fast analysis of transient acoustic wave scattering from rigid bodies using the multilevel plane wave time domain algorithm the analysis of transient wave scattering from rigid bodies using integral equation based techniques is computationally intensive if carried out using classical schemes the evaluation of the velocity potential on the surface of a three dimensional scatterer represented in terms of ns spatial basis functions for nt time steps requires o ntns2 operations the recently developed plane wave time domain pwtd algorithm permits the rapid evaluation of transient fields that are generated by bandlimited source distributions it has been shown that incorporation of the pwtd algorithm into integral equation based solvers in a two level setting reduces the computational complexity of a transient analysis to o ntns1 5 logns in this paper it is shown that casting the pwtd scheme into a multilevel framework permits the analysis of transient acoustic surface scattering phenomena in o ntnslog2ns operations using o ntns memory numerical examples that demonstrate the efficacy of the multilevel implementation are also presented

on the spatial bandwidth of scattered fields it is shown that the scattered fields are almost space bandlimited functions the effective bandwidth w is introduced and evaluated for a very general scattering system as well as the error made using functions bandlimited to w w for representing the scattered field the effective bandwidth is very simply related to the maximum dimension of the scattering system the error drops to negligible values for modest increases of w compared to w in the case of large scatterers important consequences of the above general results are finally stressed

antenna characterization in the time domain a theory for a complete far field transmit receive system characterization of short pulse antennas is derived in the time domain the transmit receive antenna system is characterized by a set of cascaded operators which transform the source waveform and power into similar quantities at the receiving antenna terminals two such sets are defined the first one is phrased in terms of the wave type time dependent effective height operator while the second one is defined in terms of the energy type gain operator both definitions fit within a complete transmit receive system description the latter being equivalent to the frequency domain friis equation however these operators are derived entirely in the context of the time domain field equation the starting point in the time domain analysis of the effective height is the slant stack transform sst of the time dependent current distribution in a manner equivalent to the spatial fourier transform used in the frequency domain the vector autocorrelation of the transmitting effective height is then used to define the time dependent gain operator under impulsive source excitation time domain reciprocity leads to the definitions of antenna parameters under receiving conditions and the corresponding equivalent circuit the parameters defined in this way fit within a consistent transmit receive convolution operator operating on the autocorrelation of the input signal this independent time domain representation is thus similar to the frequency domain representation however unlike the conventional frequency domain circuit parameters which relate voltage and current amplitudes the time domain circuit representation is based on incident and reflected wave type constituents in addition the use of appropriate norms facilitates the transformation of our operators to stand alone figures of merits the general concepts developed are demonstrated for a short dipole antenna

rapid solution of the wave equation in unbounded domains in this paper we propose and analyze a new fast method for the numerical solution of time domain boundary integral formulations of the wave equation we employ lubich s convolution quadrature method for the time discretization and a galerkin boundary element method for the spatial discretization the coefficient matrix of the arising system of linear equations is a triangular block toeplitz matrix possible choices for solving the linear system arising from the above discretization include the use of fast fourier transform fft techniques and the use of data sparse approximations by using fft techniques the computational complexity can be reduced substantially while the storage cost remains unchanged and is typically high using data sparse approximations the gain is reversed i e the computational cost is approximately unchanged while the storage cost is substantially reduced the method proposed in this paper combines the advantages of these two approaches first the discrete convolution related to the block toeplitz system is transformed into the discrete fourier image thereby arriving at a decoupled system of discretized helmholtz equations with complex wave numbers a fast data sparse e g fast multipole or panel clustering method can then be applied to the transformed system additionally significant savings can be achieved if the boundary data are smooth and time limited in this case the right hand sides of many of the helmholtz problems are almost zero and hence can be disregarded finally the proposed method is inherently parallel we analyze the stability and convergence of these methods thereby deriving the choice of parameters that preserves the convergence rates of the unperturbed convolution quadrature we also present numerical results which illustrate the predicted convergence behavior

a fast time domain integral equation based scheme for analyzing scattering from dispersive objects a fast integral equation based scheme for analyzing transient scattering from inhomogeneous dispersive bodies is presented a time domain integral equation in terms of the electric flux inside the body is constructed by invoking the volume equivalence principle i e by equating the sum of the incident electric field and that radiated by equivalent volume polarization currents to the total electric field the proposed algorithm for solving this time domain integral equation incorporates a recursive convolution scheme that updates the polarization current from knowledge of the electric flux to reduce the computational cost and memory requirement of the resulting marching on in time scheme it is augmented with the plane wave time domain algorithm numerical results that validate the proposed approach and demonstrate its accuracy are presented

