high spatial order finite element method to solve maxwell s equations in time domain this paper presents a finite element method with high spatial order for solving the maxwell equations in the time domain in the first part we provide the mathematical background of the method then we discuss the advantages of the new scheme compared to a classical finite difference time domain fdtd method several examples show the advantages of using the new method for different kinds of problems comparisons in terms of accuracy and cpu time between this method the fdtd and the finite volume time domain methods are given as well

iaa spectral estimation fast implementation using the gohberg semencul factorization we consider fast implementations of the weighted least squares based iterative adaptive approach iaa for one dimensional 1 d and two dimensional 2 d spectral estimation of uniformly sampled data iaa is a robust user parameter free and nonparametric adaptive algorithm that can work with a single data sequence or snapshot compared to the conventional periodogram iaa can be used to significantly increase the resolution and suppress the sidelobe levels however due to its high computational complexity iaa can only be used in applications involving small sized data we present herein novel fast implementations of iaa using the gohberg semencul g s type factorization of the iaa covariance matrices by exploiting the toeplitz structure of the said matrices we are able to reduce the computational cost by at least two orders of magnitudes even for moderate data sizes

the optimal symmetrical points for polynomial interpolation of real functions in the tetrahedron abstract the main result of this paper is the computation of the mean optimal symmetrical interpolation points in the tetrahedron up to degree 9 this interpoation set has the smallest lebesgue constant known today

a dimension formula for bernoulli convolutions we present a dynamical approach to the study of the singularity of infinitely convolved bernoulli measuresv for the golden section we introducev as the transverse measure of the maximum entropy measure on the repelling set invariant for contracting maps of the square the fat baker s transformation our approach strongly relies on the markov structure of the underlying dynamical system indeed if golden mean the fat baker s transformation has a very simple markov coding the ambiguity of order two of this coding which appears when projecting on the line due to passages for the central overlapping zone can be expressed by means of products of matrices of order two this product has a markov distribution inherited by the markov structure of the map the dimension of the projected measure is therefore associated to the growth of this product our dimension formula appears in a natural way as a version of the furstenberg guivarch formula our technique provides an explicit dimension formula and most important provides a formalism well suited for the multifractal analysis of this measure as we will show in a forthcoming paper

a pseudospectral method for time domain computation of electromagnetic scattering by bodies of revolution we present a multidomain pseudospectral method for the accurate and efficient time domain computation of scattering by body of revolution bor perfectly electrically conducting objects in the bor formulation of the maxwell equations the azimuthal dependence of the fields is accounted for analytically through a fourier series the numerical scheme in the r z plane is developed in general curvilinear coordinates and the method of characteristics is applied for patching field values in the individual subdomains to obtain the global solution a modified matched layer method is used for terminating the computational domain and special attention is given to proper treatment of the coordinate singularity in the scattered field formulation and correct time domain boundary conditions along edges numerical results for monochromatic plane wave scattering by smooth and nonsmooth axis symmetric objects including spheres cone spheres and finite cylinders is compared with results from the literature illustrating the accuracy and computational efficiency associated with the use of properly constructed spectral methods to emphasize the versatility of the presented framework we compute plane wave scattering by a missile and find satisfactory agreement with method of moment mom computations

multidomain spectral solution of the euler gas dynamics equations abstract we present interface treatments for computing the euler gas dynamics equations by a multidomain chebyshev spectral collocation method these treatments are suitable for use at the corners of subdomains and for patched or overlapping subdomains they can be applied to interfaces placed in subsonic supersonic or transonic regions of a flow computed results indicate that the solutions are spectrally accurate can be more accurate and more efficient than a single domain calculation and that reflections of waves at interfaces are not significant

an efficient algorithm for two dimensional autoregressive spectrum estimation an algorithm similar to the burg algorithm is given for autoregressive estimation in one dimension coefficients of the filter used to decorrelate the signal are found recursively from lower order filters the coefficients needed to get the larger sized filters can be found at each stage of the recursion from the correlations of lower order filter outputs thus the resulting estimate does not assume knowledge of ensemble averages it offers a computational saving of 25 over the commonly used method in which an estimate of the correlation matrix is first computed and then inverted

