a new rigorous expansion for the velocity potential of a circular piston source in the case of boundary value problems such as the sound scattering from a sphere placed in the nearfield of a plane piston source it is sometimes essential to express the velocity potentials in terms of the orthogonal expansion it is demonstrated in the present work that the rayleigh surface integral giving the velocity potential for a plane piston source surrounded by an infinite rigid flange reduces to a rigorous expansion of the simplest form for a circular piston as series of spherical surface harmonics the resulting equation is valid for any field points even on the piston surface sample calculations made with a microcomputer are presented with three dimensional and contour plots

optimal design of groundwater remediation systems using fuzzy set theory 1 in this study we use fuzzy sets to describe uncertainty in aquifer parameters and demonstrate the use of this information in optimal design of pump and treat systems on the basis of uncertainty in aquifer parameters two optimization models are formulated where pumping rates are represented as either deterministic or fuzzy decision variables both models with fuzzy constants and fuzzy variables are then transformed into computationally efficient algorithms through the application of fuzzy set theory the resulting models are solved by optimization algorithms such as golden section search genetic algorithm ga and direct comparison methods several examples are given to demonstrate the effectiveness of the models and algorithms presented in this study the numerical results which are also compared with the results obtained from probabilistic analysis show that the optimal solutions obtained from both models provide flexible and reliable pump and treat strategies and may increase the effectiveness of the remediation system under uncertainty

multirate digital signal processing algorithm to calculate complex acoustic pressure fields an efficient algorithm to compute complex magnitude and phase acoustic pressure field data that uses a multirate digital processing architecture is presented the algorithm is based on the discretization of the velocity potential function sampled at a rate that varies as a function of field point location and transducer geometry the algorithm can be used to determine accurate magnitude and phase information at any field point location and for any transducer geometry with a closed form velocity potential function including planar pistons spherically focused pistons and planar annular array transducers e g the nondiffracting or j0 bessel transducer numerical simulations based on this algorithm are presented together with exact field calculations wherever possible in order to make absolute error comparisons additionally results based on a standard gaussian quadrature integration scheme are presented in order to compare computational speed and accuracy in the near field results indicate improv

toward a universal adaptive finite element strategy part 3 design of meshes abstract in this third paper in our series the issue of designing h p meshes which are optimal in some sense is addressed criteria for h p meshes are derived which are based on the idea of minimizing the estimated error over a mesh with a fixed number of degrees of freedom an optimization algorithm is developed based on these criteria and is applied to several model one dimensional and two dimensional elliptic boundary value problems numerical results indicate that the approach can lead to exponential rates of convergence

modal impulse response and wave vector time domain methods to evaluate transient radiation from axisymmetric planar radiators the modal impulse response method and the wave vector time domain method are two of the existing methods to evaluate the transient acoustic field from an axisymmetric planar radiator both methods are investigated here and the wave vector time domain method is used to derive the modal impulse response for the normal velocity distribution of an arbitrary axisymmetric source representations of the transient acoustic field in the space time domain and the wave vector time domain are linked through the fourier hankel transform a piston is first addressed as a result of its simplicity which serves as a benchmark case a bessel shaded aperture is then addressed as a result of its importance clearly the piston case is a special case of the spatial bessel shading cases numerical results are presented for both cases to illustrate the procedures in using the modal impulse response and the wave vector time domain methods

steady state groundwater flow simulation with imprecise parameters a methodology based on fuzzy set theory is developed to incorporate imprecise parameters into steady state groundwater flow models in this case fuzzy numbers are used to represent parameter imprecision as such they are also used as a measure for the uncertainty associated with the hydraulic heads due to the imprecision in the input parameters the imprecise input parameters may come from indirect measurements subjective interpretation and expert judgment of available information in the methodology a finite difference method is combined with level set operations to formulate the fuzzy groundwater flow model this fuzzy modeling technique can handle imprecise parameters in a direct way without generating a large number of realizations two numerical solution methods are used to solve the fuzzy groundwater flow model the groundwater model operator method proposed in this methodology and the iterative algorithm based on conventional interval arithmetics the iterative method is simple but may overestimate the uncertainty of hydraulic heads the groundwater model operator method not only provides the hull of the solution set for the hydraulic heads but also considers the dependence of hydraulic head coefficients which are functions of imprecise parameters sensitivity analysis shows that the dependence of hydraulic head coefficients has a critical impact on the model results and neglecting this dependence may result in significant overestimation of the uncertainty of hydraulic heads a numerical model based on the methodology is tested by comparing it with the analytical solution for a homogeneous radial flow problem it is also applied to a simplified two dimensional heterogeneous flow case to demonstrate the methodology

