incomplete hypercubes since a k dimensional hypercube has 2 sup k vertices these systems are restricted to having exactly 2 sup k computing nodes because system sizes must be a power of two there are large gaps in the sizes of systems that can be built with hypercubes routing and broadcast algorithms are presented for hypercubes that are missing certain of their nodes called incomplete hypercubes unlike hypercubes incomplete hypercubes can be used to interconnect systems with any number of processors the routing and broadcast algorithms for incomplete hypercubes are shown also to be simple and deadlock free

acoustical wave propagator technique for time domain analysis of dynamic stress in a step plate in this paper we introduce an explicit acoustical wave propagator technique to describe the time domain evolution of acoustical waves in two dimensional plates this technique uses a combined scheme with chebyshev polynomial expansion and fast fourier transformation for implementation of the operation of the acoustical wave propagator we also apply the acoustical wave propagator for studying dynamic stress in a step plate in time domain

one step finite difference time domain algorithm to solve the maxwell equations we present a one step algorithm to solve the time dependent maxwell equations for systems with spatially varying permittivity and permeability we compare the results of this algorithm with those obtained from the yee algorithm and from unconditionally stable algorithms we demonstrate that for a range of applications the one step algorithm may be orders of magnitude more efficient than multiple time step finite difference time domain algorithms we discuss both the virtues and limitations of this one step approach

hamiltonian connectivity of the wk recursive network with faulty nodes a graph g is said to be hamiltonian connected if there is a hamiltonian path between every two distinct nodes of g let f denote the set of faulty nodes of g then g is f node hamiltonian connected if g f is hamiltonian connected we use k d t to denote a wk recursive network of level t each of whose basic modules is a d node complete graph compared with other networks it is rather difficult to construct a hamiltonian path between two arbitrary nodes in a faulty wk recursive network in this paper we show that k d t is d 4 node hamiltonian connected since the connectivity of k d t is d 1 the result is optimal in the worst case

numerical treatment of two dimensional interfaces for acoustic and elastic waves we present a numerical method to take into account 2d arbitrary shaped interfaces in classical finite difference schemes on a uniform cartesian grid this work extends the explicit simplified interface method esim previously proposed in 1d j comput phys 168 2001 227 248 the physical problem under study concerns the linear hyperbolic systems of acoustics and elastodynamics with stationary interfaces our method maintains near the interfaces properties of the schemes in homogeneous medium such as the order of accuracy and the stability limit moreover it enforces the numerical solution to satisfy the exact interface conditions lastly it provides subcell geometrical features of the interface inside the meshing the esim can be coupled automatically with a wide class of numerical schemes lax wendroff flux limiter schemes etc for a negligible additional computational cost throughout the paper we focus on the challenging case of an interface between a fluid and an elastic solid in numerical experiments we provide comparisons between numerical solutions and original analytic solutions showing the efficiency of the method

construction and analysis of fourth order finite difference schemes for the acoustic wave equation in nonhomogeneous media in this article we construct and analyse a family of finite difference schemes for the acoustic wave equation with variable coefficients these schemes are fourth order accurate in space and time in the case of smooth media and are designed to remain stable and optimal for reflection transmission phenomena in the case of discontinuous coefficients together with a detailed mathematical study various numerical results are presented

the complementary operators method applied to acoustic finite difference time domain simulations the complementary operators method com has recently been introduced as a mesh truncation technique for open domain radiation problems in electromagnetics the com entails the construction of two solutions that employ absorbing boundary conditions abcs with complementary behavior i e the reflection coefficients associated with the two abcs are exactly opposite each other the average of these solutions then yields a new solution in which the errors caused by artificial reflections from the termination of grid are nearly eliminated in this work com is introduced for the finite difference time domain fdtd solution of acoustics problems the development of com is presented in terms of higdon s absorbing boundary operators but generalization to non higdon operators is straightforward the effectiveness of com in comparison to other absorbing boundary conditions is demonstrated with numerical experiments in two and three dimensions