time frequency arma models and parameter estimators for underspread nonstationary random processes parsimonious parametric models for nonstationary random processes are useful in many applications here we consider a nonstationary extension of the classical autoregressive moving average arma model that we term the time frequency autoregressive moving average tfarma model this model uses frequency shifts in addition to time shifts delays for modeling nonstationary process dynamics the tfarma model and its special cases the tfar and tfma models are shown to be specific types of time varying arma ar ma models they are attractive because of their parsimony for underspread processes that is nonstationary processes with a limited time frequency correlation structure we develop computationally efficient order recursive estimators for the tfarma tfar and tfma model parameters which are based on linear time frequency yule walker equations or on a new time frequency cepstrum simulation results demonstrate that the proposed parameter estimators outperform existing estimators for time varying arma ar ma models with respect to accuracy and or numerical efficiency an application to the time varying spectral analysis of a natural signal is also discussed

model identification of a noncausal 2 d ar process using a causal 2 d ar model on the nonsymmetric half plane if a noncausal two dimensional 2 d autoregressive ar process is bi causal there exists a causal 2 d ar process on the nonsymmetric half plane having the same autocorrelations as the noncausal 2 d ar process a formula is presented to relate the ar coefficients of the noncausal 2 d ar process with those of the causal 2 d ar process on the nonsymmetric half plane the 2 d yule walker equations are derived for causal 2 d ar models on the nonsymmetric half plane a computationally efficient order recursive algorithm is proposed to solve the 2 d yule walker equations using the autocorrelation equivalence relation and the order recursive algorithm we can easily identify a noncausal 2 d ar process from its autocorrelations

multifractal analysis of bernoulli convolutions associated with salem numbers abstract we consider the multifractal structure of the bernoulli convolution where 1 is a salem number in 1 2 let q denote the l q spectrum of we show that if 0 then the level set e x r lim r 0 log x r x r log r is non empty and dim h e where denotes the legendre transform of this result extends to all self conformal measures satisfying the asymptotically weak separation condition we point out that the interval 0 is not a singleton when 1 is the largest real root of the polynomial x n x n 1 x 1 n 4 an example is constructed to show that absolutely continuous self similar measures may also have rich multifractal structures

spectral element method for elastic and acoustic waves in frequency domain numerical techniques in time domain are widespread in seismic and acoustic modeling in some applications however frequency domain techniques can be advantageous over the time domain approach when narrow band results are desired especially if multiple sources can be handled more conveniently in the frequency domain moreover the medium attenuation effects can be more accurately and conveniently modeled in the frequency domain in this paper we present a spectral element method sem in frequency domain to simulate elastic and acoustic waves in anisotropic heterogeneous and lossy media the sem is based upon the finite element framework and has exponential convergence because of the use of gll basis functions the anisotropic perfectly matched layer is employed to truncate the boundary for unbounded problems compared with the conventional finite element method the number of unknowns in the sem is significantly reduced and higher order accuracy is obtained due to its spectral accuracy to account for the acoustic solid interaction the domain decomposition method ddm based upon the discontinuous galerkin spectral element method is proposed numerical experiments show the proposed method can be an efficient alternative for accurate calculation of elastic and acoustic waves in frequency domain

stable spectral methods on tetrahedral elements a framework for the construction of stable spectral methods on arbitrary domains with unstructured grids is presented although most of the developments are of a general nature an emphasis is placed on schemes for the solution of partial differential equations defined on the tetrahedron in the first part the question of well behaved multivariate polynomial interpolation on the tetrahedron is addressed and it is shown how to extend the electrostatic analogy of the jacobi polynomials to problems beyond the line this allows for the identification of nodal sets suitable for polynomial interpolation within the tetrahedron and subsequently for the formulation of stable spectral schemes on such unstructured nodal sets the second part of this work is devoted to a discussion of weakly imposed boundary conditions and energy stable schemes are formulated for a wide class of problems exemplified by advection problems advection diffusion problems and linear symmetric hyperbolic systems finally in the third part issues related to computational efficiency and implementation of the schemes are discussed the spectral accuracy of the approximation is confirmed through an example and factorization methods for the efficient computation of derivatives on the general nodal sets within the d simplex are developed ensuring that the proposed schemes are competitive with tensor product based methods in this last part we also show that the advective operator results in an cal o n 2 restriction on the time step similar to that of spectral collocation methods employing a tensor product based approximation the performance of the proposed scheme is illustrated by solving a wave problem on a triangulated domain confirming the expected accuracy and stability

