numerical calculation of grounding system in low frequency domain based on the boundary element method a new mathematical model for accurately computing currents flowing along the high voltage ac substation s grounding system and nearby floating metallic conductors buried in the multilayer earth model has been developed in this paper which is a hybrid of the galerkin type boundary element method bem and the conventional nodal analysis method only the propagation effect of electromagnetic waves within the substation s limited area has been neglected in this model the quasi static complex image method and the closed form of green s function are introduced into this model to accelerate the mutual impedance and induction coefficients calculation the model is then implemented in a computer program which can be used to calculate current distribution of any configuration of the grounding system with or without floating metallic conductors copyright 2007 john wiley sons ltd

an optimal adaptive wavelet method without coarsening of the iterands in this paper an adaptive wavelet method for solving linear operator equations is constructed that is a modification of the method from math comp 70 2001 pp 27 75 by cohen dahmen and devore in the sense that there is no recurrent coarsening of the iterands despite this it will be shown that the method has optimal computational complexity numerical results for a simple model problem indicate that the new method is more efficient than an existing alternative adaptive wavelet method

computation of differential operators in wavelet coordinates in found comput math 2 2002 pp 203 245 cohen dahmen and devore proposed an adaptive wavelet algorithm for solving general operator equations assuming that the operator defines a boundedly invertible mapping between a hilbert space and its dual and that a riesz basis of wavelet type for this hilbert space is available the operator equation is transformed into an equivalent well posed infinite matrix vector system this system is solved by an iterative method where each application of the infinite stiffness matrix is replaced by an adaptive approximation it was shown that if the errors of the best linear combinations from the wavelet basis with n terms are o n s for some s 0 which is determined by the besov regularity of the solution and the order of the wavelet basis then approximations yielded by the adaptive method with n terms also have errors of o n s moreover their computation takes only 0 n operations provided s s assuming that each entry of the stiffness matrix is exactly available at unit cost generally these entries have to be approximated using numerical quadrature in this paper restricting ourselves to differential operators we develop a numerical integration scheme that computes these entries giving an additional error that is consistent with the approximation error whereas in each column the average computational cost per entry is 0 1 as a consequence we can conclude that the adaptive wavelet algorithm has optimal computational complexity

multiscale convergence and reiterated homogenisation this paper generalises the notion of two scale convergence to the case of multiple separated scales of periodic oscillations it allows us to introduce a multi scale convergence method for the reiterated homogenisation of partial differential equations with oscillating coefficients this new method is applied to a model problem with a finite or infinite number of microscopic scales namely the homogenisation of the heat equation in a composite material finally it is generalised to handle the homogenisation of the neumann problem in a perforated domain

measurement of regional environmental noise by use of a pc based system an application to the noise near airport g marconi in bologna abstract measurements of aircraft noise were made at the airport g marconi in bologna by using a measurement system for regional environmental noise the system is based on the model of the human auditory brain system which is based on the interplay of autocorrelators and an interaural cross correlator acting on the pressure signals arriving at the ear entrances and takes into account the specialization of left and right human cerebral hemispheres see reference 8 measurements were taken through dual microphones at ear entrances of a dummy head the aircraft noise was characterized with the following physical factors calculated from the autocorrelation function acf and interaural cross correlation function iacf for binaural signals from the acf analysis 1 energy represented at the origin of delay 0 2 effective duration of the envelope of the normalized acf e 3 the delay time of the first peak 1 and 4 its amplitude 1were extracted from the iacf analysis 5 iacc 6 interaural delay time at which the iacc is defined iacc and 7 width of the iacf at the iacc wiaccwere extracted the factor 0 can be represented as the geometrical mean of the energies at both ears a noise source may be identified by these factors as timbre

acoustical properties of aircraft noise measured by temporal and spatial factors abstract acoustical properties of aircraft noise were investigated by means of temporal and spatial factors in sound fields based on the model of auditory brain system see reference 10 the model consists of the autocorrelation and crosscorrelation mechanisms for sound signals arriving at two ears and the specialization of human cerebral hemisphere there are four temporal factors extracted from the autocorrelation function acf 1 sound energy 0 2 effective duration of acf e 3 delay time of the first peak 1 and 4 its amplitude 1 from the interaural crosscorrelation function iacf three spatial factors are extracted as 1 magnitude of the interaural crosscorrelation iacc 2 interaural delay time at iacc iacc and 3 width of the maximum peak of the iacf wiacc it is found that the acoustical properties are well represented by the factors extracted from the acf and the iacf