the pseudospectral method comparisons with finite differences for the elastic wave equation the pseudospectral or fourier method has been used recently by several investigators for forward seismic modeling the method is introduced here in two different ways as a limit of finite differences of increasing orders and by trigonometric interpolation an argument based on spectral analysis of a model equation shows that the pseudospectral method for the accuracies and integration times typical of forward elastic seismic modeling may require in each space dimension as little as a quarter the number of grid points compared to a fourth order finite difference scheme and one sixteenth the number of points as a second order finite difference scheme for the total number of points in two dimensions these factors become 1 16 and 1 256 respectively in three dimensions they become 1 64 and 1 4 096 respectively in a series of test calculations on the two dimensional elastic wave equation only minor degradations are found in cases with variable coefficients and discontinuous interfaces

galois actions on blocks and classes of finite groups abstract we consider galois actions on blocks and conjugacy classes we extend some of the results valid in the case of complex conjugation we give some counterexamples where this extension is not possible

time domain calculation of acoustical wave propagation in discontinuous media using acoustical wave propagator with mapped pseudospectral method the acoustical wave propagator awp scheme involves an effective time domain calculation of sound propagation using the combination of chebyshev polynomial expansion and the fourier pseudospectral method the accuracy of this scheme degrades when the media has discontinuities due to the well known gibbs phenomenon in this paper several issues concerning awp are addressed including an analysis of the effect of gibbs phenomenon on the accuracy a mapped pseudospectral method is proposed wherein the grid points are redistributed with the emphasis across the media discontinuities by a pre determined smooth mapping curve then the spatial derivatives are calculated through a modified fourier pseudospectral method using this method the influence of the gibbs phenomenon is effectively alleviated while the computational efficiency of awp is still maintained the superiority of this improved awp scheme is illustrated by three one dimensional 1 d numerical examples

a k space method for coupled first order acoustic propagation equations a k space method for large scale simulation of ultrasonic pulse propagation is presented the present method which solves the coupled first order differential equations for wave propagation in inhomogeneous media is derived in a simple form analogous to previous finite difference methods with staggered spatial and temporal grids like k space methods based on second order wave equations the present method is exact for homogeneous media unconditionally stable for slow c r c0 media and highly accurate for general weakly scattering media in addition unlike previous k space methods the form of the method allows straightforward inclusion of relaxation absorption and perfectly matched layer pml nonreflecting boundary conditions numerical examples illustrate the capabilities of the present k space method for weakly inhomogeneous media accurate results are obtained using coarser temporal and spatial steps than possible with comparable finite difference and pseudospectral methods the low dispers

acoustical wave propagator in this paper an explicit acoustical wave propagator awp is introduced to described the time domain evolution of acoustical waves to implement its operation on an initial state of wave motion the acoustical wave propagator is approximated as a chebyshev polynomial expansion which converges to machine accuracy the spatial gradient in each polynomial term is evaluated by a fourier transformation scheme analysis and numerical examples demonstrated that this chebyshev fourier scheme is highly accurate and computational effective in predicting time domain acoustical wave propagation and scattering

spectral methods in time for hyperbolic equations a pseudospectral numerical scheme for solving linear periodic hyperbolic problems is described it has infinite accuracy both in time and in space the high accuracy in time is achieved without increasing the computational work and memory space which is needed for a regular one step explicit scheme the algorithm is shown to be optimal in the sense that among all the explicit algorithms of a certain class it requires the least amount of work to achieve a certain given resolution the class of algorithms referred to consists of all explicit schemes which may be represented as a polynomial in the spatial operator

solving the maxwell equations by the chebyshev method a one step finite difference time domain algorithm we present a one step algorithm that solves the maxwell equations for systems with spatially varying permittivity and permeability by the chebyshev method we demonstrate that this algorithm may be orders of magnitude more efficient than current finite difference time domain fdtd algorithms