nodal high order methods on unstructured grids we present a convergent high order accurate scheme for the solution of linear conservation laws in geometrically complex domains as our main example we include a detailed development and analysis of a scheme for the time domain solution of maxwell s equations in a three dimensional domain the fully unstructured spatial discretization is made possible by the use of a high order nodal basis employing multivariate lagrange polynomials defined on the triangles and tetrahedra while the equations themselves are satisfied in a discontinuous galerkin form with the boundary conditions being enforced weakly through a penalty term accuracy stability and convergence of the semidiscrete approximation to maxwell s equations is established rigorously and bounds on the growth of the global divergence error are provided concerns related to efficient implementations are discussed in detail this sets the stage for the presentation of examples verifying the theoretical results and illustrating the versatility flexibility and robustness when solving two and three dimensional benchmark problems in computational electromagnetics pure scattering as well as penetration is discussed and high parallel performance of the scheme is demonstrated

efficient algorithms for the solution of block linear systems with toeplitz entries abstract this paper is concerned with the development of fast solvers for block linear systems with toeplitz entries two algorithms are described the first utilizes block permutations to unravel the nesting structure of the associated matrix the second has a block schur type format and features highly parallel potential

a new 3 d nonspurious discontinuous galerkin spectral element time domain dg setd method for maxwell s equations a new discontinuous galerkin spectral element time domain dg setd method for maxwell s equations based on the field variables mathbf e and mathbf b is proposed to analyze three dimensional 3 d transient electromagnetic phenomena compared to the previous setd method based on the field variables mathbf e and mathbf h the mathbf eh scheme in which different orders of interpolation polynomials for electric and magnetic field intensities are required the newly proposed method can eliminate spurious modes using basis functions with the same order interpolation for electric field intensity and magnetic flux density the mathbf eb scheme consequently it can reduce the number of unknowns and computation load domain decomposition for the mathbf eb scheme setd method is completed via the dg method in addition the mathbf eb scheme setd method is extended to the well posed time domain perfectly matched layer pml to truncate the computation domain when solving open region problems the effectiveness and advantages of the new dg setd method are validated by eigenvalue analysis and numerical results

analysis of photonic crystals using the hybrid finite element finite difference time domain technique based on the discontinuous galerkin method summary two dimensional photonic crystal structures are analyzed by a recently developed hybrid technique combining the finite element time domain fetd method and the finite difference time domain fdtd method this hybrid fetd fdtd method uses the discontinuous galerkin method as framework for domain decomposition to the best of our knowledge this is the first hybrid fetd fdtd method that allows non conformal meshes between different fetd and fdtd subdomains it is also highly parallelizable these properties are very suitable for the computation of periodic structures with curved surfaces numerical examples for the computation of the scattering parameters of two dimensional photonic bandgap structures are presented as applications of the hybrid fetd fdtd method numerical results demonstrate the efficiency and accuracy of the proposed hybrid method copyright 2012 john wiley sons ltd

computationally efficient two dimensional capon spectrum analysis we present a computationally efficient algorithm for computing the 2 d capon 1969 spectral estimator the implementation is based on the fact that the 2 d data covariance matrix will have a toeplitz block toeplitz structure with the result that the inverse covariance matrix can be expressed in closed form by using a special case of the gohberg heinig 1974 formula that is a function of strictly the forward 2 d prediction matrix polynomials furthermore we present a novel method based on a 2 d lattice algorithm to compute the needed forward prediction matrix polynomials and discuss the difference in the so obtained 2 d spectral estimate as compared with the one obtained by using the prediction matrix polynomials given by the whittle wiggins robinson 1963 1965 algorithm numerical simulations illustrate the improved resolution as well as the clear computational gain in comparison to both the well known classical implementation and the method published by liu et al see ieee trans aerosp electron syst vol 34 p 1314 19 1998

