stable algorithm for the stress field around a multiply branched crack we present an algorithm for the computation of the stress field around a branched crack the algorithm is based on an integral equation with good numerical properties our equation is obtained through a left regularization of an integral equation of fredholm s first kind complex valued functions involving repeated products of square roots appear in the regularization a new and effective scheme for correct evaluation of these functions is described for validation mode i and ii stress intensity factors are computed for simple branched geometries the relative errors in the stress intensity factors are typically as low as 10 12 a large scale example is also presented where a crack with 176 branching points is studied

development of a distributed dislocation dipole technique for the analysis of multiple straight kinked and branched cracks in an elastic half plane abstract a distributed dislocation dipole technique for the analysis of multiple straight kinked and branched cracks in an elastic half plane has been developed the dipole density distribution is represented with a weighted jacobi polynomial expansion where the weight function captures the asymptotic behaviour at each end of the crack to allow for opening and sliding at crack kinking and branching the dipole density representation contains conditional extra terms which fulfills the asymptotic behaviour at each endpoint several test cases involving straight kinked and branched cracks have been analysed and the results suggest that the accuracy of the method is within 1 provided that jacobi polynomial expansions up to at least the sixth order are used adopting even higher order jacobi polynomials yields improved accuracy the method is compared to a simplified procedure suggested in the literature where stress singularities associated with corners at kinking or branching are neglected in the representation for the dipole density distribution the comparison suggests that both procedures work but that the current procedure is superior in as much as the same accuracy is reached using substantially lower order polynomial expansions

a new cloud based hp finite element method a hybrid computational method for solving boundary value problems is introduced which combines features of the meshless hp cloud methods with features of conventional finite elements the method admits straightforward nonuniform hp type approximations easy implementation of essential boundary conditions is robust under severe distortions of the mesh and can deliver exponential rates of convergence results of numerical experiments are presented

interactive algorithms for multiple criteria nonlinear programming problems abstract in this paper several interactive procedures for solving multiple criteria nonlinear programming problems have been developed these are based on the generalized reduced gradient method for solving single objective nonlinear programming problems they can handle maximization problems with nonlinear concave objectives nonlinear convex constraints and an implicit quasi concave preference function of the decision maker the interactive procedures work with information of varying degrees of accuracy from the decision maker thereby extending and strengthening a number of existing methods

some issues in measuring and reporting solution quality of interactive multiple objective programming procedures issues in measuring and reporting solution quality are examined when value functions are used in computational experiments of interactive multiple objective programming procedures they include value functions used weights assigned to the objective functions in the value functions the size of the efficient set and the number of objective functions the feasibility and existence of the ideal and nadir points are also discussed detailed examples are presented to demonstrate these issues neither the users nor in fact the researchers may discern these issues even though they have strong impacts on the reported solution qualities common practices in the computational experiments of interactive multiple objective programming procedures are reviewed

integral equation methods and numerical solutions of crack and inclusion problems in planar elastostatics we present algorithms for crack and inclusion problems in planar linear elastostatics the algorithms are based on new integral equations for the pure crack problem the integral equations are of fredholm s second kind our algorithms show great stability and allow for solutions to problems more complex than have previously been possible our results are orders of magnitudes more accurate than those of previous investigators which rely on integral equations of fredholm s first kind

solving multiple criteria problems by interactive decomposition an interactive decomposition method is developed for solving the multiple criteria mc problem based on nonlinear programming duality theory the mc problem is decomposed into a series of subproblems and relaxed master problems each subproblem is a bicriterion problem and each relaxed master problem is a standard linear program the prime objective of the decomposition is to simplify and facilitate the process of making preference assessments and tradeoffs across many conflicting objectives therefore the decision maker s preference function is not assumed to be known explicitly rather the decision maker is required to make only limited local preference assessments in the context of feasible and nondominated alternatives also the preference assessments are of the form of ordinal paired comparisons and in most of them only two criteria are allowed to change their values simultaneously while the remaining l 2 criteria are held fixed at certain levels