super spanning connectivity on wk recursive networks abstract the wk recursive network has received much attention due to its many favorable properties such as small diameter large connectivity and high degree of scalability and expandability in this paper we consider the super spanning connectivity properties of the wk recursive network we use k d t to denote the wk recursive network of level t each of which basic modules is a d vertex complete graph where d 1 and t 1 we prove that for any two distinct vertices and there exist m node disjoint paths whose union covers all the vertices of k d t for d 4 t 1 and 1 m d 1 since the connectivity of k d t is d 1 the result is optimal in the worst case

an efficient high order algorithm for acoustic scattering from penetrable thin structures in three dimensions this paper presents a high order accelerated algorithm for the solution of the integral equation formulation of volumetric scattering problems the scheme is particularly well suited to the analysis of thin structures as they arise in certain applications e g material coatings in addition it is also designed to be used in conjunction with existing low order fft based codes to upgrade their order of accuracy through a suitable treatment of material interfaces the high order convergence of the new procedure is attained through a combination of changes of parametric variables to resolve the singularities of the green function and partitions of unity to allow for a simple implementation of spectrally accurate quadratures away from singular points accelerated evaluations of the interaction between degrees of freedom on the other hand are accomplished by incorporating two face equivalent source approximations on cartesian grids a detailed account of the main algorithmic components of the scheme are presented together with a brief review of the corresponding error and performance analyses which are exemplified with a variety of numerical results

on the gibbs phenomenon and its resolution the nonuniform convergence of the fourier series for discontinuous functions and in particular the oscillatory behavior of the finite sum was already analyzed by wilbraham in 1848 this was later named the gibbs phenomenon this article is a review of the gibbs phenomenon from a different perspective the gibbs phenomenon as we view it deals with the issue of recovering point values of a function from its expansion coefficients alternatively it can be viewed as the possibility of the recovery of local information from global information the main theme here is not the structure of the gibbs oscillations but the understanding and resolution of the phenomenon in a general setting the purpose of this article is to review the gibbs phenomenon and to show that the knowledge of the expansion coefficients is sufficient for obtaining the point values of a piecewise smooth function with the same order of accuracy as in the smooth case this is done by using the finite expansion series to construct a different rapidly convergent approximation

a comparison of different propagation schemes for the time dependent schro dinger equation abstract a comparison of three widely used time propagation algorithms for the time dependent schrodinger equation is described a typical evolution problem is chosen to demonstrate the efficiency and accuracy of the various methods on a numerical grid using a pseudo spectral fft spatial representation for scattering and bound state evolution the methods used second order differencing split operator propagation chebyshev polynomial expansion are discussed in terms of their applicability to various classes of dynamic problems a new method is introduced which is based upon a low order lanczos technique this method appears to offer an accurate and flexible alternative to the existing techniques overall the chebyshev method is recommended for time independent potentials and the lanczos method for time dependent potentials

dynamic stress concentration in a ribbed plate using the acoustical wave propagator technique this paper presents an explicit acoustical wave propagator technique to investigate the flexural wave scattering and dynamic stress concentration in a ribbed plate based on mindlin plate theory a scheme combining chebyshev polynomial expansion and fast fourier transformation is introduced to implement the operation of the acoustical wave propagator the exact analytical solutions are also presented to demonstrate the validity of the present technique the wave propagation patterns are used to investigate the effect of rib on the flexural wave scattering and distribution of dynamic stress concentration dynamic stress concentration factors around the discontinuities are examined in detail

flexural wave scattering and dynamic stress concentration in a heterogeneous plate with multiple cylindrical patches by acoustical wave propagator technique this paper presents the acoustical wave propagator technique to describe the flexural wave propagation and scattering in an elastic plate with multiple cylindrical patches the wave propagation patterns in the presence of these patches are used to investigate dynamic stress concentration an improved combined scheme of chebyshev polynomial expansion and fast fourier transformation compared with the exact analytical solutions is found to be effective in predicting the distribution of dynamic stress concentration the dynamic stress concentration factors around the patches in the time domain are also discussed in detail