an annular superposition integral for axisymmetric radiators a fast integral expression for computing the nearfield pressure is derived for axisymmetric radiators this method replaces the sum of contributions from concentric annuli with an exact double integral that converges much faster than methods that evaluate the rayleigh sommerfeld integral or the generalized king integral expressions are derived for plane circular pistons using both continuous wave and pulsed excitations several commonly used apodization schemes for the surface velocity distribution are considered including polynomial functions and a smooth piston function the effect of different apodization functions on the spectral content of the wave field is explored quantitative error and time comparisons between the new method the rayleigh sommerfeld integral and the generalized king integral are discussed at all error levels considered the annular superposition method achieves a speed up of at least a factor of 4 relative to the point source method and a factor of 3 relative to the generalized king integral without increasing the computational complexity

on axis and far field sound radiation from resilient flat and dome shaped radiators on axis and far field series expansions are developed for the sound pressure due to an arbitrary circular symmetric velocity distribution on a flat radiator in an infinite baffle these expansions are obtained by expanding the velocity distributions in terms of orthogonal polynomials r 2n 0 sigma a p n 2 sigma a 2 1 with p n the legendre polynomials the terms r 2n 0 give rise to a closed form expression for the pressure on axis as well as for the far field pressure furthermore for a large number of velocity profiles including those associated with the rigid piston the simply supported radiator and the clamped radiators as well as gaussian radiators there are closed form expressions for the required expansion coefficients in particular for the rigid simply supported and clamped radiators this results in explicit finite series expressions for both the on axis and far field pressures in the reverse direction a method of estimating velocity distributions from measured on axis pressures by matching in terms of expansion coefficients is proposed together with the forward far field computation scheme this yields a method for far field loudspeaker assessment from on axis data generalized keele scheme the forward computation scheme is extended to dome shaped radiators with arbitrary velocity distributions

adaptive h p and hp versions for boundary integral element methods recently very promising results in a so called hp version of the finite element method have been obtained the basic idea is a balanced combination of mesh refinement and increase of the polynomial degree of the shape functions this idea is applied to a boundary collocation method in this paper the new method is compared with adaptive h and p versions and it is shown in numerical examples that even in the presence of singularities in the exact solution exponential convergence is obtained

on fuzzy bayesian inference abstract the paper combines methods from bayesian statistics with ideas from fuzzy set theory to generalize bayesian methods both for samples of fuzzy data and for prior distributions with non precise parameters applying the principle of propagation of fuzziness we introduce a fuzzy valued likelihood function bayes theorem for both fuzzy data and fuzzy priors a fuzzy bayes estimator fuzzy predictive densities and distributions and fuzzy h p d regions

ultrasonic field modeling by distributed point source method for different transducer boundary conditions several investigators have modeled ultrasonic fields in front of transducers by huygens fresnel superposition principle that integrates the contributions of a number of point sources distributed on the transducer face this integral solution also known as the rayleigh integral or rayleigh sommerfeld integral solution assumes the strengths of the point sources distributed over the transducer face a newly developed technique called distributed point source method dpsm offers an alternative approach for modeling ultrasonic fields dpsm is capable of modeling the field for prescribed source strength distribution as well as for prescribed interface conditions with unknown source strengths it is investigated how the ultrasonic field in front of the transducer varies in different situations 1 when the point source strengths are known 2 when the point source strengths are unknown but obtained from the interface condition that only the normal component of the transducer velocity is continuous across th

an efficient grid sectoring method for calculations of the near field pressure generated by a circular piston an analytical expression is derived for time harmonic calculations of the near field pressure produced by a circular piston the near field pressure is described by an efficient integral that eliminates redundant calculations and subtracts the singularity which in turn reduces the computation time and the peak numerical error the resulting single integral expression is then combined with an approach that divides the computational grid into sectors that are separated by straight lines the integral is computed with gauss quadrature in each sector and the number of gauss abscissas in each sector is determined by a linear mapping function that prevents large errors from occurring in the axial region by dividing the near field region into 10 sectors the raw computation time is reduced by nearly a factor of 2 for each expression evaluated in this grid the grid sectoring approach is most effective when the computation time is reduced without increasing the peak error and this is consistently accomplished with the efficient integral formulation of the four single integral expressions evaluated with grid sectoring the efficient formulation that eliminates redundant calculations and subtracts the singularity demonstrates the smallest computation time for a specified value of the maximum error

evaluation of angle dependent spectral distortion for infinite planar elastic media via angular spectrum decomposition the angle dependent spectral distortion for an infinite planar interface ip asd is examined for the case of fluid fluid and fluid solid elastic interfaces the results are based on computation of the angular spectrum plane wave decomposition of the acoustic pressure field as radiated by an equivalent image source transducer for each frequency of interest the exact incident angle dependent reflection coefficient of the interface may thus be used in the computation versus approximate methods previously required d p orofino and p c pedersen j acoust soc am 92 2883 2899 1992 comparisons of the previous approximate ip asd results to the current exact results are made ip asd results for elastic parallel plates are also presented for a variety of plate orientations and geometries for the special case of normal incidence a comparison of the ip asd result to a previously published result is made the ip asd is additionally examined for a reduced subset of plane wave components that appro

