analytical approach to network inference investigating degree distribution when the network is reconstructed two types of errors can occur false positive and false negative errors about the presence or absence of links in this paper the influence of these two errors on the vertex degree distribution is analytically analyzed moreover an analytic formula of the density of the biased vertex degree distribution is found in the inverse problem we find a reliable procedure to reconstruct analytically the density of the vertex degree distribution of any network based on the inferred network and estimates for the false positive and false negative errors based on e g simulation studies

improved conditioning of infinite elements for exterior acoustics an optimized version of the so called mapped wave envelope elements also known as astley leis elements is introduced these elements extend to infinity in one dimension and therefore provide an approach to the simulation of exterior acoustical problems in both frequency and time domains their formulation is improved significantly through the proper choice of polynomial bases in the direction of radiation in particular certain jacobi polynomials are identified which behave well with respect to conditioning of the system matrices as a consequence the size of the finite element discretization may reduce considerably without any loss of accuracy in addition the new polynomial bases lead to superior performance of the infinite elements in conjunction with iterative solvers

a comparison of approximate boundary conditions and infinite element methods for exterior helmholtz problems we compare the accuracy of a variety of approximate boundary conditions abcs and two versions of an infinite element method iem for approximating solutions of exterior helmholtz problems the infinite elements are of variable order in the radial direction and differ only in whether the test functions in the weak formulation are conjugated or not we find that the accuracy of the abcs decreases with increasing frequency and that at higher frequencies their accuracy is several orders of magnitude lower than that obtained with the iems we show that the convergence rate of the conjugated element is slower than the rate for the unconjugated element and that the latter element fails to converge in the far field

a reflective newton method for minimizing a quadratic function subject to bounds on some of the variables we propose a new algorithm a reflective newton method for the minimization of a quadratic function of many variables subject to upper and lower bounds on some of the variables this method applies to a general indefinite quadratic function for which a local minimizer subject to bounds is required and is particularly suitable for the large scale problem our new method exhibits strong convergence properties global and quadratic convergence and appears to have significant practical potential strictly feasible points are generated experimental results on moderately large and sparse problems support the claim of practicality for large scale problems

a quadratic programming approach to blind equalization and signal separation blind equalization and signal separation are two well established signal processing problems in this paper we present a quadratic programming algorithm for fast blind equalization and signal separation by introducing a special non mean square error mse objective function we reformulate fractionally spaced blind equalization into an equivalent quadratic programming problem based on a clear geometric interpretation and a formal proof we show that a perfect equalization solution is obtained at every local optimum of the quadratic program because blind source separation is by nature and mathematically a closely related problem we also generalize the algorithm for blind signal separation we show that by enforcing source orthogonalization through successive processing the quadratic programming approach can be applied effectively moreover the quadratic program is easily extendible to incorporate additional practical conditions such as jamming suppression constraints we also provide evidence of good performance through computer simulations

a fast subspace method for image deblurring image deblurring problems appear frequently in astronomical image analysis for image deblurring problems it is reasonable to add a non negativity constraint because of the physical meaning of the image previous research works are mainly full space methods i e solving a regularized optimization problem in a full space to solve the problem more efficiently we propose a subspace method we first formulate the problem from full space to subspace and then use an interior point trust region method to solve it the numerical experiments show that this method is suitable for ill posed image deblurring problems

diffraction from simple shapes by a hybrid asymptotic finite element method the application of a hybrid asymptotic finite element method to the problem of scattering from two dimensional submerged objects is considered the hybrid method is based on patching a short wavelength asymptotic expansion of the scattered field to a finite element interpolation of the near field in patching the diffracted field shape functions with unknown amplitude are forced to agree smoothly with the solution in the near field along a curve at a prescribed distance from the diffraction points a new hybrid finite element on this artificial boundary represents the effect of the outer domain on the solution within this new boundary this allows the replacement of the original boundary value problem with an asymptotically equivalent boundary value problem the domain of which is small and efficiently discretized the method is applied to diffraction by a blunted wedge which in this context represents a degenerate prism the hybrid scattering solution shall be compared to an analytic field representat

wave envelope examples for progressive waves the wave envelope method due to astley 1 is applied to some simple propagating wave problems governed by the helmholtz equation and similar equations it is shown that the method yields solutions which for some of the problems are exact and for the others are approximate and complex in these cases however when the number of elements is increased the trial function becomes a better approximation