a hybrid approach to high resolution two dimensional spectrum analysis the 2 d spectrum estimation is divided into the two consecutive 1 d spectrum estimations a multichannel spectrum estimation in the time domain and a scalar spectrum estimation in the frequency domain the first is a purely parametric estimation while the second is a mixture of parametric and nonparametric estimation the maximum entropy method is used in each estimation in order to utilize the high resolution performance of the maximum entropy method on the one hand and to avoid the highly nonlinear nature of the maximum entropy method for 2 d problems on the other hand the estimate obtained by this procedure satisfies the covariance matching property and exhibits remarkably high resolution a simplified version of the multichannel levinson durbin algorithm is derived based on the special structure of the covariance data of homogeneous random fields the related extendibility of the covariance array is discussed it is shown that this method is particularly suitable for a class of random fields having some shift invariance

finite orbits in multivalued maps and bernoulli convolutions abstract bernoulli convolutions are certain measures on the unit interval depending on a parameter between 1 and 2 in spite of their simple definition they are not yet well understood we study their two dimensional density which exists by a theorem of solomyak to each bernoulli convolution there is an interval d called the overlap region and a map which assigns two values to each point of d and one value to all other points of 0 1 there are two types of finite orbits of these multivalued maps which correspond to zeros and potential singularities of the density respectively orbits which do not meet d belong to an ordinary map called transformation and exist for all 1 6182 they were studied by erdos joo komornik sidorov de vries and others as points with unique addresses and by jordan shmerkin and solomyak as points with maximal local dimension in the two dimensional view these orbits form address curves related to the milnor thurston itineraries in one dimensional dynamics the curves depend smoothly on the parameter and represent quantiles of all corresponding bernoulli convolutions finite orbits which intersect d have a network like structure and can exist only at perron parameters their points are intersections of extended address curves and can have finite or countable number of addresses as found by sidorov for an uncountable number of parameters the central point 1 2 has only two addresses the intersection of periodic address curves can lead to singularities of the measures we give examples which are not pisot or salem parameters

spectral methods on arbitrary grids stable and spectrally accurate numerical methods are constructed on arbitrary grids for partial differential equations these new methods are equivalent to conventional spectral methods but do not rely on specific grid distributions specifically we show how to implement legendre galerkin legendre collocation and laguerre galerkin methodology on arbitrary grids

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

vector time frequency ar models for nonstationary multivariate random processes we introduce the vector time frequency autoregressive vtfar model for a parsimonious parametric description of nonstationary vector random processes the vtfar model generalizes the recently proposed scalar tfar model to the multivariate case it is physically meaningful because nonstationarity and spectral correlation are represented in terms of frequency shifts and it is parsimonious for the practically relevant class of underspread vector processes i e nonstationary vector processes with rapidly decaying correlation in time and frequency for vector processes with decaying correlation across the signals we introduce a variant of the vtfar model with banded parameter matrices furthermore we present a vtfar parameter estimator that is based on a system of linear equations with two level block toeplitz structure and we develop an efficient order recursive algorithm for solving these equations we also present information criteria for estimating the vtfar model order and the matrix bandwidth of the banded vtfar model the performance of the proposed vtfar parameter and order estimators is assessed through numerical simulations finally an application to nonstationary multivariate spectral analysis is presented

on the recursive computation of interpolators with nonrectangular masks an algorithm is presented for the recursive computation of finite order interpolators and predictors for scalar random processes on multidimensional parameter sets the algorithm is able to achieve computational savings even for interpolation filters with nonrectangularly shaped support because it avoids direct exploitation of toeplitz structure in the normal equations by using the displacement invariance structure of the interpolation filter and the low displacement rank properties of the correlation matrix the paper presents the method for step by step growth of the interpolation support and shows that an interpolation filter can be constructed from the interpolator of the previous step along with certain interpolators corresponding to the boundary points of the filter support in the previous step when restricted to rectangularly shaped masks the algorithm has the same order of complexity as previous algorithms for solving toeplitz block toeplitz systems