the regular fourier matrices and nonuniform fast fourier transforms for any triple of positive integers m n q the matrix f m n q called the m n q regular fourier matrix is defined the regular fourier matrices f m n q are then applied to set up new algorithms for nonuniform fast fourier transforms numerical results show that the accuracies obtained by our algorithms are much better than previously reported results with the same computation complexity the algorithms require o n cdot log 2n arithmetic operations where n is the number of data points

mappings and accuracy for chebyshev pseudo spectral approximations abstract the effect of mappings on the approximation by chebyshev collocation of functions which exhibit localized regions of rapid variation is studied a general strategy is introduced whereby mappings are adaptively constructed which map specified classes of rapidly varying functions into low order polynomials a particular family of mappings constructed in this way is tested on a variety of rapidly varying functions similar to those occurring in applications it is shown that the mapped function can be approximated much more accurately by chebyshev polynomial approximations than the original function the effect on the approximation of introducing subdomains is also studied the accuracy of the pseudo spectral approximation is very sensitive to the location of the interface although this sensitivity is reduced when mappings are employed within the subdomains

acoustical wave propagator for time domain flexural waves in thin plates in this paper an explicit acoustical wave propagator technique is introduced to describe the time domain evolution of acoustical waves in two dimensional plates a combined scheme with chebyshev polynomial expansion and fast fourier transformation is used to implement the operation of the acoustical wave propagator through this operation the initial wave packet at t 0 is mapped into the wave packet at any instant t 0 by comparison of the results of the exact analytical solution and the euler numerical method we find that this new chebyshev fourier scheme is highly accurate and computationally effective in predicting the acoustical wave propagation in thin plates this method offers an opportunity for future study of dynamic stress concentration and time domain energy flow in coupled structures

embedding graphs onto the supercube in this paper we consider the supercube a new interconnection network derived from the hypercube the supercube introduced by a sen 1989 has the same diameter and connectivity as a hypercube but can be realized for any number of nodes not only powers of 2 we study the supercube s ability to execute parallel programs using graph embedding techniques we show that complete binary trees and bidimensional meshes with a side length power of 2 are spanning subgraphs of the supercube we then prove that the supercube is hamiltonian and when the number of nodes is not a power of 2 it contains all cycles of length greater than 3 as subgraphs

time compact difference methods for wave propagation in discontinuous media in b gustafsson and e mossberg siam j sci comput 26 2004 pp 259 271 a fourth order one step method was constructed for the solution of wave propagation problems the method is based on the first order system form of the pde and uses a staggered grid both in space and time the method was also applied with good results to a problem with discontinuous coefficients without using any special procedure across the discontinuity in this paper we will analyze a model problem from acoustics and demonstrate the theoretical foundation for this behavior furthermore we shall present more detailed numerical experiments which confirm the theoretical results

on the gibbs phenomenon v recovering exponential accuracy from collocation point values of a piecewise analytic function this paper presents a method to recover exponential accuracy at all points including at the discontinuities themselves from the knowledge of an approximation to the interpolation polynomial or trigonometrical polynomial we show that if we are given the collocation point values or a highly accurate approximation at the gauss or gauss lobatto points we can reconstruct an uniform exponentially convergent approximation to the function f x in any sub interval of analyticity the proof covers the cases of fourier chebyshev legendre and more general gegenbauer collocation methods a numerical example is also provided

on vertex pancyclicity and edge pancyclicity of the wk recursive network abstract in this paper we study the pancyclic properties of the wk recursive networks we show that a wk recursive network with amplitude w and level l is vertex pancyclic for w 6 that is each vertex on them resides in cycles of all lengths ranging from 3 to n where n is the size of the interconnection network on the other hand we also investigate the m edge pancyclicity of the wk recursive network we show that the wk recursive network is strictly 3 2 l 1 edge pancyclic for w 7 and l 1 that is each edge on them resides in cycles of all lengths ranging from 3 2 l 1 to n and the value 3 2 l 1 reaches the lower bound of the problem