integral equation methods for elliptic problems with boundary conditions of mixed type laplace s equation with mixed boundary conditions that is dirichlet conditions on parts of the boundary and neumann conditions on the remaining contiguous parts is solved on an interior planar domain using an integral equation method rapid execution and high accuracy is obtained by combining equations which are of fredholm s second kind with compact operators on almost the entire boundary with a recursive compressed inverse preconditioning technique then an elastic problem with mixed boundary conditions is formulated and solved in an analogous manner and with similar results this opens up for the rapid and accurate solution of several elliptic problems of mixed type

estimation of variable coefficients in parabolic distributed systems we present techniques based on cubic spline approximations for estimating coefficients e g diffusion convector velocity etc depending on time and the spatial variable in parabolic distributed systems such as those that arise in transport models convergence results and a summary of numerical performance of the resulting algorithms are given

an efficient numerical algorithm for cracks partly in frictionless contact an algorithm for a loaded crack partly in frictionless contact is presented the problem is nonlinear in the sense that the equations of linear elasticity are supplemented by certain contact inequalities the location of a priori unknown contact zones and the solutions to the field equations must be determined simultaneously the algorithm is based on a rapidly converging sequence of relaxed fredholm integral equations of the second kind in which the contact problem is viewed as a perturbation of a noncontacting crack problem the algorithm exhibits great stability and speed the numerical results are orders of magnitudes more accurate than those of previous investigators

higher order extended finite elements with harmonic enrichment functions for complex crack problems summary in this paper we analyze complex crack problems in elastic media using harmonic enrichment functions in a higher order extended finite element implementation the numerically computed enrichment function of a crack is the solution of the laplace equation with discontinuous dirichlet boundary condition along the crack and its interaction with branches or other cracks is realized by imposing vanishing neumann boundary conditions along those cracks the classical finite element displacement approximation is enriched by adding the enrichment function of a crack through the framework of partition of unity a nested subgrid mesh is used in the laplace solve with a rasterized approximation of a crack which simplifies the numerical integration no partitioning of finite elements is required harmonic enrichment functions readily permit the extension to handle multiple interacting and branched cracks without any special treatment around the junction points several numerical examples are presented that arm the accuracy and eectiveness of the method when applied to complex crack

interactive multiobjective complex search abstract an interactive procedure based on box s complex search is used to solve the vector maximization problem this method has the advantage that the decision maker s underlying value function need not be explicitly specified also the problem may have nonlinear objective functions and nonlinear constraints several example problems are presented

an interactive multiple objective linear programming method for a class of underlying nonlinear utility functions this paper develops a method for interactive multiple objective linear programming assuming an unknown pseudo concave utility function satisfying certain general properties the method is an extension of our earlier method published in this journal zionts s wallenius j 1976 an interactive programming method for solving the multiple criteria problem management sci 22 6 652 663 various technical problems present in predecessor versions have been resolved in addition to presenting the supporting theory and algorithm we discuss certain options in implementation and summarize our practical experience with several versions of the method

a new variable order singular boundary element for two dimensional stress analysis a new variable order singular boundary element for two dimensional stress analysis is developed this element is an extension of the basic three node quadratic boundary element with the shape functions enriched with variable order singular displacement and traction fields which are obtained from an asymptotic singularity analysis both the variable order of the singularity and the polar profile of the singular fields are incorporated into the singular element to enhance its accuracy the enriched shape functions are also formulated such that the stress intensity factors appear as nodal unknowns at the singular node thereby enabling direct calculation instead of through indirect extrapolation or contour integral methods numerical examples involving crack notch and corner problems in homogeneous materials and bimaterial systems show the singular element s great versatility and accuracy in solving a wide range of problems with various orders of singularities the stress intensity factors which are obtained agree very well with those reported in the literature copyright 2002 john wiley sons ltd

corner singularities for elliptic problems integral equations graded meshes quadrature and compressed inverse preconditioning we take a fairly comprehensive approach to the problem of solving elliptic partial differential equations numerically using integral equation methods on domains where the boundary has a large number of corners and branching points use of non standard integral equations graded meshes interpolatory quadrature and compressed inverse preconditioning are techniques that are explored developed mixed and tested on some familiar problems in materials science the recursive compressed inverse preconditioning the major novelty of the paper turns out to be particularly powerful and when it applies eliminates the need for mesh grading completely in an electrostatic example for a multiphase granular material with about two thousand corners and triple junctions and a conductivity ratio between phases up to a million we compute a common functional of the solution with an estimated relative error of 10 1 2 in another example five times as large but with a conductivity ratio of only a hundred we achieve an estimated relative error of 10 1 4