simplified understanding and efficient decoding of a class of algebraic geometric codes an efficient decoding algorithm for algebraic geometric codes is presented for codes from a large class of irreducible plane curves including hermitian curves it can correct up to d 1 2 errors where d is the designed minimum distance with it we also obtain a proof of d sub min spl ges d without directly using the riemann roch theorem the algorithm consists of gaussian elimination on a specially arranged syndrome matrix followed by a novel majority voting scheme a fast implementation incorporating block hankel matrix techniques is obtained whose worst case running time is o mn sup 2 where m is the degree of the curve applications of our techniques to decoding other algebraic geometric codes to decoding bch codes to actual minimum distance and to two dimensional shift register synthesis are also presented

dimension of a family of singular bernoulli convolutions abstract let x n n 0 be a sequence of i i d bernoulli random variables i e x n takes values 0 1 with probability 1 2 each let x n 0 n x n and let be the corresponding probability measure erdos salem proved that if 1 2 1 is a p v number then is singular in this paper we study the algebraic structure of and the singularity of the correspondent in more detail we introduce a new class of algebraic numbers containing the p v numbers and make use of the self similar property determined by such numbers to calculate the exact mean quadratictariation dimension of this dimension is most relevant to strichartz s recent work on fourier asymptotics of fractal measures

an isoparametric spectral element method for solution of the navier stokes equations in complex geometry abstract an isoparametric spectral element technique is presented for solution of the two dimensional navier stokes equations in arbitrary curvy geometries the spatial discretization is described and the method is illustrated by solution of poisson s equation in a cylindrical annulus a fractional step navier stokes solver based on a discretely consistent poisson equation for the pressure is then presented and exponential convergence in space is demonstrated for the case of separated flow between eccentric rotating cylinders the technique is made efficient by the use of explicit collocation rather than galerkin operators for the convective terms and use of static condensation to solve the elliptic equations resulting from the stokes problem the algorithm is amenable to a high degree of parallelism in both multiprocessor and vector pipeline environments

a comparative study of three finite element based explicit numerical schemes for solving maxwell s equations three finite element based explicit numerical algorithms named the dual field domain decomposition at the element level dfdd eld the discontinuous galerkin time domain method with upwind fluxes dgtd upwind and the discontinuous galerkin time domain method with central fluxes dgtd central are investigated and compared in terms of accuracy and efficiency all three algorithms can perform an efficient domain decomposition and avoid the inversion of a global system matrix yet the study shows that they differ from each other in terms of accuracy and efficiency hybrid implicit explicit schemes which can relax the restriction on the time step size imposed by the smallest elements in the computational domain are also investigated for both dfdd and dgtd and compared in terms of efficiency

a new triangular and tetrahedral basis for high order hp finite element methods in this paper we describe the foundations of a new hierarchical modal basis suitable for high order hp finite element discretizations on unstructured meshes it is based on a generalized tensor product of mixed weight jacobi polynomials the generalized tensor product property leads to a low operation count with the use of sum factorization techniques variable p order expansions in each element are readily implemented which is a crucial property for efficient adaptive discretizations numerical examples demonstrate the exponential convergence for smooth solutions and the ability of this formulation to handle easily very complex two and three dmensional computational domains employing standard meshes

multifractal measures and a weak separation condition abstract we define a new separation property on the family of contractive similitudes that allows certain overlappings this property is weaker than the open set condition of hutchinson it includes the well known class of infinite bernoulli convolutions associated with the p v numbers and the solutions of the two scale dilation equations our main purpose in this paper is to prove the multifractal formalism under such condition

modeling 2 d ar processes with various regions of support we show that there exists a causal 2 d linear process in the nonsymmetric half plane having the same autocorrelations as a noncausal 2 d linear process in the whole plane this property is called the autocorrelation equivalence relation and can be used for practical fitting and modeling of 2 d processes some causal 2 d autoregressive ar models with various regions of support are considered such as half cross half diamond quarter plane square half square half hexagon half octagon and half circle considerations of parsimony in 2 d model fitting are then focused not only on the number of parameters in our model but also most importantly on the optimal shape of the region of support their 2 d yule walker equations are derived and a computationally efficient order recursive algorithm is proposed to solve them the autocorrelation equivalence relation and the order recursive algorithm are utilized to specify a noncausal 2 d ar process as well as its spectrum from a given realization of a random field