geostatistics utilizing imprecise fuzzy information abstract fuzzy set theory specifically fuzzy number arithmetic and the extension principle is employed to utilize imprecise data in a geostatistical analysis this formulation is an alternative of soft kriging imprecise data are defined as fuzzy numbers and lead to fuzzy experimental and fuzzy theoretical variograms then a fuzzy geostatistical operation termed fuzzy kriging type 3 is performed and the kriged estimates are represented as fuzzy numbers the width of the fuzzy kriged estimate is interpreted as an uncertainty measure which depends on the data and characterizes local inhomogeniety the estimation variance is also a fuzzy number the illustrative example refers to permeability field predictions for a soil liner a typical case where imprecise measurement data may be available and should be utilized

aleatoric and epistemic uncertainty in groundwater flow and transport simulation 1 the characterization of aleatory hydrogeological parameter uncertainty has traditionally been accomplished using probability theory however when consideration is given to epistemic as well as aleatory uncertainty probability theory is not necessarily appropriate this is especially the case where expert opinion is regarded as a suitable source of information when experts opine upon the uncertainty of a parameter value both aleatoric and epistemic uncertainties are introduced and must be modeled appropriately a novel approach to expert provided parameter uncertainty characterization can be defined that bridges an historical gap between probability theory and fuzzy set theory herein a random set a generalization of a random variable is employed to formalize expert knowledge and fuzzy sets are used to propagate this uncertainty to model estimates of contaminant transport the resultant random set based concentration estimates are shown to be more general than the corresponding random variable estimates in some cases the random set based results are shown as upper and lower probabilities that bound the corresponding random variable s cumulative distribution function

simplified expansions for radiation from a baffled circular piston computation of acoustic radiation from a baffled circular piston continues to be an active area of investigation both as a canonical problem and because of numerous practical applications for time harmonic radiation exact series expansions are an attractive approach because they do not require numerical integration or limiting approximations here series expansions due to hasegawa inoue and matsuzawa j acoust soc am 74 1044 1047 1983 75 1048 1051 1984 are shown to reduce to simpler expressions suitable for numerical computations for the region r a where a is the piston radius and r is the distance from the piston center an exact solution is given by a series of spherical hankel functions and legendre polynomials with explicit closed form position independent coefficients for the paraxial region w a where w is the distance from the piston axis a second exact series expansion is valid for all axial distances z and reduces to the known analytic solution for w 0 these two expansions allow the radiated field to be computed at any point with rapid convergence except for points near the circle bounding the piston example numerical results illustrate application of this method to ultrasonic sources

a fast near field method for calculations of time harmonic and transient pressures produced by triangular pistons analytical expressions are demonstrated for fast calculations of time harmonic and transient near field pressures generated by triangular pistons these fast expressions remove singularities from the impulse response thereby reducing the computation time and the peak numerical error with a general formula that describes the near field pressure produced by any triangular piston geometry the time domain expressions are further accelerated by a time space decomposition approach that analytically separates the spatial and temporal components of the numerically computed transient pressure applied to a hanning weighted input pulse time space decomposition converts each spatio temporal integral into six spatial integral evaluations at each field point time harmonic and transient calculations are evaluated for an equilateral triangle with sides equal to four wavelengths and the resulting errors are compared to pressures obtained with exact and approximate implementations of the impulse response method the results show that the fast near field method achieves smaller maximum errors and is consistently faster than the impulse response and methods that approximate the impulse response

a gaussian finite element method for description of sound diffraction a new method for solving diffraction problems is presented it is based on the use of gaussian diffraction theory comparison of the gaussian beam expansion and fourier series expansion reveals that the gaussian expansion is a more general and more powerful technique the new method combines the gaussian beam superposition technique wen and breazeale j acoust soc am 83 1752 1756 1988 and the numerical finite element solution to the parabolic equation huang j acoust soc am 84 1405 1413 1988 the new method is capable of solving for the sound field even in an inhomogeneous medium or in the presence of reflection as shown by computer modeling the source may be a gaussian source or a distributed source calculated results are compared with experimental results in a laboratory water tank

