an efficient 3 d infinite element for water wave diffraction problems an efficient and simple infinite element for modelling the far field potential of water wave diffraction problems is presented the shape functions in the radial direction comprise the first two terms of the asymptotic expansions of hankel functions the integrals with infinite limit for calculating the coefficient matrix have been worked out numerical tests on the diffraction by a surface piercing circular cylinder give surprisingly accurate resultant forces even if the infinite elements are placed very near to the cylinder other typical three dimensional examples also show that satisfactory results can be obtained by the use of this simple infinite element a computer program waload has been developed for computing the wave forces on fixed two and three dimensional bodies

investigation of nonplanar perfectly matched absorbers for finite element mesh truncation we present a detailed theoretical and numerical investigation of the perfectly matched layer pml concept as applied to the problem of mesh truncation in the finite element method fem we show that it is possible to extend the cartesian pml concepts involving half spaces to cylindrical and spherical geometries appropriate for closed boundaries in two and three dimensions by defining lossy anisotropic layers in the relevant coordinate systems by using the method of separation of variables it is possible to solve the boundary value problems in these geometries the analytical solutions demonstrate that under certain conditions outgoing waves are absorbed with negligible reflection and the transmitted wave is attenuated within the pml to reduce the white space in radiation or scattering problems conformal pmls are constructed via parametric mappings it is also verified that the pml concept which was originally introduced for problems governed by maxwell s equations can be extended to cases governed by the scalar helmholtz equation finally numerical results are presented to demonstrate the use of the pml in fem mesh truncation

exterior stable domain segmentation integral equation method for scattering problems this paper is concerned with the development of an exterior domain segmentation method for the solution of two or three dimensional time harmonic scattering problems in acoustic media this method based on a variational localized symmetric boundary integral equation formulation leads upon discretization to a sparse system of algebraic equations whose solution requires only o n multiplications where n is the number of unknown nodal pressures on the scatterer surface the new procedure is analogous to the one developed recently1 except that in the present formulation we avoid completely the use of the hypersingular operator thereby reducing the computational complexity numerical experiments for a rigid circular cylindrical scatterer subjected to a plane incident wave serve to assess its accuracy for normalized wave numbers ka ranging from 0 to 30 both directly on the scatterer and in the far field and to confirm that contrary to standard boundary integral equation formulations the present procedure is valid for critical frequencies

higher order boundary infinite elements abstract higher order approximations are implemented in a novel approach to infinite element formulations for exterior problems of time harmonic acoustics this approach is based on a functional which provides a general framework for domain based computation of exterior problems two prominent features of this formulation simplify the task of discretization the lack of integration over the unbounded domain and weak enforcement of continuity between finite elements and infinite elements consequently the infinite elements mesh the interface only and need not match the finite elements on the interface various infinite element approximations for two dimensional configurations with circular interfaces are presented numerical results demonstrate the good performance of this scheme

a new mesh generation scheme for arbitrary planar domains this paper describes a new algorithm to generate interior nodes within any arbitrary multi connected regions the boundary nodes and the interior nodes are then linked up to form the best possible triangular elements by a completely revised technique in an efficient and stable manner owing to the generality of the central generation program the global domain is allowed to be divided into as many irregular subdomains as desired in order to model closely the actual physical situation moreover the boundaries of the sub domains are updated from time to time when necessary to include the possibilities of progressive refinement around a sharp corner generating radiating mesh from a prescribed node generating mesh between two circular arcs etc despite its flexibility and capabilities data for triangulation have been kept to a minimum by a logical input module no connectivity information between subregions is needed and common boundaries are defined once only all these features have contributed to a powerful method to generate 3 node or 6 node triangular element meshes of great variety within the most irregular heterogeneous regions