fractal measures and mean p variations abstract recently strichartz proved that if is locally uniformly dimensional on r d then where 0 d and bt denotes the ball of radius t center at 0 if is self similar and satisfies a certain open set condition he also obtained a formula for the so that 0 lim sup t 1 t d b t f s 2 the can serve in some sense as the dimensional index of the measure by using the mean p variation and the tauberian theorems we extend the first inequality and its variants to p q forms and give necessary and sufficient conditions on for such inequalities to hold we then use the mean quadratic variation to study some self similar measures on r which do not satisfy the open set condition the s that are constructed from s 1 x x s 2 x x 1 1 2 with weights 1 2 each the index for corresponding to 5 1 2 is calculated the expression for such is significantly different from the one obtained by strichartz

efficient inversion of toeplitz block toeplitz matrix an iterative algorithm for the inversion of a toeplitz block toeplitz matrix consisting of m m blocks of size p p is described the algorithm presented exploits the structure of the toeplitz block toeplitz matrix and outperforms akaike s algorithm by a factor of max 2 p m 2 the use of this algorithm for an iterative solution of a toeplitz block toeplitz set of linear equations is also presented

monomial cubature rules since stroud a compilation a bibliography of references to cubature rules which have appeared since the publication of stroud s book 1971 is presented the standard regions that are treated in this paper are the n cube the n simplex the n sphere and the entire space

discontinuous galerkin methods for dispersive and lossy maxwell s equations and pml boundary conditions in this paper we will present a unified formulation of discontinuous galerkin method dgm for maxwell s equations in linear dispersive and lossy materials of debye type and in the artificial perfectly matched layer pml regions an auxiliary differential equation ade method is used to handle the frequency dependent constitutive relations with the help of auxiliary polarization currents in the computational and pml regions the numerical flux for the dispersive lossy maxwell s equations with the auxiliary polarization current variables is derived various numerical results are provided to validate the proposed formulation

a theorem on the asymptotic eigenvalue distribution of toeplitz block toeplitz matrices we extend szego s eigenvalue distribution theorem to block toeplitz matrices a sequence of such matrices arises from the autocorrelation of a 2 d discrete random process we show that the eigenvalues of the matrix sequence are asymptotically distributed like the samples of the random process 2 d power spectrum

new algorithm for solving block matrix equations with applications in 2 d ar spectral estimation the author presents an iterative algorithm to solve toeplitz and non toeplitz block matrix equations the development is based upon some well known matrix iterative techniques the algorithm is developed for the ideal case where the individual blocks in the autocorrelation matrix are toeplitz and it is then extended to a more general least squares data formulation case it is shown that the algorithm requires fewer computations than the direct matrix inversion methods and is very simple to implement the algorithm is applied to compute the spectral estimates of 2 d data of very small size based on the least squares data formulation with a quarter plane support

the limited rademacher functions and bernoulli convolutions associated with pisot numbers abstract in this paper we give a systematical study of the local structures and fractal indices of the limited rademacher functions and bernoulli convolutions associated with pisot numbers for a given pisot number in the interval 1 2 we construct a finite family of non negative matrices maybe non square such that the corresponding fractal indices can be re expressed as some limits in terms of products of these non negative matrices we are especially interested in the case that the associated pisot number is a simple pisot number i e the unique positive root of the polynomial x k x k 1 x 1 k 2 3 in this case the corresponding products of matrices can be decomposed into the products of scalars based on which the precise formulas of fractal indices as well as the multifractal formalism are obtained

a new efficient 3d discontinuous galerkin time domain dgtd method for large and multiscale electromagnetic simulations a new discontinuous galerkin time domain dgtd method for solving the 3d time dependent maxwell s equations via the electric field intensity e and magnetic flux density b fields is proposed for the first time it uses curl conforming and divergence conforming basis functions for e and b respectively with the same order of interpolation in this way higher accuracy is achieved at lower memory consumption than the conventional approach based on the field variables e and h the centered flux and riemann solver are both used to treat interfaces with non conforming meshes and both explicit runge kutta method and implicit crank nicholson method are implemented for time integration numerical examples for realistic cases will be presented to verify that the proposed method is a non spurious and efficient dgtd scheme