hierarchal vector basis functions of arbitrary order for triangular and tetrahedral finite elements new vector finite elements are proposed for electromagnetics the new elements are triangular or tetrahedral edge elements tangential vector elements of arbitrary polynomial order they are hierarchal so that different orders can be used together in the same mesh and p adaption is possible they provide separate representation of the gradient and rotational parts of the vector field explicit formulas are presented for generating the basis functions to arbitrary order the basis functions can be used directly or after a further stage of partial orthogonalization to improve the matrix conditioning matrix assembly for the frequency domain curl curl equation is conveniently carried out by means of universal matrices application of the new elements to the solution of a parallel plate waveguide problem demonstrates the expected convergence rate of the phase of the reflection coefficient for tetrahedral elements to order 4 in particular the full order elements have only the same asymptotic convergence rate as elements with a reduced gradient space such as the whitney element however further tests reveal that the optimum balance of the gradient and rotational components is problem dependent

cubic spline interpolation based time domain equivalent source method for modeling transient acoustic radiation abstract transient acoustic radiation from an arbitrarily shaped source is modeled using a cubic spline interpolation based time domain equivalent source method in the method the cubic spline interpolation function is introduced to approximate the equivalent source strengths in the time domain for establishing the relationships between the acoustic quantities in the field the normal acceleration on the source surface and the equivalent sources and the least squares solution of the equivalent source strengths at each time step is determined by an iterative solving process with the singular value decomposition technique the proposed method has the abilities of calculating the acoustic quantities directly in the time domain and applying to arbitrarily shaped sources numerical examples of calculating the transient acoustic fields from a baffled planar piston and an impulsively accelerating sphere demonstrate that the proposed method can model the transient acoustic radiation very well the experimental results also further verify the validity of the proposed method

on the sound field of a resilient disk in an infinite baffle the rayleigh integral describing the near field pressure of an axisymmetric planar monopole source with an arbitrary velocity distribution is solved with a method similar to that used by mast and yu j acoust soc am 118 6 3457 3464 2005 for a rigid disk in an infinite baffle the closed form solution is in the form of a double expansion which is valid for distances from the observation point to the center of the source that are greater than its radius however for the remaining immediate near field the king integral is solved using a combination of gegenbauer s summation theorem and the lommel expansion resulting in a solution which is in the form of a triple expansion reducing to a double expansion along the source s axis of symmetry these relatively compact solutions in analytic form do not require numerical integration and therefore present no numerical difficulties except for a singularity at the rim as an example of a monopole source with an arbitrary velocity distribution equations

toward a universal h p adaptive finite element strategy part 2 a posteriori error estimation abstract in this second paper of the series on h p adaptive finite element methods we present five different techniques for a posteriori error estimation of h p methods for linear elliptic boundary value problems the techniques are referred to as the residual estimation method the duality method the subdomain residual method a method based on interpolation theory and a post processing method the present study examines the theory and behavior of such techniques applied specifically to h p adaptive finite element methods several numerical examples illustrate the efficiency of the methods

a radial propagator for axisymmetric pressure fields the concept of a propagator is central to the angular spectrum formulation of diffraction theory which expresses the pressure field diffracted by a two dimensional aperture as a superposition of a continuum of plane waves in the conventional form an exponential term known as a propagator is multiplied by the wavenumber spectrum obtained from a two dimensional spatial fourier transform of the aperture boundary condition to obtain the wavenumber spectrum in a plane parallel to the boundary offset by some distance specified in the propagator by repeated use of this propagator and fourier inversion it is possible to completely construct the homogeneous part of the pressure field in the positive half space beyond the planar boundary containing the aperture drawing upon preceding work relating the boundary condition to the axial pressure pees j acoust soc am 127 3 1381 1390 2010 it is shown in this article that when the aperture is axially symmetric an alternative type of propagator can b

multilevel methods for p adaptive finite element analysis of electromagnetic scattering in p adaptive finite element analysis the large sparse matrix that arises can be block structured according to the hierarchical level of the unknowns a multilevel preconditioner for the matrix is a v cycle that starts by applying gauss seidel to the highest level then the next level down and so on on the other side of the v gauss seidel is applied in the reverse order at the bottom of the v is the lowest order system which typically is solved exactly with a direct solver however for a complex geometry even the lowest order system may be too large for direct factorization here an alternative is proposed to continue the v cycle downwards first into a set of auxiliary node based spaces then through a series of progressively smaller matrices generated by an algebraic multigrid method the smallest matrix is solved by factorization the method is applied to p adaptive analysis of a five resonator iris filter a split ring resonator loaded waveguide a buckyball metallic frame surrounding a conducting sphere and a noncommensurate frequency selective surface tetrahedral elements up to fourth order are used the largest matrix has over 12 million rows and 0 6 billion nonzero entries