solution of the schrodinger equation by a spectral method abstract a new computational method for determining the eigenvalues and eigenfunctions of the schrodinger equation is described conventional methods for solving this problem rely on diagonalization of a hamiltonian matrix or iterative numerical solutions of a time independent wave equation the new method in contrast is based on the spectral properties of solutions to the time dependent schrodinger equation the method requires the computation of a correlation function r 0 r t from a numerical solution r t fourier analysis of this correlation function reveals a set of resonant peaks that correspond to the stationary states of the system analysis of the location of these peaks reveals the eigenvalues with high accuracy additional fourier transforms of r t with respect to time generate the eigenfunctions the effectiveness of the method is demonstrated for a one dimensional asymmetric double well potential and for the two dimensional henon heiles potential

a domain decomposition method for the acoustic wave equation with discontinuous coefficients and grid change a domain decomposition technique is proposed for the computation of the acoustic wave equation in which the bulk modulus and density fields are allowed to be discontinuous at the interfaces inside each subdomain the method presented coincides with the second order finite difference schemes traditionally used in geophysical modeling however the possibility of assigning to each subdomain its own space step makes numerical simulations much less expensive another interest of the method lies in the fact that its hybrid variational formulation naturally leads to exact equations for gridpoints on the interfaces transposing babuska brezzi s formalism on mixed and hybrid finite elements provides a suitable functional framework for this domain decomposition formulation and shows that the inf sup condition remains the basic requirement for convergence to occur

an improved acoustical wave propagator method and its application to a duct structure the pseudospectral time domain method has long been used to describe the acoustical wave propagation however due to the limitation and difficulties of the fast fourier transform fft in dealing with nonperiodic problems the dispersion error is inevitable and the numerical accuracy greatly decreases after the waves arrive at the boundary to resolve this problem the lagrange chebyshev interpolation polynomials were used to replace the previous fft which however brings in an additional restriction on the time step in this paper a mapped chebyshev method is introduced providing the dual benefit of preserving the spectral accuracy and overcoming the time step restriction at the same time three main issues are addressed to assess the proposed technique a spatial derivatives in the system operator and the boundary treatment b parameter selections and c the maximum time step in the temporal operator furthermore a numerical example involving the time domain evolution of wave propagation in

complete path embeddings in crossed cubes crossed cubes are popular variants of hypercubes in this paper we study path embeddings between any two distinct nodes in crossed cubes we prove two important results in the n dimensional crossed cube a for any two nodes all paths whose lengths are greater than or equal to the distance between the two nodes plus 2 can be embedded between the two nodes with dilation 1 b for any two integers n 2 and l with 1

acoustical wave propagator technique for time domain reflection and transmission of flexural wave packets in one dimensional stepped beams this paper applies the acoustical wave propagator technique to wave packet propagation in a one dimensional stepped beam the time domain analytical solutions of this structure subjected to an initial value problem with the specific gaussian waveform were derived and compared with the predicted results obtained by the acoustical wave propagator technique it is shown that this technique is efficient and accurate in predicting wave propagation in one dimensional structure with thickness discontinuity the effects of near field waves on reflection and transmission coefficients and transmission efficiencies are also studied in detail furthermore an experiment was carried out to investigate the reflection and transmission of flexural waves in a stepped beam structure

character heights and p length in blocks of p solvable groups abstract we give the lower bounds 2 l and 2 l 2 2 l 4 for the number of irreducible characters of height zero and positive height respectively in a p block of a p solvable group where l is the p length of an associated p solvable group we also prove some results on extensions of linear characters in p subgroups of p solvable groups