convergent cartesian grid methods for maxwell s equations in complex geometries a convergent second order cartesian grid finite difference scheme for the solution of maxwell s equations is presented the scheme employs a staggered grid in space and represents the physical location of the material and metallic boundaries correctly hence eliminating problems caused by staircasing and contrary to the popular yee scheme enforces the correct jump conditions on the field components across material interfaces a detailed analysis of the accuracy of the new embedding scheme is presented confirming its second order global accuracy furthermore the scheme is proven to be a bounded error scheme and thus convergent conditions for fully discrete stability is furthermore established this enables the derivation of bounds for fully discrete stability with cfl restrictions being almost identical to those of the much simpler yee scheme the analysis exposes that the effects of staircasing as well as a lack of properly enforced jump conditions on the field components have significant consequences for the global accuracy it is among other things shown that for cases in which a field component is discontinuous along a grid line as happens at general two and three dimensional material interfaces the yee scheme may exhibit local divergence and loss of global convergence to validate the analysis several one and two dimensional test cases are presented showing an improvement of typically 1 to 2 orders of accuracy at little or no additional computational cost over the yee scheme which in most cases exhibits first order accuracy c 2001 academic press

regular article spectral collocation time domain modeling of diffractive optical elements a spectral collocation multi domain scheme is developed for the accurate and efficient time domain solution of maxwell s equations within multi layered diffractive optical elements special attention is being paid to the modeling of out of plane waveguide couplers emphasis is given to the proper construction of high order schemes with the ability to handle very general problems of considerable geometric and material complexity central questions regarding efficient absorbing boundary conditions and time stepping issues are also addressed the efficacy of the overall scheme for the time domain modeling of electrically large and computationally challenging problems is illustrated by solving a number of plane as well as non plane waveguide problems

tetrahedralhpfinite elements we present a new discretisation for the incompressible navier stokes equations that extends spectral methods to three dimensional complex domains consisting of tetrahedral subdomains the algorithm is based on standard concepts ofhpfinite elements as well as tensorial spectral elements this new formulation employs a hierarchical modal basis constructed from a new apex co ordinate system which retains a generalised tensor product these properties enable the development of computationally efficienct algorithms for use on standard finite volume unstructured meshes a detailed analysis is presented that documents the stability and exponential convergence of the method and several flow cases are simulated and compared with analytical and experimental results

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

toeplitz properties of the block matrices encountered in the processing of spatiotemporal signals various signal processing applications such as system identification fir finite impulse response wiener filtering linear prediction and spectral estimation are known to lead to the solution of toeplitz systems for the case of one dimensional signals and to toeplitz block toeplitz systems for the case of two dimensional signals the authors investigate such systems for the case of l dimensional signals with l 2 and emphasize their block and persymmetrical nature such important characteristics allow the use of fast algorithms for signals of any dimension the case of three dimensional signals is treated in detail not only because it is of special interest for video applications but also because the reasoning used for this case can be straightforwardly applied to higher dimension signals

two dimensional linear prediction model based decorrelation method a unified feature extraction scheme the two dimensional 2 d linear prediction model based decorrelation method is presented by applying 2 d causal linear prediction model to decorrelate a textured image the very heavy computation load required when using a whitening operator to decorrelate the image or the significant information loss when using the gradient operator to approximately whiten the image is avoided the texture model based decorrelation provides three sets of features to perform texture classification the coefficients of the 2 d linear prediction the moments of error residuals and the autocorrelation values an optimum feature selection scheme using modified branch and bound method was introduced to reduce information redundancy after feature selection 100 classification accuracy was achieved for a 20 class texture problem experiments show that this feature extraction scheme is truly information lossless effective and fast