adaptive multiresolution antenna modeling using hierarchical mixed order tangential vector finite elements hierarchical mixed order tangential vector finite elements tvfes for tetrahedra are attractive for accurate and efficient finite element or hybrid finite element boundary integral fe bi simulation of complicated electromagnetic problems they provide versatility in the geometrical modeling of physical structures guarantee solutions free of spurious modes and allow a local increase of resolution by combination of mixed order tvfes of different orders within a computational domain regions with higher order mixed order tvfes can be selected a priori or be found adaptively via methods for a posteriori error estimation or indication this paper demonstrates the merits of various explicit residual methods for a posteriori error indication via adaptive refinement of fe bi solutions of electromagnetic radiation problems using hierarchical mixed order tvfes for tetrahedra

rapid calculations of time harmonic nearfield pressures produced by rectangular pistons a rapid method for calculating the nearfield pressure distribution generated by a rectangular piston is derived for time harmonic excitations this rapid approach improves the numerical performance relative to the impulse response with an equivalent integral expression that removes the numerical singularities caused by inverse trigonometric functions the resulting errors are demonstrated in pressure field calculations using the time harmonic impulse response solution for a rectangular source 5 wavelengths wide by 7 5 wavelengths high simulations using this source geometry show that the rapid method eliminates the singularities introduced by the impulse response the results of pressure field computations are then evaluated in terms of relative errors and computational speeds the results show that when the same number of gauss abscissas are applied to both approaches for time harmonic pressure field calculations the rapid method is consistently faster than the impulse response and the rapid method consistently produces smaller maximum errors than the impulse response for specified maximum error values of 10 and 1 the rapid method is 2 6 times faster than the impulse response for pressure field calculations performed on a 61 by 101 point grid the rapid approach achieves even greater reductions in the computation time for smaller errors and larger grids

some extensions of the gaussian beam expansion radiation fields of the rectangular and the elliptical transducer a straightforward extension of gaussian beam expansion is presented for calculation of the fresnel field integral j j wen and m a breazeale j acoust soc am 83 1752 1756 1988 the source distribution function is expanded into the superposition of a series of two dimensional gaussian functions the corresponding radiation field is expressed as the superposition of these two dimensional gaussian beams and is then reduced to the computation of these simple functions this treatment overcomes the limit that the shape of source is of circular axial symmetry the numerical examples are presented for the field of the uniform elliptical and the rectangular piston transducers and agree well with the results given by complicated computation

latin hypercube lattice sample selection strategy for correlated random hydraulic conductivity fields 1 given an established probabilistic description of hydraulic conductivity realizations of the hydraulic conductivity field can be generated using a lattice sampling technique a special case of latin hypercube sampling and subsequently input to a groundwater flow and transport model realizations of dependent variables such as contaminant concentration are obtained as the output of the model and their corresponding statistics can be calculated compared with the other three alternative methods for generating a random hydraulic conductivity field the suggested method is more efficient in terms of computational effort because it needs fewer samples to achieve the same statistical accuracy

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

a joint wavenumber time domain technique to determine the transient acoustic radiation loading on planar vibrators abstract a new method is presented to determine the transient radiation loading on planar vibrators mounted on rigid infinite baffles by using a wave vector time domain technique the specified non uniform velocity of the vibrator is expressed as a time dependent modal expansion where the modes are solutions to the homogeneous problem the time dependent acoustic modal forces can then be expressed as a sum of the modal radiation impulse responses convolved with the modal velocities in order to evaluate the radiation impulse responses the relationship between the fourier and hankel transforms of circular symmetric functions is first used to express the green s function for the problem as an integral over wave vector space the integral form of the green s function is then used to reduce the expression for the radiation impulse responses from a double surface integral over the vibrator to an integral over the wave vector space in contrast to the double surface integral which is difficult to evaluate the integral over the wave vector space can be evaluated easily numerical results are presented for clamped circular plates and simply supported square plates

higher order frequency domain computational electromagnetics a review of the higher order computational electromagnetics cem for antenna wireless and microwave engineering applications is presented higher order cem techniques use current field basis functions of higher orders defined on large e g on the order of a wavelength in each dimension curvilinear geometrical elements which greatly reduces the number of unknowns for a given problem the paper reviews all major surface volume integral and differential equation electromagnetic formulations within a higher order computational framework focusing on frequency domain solutions with a systematic and unified review of generalized curved parametric quadrilateral triangular hexahedral and tetrahedral elements and various types of higher order hierarchical and interpolatory vector basis functions in both divergence and curl conforming arrangements a large number of actual higher order techniques representing various combinations of formulations elements bases and solution procedures are identified and discussed the examples demonstrate the accuracy efficiency and versatility of higher order techniques and their advantages over low order discretizations the most important one being a much faster higher order convergence of the solution it is demonstrated that both components of the higher order modeling namely higher order geometrical modeling and higher order current field modeling are essential for accurate and efficient cem analysis of general antenna scattering and microwave structures