kubik an automatic three dimensional finite element mesh generator this paper describes an automatic mesh generator for finite element problems in three dimensions called kubik kubik is based on a modular concept first a set of modules is generated each with its own mesh inside then the modules are placed in contact and a matrix describing the connectivity of the entire mesh is determined finally the geometry of the mesh is specified and all nodal co ordinates are determined by the computer the user s labour required to specify a mesh which represents a certain physical configuration resumbles the labour involved when the configuration has to be specified to the machine shop workers who are supposed to build it the modules are independent except for the compatibility requirements between modules which are to be placed in contact structures of any degree of complexity can in principle be obtained using kubik only two types of modules are required except when helicoidal structures are to be generated in which case it is convenient to use a third type the finite elements used are distorted cubes but they can be divided into tetrahedra prisms of pyramids nodes are placed at the corners of the cubes and additional nodes can be introduced if desired in order to obtain other types of finite elements in use infinite elements of quadrilateral cross section are also a standard feature of kubik and can be divided in order to obtain infinite prisms of triangular cross section kubik can also generate two dimensional meshes including meshing of a three dimensional surface for use with boundary elements

a faster combinatorial approximation algorithm for scheduling unrelated parallel machines we consider the problem of scheduling n independent jobs on m unrelated parallel machines without preemption job i takes processing time p i j on machine j and the total time used by a machine is the sum of the processing times for the jobs assigned to it the objective is to minimize makespan the best known approximation algorithms for this problem compute an optimum fractional solution and then use rounding techniques to get an integral 2 approximation in this paper we present a combinatorial approximation algorithm that matches this approximation quality it is much simpler than the previously known algorithms and its running time is better this is the first time that a combinatorial algorithm always beats the interior point approach for this problem our algorithm is a generic minimum cost flow algorithm without any complex enhancements tailored to handle unsplittable flow it pushes unsplittable jobs through a two layered bipartite generalized network defined by the scheduling problem in our analysis we take advantage from addressing the approximation problem directly in particular we replace the classical technique of solving the lp relaxation and rounding afterwards by a completely integral approach we feel that this approach will be helpful also for other applications

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

a polynomial combinatorial algorithm for generalized minimum cost flow we propose the first combinatorial solution to the generalized minimum cost flow problem flow with losses and gains despite a rich history dating back to kantorovich and dantzig until now the only known way to solve the problem in polynomial time was via general purpose linear programming techniques polynomial combinatorial algorithms were previously known only for the version of our problem without costs we design the first such algorithms for the version with costs our algorithms also find provably good solutions faster than optimal ones providing the first strongly polynomial approximation schemes for the problem our techniques extend to optimize linear programs with two variables per inequality polynomial combinatorial algorithms were previously developed for testing the feasibility of such linear programs we propose the first such methods for the optimization version

a faster combinatorial algorithm for the generalized circulation problem this paper presents a modified version of algorithm mcf proposed by goldberg plotkin and tardos for the generalized circulation problem this new combinatorial algorithm has a worst case complexity that is better than the complexities of the mcf and fat path combinatorial algorithms of goldberg plotkin and tardos goldberg a v s a plotkin e tardos 1991 combinatorial algorithms for the generalized circulation problem math oper res 16 351 379

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

fast and simple approximation schemes for generalized flow we present fast and simple fully polynomial time approximation schemes fptas for generalized versions of maximum flow multicommodity flow minimum cost maximum flow and minimum cost multicommodity flow we extend and refine fractional packing frameworks introduced in fptas s for traditional multicommodity flow and packing linear programs our fptas s dominate the previous best known complexity bounds for all of these problems some by more than a factor of n2 where n is the number of nodes this is accomplished in part by introducing an efficient method of solving a sequence of generalized shortest path problems our generalized multicommodity fptas s are now as fast as the best non generalized ones we believe our improvements make it practical to solve generalized multicommodity flow problems via combinatorial methods

inverse iteration for damped natural vibration abstract inverse iteration is extended to internally and or externally damped natural vibration each iteration involves one matrix multiplication and one linear equation solution of order n the symmetric band form of the original undamped eigenvalue problem is preserved if the undamped mode is taken as the first approximation the inverse iteration will converse to the corresponding damped mode in about four iterations however the one step method is divergent for heavy damping therefore it is advisible to subdivide the damping into successive steps if inverse iteration does not converge in say five iterations the method is successful for both discrete systems and distributed systems the implementation is very simple by means of complex arithmetic which is readily available in many fortran compilers