a general approach for the stability analysis of the time domain finite element method for electromagnetic simulations this paper presents a general approach for the stability analysis of the time domain finite element method tdfem for electromagnetic simulations derived from the discrete system analysis the approach determines the stability by analyzing the root locus map of a characteristic equation and evaluating the spectral radius of the finite element system matrix the approach is applicable to the tdfem simulation involving dispersive media and to various temporal discretization schemes such as the central difference forward difference backward difference and newmark methods it is shown that the stability of the tdfem is determined by the material property and by the temporal and spatial discretization schemes the proposed approach is applied to a variety of tdfem schemes which include 1 time domain finite element modeling of dispersive media 2 time domain finite element boundary integral method 3 higher order tdfem and 4 orthogonal tdfem numerical results demonstrate the validity of the proposed approach for stability analysis

the local dimensions of the bernoulli convolution associated with the golden number let x1 x2 be a sequence of i i d random variables each taking values of 1 and 1 with equal probability for 1 2 p xi for any x in the range of s let d 4 x lim log 4 x r x r logr be the local dimension of u at x whenever the limit exists we prove that log 2 and a log 6 log 2 log p s log p log p where 6 v51 2 are respectively the maximum and minimum values of the local dimensions if s 2 then p is the golden number and the approximate numerical values are ce 1 4404 and ce 0 9404

a 3 d discontinuous spectral element time domain method for maxwell s equations a discontinuous spectral element time domain method is proposed to analyze transient electromagnetic properties of general 3 d structures this method is advantageous in that its mass matrices are block diagonal due to the gauss lobatto legendre polynomials and it allows different orders of basis functions for each subdomain the riemann solver is employed in the boundary integral terms to communicate fields between adjacent subdomains perfectly matched layers are utilized to truncate the computational domain galerkin method is used for spatial discretization and a fourth order runge kutta scheme is employed for the time integration the validity of the proposed approach is demonstrated through several numerical examples of initial value problems and scattering problems

the effect of filtering on the pseudospectral solution of evolutionary partial differential equations abstract this paper examines the effect of filtering on the solution of time dependent partial differential equations by the pseudospectral method it is shown that if spatial discretisation is effected using the fourier pseudospectral method the computed solution will be an approximation to the solution of a modified differential equation the changes in dispersive and dissipative properties induced by the modification are examined and numerical results are presented which illustrate these changes for both linear and nonlinear equations numerical results are also presented which show the effect of filtering on chebyshev pseudospectral solutions of time dependent equations

stable spectral methods for conservation laws on triangles with unstructured grids this paper presents an asymptotically stable scheme for the spectral approximation of linear conservation laws defined on a triangle lagrange interpolation on a general two dimensional nodal set is employed and by imposing the boundary conditions weakly through a penalty term the scheme is proven stable in l 2 this result is established for a general unstructured grid in the triangle a special case for which the nodes along the edges of the triangle are chosen as the legendre gauss lobatto quadrature points is discussed in detail the eigenvalue spectrum of the approximation to the advective operator is computed and is shown to result in an o n 2 restriction on the time step when considering explicit time stepping c 1999 elsevier science s a all rights reserved

a stable penalty method for the compressible navier stokes equations iii multidimensional domain decomposition schemes this paper concluding the trilogy develops schemes for the stable solution of wave dominated unsteady problems in general three dimensional domains the schemes utilize a spectral approximation in each subdomain and asymptotic stability of the semidiscrete schemes is established the complex computational domains are constructed by using nonoverlapping quadrilaterals in the two dimensional case and hexahedrals in the three dimensional space to illustrate the ideas underlying the multidomain method a stable scheme for the solution of the three dimensional linear advection diffusion equation in general curvilinear coordinates is developed the analysis suggests a novel yet simple stable treatment of geometric singularities like edges and vertices the theoretical results are supported by a two dimensional implementation of the scheme the main part of the paper is devoted to the development of a spectral multidomain scheme for the compressible navier stokes equations on conservation form and a unified approach for dealing with the open boundaries and subdomain boundaries is presented well posedness and asymptotic stability of the semidiscrete scheme is established in a general curvilinear volume with special attention given to a hexahedral domain the treatment includes a stable procedure for dealing with boundary conditions at a solid wall the efficacy of the scheme for the compressible navier stokes equations is illustrated by obtaining solutions to subsonic and supersonic boundary layer flows with various types of boundary conditions the results are found to agree with the solution of the compressible boundary layer equations