an explicit a posteriori error indicator for electromagnetic finite element boundary integral analysis within the finite element method fem there is always an error associated with the solution quantifying this error is a very important aspect of fe analysis since it can increase confidence in a solution and can be used to drive adaptive refinements of the discretization optimizing the quality of the solution relative to the number of degrees of freedom and in turn reducing computational cost this paper presents an a posteriori error indicator for time harmonic electromagnetic analysis in three dimensions when using a galerkin fe approach with curl conforming elements and including a nonlocal boundary integral boundary condition as well as a dominant mode port boundary condition the error indicator is residual based of an explicit nature and constitutes a bound on an error energy measure the error indicator is evaluated by presenting results relating to common microwave engineering applications which shows that it can be used successfully to estimate the relative error distribution and that it can successfully serve within an adaptive algorithm

random sets and fuzzy interval analysis abstract a general expression of function with random set valued arguments is stated which encompasses zadeh s extension principle as well as functions of random variables and interval analysis a monotonicity property is derived for algebraic operations performed between random set valued variables this property extends the monotonicity of functions with set valued arguments in the sense of inclusion the application of this result to the approximate calculation of functions of random variables is suggested and illustrated by an example

suppressing the onset of instabilities in the time domain equivalent source method using a multistep approach numerical instability is an important issue that should be addressed in the time domain equivalent source method tesm this study proposes a multistep method to stabilize tesm when using the measured acoustic pressure data to optimize equivalent source strengths unlike the conventional single step method that solves each time step in the time marching process of tesm the proposed method performs a one time solution for several time steps the multistep solution can potentially reduce the accumulation rate of error and improves filtering effects by changing the structure of the matrix that needs to be inverted when the truncated singular value decomposition or tikhonov regularization is used in the time marching process numerical simulations with three examples demonstrate the effectiveness of the multistep method in improving the stability of solutions compared with the single step method effects of the number of merged time steps on the solutions are also discussed to guide the selection process finally the sensitivity of the multistep method to numerical parameters is investigated to demonstrate its consistency under different configurations of numerical parameters

a posteriori error indicators for maxwell s equations abstract in this paper we shall analyze a class of a posteriori error indicators for an electromagnetic scattering problem for maxwell s equations in the presence of a bounded inhomogeneous and anisotropic scatterer problems of this type arise when computing the interaction of electromagnetic radiation with biological tissue we briefly recall existence and uniqueness theory associated with this problem then we show how a posteriori error indicators can be derived using an adjoint equation approach the error indicators use both the jump in normal and tangential components of the field across faces in the mesh

fuzzy regression in hydrology a general methodology for fuzzy regression is developed and illustrated by an actual hydrological case study fuzzy regression may be used whenever a relationship between variables is imprecise and or data are inaccurate and or sample sizes are insufficient in such cases fuzzy regression may be used as a complement or an alternative to statistical regression analysis in fuzzy regression several goodness of fit criteria may be used such as the maximum average vagueness criterion and the prediction vagueness criterion the technique is illustrated by means of a case study involving the relationship between soil electrical resistivity and hydraulic permeability this relationship is imprecise and based on only a few data points in the present case a curvilinear relationship is fitted using fuzzy regression with six calculated resistivities and six measured permeabilities prediction vagueness criteria appears to yield a more robust fuzzy regression than the maximum average vagueness criteria potential application areas of fuzzy regression in hydrology are discussed further the methodology is relatively simple and the results can be interpreted to provide a valuable hydrological decision making aid

a 2d fast near field method for calculating near field pressures generated by apodized rectangular pistons analytical two dimensional 2d integral expressions are derived for fast calculations of time harmonic and transient near field pressures generated by apodized rectangular pistons these 2d expressions represent an extension of the fast near field method fnm for uniformly excited pistons after subdividing the rectangular piston into smaller rectangles the pressure produced by each of the smaller rectangles is calculated using the uniformly excited fnm expression for a rectangular piston and the total pressure generated by an apodized rectangular piston is the superposition of the pressures produced by all of the subdivided rectangles by exchanging summation variables and performing integration by parts a 2d apodized fnm expression is obtained and the resulting expression eliminates the numerical singularities that are otherwise present in numerical models of pressure fields generated by apodized rectangular pistons a simplified time space decomposition method is also described and this method further reduces the computation time for transient pressure fields the results are compared with the rayleigh sommerfeld integral and the field ii program for a rectangular source with each side equal to four wavelengths for time harmonic calculations with a 0 1 normalized root mean square error nrmse the apodized fnm is 4 14 times faster than the rayleigh sommerfeld integral and 59 43 times faster than the field ii program and for a 0 01 nrmse the apodized fnm is 12 50 times faster than the rayleigh sommerfeld integral and 155 06 times faster than the field ii program for transient calculations with a 0 1 nrmse the apodized fnm is 2 31 times faster than the rayleigh sommerfeld integral and 4 66 times faster than the field ii program and for a 0 01 nrmse the apodized fnm is 11 90 times faster than the rayleigh sommerfeld integral and 24 04 times faster than the field ii program thus the 2d apodized fnm is ideal for fast pressure calculations and for accurate reference calculations in the near field region