numerical simulation of substation grounding grids buried in both horizontal and vertical multilayer earth model in the simulation of quasi static electromagnetic fields produced by a point source located in both horizontal and vertical multilayer media the conventional image method requires an infinite number of images to get an accurate solution while the method of quasi static complex images needs only a few ones based on the method of quasi static complex images the closed form of green s function of a point source in both horizontal and vertical multilayer earth model is derived through matrix pencil mp approach the fast convergent galerkin s type of boundary element method bem is taken to simulate and analyse a grounding system including floating electrode with any complicated structure which can be located anywhere in horizontal or vertical multilayer earth model copyright 2006 john wiley sons ltd

composite wavelet bases for operator equations this paper is concerned with the construction of biorthogonal wavelet bases defined on a union of parametric images of the unit n cube these bases are to satisfy certain requirements imposed by applications to a class of operator equations acting on such domains this covers also elliptic boundary value problems although this study is primarily motivated by our previous analysis of wavelet methods for pseudo differential equations with special emphasis on boundary integral equations in this case it is natural to model the boundary surface as a union of parametric images of the unit cube it will be shown how to construct wavelet bases on the surface which are composed of wavelet bases defined on each surface patch here the relevant properties are the validity of norm equivalences in certain ranges of sobolev scales as well as appropriate moment conditions

a boundary element numerical approach for grounding grid computation abstract analysis and design of substation earthing involves computing the equivalent resistance of grounding systems as well as distribution of potentials on the earth surface due to fault currents 1 2 while very crude approximations were available in the 1960s several methods have been proposed in the last two decades most of them on the basis of intuitive ideas such as superposition of punctual current sources and error averaging 3 4 although these techniques represented a significant improvement in the area of earthing analysis a number of problems have been reported namely large computational requirements unrealistic results when segmentation of conductors is increased and uncertainty in the margin of error 4 a boundary element approach for the numerical computation of substation grounding systems is presented in this paper several widespread intuitive methods such as the average potential method can be identified in this general formulation as the result of suitable assumptions introduced in the bem formulation to reduce computational cost for specific choices of the test and trial functions on the other hand this general approach allows the use of linear and parabolic leakage current elements to increase accuracy efforts have been made particularly in getting a drastic reduction in computing time by means of completely new analytical integration techniques while semi iterative methods have proven to be specially efficient for solving the involved system of linear equations this bem formulation has been implemented in a specific computer aided design system for grounding analysis developed within the last years the feasibility of this approach is finally demonstrated by means of its application to two real problems

numerical analysis of earthing grids buried in horizontally stratified multilayer earth this paper describes a new numerical procedure for analysing earthing grids buried in horizontally stratified multilayer earth the procedure is very efficient and general the total number of layers and the total number of metallically disconnected earthing grids are completely arbitrary a single earthing grid can be positioned in several layers the procedure is based on an integral equation formulation earthing grid conductors are subdivided into segments and the average potential method is used efficiency and generality of the computation procedure are based on the successful application of numerical approximations of two kernel functions of the integral expression for the potential distribution within a single layer which is caused by a point current source each kernel function of the observed layer is approximated using a linear combination of 15 exponential functions extension from the point source to a segment of the earthing grid conductor is done by integrating the potential contribution due to a line of point current sources along the segment axis this computational procedure gives highly accurate results in a short execution time 1998 john wiley sons ltd

an optimal adaptive wavelet method for nonsymmetric and indefinite elliptic problems in this paper we modify the adaptive wavelet algorithm from gantumur et al an optimal adaptive wavelet method without coarsening of the iterands technical report 1325 department of mathematics utrecht university march 2005 math comp to appear so that it applies directly i e without forming the normal equation not only to self adjoint elliptic operators but also to operators of the form l a b where a is self adjoint elliptic and b is compact assuming that the resulting operator equation is well posed we show that the algorithm has optimal computational complexity

