods remapping is an essential part of most arbitrary lagrangian eulerian ale methods in this paper we focus on the part of the remapping algorithm that performs the interpolation of the fluid velocity field from the lagrangian to the rezoned computational mesh in the context of a staggered discretization standard remapping algorithms generate a discrepancy between the remapped kinetic energy and the kinetic energy that is obtained from the remapped nodal velocities which conserves momentum in most ale codes this discrepancy is redistributed to the internal energy of adjacent computational cells which allows for the conservation of total energy this approach can introduce oscillations in the internal energy field which may not be acceptable we analyze the approach introduced in bailey 1984 11 which is not supposed to introduce dissipation on a simple example we demonstrate a situation in which this approach fails a modification of this approach is described which eliminates when it is possible or reduces the energy discrepancy

parallel vlsi matrix pencil algorithm for high resolution direction finding algorithms to find the directions of arrival doas of multiple signals from measurements on an array of antenna doublets esprit method and their parallel vlsi implementation are discussed in particular algorithms that allow large scale pipelining and use only robust unitary transformations are identified this problem is solved by a matrix pencil approach in which the generalized eigenvalues of a pair of data matrices are determined a modified stewart jacobi approach is used for which convergence is improved and parameter computations are simplified the resulting architecture is a two layer jacobi array that can handle all the subproblems two qr factorizations two svds and a single generalized schur decomposition the mapping of the subproblems on a single parallel array of cordic processors is considered

calf a cordic adaptive lattice filter calf is a cordic processor implementation of the adaptive lattice filter unlike previously reported results which simply use the cordic processor to implement the lattice algorithm formulated for conventional multiply and accumulate type arithmetic units a novel adaptive normalized lattice algorithm which directly updates the rotation angles rather than the reflection coefficients is reported thus this angle updating lattice algorithm is derived specifically for implementation with a vlsi cordic processor moreover this algorithm was further modified to a sign sign algorithm to take advantage of the fact that the cordic processors only rotate a finite number of distinct rotation angles computer simulation results showed good converging properties even at rather coarsely quantized angles

angular momentum preserving cell centered lagrangian and eulerian schemes on arbitrary grids we address the conservation of angular momentum for cell centered discretization of compressible fluid dynamics on general grids we concentrate on the lagrangian step which is also sufficient for eulerian discretization using lagrange remap starting from the conservative equation of the angular momentum we show that a standard riemann solver a nodal one in our case can easily be extended to update the new variable this new variable allows to reconstruct all solid displacements in a cell and is analogous to a partial discontinuous galerkin dg discretization we detail the coupling with a second order muscl extension all numerical tests show the important enhancement of accuracy for rotation problems and the reduction of mesh imprint for implosion problems the generalization to axi symmetric case is detailed

design of subarrayed linear and planar array antennas with sll control based on an excitation matching approach in this paper the synthesis of subarrayed antennas with subarrays having different weights and dimensions is considered the problem is formulated as the definition of the element clustering into spatially contiguous subarrays and the corresponding weights to obtain a pattern with the lowest i e minimum achievable sidelobe level sll the problem is addressed with an unconstrained approach based on an excitation matching method where the synthesis of subarray weights and sizes is simultaneously carried out successively a hybrid version of such an approach is proposed to directly enforce into the optimization procedure the sll constraints a set of representative results concerned with both sum and difference patterns are shown furthermore some comparisons with state of the art hybrid evolutionary based techniques are reported as well

an innovative approach based on a tree searching algorithm for the optimal matching of independently optimum sum and difference excitations an innovative approach for the optimal matching of independently optimum sum and difference patterns through sub arrayed monopulse linear arrays is presented by exploiting the relationship between the independently optimal sum and difference excitations the set of possible solutions is considerably reduced and the synthesis problem is recast as the search of the best solution in a noncomplete binary tree towards this end a fast resolution algorithm that exploits the presence of elements more suitable to change subarray membership is presented the results of a set of numerical experiments are reported in order to validate the proposed approach pointing out its effectiveness also in comparison with state of the art optimal matching techniques

triangular processor array for computing singular values a triangular processor array for computing the singular values of an m n m n matrix is proposed a jacobi type algorithm is used to first triangularize the given matrix and then diagonalize the resultant triangular form the requirements are 14n2 o n processors and o m ns time where s denotes the number of sweeps the triangular array can be extended to a rectangular one with 12mn o m processors for the computational of singular vectors

complex weight sparse linear array synthesis by bayesian compressive sampling an innovative method for the synthesis of maximally sparse linear arrays matching arbitrary reference patterns is proposed in the framework of sparseness constrained optimization the approach exploits the multi task mt bayesian compressive sensing bcs theory to enable the design of complex non hermitian layouts with arbitrary radiation and geometrical constraints by casting the pattern matching problem into a probabilistic formulation a relevance vector machine rvm technique is used as solution tool the numerical assessment points out the advances of the proposed implementation over the extension to complex patterns of and it gives some indications about the reliability flexibility and numerical efficiency of the mt bcs approach also in comparison with state of the art sparse arrays synthesis methods