the stability of infinite element schemes for transient wave problems the transformation of conjugated infinite elements from the frequency domain to the time domain is described this procedure yields discrete numerical models for transient acoustics which are local in space and time these can be integrated in time to solve unsteady problems of radiation or scattering in infinite domains provided that the discrete equations themselves are stable with time the conditions under which this is true are investigated in this article a numerical study is presented which shows that the stability of the numerical scheme depends critically upon the form of the inner surface of the infinite element domain solutions for test problems are presented to demonstrate that such criteria also apply when the equations are discretised in time and that stable solutions can be obtained using implicit time integration schemes when simple criteria are correctly applied axisymmetric spherical and spheroidal formulations are considered

entropy satisfying schemes for computing selection dynamics in competitive interactions in this paper we present entropy satisfying schemes for solving an integro differential equation that describes the evolution of a population structured with respect to a continuous trait in p e jabin and g raoul j math biol 63 2011 pp 493 517 solutions are shown to converge toward the so called evolutionary stable distribution esd as time becomes large using the relative entropy at the discrete level the esd is shown to be the solution to a quadratic programming problem and can be computed by any well established nonlinear programing algorithm the schemes are then shown to satisfy the entropy dissipation inequality on the set where initial data are positive and the numerical solutions tend toward the discrete esd in time an alternative algorithm is presented to capture the global esd for nonnegative initial data which is made possible due to the mutation mechanism built into the modified scheme a series of numerical tests are given to confirm both accuracy and the entropy satisf

class number three ramanujan type series for 1 p abstract there is a class of remarkable series for 1 of the form c 3 n 0 a nb c 3n 6n 3n n 3 where a b c are certain algebraic numbers these were first examined by ramanujan these examples arise by computing singular invariants for j and the constants involved will have degree equal to the class number of the associated imaginary quadratic field our intention is compute all such class number three examples the largest such example with discriminant 907 adds 37 additional digit accuracy per term a class number four example with discriminant 1555 gives 50 digits per term

transient spheroidal elements for unbounded wave problems a wave envelope element numerical scheme is applied to the solution of unbounded wave problems the scheme is based on a fourier transformation of a discrete model formulated in the frequency domain this yields a discrete system of ordinary differential equations in time which are local in space oblate and prolate spheroidal element geometries are used the accuracy of the scheme is demonstrated by a comparison of computed and analytic solutions for axisymmetric test cases time harmonic and transient solution are presented an indirect solution procedure is also presented which permits the sparsity of the transient equations to be utilised more effectively

a new active set algorithm for box constrained optimization an active set algorithm asa for box constrained optimization is developed the algorithm consists of a nonmonotone gradient projection step an unconstrained optimization step and a set of rules for branching between the two steps global convergence to a stationary point is established for a nondegenerate stationary point the algorithm eventually reduces to unconstrained optimization without restarts similarly for a degenerate stationary point where the strong second order sufficient optimality condition holds the algorithm eventually reduces to unconstrained optimization without restarts a specific implementation of the asa is given which exploits the recently developed cyclic barzilai borwein cbb algorithm for the gradient projection step and the recently developed conjugate gradient algorithm cg descent for unconstrained optimization numerical experiments are presented using box constrained problems in the cuter and minpack 2 test problem libraries

three dimensional finite element calculations in acoustic scattering using arbitrarily shaped convex artificial boundaries we report on a generalization of the bayliss gunzburger turkel non reflecting boundary conditions to arbitrarily shaped convex artificial boundaries for elongated scatterers such as submarines we show that this generalization can improve significantly the computational efficiency of finite element methods applied to the solution of three dimensional acoustic scattering problems copyright 2001 john wiley sons ltd

a survey of finite element methods for time harmonic acoustics many of the current issues and methodologies related to finite element methods for time harmonic acoustics are reviewed the effective treatment of unbounded domains is a major challenge most prominent among the approaches that have been developed for this purpose are absorbing boundary conditions infinite elements and absorbing layers standard computational methods are unable to cope with wave phenomena at short wave lengths due to resolutions required to control dispersion and pollution errors leading to prohibitive computational demands since computation naturally separates the scales of a problem according to the mesh size multiscale considerations provide a useful framework for viewing these difficulties and developing methods to counter them other issues addressed are related to the efficient solution of systems of specialized algebraic equations and inverse problems of acoustics the tremendous progress that has been made in all of the above areas in recent years will surely continue leading to many more exciting developments