combinatorial algorithms for the generalized circulation problem we consider a generalization of the maximum flow problem in which the amounts of flow entering and leaving an arc are linearly related more precisely if x e units of flow enter an arc e x e e units arrive at the other end for instance nodes of the graph can correspond to different currencies with the multipliers being the exchange rates we require conservation of flow at every node except a given source node the goal is to maximize the amount of flow excess at the source this problem is a special case of linear programming and therefore can be solved in polynomial time in this paper we present the first polynomial time combinatorial algorithms for this problem the algorithms are simple and intuitive

a coupled fe and boundary integral equation method based on exterior domain decomposition for fluid structure interface problems abstract a coupled finite element and exterior domain decomposition based boundary integral formulations for the solutions of two or three dimensional time harmonic fluid structure interaction problems is described in this paper it is known that the memory limitation of computers has been one of the major obstacles for solving large scale high frequency fluid structure interface systems using various existing nonlocal finite element and boundary integral equation coupling techniques due to the fully populated resultant matrix generated from the boundary integral equation representation the essence of this study is to decompose through domain decomposition of the exterior region the original exterior problem into arbitrary subproblems with data sharing only at the interfaces by decomposing the exterior infinite domain into an appropriate number of infinite subdomains this method not only ensures the validity of the formulation for all frequencies but also leads to a diagonalized blockwise banded system of discretized equations the size of an individual submatrix i e a block that is associated with an exterior subdomain may be decided by the user and may be selected such that the restriction due to the memory limitation of a given computer may be accommodated in addition the method is suited for parallel processing since the data associated with each subdomain impedance matrices load vectors etc may be generated in parallel and the communication needed will be only for the interface values most significantly unlike the existing coupled finite element and boundary integral equation techniques that are valid for all frequencies our method avoids the use of both the hypersingular operator and the double integrals therefore reducing the computational complexity numerical experiments have been performed for elastic cylindrical shells subjected to a plane incident wave the results have demonstrated the accuracy of the method for wavenumbers ranging from 0 to 30 both directly on the shell and in the far field and have confirmed that the procedure is valid for all frequencies

large displacement transient analysis of flexible structures a new approach for numerical analysis of flexible space frames subjected to impact forces is presented the method is particularly effective in the analysis of large amplitude vibration and dynamic stability found in extremely flexible structures the proposed method of analysis is based on a concept of updated material frame which allows the algorithm of handling large rotations exceeding 360 and extensions longer than 100 per cent without numerical difficulty and the need for iterations thus an efficient explicit integration finite element algorithm can be adopted the method is convenient for non linear and inelastic material models the basic coding procedure is similar to the popular co rotational approach existing codes can be easily modified to solve transient dynamic problems the modification steps necessary for the implementation are outlined in the paper several numerical examples are presented comparison with the standard co rotational approach and large deformation finite element formulations such as the updated lagrangian approach are presented

mapped infinite elements for exterior wave problems recently a new type of infinite elements which uses r 1 decay was proposed they were applied to exterior wave problems and good results were obtained in two dimensional problems however it was necessary to move the origin of the r 1 decay in order to model the outgoing wave more accurately because it decays roughly as r 1 2 in this paper the mapped infinite elements with r 1 2 decay and the necessary numerical integration procedure are presented these elements do not require any artificial movement of the origin several example problems are solved the results show that the infinite elements with r 1 2 decay here give much more accurate values than the infinite elements with exponential decay and any damper elements

delaunay triangulation of non convex planar domains this paper investigates the possibility of integrating the two currently most popular mesh generation techniques namely the method of advancing front and the delaunay triangulation algorithm the merits of the resulting scheme are its simplicity efficiency and versatility with the introduction of non delaunay line segments the concept of using delaunay triangulation as a means of mesh generation is clarified an efficient algorithm is proposed for the construction of delaunay triangulations over non convex planar domains interior nodes are first generated within the planar domain these interior nodes and the boundary nodes are then linked up together to produce a valid triangulation in the mesh generation process the delaunay property of each triangle is ensured by selecting a node having the smallest associated circumcircle in contrast to convex domains intersection between the proposed triangle and the domain boundary has to be checked this can be simply done by considering only the non delaunay segments on the generation front through the study of numerous examples of various characteristics it is found that high quality triangular element meshes are obtained by the proposed algorithm and the mesh generation time bears a linear relationship with the number of elements nodes of the triangulation