fast fourier transforms for nonequispaced data a group of algorithms is presented generalizing the fast fourier transform to the case of noninteger frequencies and nonequispaced nodes on the interval pi pi the schemes of this paper are based on a combination of certain analytical considerations with the classical fast fourier transform and generalize both the forward and backward ffts each of the algorithms requires o n cdot log n n cdot log 1 varepsilon arithmetic operations where varepsilon is the precision of computations and n is the number of nodes the efficiency of the approach is illustrated by several numerical examples

time domain modeling of acoustic propagation with acoustic wave propagator and absorbing boundary conditions the acoustic wave propagator awp is the application of the time evolution operator on the acoustic wave equation for stationary systems in a polynomial expansion of chebychev polynomials it allows to increase the time step by more than one order of magnitude compared to finite difference time domain fdtd codes in contrast to other implementations of the awp the spatial differentiation is carried out with finite difference techniques because this allows the use of the perfectly matched layer formulation as absorbing boundary conditions the formulation includes the direct implementation of acoustic sources with sinusoidal time evolution other sources can be synthesized by their fourier components for the calculation of large areas the explicit formulation of a large system matrix can be avoided by calculating the propagation equations for each time step at row and column level repeatedly which reduces memory requirements notably this procedure and the suitability of the finite difference approach

blocks of defect zero and products of elements of orderp abstract suppose thatgis a finite group and thatfis a field of characteristicp 0 which is a splitting field for all subgroups ofg lete0be the sum of the block idempotents of defect zero infg and let be the set of solutions togp 1 ing we show thate0 2 whenpis odd ande0 3 whenp 2 in the latter case 2 r whereris the set of real elements of 2 defect zero soe0 r r 2 we also show thate0 4 4 2 whenp 2 where 4is the set of solutions tog4 1 these results give us various criteria for the existence ofp blocks of defect zero

an eigenfunction expansion method to efficiently evaluate spatial derivatives for media with discontinuous properties pseudo spectral methods are often used as an alternative to the finite difference time domain fdtd method to model wave propagation in heterogeneous moving media the fdtd method is robust and accurate but is numerically expensive pseudo spectral methods make use of the wavelike nature of the solution to obtain more efficient time domain algorithms the most straightforward of the pseudo spectral methods is the fourier method in which a spatial fourier transform is used to evaluate the spatial derivatives in the wave equation whereas this method is accurate for a weakly heterogeneous moving medium it degenerates for media with discontinuous properties the eigenfunction expansion method presented here is a way to accurately and efficiently evaluate spatial derivatives in media with interfaces as in the fourier method transforms may be calculated using fft s and spatial sampling is limited only by the nyquist condition the performance of the method is shown in a time domain implementation for media

real 2 regular classes and 2 blocks abstract suppose that g is a finite group we show that every 2 block of g has a defect class which is real as a partial converse we show that if g has a real 2 regular class with defect group d and if n d d has no dihedral subgroup of order 8 then g has a real 2 block with defect group d more generally we show that every 2 block of g which is weakly regular relative to some normal subgroup n has a defect class which is real and contained in n we give several applications of these results and also investigate some consequences of the existence of non real 2 blocks

the k space formulation of the scattering problem in the time domain an improved single propagator formulation the storage allocation requirement and solution speed of the k space formulation of the scattering problem in the time domain developed by this author n bojarski j acoust soc am 72 570 584 1982 were improved by a factor of 2 and 4 respectively by the replacement of the earlier two temporal propagators by a single more accurate propagator and the utilization of the special case real to complex fft algorithm it is shown that for problems of the size of about one million spatially discretized cells this method is about five times slower than an ideal solution and requires about five times as much in core storage allocation as an ideal solution it is shown that for a modern array processor this solution is i o bound it is pointed out that this method is ideally suited for parallel array processor implementation resulting in even greater speed

defect groups conjugacy classes and the robinson map abstract we prove a generalization of the brauer nesbitt theorem we study the robinson map and relations between p regular conjugacy classes and block idempotents with common defect group we characterize defect classes and those class sums whose images under the brauer map are not nilpotent