superlinear convergence of affine scaling interior point newton methods for infinite dimensional nonlinear problems with pointwise bounds we develop and analyze a superlinearly convergent affine scaling interior point newton method for infinite dimensional problems with pointwise bounds in lp space the problem formulation is motivated by optimal control problems with lp controls and pointwise control constraints the finite dimensional convergence theory by coleman and li siam j optim 6 1996 pp 418 445 makes essential use of the equivalence of norms and the exact identifiability of the active constraints close to an optimizer with strict complementarity since these features are not available in our infinite dimensional framework algorithmic changes are necessary to ensure fast local convergence the main building block is a newton like iteration for an affine scaling formulation of the kkt condition we demonstrate in an example that a stepsize rule to obtain an interior iterate may require very small stepsizes even arbitrarily close to a nondegenerate solution using a pointwise projection instead we prove superlinear convergence under a weak strict complementarity condition and convergence with mbox q rate 1 under a slightly stronger condition if a smoothing step is available we discuss how the algorithm can be embedded in the class of globally convergent trust region interior point methods recently developed by m heinkenschloss and the authors numerical results for the control of a heating process confirm our theoretical findings

solution of 3d laplace and helmholtz equations in exterior domains using hp infinite elements abstract this work is devoted to a convergence study for infinite element discretizations for laplace and helmholtz equations in exterior domains the proposed approximation applies to separable geometries only combining an hp fe discretization on the boundary of the domain with a spectral like representation resulting from the separation of variables in the radial direction the presentation includes a convergence proof for the laplace equation and a stability analysis for the variational formulation of the helmholtz equation in weighted sobolev spaces the theoretical investigations are verified and illustrated with numerical examples for the exterior spherical domain

model reduction for large scale systems with high dimensional parametric input space a model constrained adaptive sampling methodology is proposed for the reduction of large scale systems with high dimensional parametric input spaces our model reduction method uses a reduced basis approach which requires the computation of high fidelity solutions at a number of sample points throughout the parametric input space a key challenge that must be addressed in the optimization control and probabilistic settings is the need for the reduced models to capture variation over this parametric input space which for many applications will be of high dimension we pose the task of determining appropriate sample points as a pde constrained optimization problem which is implemented using an efficient adaptive algorithm that scales well to systems with a large number of parameters the methodology is demonstrated using examples with parametric input spaces of dimension 11 and 21 which describe thermal analysis and design of a heat conduction fin and compared with statistically based sampling methods for these examples the model constrained adaptive sampling leads to reduced models that for a given basis size have error several orders of magnitude smaller than that obtained using the other methods

estimating the concentration of optically active constituents of sea water by takagi sugeno models with quadratic rule consequents determining the concentrations of chlorophyll suspended particulate matter and coloured dissolved organic matter in the sea water is basic to support the monitoring of upwelling phenomena algae blooms and changes in the marine ecosystem since these concentrations affect the spectral distribution of the solar light back scattered by the water body their estimation can be computed by using a set of remotely sensed multispectral measurements of the reflected sunlight in this paper the relation between the concentrations of interest and the average subsurface reflectances is modelled by means of a set of second order takagi sugeno ts fuzzy rules unlike first order ts rules which adopt linear functions as consequent second order ts rules exploit quadratic functions thus improving the modelling capability of the rule in the subspace determined by the antecedent first we show how we can build a second order ts model through a simple transformation which allows estimating the consequent parameters using standard linear least squares algorithms and by adopting one of the most used methods proposed in the literature to generate first order ts models then we compare first order and second order ts models against mean square error and interpretability of rules we highlight how second order ts models allow us to achieve better approximation than first order ts models though maintaining interpretability of the rules finally we show how second order ts models perform considerably better the mean square error is lower by two orders of magnitude than the specific implementations of radial basis function networks and multi layer perceptron networks used in previous papers for the same application domain

a polynomial time interior point method for conic optimization with inexact barrier evaluations we consider a primal dual short step interior point method for conic convex optimization problems for which exact evaluation of the gradient and hessian of the primal and dual barrier functions is either impossible or prohibitively expensive as our main contribution we show that if approximate gradients and hessians of the primal barrier function can be computed and the relative errors in such quantities are not too large then the method has polynomial worst case iteration complexity in particular polynomial iteration complexity ensues when the gradient and hessian are evaluated exactly in addition the algorithm requires no evaluation or even approximate evaluation of quantities related to the barrier function for the dual cone even for problems in which the underlying cone is not self dual