new algorithms for generalized network flows this paper of which a preliminary version appeared in istcs 92 is concerned with generalized network flow problems in a generalized network each edgee u v has a positive flow multiplier a e associated with it the interpretation is that if a flow ofx e enters the edge at nodeu then a flow ofa e x e exits the edge atv the uncapacitated generalized transshipment problem ugt is defined on a generalized network where demands and supplies real numbers are associated with the vertices and costs real numbers are associated with the edges the goal is to find a flow such that the excess or deficit at each vertex equals the desired value of the supply or demand and the sum over the edges of the product of the cost and the flow is minimized adler and cosares operations research 39 1991 955 960 reduced the restricted uncapacitated generalized transshipment problem where only demand nodes are present to a system of linear inequalities with two variables per inequality the algorithms presented by the authors in siam journal on computing to appear result in a faster algorithm for restricted ugt generalized circulation is defined on a generalized network with demands at the nodes and capacity constraints on the edges i e upper bounds on the amount of flow the goal is to find a flow such that the excesses at the nodes are proportional to the demands and maximized we present a new algorithm that solves the capacitated generalized flow problem by iteratively solving instances of ugt the algorithm can be used to find an optimal flow or an approximation thereof when used to find a constant factor approximation the algorithm is not only more efficient than previous algorithms but also strongly polynomial it is believed to be the first strongly polynomial approximation algorithm for generalized circulation the existence of such an approximation algorithm is interesting since it is not known whether the exact problem has a strongly polynomial algorithm

infinite domain elements a parametric element is formulated which enables the economic modelling of infinite domain type problmes a typical problem is an opening in a stress field in an infinite medium either in two or three dimensions the strategy is to model around the opening with two or three layers of conventional isoparametric finite elements and surround these with a single layer of infinite domain elements several sample problems has been analysed for circular square and spherical openings in infinite media and the results compared with either theoretical or boundary element solutions which include the infinite boundary in their solution technique copyright

a novel boundary infinite element a new improved infinite element based on mapping is proposed for modelling unbounded domain problems mapping has previously been used in such problems not only for the entire domain but also for the infinite element itself the novelty of the present approach is the simplicity of the mapping and the retention of standard integration abscissae and weights the implementation of these elements is very straightforward and they are ideally suited for the analysis of infinite domain static problems in two and three dimensions

inverse iteration for the quadratic eigenvalue problem the inverse iteration method for the linear eigenvalue problem is extended to the quadratic eigenvalue problem based on the famous newtonian iteration for algebraic equations the process is shown to converge to the desired modes by means of a newly introduced continuation parameter for highly non conservative systems only physical co ordinates are involved and the sparsity of the original matrices is preserved to achieve high computational efficiency the required orthonormalization condition and the generalized rayleigh s quotient are given the method can handle complex eigensolution without difficulties

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

the numerical methods for oscillating singularities in elliptic boundary value problems the singularities near the crack tips of homogeneous materials are monotone of type r and r log r depending on the boundary conditions along nonsmooth domains however the singularities around the interfacial cracks of the heterogeneous bimaterials are oscillatory of type r sin e log r the method of auxiliary mapping mam introduced by babuska and oh was proven to be successful in dealing with r type singularities however the effectiveness of mam is reduced in handling oscillating singularities this paper deals with oscillating singularities as well as the monotone singularities by extending mam through introducing the power auxiliary mapping and the exponential auxiliary mapping

finding minimum cost circulations by canceling negative cycles a classical algorithm for finding a minimum cost circulation consists of repeatedly finding a residual cycle of negative cost and canceling it by pushing enough flow around the cycle to saturate an arc we show that a judicious choice of cycles for canceling leads to a polynomial bound on the number of iterations in this algorithm this gives a very simple strongly polynomial algorithm that uses no scaling a variant of the algorithm that uses dynamic trees runs in o nm log n min log nc m log n time on a network of n vertices m arcs and arc costs of maximum absolute value c this bound is comparable to those of the fastest previously known algorithms