time domain adaptive integral method for surface integral equations an efficient marching on in time mot scheme is presented for solving electric magnetic and combined field integral equations pertinent to the analysis of transient electromagnetic scattering from perfectly conducting surfaces residing in an unbounded homogenous medium the proposed scheme is the extension of the frequency domain adaptive integral pre corrected fast fourier transform fft method to the time domain fields on the scatterer that are produced by space time sources residing on its surface are computed 1 by locally projecting for each time step all sources onto a uniform auxiliary grid that encases the scatterer 2 by computing everywhere on this grid the transient fields produced by the resulting auxiliary sources via global multilevel blocked space time ffts 3 by locally interpolating these fields back onto the scatterer surface as this procedure is inaccurate when source and observer points reside close to each other and 4 near fields are computed classically albeit pre corrected for errors introduced through the use of global ffts the proposed scheme has a computational complexity and memory requirement of o n sub t n sub s log sup 2 n sub s and o n sub s sup 3 2 when applied to quasiplanar structures and of o n sub t n sub s sup 3 2 log sup 2 n sub s and o n sub s sup 2 when used to analyze scattering from general surfaces here n sub s and n sub t denote the number of spatial and temporal degrees of freedom of the surface current density these computational cost and memory requirements are contrasted to those of classical mot solvers which scale as o n sub t n sub s sup 2 and o n sub s sup 2 respectively a parallel implementation of the scheme on a distributed memory computer cluster that uses the message passing interface is described simulation results demonstrate the accuracy efficiency and the parallel performance of the implementation

accuracy and stability improvements of integral equation models using the partial element equivalent circuit peec approach the partial element equivalent circuit peec technique is a formulation which transforms an electric field integral equation efie into a full wave equivalent circuit solution in this paper improvements are made to the peec model through the development of a refined method of computing both the partial inductances as well as the coefficients of potential the method does not increase the number of unknowns in addition damping is added to the peec model in order to further reduce nonphysical resonances which may occur above the useful frequency range the observations and solutions presented in this paper are especially important for time domain solvers the effectiveness of the method is illustrated with several examples

a direct boundary element method for acoustic radiation and scattering from mixed regular and thin bodies in this paper the direct boundary element method is applied to acoustic radiation and scattering from mixed regular and thin bodies a typical application problem involves a regular body with thin fins either attached to or in the neighborhood of the body it is shown that the mixed body integral formulation requires interactions between the conventional helmholtz integral equation and the hypersingular thin body integral equation if at least one regular body is involved in a mixed body environment the direct integral formulation possesses the well known nonuniqueness difficulty this nonuniqueness difficulty is overcome by either the chief method or the burton and miller method since both the thin body integral equation and the burton and miller equation contain a hypersingular integral a regularized form recently derived by krishnasamy et al asme j appl mech 57 404 414 1990 is adopted in this paper numerical results show excellent agreement with a multidomain boundary element solution and a point source solution

a comparison of techniques for overcoming non uniqueness of boundary integral equations for the collocation partition of unity method in two dimensional acoustic scattering the partition of unity method has become an attractive approach for extending the allowable frequency range for wave simulations beyond that available using piecewise polynomial elements the non uniqueness of solution obtained from the conventional boundary integral equation cbie is well known the cbie derived through green s identities suffers from a problem of non uniqueness at certain characteristic frequencies two of the standard methods of overcoming this problem are the so called combined helmholtz integral equation formulation chief method and that of burton and miller the latter method introduces a hypersingular integral which may be treated in various ways in this paper we present the collocation partition of unity boundary element method pubem for the helmholtz problem and compare the performance of chief against a burton miller formulation regularised using the approach of li and huang

an interpolation based fast multipole accelerated boundary integral equation method for the three dimensional wave equation a new fast multipole method fmm is proposed to accelerate the time domain boundary integral equation method tdbiem for the three dimensional wave equation the proposed algorithm is an enhancement of the interpolation based fmm for the time domain case adopting the notion of the plane wave time domain algorithm with the application being targeted at a low frequency regime the proposed time domain interpolation based fmm can reduce the computational complexity of the tdbiem from o n s 2 n t to o n s 1 n t where 1 3 or 1 2 with the help of multilevel space time hierarchy where n s and n t are the spatial and temporal degrees of freedom respectively the computational accuracy and speed of the proposed accelerated tdbiem are verified in comparison with those of the conventional direct tdbiem via numerical experiments

analysis of three dimensional transient acoustic wave propagation using the boundary integral equation method this paper describes a boundary integral equation boundary element method for the solution of a variety of transient acoustic problems the spatial and temporal discretization employs quadratic isoparametric elements with high order gauss quadrature and the ensuing equations are implicit the implicit formulation both eliminates the instabilities reported in explicit treatments and permits a freedom of choice of timestep which can reduce costs dramatically the accuracy of the approach is demonstrated by comparison with the analytical solution for a sphere results for more demanding sphere cone sphere geometries extending to seven wavelengths long are presented and compared to those obtained from a related frequency domain approach