non reflecting boundary conditions for acoustic propagation in ducts with acoustic treatment and mean flow we consider a time harmonic acoustic scattering problem in a 2d infinite waveguide with walls covered with an absorbing material in the presence of a mean flow assumed uniform far from the source to make this problem suitable for a finite element analysis the infinite domain is truncated this paper concerns the derivation of a non reflecting boundary condition on the artificial boundary by means of a dirichlet to neumann dtn map based on a modal decomposition compared with the hard walled guide case several difficulties are raised by the presence of both the liner and the mean flow in particular acoustic modes are no longer orthogonal and behave asymptotically like the modes of a soft walled guide however an accurate approximation of the dtn map can be derived using some bi orthogonality relations valid asymptotically for high order modes numerical validations show the efficiency of the method the influence of the liner with or without mean flow is illustrated

modelling of short wave diffraction problems using approximating systems of plane waves this paper describes a finite element model for the solution of helmholtz problems at higher frequencies that offers the possibility of computing many wavelengths in a single finite element the approach is based on partition of unity isoparametric elements at each finite element node the potential is expanded in a discrete series of planar waves each propagating at a specified angle these angles can be uniformly distributed or may be carefully chosen they can also be the same for all nodes of the studied mesh or may vary from one node to another the implemented approach is used to solve a few practical problems such as the diffraction of plane waves by cylinders and spheres the wave number is increased and the mesh remains unchanged until a single finite element contains many wavelengths in each spatial direction and therefore the dimension of the whole problem is greatly reduced issues related to the integration and the conditioning are also discussed

model based subspace projection beamforming for deep interference nulling this paper considers the problem of adaptive array processing for interference canceling to drive very deep nulls in difficult signal environments in many practical scenarios the achievable null depth is limited by covariance matrix estimation error leading to poor identification of the interference subspace we address the particularly troublesome cases of low interference to noise ratio inr relatively rapid interference motion and correlated noise across the receiving array a polynomial based model is incorporated in the proposed algorithm to track changes in the array covariance matrix over time mitigate interference subspace estimation errors and improve canceler performance the application of phased array feeds for radio astronomical telescopes is used to illustrate the problem and proposed solution here even weak residual interference after cancellation may obscure a signal of interest so very deep beampattern nulls are required performance for conventional subspace projection sp is compared with polynomial augmented sp using simulated and real experimental data showing null depth improvement of 6 to 30 db

acoustic infinite elements for non separable geometries we present new infinite element formulations for solving acoustic scattering and radiation problems in the exterior of long slender bodies the new infinite elements are geometrically constructed from a prolate spheroid inscribed by the scatterer these elements need not begin on a level surface of the prolate spheroidal coordinate system instead they may be attached to any convex surface including that of the scatterer itself this scheme reduces or even completely eliminates finite element modeling of the exterior medium the formulations may easily be extended to the cases of an interior oblate spheroid or ellipsoid we present both conjugated and unconjugated formulations without any weighting factors although it would be simple to include them we describe a fast numerical scheme for computing the element integrals based on chebychev approximation we include numerical results for scattering from spheres and capped cylinders these results demonstrate the accuracy and the dramatic reduction in computational expense of our new formulations compared to other coupled finite element infinite element methods

on the divergence free condition in godunov type schemes for ideal magnetohydrodynamics the upwind constrained transport method we present a general framework to design godunov type schemes for multidimensional ideal magnetohydrodynamic mhd systems having the divergence free relation and the related properties of the magnetic field b as built in conditions our approach mostly relies on the constrained transport ct discretization technique for the magnetic field components originally developed for the linear induction equation which assures b num 0 and its preservation in time to within machine accuracy in a finite volume setting we show that the ct formalism when fully exploited can be used as a general guideline to design the reconstruction procedures of the b vector field to adapt standard upwind procedures for the momentum and energy equations avoiding the onset of numerical monopoles of o 1 size and to formulate approximate riemann solvers for the induction equation this general framework will be named here upwind constrained transport uct to demonstrate the versatility of our method we apply it to a variety of schemes which are finally validated numerically and compared a novel implementation for the mhd case of the second order roetype positive scheme by lin and lax j comput fluid dyn 5 1996 133 and both the second and third order versions of a central type mhd scheme presented by londrillo and del zanna astrophys j 530 2000 508 where the basic uct strategies have been first outlined