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

maximum network flows with concave gains this paper deals with a generalized maximum flow problem with concave gains which is a nonlinear network optimization problem optimality conditions and an algorithm for this problem are presented the optimality conditions are extended from the corresponding results for the linear gain case the algorithm is based on the scaled piecewise linear approximation and on the fat path algorithm described by goldberg plotkin and tardos for linear gain cases the proposed algorithm solves a problem with piecewise linear concave gains faster than the naive solution by adding parallel arcs

fibonacci heaps and their uses in improved network optimization algorithms in this paper we develop a new data structure for implementing heaps priority queues our structure fibonacci heaps abbreviated f heaps extends the binomial queues proposed by vuillemin and studied further by brown f heaps support arbitrary deletion from an n item heap in o log n amortized time and all other standard heap operations in o 1 amortized time using f heaps we are able to obtain improved running times for several network optimization algorithms in particular we obtain the following worst case bounds where n is the number of vertices and m the number of edges in the problem graph o n log n m for the single source shortest path problem with nonnegative edge lengths improved from o m log m n 2 n o n 2 log n nm for the all pairs shortest path problem improved from o nm log m n 2 n o n 2 log n nm for the assignment problem weighted bipartite matching improved from o nm log m n 2 n o m m n for the minimum spanning tree problem improved from o m log log m n 2 n where m n min i u log i n m n note that m n log n if m n of these results the improved bound for minimum spanning trees is the most striking although all the results give asymptotic improvements for graphs of appropriate densities

the numerical manifold method for exterior problems abstract the numerical manifold method nmm a galerkin type numerical method has been successful in the solution of problems with finite definition domains yet it has never been applied to problems with unbounded domains or exterior problems this study aims to fill the big gap by constructing infinite patches together with the finite patches to cover the unbounded domain the local approximations of infinite patches can take the asymptotic estimations of the solutions at infinity which are available for all those well established boundary value problems compared with the infinite element methods in the finite element method fem the construction of the trial functions by nmm is more elegant in theory and more systematical in methodology resulting in more accurate solutions some typical examples in potential and half space elasticity problems are investigated to illustrate the applicability and accuracy of the proposed method

an infinite element and a formula for numerical quadrature over an infinite interval in this publication we present a new infinite element and discuss a formula for numerical quadrature over infinite regions both the element and the formula are based on the properties of a set of orthonormal functions obtained by mapping the legendre polynomials on the infinite interval the element can represent any physical function over the entire infinite region and the formula can integrate most integrands over the infinite interval they are thus very convenient for implementation in a general computer program which could then be used to solve different problems with no restrictions concerning the asymptotic behaviour of the solutions or the form of integrands to be integrated over the infinite interval however the element and the formula will perform at their best when used in conjunction and for problems of electrostatic magnetostatic etc potential the formula was compared with other existing formulae and found to be either superior or satisfactory in practically all cases as shown by the results of many numerical experiments expressions of shape functions are given for the element a test problem was solved using the element and the formula and the results are shown to be more accurate than those obtained when solving the same problem using infinite elements with exponential decay and gauss laguerre numerical quadrature

an algorithm for matrix polynomial eigenproblems abstract when a system is described by higher order differential equations with time as the independent variable the solution for the homogeneous system is defined by a matrix polynomial eigenproblem a method alternative to the classical companion matrix method is introduced to expand the determinant algebraically to result in a scalar polynomial equation for the eigenvalues the eigenvectors are obtained by inverse iteration it is shown that the new method is computationally more advantageous than the conventional companion matrix method a computer program is given for general matrix polynomials as well as hermitian matrix polynomials defective eigenproblems can be handled without special attention

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

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

faster algorithms for the generalized network flow problem we consider the generalized network flow problem each arc e in the network has a gain factor e if f e units of flow enter arc e then f e e units arrive at the other end of e the objective is to maximize the net flow into one specific node the sink the constraints are the conservation of flow at nodes and the capacities of arcs we present a combinatorial algorithm which solves this problem in o m2 m n log log b log b time where n is the number of nodes m is the number of arcs and b is the largest integer used to represent the gain factors the capacities and the initial supplies at the nodes if m is o n4 3 e and b is not extremely large then our bound is better than the previous best upper bound for this problem we also improve the best known upper bound for the approximate generalized flow problem by showing that a solution whose value is within a factor of 1 from the optimum can be computed in o m m n log log b log 1 time plus o mn2 log b time for preprocessing