spatial impulse responses from a flexible baffled circular piston the theory of orthogonal polynomial zernike expansions of functions on a disk as used in the diffraction theory of optical aberrations is applied to obtain semi analytical expressions for the spatial impulse responses arising from a non uniformly moving baffled circular piston these expressions are in terms of the expansion coefficients of the non uniformity and the responses of the orthogonal expansion functions the latter impulse responses have a closed formas finite series involving legendre functions and the sinc function the method is compared with a similar method proposed in p r stepanishen j acoust soc am 70 1176 1181 1981 where zero th orderorthogonal bessel functions rather than zernike polynomials are used as expansion functions the method is also considered for retrieval of a non uniform velocity profile from measured spatial impulseresponses on the level of expansion coefficients which can be applied to acoustic holography for loudspeakers

analysis of the time reversal operator for scatterers of finite size recently it was shown that the time reversal operator for a single small spherical scatterer could have up to four distinguishable eigenstates chambers and gautesen j acoust soc am 109 2616 2624 2001 in this paper that analysis is generalized for scatterers of arbitrary shape and larger size it is shown that the time reversal operator may have an indefinitely large number of distinguishable eigenstates with the exact number depending on the nature of the scatterer and the geometry of the time reversal mirror in addition the case of a multiple number of well separated scatterers is investigated with the result that the total spectrum is the direct combination of the eigenstates associated with each scatterer as an example the singular value spectrum of the time reversal operator for a linear array is calculated explicitly for bubbles and hard rubber spheres of finite size both resonance peaks and apparent crossing points can be observed in the spectrum as the size of the scatterer increases

transient field of a baffled planar piston having an arbitrary vibration amplitude distribution a theoretical model is presented for evaluating the transient velocity potential and pressure fields radiated by a pulsed planar piston set in an infinite rigid baffle and having an arbitrary spatial velocity distribution the method is based on the development of a generalized spatial impulse response function which describes the velocity potential either at a point or averaged over a finite receiving surface resulting from the velocity impulse excitation of a uniformly or nonuniformly vibrating piston source for the specific case of a circular source and receiver this function is plotted using several source distributions and receiver sizes then corresponding plots are presented for two piston velocity waveforms a gaussian pulse and a gaussian modulated sinusoidal burst these plots are compared and the effects of a nonuniformly vibrating source and finite receiver are discussed lastly a previous solution by schoch in which the field of a rigid piston is separated into geometrical and boundary d

fuzzy probabilistic design of water distribution networks 1 the primary aim of this paper is to present a fuzzy probabilistic approach for optimal design and rehabilitation of water distribution systems combining aleatoric and epistemic uncertainties in a unified framework the randomness and imprecision in future water consumption are characterized using fuzzy random variables whose realizations are not real but fuzzy numbers and the nodal head requirements are represented by fuzzy sets reflecting the imprecision in customers requirements the optimal design problem is formulated as a two objective optimization problem with minimization of total design cost and maximization of system performance as objectives the system performance is measured by the fuzzy random reliability defined as the probability that the fuzzy head requirements are satisfied across all network nodes the satisfactory degree is represented by necessity measure or belief measure in the sense of the dempster shafer theory of evidence an efficient algorithm is proposed within a monte carlo procedure to calculate the fuzzy random system reliability and is effectively combined with the nondominated sorting genetic algorithm ii nsgaii to derive the pareto optimal design solutions the newly proposed methodology is demonstrated with two case studies the new york tunnels network and hanoi network the results from both cases indicate that the new methodology can effectively accommodate and handle various aleatoric and epistemic uncertainty sources arising from the design process and can provide optimal design solutions that are not only cost effective but also have higher reliability to cope with severe future uncertainties