an hp adaptive finite element method for electromagnetics part 3 a three dimensional infinite element for maxwell s equations this paper is a continuation of reference 26 cecot demkowicz and rachowicz computer methods in applied mechanics and engineering 2000 188 625 643 and describes an implementation of the infinite element for three dimensional time harmonic maxwell s equations proposed in reference 15 demkowicz and pal computer methods in applied mechanics and engineering 1998 164 77 94 the element is compatible with the hp finite element discretizations for maxwell s equations in bounded domains reported in references 16 18 computer methods in applied mechanics and engineering 1998 152 103 124 1999 169 331 344 2000 187 307 337 copyright 2003 john wiley sons ltd

the performance of spheroidal infinite elements a number of spheroidal and ellipsoidal infinite elements have been proposed for the solution of unbounded wave problems in the frequency domain i e solutions of the helmholtz equation these elements are widely believed to be more effective than conventional spherical infinite elements in cases where the radiating or scattering object is slender or flat and can therefore be closely enclosed by a spheroidal or an ellipsoidal surface the validity of this statement is investigated in the current article the radial order which is required for an accurate solution is shown to depend strongly not only upon the type of element that is used but also on the aspect ratio of the bounding spheroid and the non dimensional wave number the nature of this dependence can partially be explained by comparing the non oscillatory component of simple source solutions to the terms available in the trial solution of spheroidal elements numerical studies are also presented to demonstrate the rates at which convergence can be achieved in practice by unconjugated burnett and conjugated astley leis type elements it will be shown that neither formulation is entirely satisfactory at high frequencies and high aspect ratios

a new mapped infinite wave element for general wave diffraction problems and its validation on the ellipse diffraction problem the theory for an improved infinite element for wave diffraction is presented the improvement is on the original wave element presented by bettess zienkiewicz and others the modification involves the introduction of one extra term in the original shape function derivatives and a change in the numerical integration sequence the modification enables the element to be used with elliptical and other non circular meshes similar mappings have already been used with wave envelope infinite elements by astley and others as a test of the element accurate results are demonstrated for a range of elliptical cylinder diffraction problems the element has not yet been tested for other non circular problems

a randomized maximum a posteriori method for posterior sampling of high dimensional nonlinear bayesian inverse problems we present a randomized maximum a posteriori rmap method for generating approximate samples of posteriors in high dimensional bayesian inverse problems governed by large scale forward problems we derive the rmap approach by 1 casting the problem of computing the map point as a stochastic optimization problem 2 interchanging optimization and expectation and 3 approximating the expectation with a monte carlo method for a specific randomized data and prior mean rmap reduces to the randomized maximum likelihood rml approach it can also be viewed as an iterative stochastic newton method an analysis of the convergence of the rmap samples is carried out for both linear and nonlinear inverse problems each rmap sample requires solution of a pde constrained optimization problem to solve these problems we employ a state of the art trust region inexact newton conjugate gradient method with sensitivity based warm starts an approximate metropolization approach is presented to reduce the bias in rma

the ill conditioning of infinite element stiffness matrices abstract in this paper a method for improving the conditioning of infinite element stiffness matrices is proposed and examined for one dimensional and two dimensional infinite elements this method is a preconditioning technique which is based on a gram schmidt like transformation induced by general sesquilinear forms although the preconditioning method can be applied to many types of infinite elements it will be applied to improve the conditioning of the popular multipole infinite element the paper is concluded with numerical examples demonstrating improved conditioning and convergence properties of the preconditioned multipole infinite elements

approximate solution of the trust region problem by minimization over two dimensional subspaces the trust region problem minimization of a quadratic function subject to a spherical trust region constraint occurs in many optimization algorithms in a previous paper the authors introduced an inexpensive approximate solution technique for this problem that involves the solution of a two dimensional trust region problem they showed that using this approximation in an unconstrained optimization algorithm leads to the same theoretical global and local convergence properties as are obtained using the exact solution to the trust region problem this paper reports computational results showing that the two dimensional minimization approach gives nearly optimal reductions in then dimension quadratic model over a wide range of test cases we also show that there is very little difference in efficiency and reliability between using the approximate or exact trust region step in solving standard test problems for unconstrained optimization these results may encourage the application of similar approximate trust region techniques in other contexts