application of infinite elements to phase change situations on deforming meshes in recent years progress has been made in applying moving and deforming mesh systems to phase change problems this allows the numerical attention where it is needed near the migrating phase change zone in spatially unbounded problems one hopes that numerically finite outer boundaries either escape significant activity or are automatically pushed further away as activity nears not infrequently this approach fails temperature activity often spreads more rapidly than phase change thereby reaching far boundaries stretching of the mesh by movement of far boundaries can challenge mesh control and cause ill conditioning in this paper the advantages of time dependent mesh adaption are enhanced by the joining of a new formulation for infinite elements to far boundaries this is accomplished through a co ordinate transformation within the framework of conventional 2 d quadratic biquadratic and linear quadratic elements standard 2 by 2 gauss legendre quadrature suffices throughout and normal galerkin finite element features are undisturbed including strict conservation of energy the formulation is independent of global co ordinates entails no restrictions on the unknown function and should be applicable to other problem types all test cases on quadrilateral and triangular grids show very significant improvements with infinite elements relative to comparable solution systems using strictly finite grids

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

an e relaxation method for separable convex cost generalized network flow problems cover title the extended abstract of this article appeared in the proceedings of the 5th international ipco conference vancouver june 1996 p 1

an ellipsoidal acoustic infinite element abstract in previous papers the authors presented new 3 d time harmonic prolate and oblate spheroidal acoustic infinite elements based on new prolate and oblate spheroidal multipole expansions for modeling acoustic fields in unbounded domains here we present the development of an ellipsoidal infinite element which is the logical generalization of those elements this development is also based on a new multipole expansion as well as a new system of ellipsoidal coordinates the element stiffness radiation damping and mass matrices are developed and presented in sufficient detail to enable their software implementation both the new coordinate system and the new element include the previous spheroidal coordinate systems and spheroidal elements as limiting cases therefore all the previously reported performance data for the spheroidal elements apply to this ellipsoidal element when used in spheroidal form since the three axes of an ellipsoid can be chosen independently an ellipsoid can circumscribe any structural shape at least as closely and generally more closely than a prolate or oblate spheroid the resulting reduction in size of the finite computational domain will result in even greater computational speeds than those already reported for the spheroidal elements the element may be used to model problems in free space 4 steradians half space 2 quarter space or eighth space 2 since this infinite element provides maximum computational efficiency for structures of all shapes software element libraries would need only this one element for all problems in unbounded domains

two step component mode synthesis for the eigensolution of large systems component mode synthesis is a dynamic substructuring technique for approximate eigensolutions of large degree of freedom systems divisible into two or more components system synthesis using component modes results in approximate eigenparameters the approximation is improved by using more component modes in synthesis typically all component modes up to x times the frequency range of interest are required to ensure reasonable accuracy where x varies from 2 to 10 a two step component mode synthesis approach is presented the first step involves system synthesis using the minimum number of component modes required to obtain approximate cigenvalues up to a preselected frequency and the second step uses additional component modes in a convergence scheme operating on the system eigenparameters calculated in the first step this results in an infinite series eigenvalue problem that is solved by a modified shooting method a perturbation approach is adopted to derive the convergence scheme in which separate iterations are performed for each eigenvalue and eigenvector in each step selection of initial values for the convergence scheme is also presented in a few instances an eigenvalue nearly reached the convergence tolerance but then wandered away and converged to an adjacent value the algorithm was modified to automatically detect this problem and abort iteration with a small penalty in accuracy this two step approach provides the analyst with some insight into the convergence and accuracy of the eigenparameters without resolving an increasingly larger system over and over with more component modes numerical examples are included to demonstrate the applicability of the method

the weighted finite element method for elasticity equations on unbounded domains abstract by introducing the weighted riesz galerkin method with a special weight function oh jou 23 made it possible to apply mam the method of auxiliary mapping introduced by babuska oh to general elliptic boundary value problems on unbounded domains in this paper this method is further generalized to yield highly accurate approximate solutions for linear elasticity problems on unbounded domains with bounded or unbounded boundaries it is shown that in the framework of the p version of the fem this method does efficiently handle elasticity problems on unbounded domains and yields accurate solutions at low cost