element by element construction of wavelets satisfying stability and moment conditions in this paper we construct a class of locally supported wavelet bases for c0 lagrange finite element spaces on possibly nonuniform meshes on n dimensional domains or manifolds the wavelet bases are stable in the sobolev spaces mathcal h s for s frac 3 2 s leq 1 on lipschitz manifolds and the wavelets can in principle be arranged to have any desired order of vanishing moments as a consequence these bases can be used e g for constructing an optimal solver of discretized mathcal h s elliptic problems for s in above ranges the construction of the wavelets consists of two parts an implicit part involves some computations on a reference element which for each type of finite element space have to be performed only once in addition there is an explicit part which takes care of the necessary adaptations of the wavelets to the actual mesh the only condition we need for this construction to work is that the refinements of initial elements are uniform we will show that the wavelet bases can be implemented efficiently

loudness of subcritical sounds as a function of bandwidth center frequency and level level differences at equal loudness between band pass noise and pure tones with a frequency equal to the center frequency of the noise were measured in normal hearing listeners using a loudness matching procedure the center frequencies were 750 1500 and 3000 hz and noise bandwidths from 5 to 1620 hz were used the level of the reference pure tone was 30 50 or 70 db for all center frequencies and reference levels the level at equal loudness was close to 0 db for the narrowest bandwidth increased with bandwidth for bandwidths smaller than the critical bandwidth and decreased for bandwidths larger than the critical bandwidth for bandwidths considerably larger than the critical bandwidth the level difference was negative the maximum positive level difference was measured for a bandwidth close to the critical bandwidth this maximum level difference decreased with increasing reference level a similar effect was found when the level differences were derived from data of an additional categorical loudness scaling experiment the results indicate that the decrease of loudness at equal level with increasing subcritical bandwidth is a common property of the auditory system which is not taken into account in current loudness models

adaptive wavelet algorithms for elliptic pde s on product domains with standard isotropic approximation by piecewise polynomials of fixed order in a domain d subset of r d the convergence rate in terms of the number n of degrees of freedom is inversely proportional to the space dimension d this so called curse of dimensionality can be circumvented by applying sparse tensor product approximation when certain high order mixed derivatives of the approximated function happen to be bounded in l 2 it was shown by nitsche 2006 that this regularity constraint can be dramatically reduced by considering best n term approximation from tensor product wavelet bases when the function is the solution of some well posed operator equation dimension independent approximation rates can be practically realized in linear complexity by adaptive wavelet algorithms assuming that the infinite stiffness matrix of the operator with respect to such a basis is highly compressible applying piecewise smooth wavelets we verify this compressibility for general non separable elliptic pdes in tensor domains applications of the general theory developed include adaptive galerkin discretizations of multiple scale homogenization problems and of anisotropic equations which are robust i e independent of the scale parameters resp of the size of the anisotropy

wavelets with patchwise cancellation properties we construct wavelets on general n dimensional domains or manifolds via a domain decomposition technique resulting in so called composite wavelets with this construction wavelets with supports that extend to more than one patch are only continuous over the patch interfaces normally this limited smoothness restricts the possibility for matrix compression and with that the application of these wavelets in adaptive methods for solving operator equations by modifying the scaling functions on the interval and with that on the n cube that serves as parameter domain we obtain composite wavelets that have patchwise cancellation properties of any required order meaning that the restriction of any wavelet to each patch is again a wavelet this is also true when the wavelets are required to satisfy zeroth order homogeneous dirichlet boundary conditions on part of the boundary as a result compression estimates now depend only on the patchwise smoothness of the wavelets that one may choose also taking stability into account our composite wavelets have all the properties for the application to the adaptive solution of well posed operator equations of orders 2t for t 3 2

pitch strength of iterated rippled noise two versions of a cascade add attenuate and delay circuit were used to generate iterated rippled noise irn stimuli irn stimuli produce a repetition pitch whose pitch strength relative to the noise percept can be varied by changing the type of circuit the attenuation or the number of iterations in the circuit listeners were asked to use pitch strength to discriminate between various pairs of irn stimuli which differed in the type of network used to generate the sounds the number of iterations and the attenuation in the network a description based on an exponential function of the first peak of the autocorrelation function of irn stimuli is consistent with the results the discrimination data were well fit by a function based on the difference in the exponential functions of the first peak of the autocorrelation functions a magnitude estimation experiment indicated that pitch strength was an exponential function of the height of the first peak in the autocorrelation function these results suggest that the strength of the pitch of irn stimuli is based on temporal processing as might be revealed by autocorrelation

loudness in relation to iterated rippled noise abstract this study examined the loudness of iterated rippled noises irns with different number of iterations under conditions of equal sound pressure the scale values of loudness were obtained using a paired comparison method the results showed that the loudness of irns was not constant even though the sound pressure level was equivalent the loudness of irns increased with increasing iteration number this indicated that repetitive components of sounds might affect their loudness