mapped wave envelope elements for acoustical radiation and scattering wave envelope elements provide an alternative to boundary element methods for the solution of exterior wave problems applications to date have been to axisymmetric geometries and have involved the use of large but finite wave envelope meshes compatibly matched to denser near field meshes of conventional elements in the present paper the wave envelope idea is extended by the inclusion of an element mapping taken directly from infinite element methodology and by modifications to the residual formulation taken in conjunction these two measures permit the outer boundary of the wave envelope region to be moved to infinity while preserving the boundedness of the acoustic mass and stiffness integrals the present formulation is developed initially with reference to a simple one dimensional model and is then applied in two and three dimensions comparisons between computed results and those obtained from analytic solutions where applicable and from boundary element codes demonstrate the effectiveness of the method

compactness and convergence rates in the combinatorial integral approximation decomposition the combinatorial integral approximation decomposition splits the optimization of a discrete valued control into two steps solving a continuous relaxation of the discrete control problem and computing a discrete valued approximation of the relaxed control different algorithms exist for the second step to construct piecewise constant discrete valued approximants that are defined on given decompositions of the domain it is known that the resulting discrete controls can be constructed such that they converge to a relaxed control in the hbox weak topology of l infty if the grid constant of this decomposition is driven to zero we exploit this insight to formulate a general approximation result for optimization problems which feature discrete and distributed optimization variables and which are governed by a compact control to state operator we analyze the topology induced by the grid refinements and prove convergence rates of the control vectors for two problem classes we use a reconstruction problem from signal processing to demonstrate both the applicability of the method outside the scope of differential equations the predominant case in the literature and the effectiveness of the approach

a finite element alternative to infinite elements abstract in this paper a simple idea based on midpoint integration rule is utilized to solve a particular class of mechanics problems namely static problems defined on unbounded domains where the solution is required to be accurate only in an interior and not in the far field by developing a finite element mesh that approximates the stiffness of an unbounded domain directly without approximating the far field displacement profile first the current formulation provides a superior alternative to infinite elements ies that have long been used to incorporate unbounded domains into the finite element method fem in contrast to most ies the present formulation a requires no new shape functions or special integration rules b is proved to be both accurate and efficient and c is versatile enough to handle a large variety of domains including those with anisotropic stratified media and convex polygonal corners in addition to this the proposed model leads to the derivation of a simple error expression that provides an explicit correlation between the mesh parameters and the accuracy achieved this error expression can be used to calculate the accuracy of a given mesh a priori this in turn allows one to generate the most efficient mesh capable of achieving a desired accuracy by solving a mesh optimization problem we formulate such an optimization problem solve it and use the results to develop a practical mesh generation methodology this methodology does not require any additional computation on the part of the user and can hence be used in practical situations to quickly generate an efficient and near optimal finite element mesh that models an unbounded domain to the required accuracy numerical examples involving practical problems are presented at the end to illustrate the effectiveness of this method

parallel minimum p norm solution of the neuromagnetic inverse problem for realistic signals using exact hessian vector products in the neuromagnetic inverse problem one is interested in determining the current density inside the human brain from measurements of the magnetic field recorded outside the head from a numerical point of view the solution of this inverse problem is challenging not only in terms of nonuniqueness and time complexity but also with respect to numerical stability an efficient and robust computational technique is presented that finds the minimum p norm solution of the neuromagnetic inverse problem the approach is based on carefully combining a subspace trust region algorithm for the solution of an unconstrained nonlinear optimization problem automatic differentiation for the truncation error free evaluation of first and second order derivatives and shared memory parallelization using the openmp programming paradigm using actual measurements obtained from a head phantom model as well as realistic data sets of middle latency auditory evoked field data it is demonstrated that a valid reconstruction of neuromagnetic activity is achieved for values of p less than 2