coupling discontinuous galerkin methods and retarded potentials for transient wave propagation on unbounded domains this work deals with the numerical simulation of wave propagation on unbounded domains with localized heterogeneities to do so we propose to combine a discretization based on a discontinuous galerkin method in space and explicit finite differences in time on the regions containing heterogeneities with the retarded potential method to account the unbounded nature of the computational domain the coupling formula enforces a discrete energy identity ensuring the stability under the usual cfl condition in the interior moreover the scheme allows to use a smaller time step in the interior domain yielding to quasi optimal discretization parameters for both methods the aliasing phenomena introduced by the local time stepping are reduced by a post processing by averaging in time obtaining a stable and second order consistent in time coupling algorithm we compute the numerical rate of convergence of the method for an academic problem the numerical results show the feasibility of the whole discretization procedure

general model of a cascade of reactions with time delays global stability analysis abstract the problem considered in this paper consists of a cascade of reactions with discrete as well as distributed delays which arose in the context of hes1 gene expression for the abstract general model sufficient conditions for global stability are presented then the abstract result is applied to the hes1 model

stability and convergence of collocation schemes for retarded potential integral equations time domain boundary integral formulations of transient scattering problems involve retarded potential integral equations solving such equations numerically is both complicated and computationally intensive and numerical methods often prove to be unstable collocation schemes are easier to implement than full finite element formulations but little appears to be known about their stability and convergence here we derive and analyze some new stable collocation schemes for the single layer equation for transient acoustic scattering and use spatial fourier and temporal laplace transform techniques to demonstrate that such stable schemes are second order convergent

stability properties of the time domain electric field integral equation using a separable approximation for the convolution with the retarded potential the state of art of time domain integral equation tdie solvers has grown by leaps and bounds over the past decade during this time advances have been made in i the development of accelerators that can be retrofitted with these solvers and ii understanding the stability properties of the electric field integral equation as is well known time domain electric field integral equation solvers have been notoriously difficult to stabilize research into methods for understanding and prescribing remedies have been on the uptick the most recent of these efforts are i lubich quadrature and ii exact integration in this paper we re examine the solution to this equation using i the undifferentiated form of the time domain electric field integral equation tdefie and ii a separable approximation to the spatio temporal convolution the proposed scheme can be constructed such that the spatial integrand over the source and observer domains is smooth and integrable as several numerical results will demonstrate the proposed scheme yields stable results for long simulation times and a variety of targets both of which have proven extremely challenging in the past

multistep and multistage convolution quadrature for the wave equation algorithms and experiments we describe how a time discretized wave equation in a homogeneous medium can be solved by boundary integral methods the time discretization can be a multistep runge kutta or a more general multistep multistage method the resulting convolutional system of boundary integral equations belongs to the family of convolution quadratures of lubich the aim of this work is twofold it describes an efficient robust and easily parallelizable method for solving the semidiscretized system the resulting algorithm has the main advantages of time stepping methods and of fourier synthesis at each time step a system of linear equations with the same system matrix needs to be solved yet computations can easily be done in parallel the computational cost is almost linear in the number of time steps and only the laplace transform of the time domain fundamental solution is needed the new aspect of the algorithm is that all this is possible without ever explicitly constructing the weights of the convolution quadrature this approach also readily allows the use of modern data sparse techniques to efficiently perform computation in space we investigate theoretically and numerically to which extent hierarchical matrix mathcal h matrix techniques can be used to speed up the space computation the second aim of this article is to perform a series of large scale 3d experiments with a range of multistep and multistage time discretization methods the backward difference formula of order 2 bdf2 the trapezoid rule and the 3 stage radau iia methods are investigated in detail one of the conclusions of the experiments is that the radau iia method often performs overwhelmingly better than the linear multistep methods especially for problems with many reflections yet in connection with hyperbolic problems bdfs have so far been predominant in the literature on convolution quadrature

the thin shape breakdown tsb of the helmholtz integral equation many numerical implementations of the helmholtz integral equation exist today that can predict routinely the field scattered by a volume holding body one such object is the ellipsoidal core of a typical airborne or submerged vehicle stripped of its thin appendages i e stripped of its finlike control surfaces etc the reason for these omissions has often been an inherent limitation of the cited modeling tools rather than a rational dismissal of the potential effect of these neglected appendages on the complete body s expected scattering cross section the limitation of existing techniques is this the standard form of gauss theorem on which they are based that leads to the helmholtz integral becomes meaningless when the thickness of the shape addressed tapers down to zero even over only part of the structure this paper exposes analytically the fundamental cause of this thin shape breakdown tsb and in the process derives an alternate boundary element formulation for its cure