loudness of sharply 2068 db octave filtered noises in relation to the factors extracted from the autocorrelation function this study examines the loudness of bandpass noises with center frequencies of 250 500 and 1000hz while changing the autocorrelation function acf the bandwidth of the source signal was altered with a 2068 db octave sharp filter to control the acf of the source signal the scale values of loudness were obtained using a paired comparison method it is shown that the loudness of the bandpass noises inside the critical band is not constant the loudness of the pure tone is greater than that of sharply filtered noises the loudness of the bandpass noises increases with increasing effective duration of the acf e of the source signal

diagnostic system based on the human auditory brain model for measuring environmental noise an application to railway noise abstract measurements of railway noise were conducted by use of a diagnostic system of regional environmental noise the system is based on the model of the human auditory brain system the model consists of the interplay of autocorrelators and an interaural crosscorrelator acting on the pressure signals arriving at the ear entrances and takes into account the specialization of left and right human cerebral hemispheres different kinds of railway noise were measured through binaural microphones of a dummy head to characterize the railway noise physical factors extracted from the autocorrelation functions acf and interaural crosscorrelation function iacf of binaural signals were used the factors extracted from acf were 1 energy represented at the origin of the delay 0 2 effective duration of the envelope of the normalized acf e 3 the delay time of the first peak 1 and 4 its amplitude o 1 the factors extracted from iacf were 5 iacc 6 interaural delay time at which the iacc is defined iacc and 7 width of the iacf at the iacc w iacc the factor 0 can be represented as a geometrical mean of energies at both ears as listening level ll

multiresolution weighted norm equivalences and applications we establish multiresolution norm equivalences in weighted spaces l2w 0 1 with possibly singular weight functions w x 0 in 0 1 our analysis exploits the locality of the biorthogonal wavelet basis and its dual basis functions the discrete norms are sums of wavelet coefficients which are weighted with respect to the collocated weight function w x within each scale since norm equivalences for sobolev norms are by now well known our result can also be applied to weighted sobolev norms we apply our theory to the problem of preconditioning p version fem and wavelet discretizations of degenerate elliptic and parabolic problems from finance

adaptive wavelet methods for elliptic operator equations convergence rates this paper is concerned with the construction and analysis of wavelet based adaptive algorithms for the numerical solution of elliptic equations these algorithms approximate the solution u of the equation by a linear combination of n wavelets therefore a benchmark for their performance is provided by the rate of best approximation to u by an arbitrary linear combination of n wavelets so called n term approximation which would be obtained by keeping the n largest wavelet coefficients of the real solution which of course is unknown the main result of the paper is the construction of an adaptive scheme which produces an approximation to u with error o n s in the energy norm whenever such a rate is possible by n term approximation the range of s 0 for which this holds is only limited by the approximation properties of the wavelets together with their ability to compress the elliptic operator moreover it is shown that the number of arithmetic operations needed to compute the approximate solution stays proportional to n the adaptive algorithm applies to a wide class of elliptic problems and wavelet bases the analysis in this paper puts forward new techniques for treating elliptic problems as well as the linear systems of equations that arise from the wavelet discretization

composite wavelet bases with extended stability and cancellation properties the efficient solution of operator equations using wavelets requires that they generate a riesz basis for the underlying sobolev space and that they have cancellation properties of a sufficiently high order suitable biorthogonal wavelets were constructed on reference domains as the n cube via a domain decomposition approach these bases have been used as building blocks to construct biorthogonal wavelets on general domains or manifolds where in order to end up with local wavelets biorthogonality was realized with respect to a modified l 2 scalar product the use of this modified scalar product restricts the application of these so called composite wavelets to problems of orders strictly larger than 1 moreover those wavelets with supports that extend to more than one patch generally have no cancellation properties in this paper we construct local composite wavelets that are close to being biorthogonal with respect to the standard l 2 scalar product as a consequence they generate riesz bases for the sobolev spaces h s for the full range of s allowed by the continuous gluing of functions over the patch interfaces the properties of the primal and dual approximation spaces on the reference domain and in the manifold case by the regularity of the manifold moreover all these wavelets have cancellation properties of the full order induced by the approximation properties of the dual spaces on the reference domain we illustrate our findings by a concrete realization of wavelets on a perturbed sphere