treatment of frequency dependent admittance boundary conditions in transient acoustic finite infinite element models the paper addresses the handling of frequency dependent local admittance boundary conditions in acoustic transient finite infinite element models the proposed approach avoids the evaluation of a convolution integral along the related boundary based on a similar technique developed in an aeroacoustic finite difference context the spatially local boundary condition is rewritten in a discrete form that involves normal accelerations and pressure time derivatives at the current time step and few steps before the incorporation of such a discrete in time boundary condition in a finite infinite element context is addressed the infinite element scheme selected for that purpose relies on the conjugated astley leis formulation implementation aspects cover the handling of frequency dependent boundary conditions along both finite and infinite element edges numerical examples waveguide single source in a half space bounded by an impedance plane diffraction by an acoustically treated screen are presented in order to demonstrate the efficiency of the proposed approach

a new affine scaling interior point algorithm for nonlinear optimization subject to linear equality and inequality constraints in this paper we propose a new interior affine scaling region algorithm with nonmonotonic interior point backtracking technique for nonlinear optimization subject to linear equality and inequality constraints the trust region subproblem in the proposed algorithm is defined by minimizing a quadratic function subject only to an affine scaling ellipsoidal constraint in a null subspace of the extended equality constraints using both trust region strategy and line search technique the affine scaling trust region subproblem at each iteration generates backtracking interior step to obtain a new accepted step the global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions a nonmonotonic criterion should bring about speeding up the convergence progress in some ill conditioned cases

on two dimensional infinite elements utilizing basis functions with compact support in this paper improvements are made in the numerical conditioning of infinite element stiffness matrices by replacing the characteristic eigenfunction basis functions which have global support with basis functions which have local support and appropriate preconditioning the conditioning and convergence properties of these new infinite elements are presented in solving two dimensional exterior problems for the helmholtz equation

diffraction of short waves modelled using new mapped wave envelope finite and infinite elements we consider a two dimensional wave diffraction problem from a closed body such that the complex progressive wave potential satisfies the sommerfield condition and the helmholtz equation we are interested in the case where the wavelength is much smaller than any other length dimensions of the problem we introduce new mapped wave envelope infinite elements to model the potential in the far field and test them for some simple dirichlet boundary condition problems they are used in conjuction with wave envelope finite elements developed earlier 1 to model the potential in the near field an iterative procedure is used in which an initial estimate of the phase is iteratively improved the iteration scheme by which the wave envelope and phase are recovered is described in detail copyright 1999 john wiley sons ltd

a subspace interior and conjugate gradient method for large scale bound constrained minimization problems a subspace adaptation of the coleman li trust region and interior method is proposed for solving large scale bound constrained minimization problems this method can be implemented with either sparse cholesky factorization or conjugate gradient computation under reasonable conditions the convergence properties of this subspace trust region method are as strong as those of its full space version computational performance on various large test problems is reported advantages of our approach are demonstrated our experience indicates that our proposed method represents an efficient way to solve large bound constrained minimization problems

element free galerkin solutions for helmholtz problems fomulation and numerical assessment of the pollution effect abstract the element free galerkin method efgm a particular case of the meshless methods is examined in its application to acoustic wave propagation addressed by the helmholtz equation dispersion and pollution effects two problems encountered by the classical numerical methods are reviewed numerical tests on two dimensional problems focus on the parameters governing the formulation of the efgm they also demonstrate that the efgm is affected by dispersion and pollution effects as well as fem but these effects are rather low showing that the efgm is a promising method

a coupled interpolating meshfree method for computing sound radiation in infinite domain summary in this paper the coupling of the improved interpolating element free galerkin iiefg method and the variable order infinite acoustic wave envelope element wee method is studied a coupled iiefg wee method for computing sound radiation is proposed to make use of their advantages while evading their disadvantages the coupling is achieved by constructing the hybrid shape function of continuity and compatibility on the interface between the iiefg and wee domains in the iiefg domain the improved interpolating moving least squares iimls method is employed to form the shape functions satisfying the kronecker delta condition while nonsingular weight functions can be used the impacts of the size of the influence domain and the shape parameter on the performance of this coupled method are investigated the numerical results show that the coupled iiefg wee method can take full advantage of both the iiefg and wee methods and that it not only can achieve higher accuracy but also has a faster convergence speed than the conventional method of the finite element coupled with the wee the experimental results show that the method is very flexible for acoustic radiation prediction in the infinite domain this article is protected by copyright all rights reserved

spectral gradient flow and equilibrium configurations of point vortices we formulate the problem of finding equilibrium configurations of n point vortices in the plane in terms of a gradient flow on the smallest singular value of a skew symmetric matrix m whose nullspa