time domain bie analysis of large three dimensional electromagnetic scattering problems a time domain boundary integral equation bie solution of the magnetic field integral equation mfie for large electromagnetic scattering problems is presented it employs isoparametric curvilinear quadratic elements to model fields geometry and time dependence eliminating staircasing problems the approach is implicit which seems to provide both stability and permits arbitrary local mesh refinement to model geometrically difficult regions without the significant cost penalty explicit methods suffer error dependence on discretization is investigated accurate results are obtained with as few as five nodes per wavelength the performance both on large scatterers and on low radar cross section rcs scatterers is demonstrated including the six wavelength nasa almond two spheres a thirteen wavelength missile and a high q cavity

on a way to save memory when solving time domain boundary integral equations for acoustic and vibroacoustic applications abstract solving acoustic equations in the time domain possibly coupled with the description of flexible structure dynamics remains attractive as compared to solving the same in the frequency domain this allows for better consideration of local non linearities acoustics structure and the boundary integral formulation also known as bem offers an exact description of the infinite acoustic field based on a simple surface mesh no need for 3d volume discretization some issues remain however the required memory space and computation time continue to grow rapidly when the number of elements of the surface mesh increases in the case of a structure with a regular non slender shape the computational cost measured in terms of required memory space varies by helmholtz number to the power of 4 this paper illustrates how the accelerating method called ngtd helps overcome this difficulty this paper shows the applicability of 2 level ngtd to acoustic and vibroacoustic problems described solely by the hypersingular formulation for surfaces it goes into more detail on some important aspects of the interpolation process and on the memory saving obtained implementation within the mot march on time astryd code shows the benefits of this method the memory requirement shows an estimated trend lower than power 1 35 of the number of surface elements

a transpose free quasi minimal residual algorithm for non hermitian linear systems the biconjugate gradient method bcg for solving general non hermitian linear systems ax b and its transpose free variant the conjugate gradients squared algorithm cgs both typically exhib

optimal interpolation of radiated fields over a sphere an optimal sampling interpolation algorithm is developed that allows the accurate recovery of scattered or radiated fields over a sphere from a minimum number of samples using the concept of the field equivalent spatial bandwidth a central interpolation scheme is developed to compute the field in theta phi coordinates starting from its samples the maximum allowable sample spacing and error upper bounds are also rigorously derived several simulated examples of pattern reconstruction are presented for both the cases of field and power pattern interpolation the interpolation error as a function of the retained sample number has been also evaluated and compared with the theoretical upper bounds the algorithm stability versus randomly distributed errors added to the exact samples is demonstrated

fast transient analysis of acoustic wave scattering from rigid bodies using a two level plane wave time domain algorithm it is well known that the computational cost associated with the application of classical time domain integral equation methods to the analysis of scattering from acoustical targets scales unfavorably with problem size indeed performing a three dimensional scattering analysis using these methods requires o ntns2 operations where ns denotes the number of basis functions that model the spatial field distribution over the surface of the scatterer and nt is the number of time steps in the analysis recently novel plane wave time domain algorithms that augment these classical methods and thereby reduce their high computational cost have been introduced this paper describes such a plane wave time domain algorithm within the context of the analysis of acoustic scattering from rigid bodies and outlines its incorporation into a time domain integral equation solver in a two level setting it is shown that the resulting scheme has a computational complexity of o ntns1 5 log ns examples comparing the accuracy

a fast spherical filter with uniform resolution this paper introduces a fast algorithm for obtaining a uniform resolution representation of a function known at a latitude longitude grid on the surface of a sphere equivalent to a triangular isotropic truncation of the spherical harmonic coefficients for the function the proposedspectral truncation method which is based on the fast multipole method and the fast fourier transform projects the function to a space with uniform resolution while avoiding surface harmonic transformations the method requireso n2logn operations foro n2 grid points as opposed too n3 operations for the standard spectral transform method providing a reduced complexity spectral method obviating the pole problem in the integration of time dependent partial differential equations on the sphere the filter s performance is demonstrated with numerical examples

a galerkin scheme for the time domain integral equation of acoustic scattering from a hard surface the transient acoustic scattered wave from a hard surface is computed using a space time integral equation a variational formulation of this integral equation is obtained from an energy identity leading to a galerkin type numerical procedure by choosing an appropriate basis for the discretized functional space this scheme is of the marching in time type with matrix coefficients this technique is applied to a sphere a box and dihedron targets