imprecise probabilistic evaluation of sewer flooding in urban drainage systems using random set theory 1 uncertainty analysis is widely applied in water system modeling to quantify prediction uncertainty from models and data conventional methods typically handle various kinds of uncertainty using a single characterizing approach be it probability theory or fuzzy set theory however using a single approach may not be appropriate particularly when uncertainties are of different types for example in sewer flood estimation problems random rainfall variables are used as model inputs and imprecise or subjective information is used to define model parameters this paper presents a general framework for sewer flood estimation that enables simultaneous consideration of two types of uncertainty randomness from rainfall data represented using imprecise probabilities and imprecision from model parameters represented by fuzzy numbers these two types of uncertainties are combined using random set theory and then propagated through a hydrodynamic urban drainage model two propagation methods i e discretization and monte carlo based methods are presented and compared with the latter shown to be much more computationally efficient and hence recommended for high dimensional problems the model output flood depth is generated in the form of lower and upper cumulative probabilities which are best estimates given the various stochastic and epistemic uncertainties considered and which embrace the unknown true cumulative probability the distance between the cumulative probabilities represents the extent of imprecise incomplete or conflicting information and can be reduced only when more knowledge is available the proposed methodology has a more complete and thus more accurate representation of uncertainty in data and models and can effectively handle different uncertainty characterizations in a single integrated framework for sewer flood estimation

on the variational formulation of hybrid finite element boundary integral techniques for electromagnetic analysis this paper addresses the time harmonic electromagnetic analysis of a three dimensional inhomogeneous radiator scatterer in free space such analysis can be carried out by combining the finite element method fem with the method of moments mom which yields finite element boundary integral fe bi formulations a general framework is presented within which stationary fe bi formulations can be established variational boundary value problems which relate to equivalent underlying variational principles stationary functionals the formulations are shown to be accurate robust and computationally efficient they avoid the problem of interior resonances without resorting to the combined field integral equation and they result in symmetric system matrices which preserve reciprocity explicitly thus the stationary fe bi framework combines the fem and mom on the continuous level as opposed to the usual approach of hybridization after discretization which generally leads to asymmetric matrices the stationary fe bi framework allows one to solve either for the electric and magnetic fields on the volume of the problem domain or for one volume and one exterior surface field quantity with only marginal differences in computational cost the volume surface formulations have the same storage requirements as previous fe bi formulations and can be more efficiently solved the volume volume formulations provide simultaneous solutions of the electric and magnetic fields which could for instance be used to construct error estimators directly based on maxwell s equations

effective and practical h p version adaptive analysis procedures for the finite element method two practical and effective h p type finite element adaptive procedures are presented the procedures allow not only the final global energy norm error to be well estimated using hierarchic p refinement but in addition give a nearly optimal mesh the design of this is guided by the local information computed on the previous mesh the desired accuracy can always be obtained within one or at most two h p refinements the rate of convergence of the adaptive h p version analysis procedures has been tested for some examples and found to be very strong the presented procedures can easily be incorporated into existing p or h type code structures

time domain comparisons of power law attenuation in causal and noncausal time fractional wave equations the attenuation of ultrasound propagating in human tissue follows a power law with respect to frequency that is modeled by several different causal and noncausal fractional partial differential equations to demonstrate some of the similarities and differences that are observed in three related time fractional partial differential equations time domain green s functions are calculated numerically for the power law wave equation the szabo wave equation and for the caputo wave equation these green s functions are evaluated for water with a power law exponent of y 2 breast with a power law exponent of y 1 5 and liver with a power law exponent of y 1 139 simulation results show that the noncausal features of the numerically calculated time domain response are only evident very close to the source and that these causal and noncausal time domain green s functions converge to the same result away from the source when noncausal time domain green s functions are convolved with a short pulse no evidence of noncausal behavior remains in the time domain which suggests that these causal and noncausal time fractional models are equally effective for these numerical calculations

a posteriori error estimators for stationary convection diffusion problems a computational comparison abstract we consider the scalar convection diffusion problem in 2 d present standard and stabilized finite element methods and give a survey of different a posteriori error estimators these estimators are either based on the evaluation of local residuals or on the solution of discrete local neumann problems besides that a heuristic indicator based on local averaging techniques for the solution gradient is presented and compared with the estimators we give an overview of another aspect of adaptive mesh refinement namely the decision which elements have to be marked for refinement several marking strategies are described and compared

adaptive finite element boundary integral analysis for electromagnetic fields in 3 d this paper presents a complete adaptive finite element boundary integral fe bi analysis scheme for the time harmonic electromagnetic analysis of three dimensional inhomogeneous scatterers radiators in free space the adaptive scheme is based on an fe bi formulation which yields electric and magnetic field solutions simultaneously it employs a posteriori error estimates which exploit the availability of both field solutions and estimates error distributions and global solution quality for the electric and magnetic fields separately it automatically determines which elements should be refined in order to equi distribute the estimated error based on the type of refinement requested h p or hp this automatic determination is based on extrapolating the elemental error estimates the algorithm terminates when specified tolerance levels are reached by the electric and or magnetic field global solution quality estimates the only required user specifications within the algorithm are the termination tolerances and the types of refinements to effect results are presented which show that within the scope of the presented error measures significant reductions in computational cost may be achieved the proposed scheme could be used with other types of error estimates and it could be adapted to other fe or fe bi formulations