an accurate and fast analysis for strongly interacting multiple crack configurations including kinked v and branched y cracks in this study multiple interacting cracks in an infinite plate are analyzed to determine the overall stress field as well as stress intensity factors for crack tips and singular wedges at crack kinks the problem is formulated using integral equations expressed in terms of unknown edge dislocation distributions along crack lines these distributions derive from an accurate representation of the crack opening displacements using power series basis terms obtained through wedge eigenvalue analysis which leads to both polynomial and non polynomial power series the process is to choose terms of the series and their exponents such that the tractions on the crack faces are virtually zero compared to the far field loading applying the method leads to a set of linear algebraic equations to solve for the unknown weighting coefficients for the power series basis terms since no numerical integration is required unlike in other methods in most cases solution takes just a few seconds on a pc the accuracy and efficiency of the method are first demonstrated with a simple example of three aligned cracks with small ligaments between their tips under tensile loading the results are compared to exact results as well as to those of other numerical methods including recent fie fem and bem approaches said to have fast computation times thereafter some new and challenging crack interaction problems including branched y cracks two kinked v cracks are solved from a parametric study of the various crack configurations stress intensity factors are graphed and tabulated to demonstrate subtleties in the magnitudes of the crack interactions

an interactive branch and bound algorithm for multiple criteria optimization we present a new interactive algorithm for multiple criteria optimization the algorithm is of the branch and bound type and differs from previous interactive algorithms in several ways first the field of application is wider because it applies to two important classes of multiple criteria decision problems those for which the feasible set is convex and those for which the feasible set is discrete secondly the algorithm does not require a great deal from the decision maker he is merely required to indicate his preference between two vectors whenever the algorithm so demands

integral equation methods for stokes flow and isotropic elasticity in the plane we present a class of integral equation methods for the solution of biharmonic boundary value problems with applications to two dimensional stokes flow and isotropic elasticity the domains may be multiply connected and finite infinite or semi infinite in extent our analytic formulation is based on complex variables and our fast multipole based iterative solution procedure requireso n operations wherenis the number of nodes in the discretization of the boundary the performance of the methods is illustrated with several large scale numerical examples

on the numerical solution of the biharmonic equation in the plane the biharmonic equation arises in a variety of problems in applied mathematics most notably in plane elasticity and in viscous incompressible flow integral equation methods are natural candidates for the numerical solution of such problems since they discritize the boundary alone are easy to apply in the case of free or moving boundaries and achieve superalgebraic convergence rates on sufficiently smooth domains regardless of shape in this paper we follow the work of mayo and greenbaum and make use of the sherman lauricella integral equation which is a fredholm equation with bounded kernel we describe a fast algorithm for the evaluation of the integral operators appearing in that equation when combined with a conjugate gradient like algorithm we are able to solve the discretized integral equation in an amount of time proportional to n where n is the number of nodes in the discretization of the boundary

stress calculations on multiply connected domains the outstanding problem of finding a simple muskhelishvili type integral equation for stress problems on multiply connected domains is solved complex potentials are represented in a way which allows for the incorporation of cracks and inclusions several numerical examples demonstrate the generality and extreme stability of the approach the stress field is resolved with a relative error of less than 10 10 on a large yet simply reproducible setup with a loaded square plate containing 4096 holes and cracks comparison with previous results in the literature indicates that general purpose finite element software may perform better than many special purpose codes

efficient algorithm for edge cracked geometries the stress field in a finite edge cracked specimen under load is computed using algorithms based on two slightly different integral equations of the second kind these integral equations are obtained through left regularizations of a first kind integral equation in numerical experiments it is demonstrated that the stress field can be accurately computed highly accurate stress intensity factors and t stresses are presented for several setups and extensive comparisons with results from the literature are made for simple geometries the algorithms presented here achieve relative errors of less than 10 10 it is also shown that the present algorithms can accurately handle both geometries with arbitrarily shaped edge cracks and geometries containing several hundred edge cracks all computations were performed on an ordinary workstation copyright c 2005 john wiley sons ltd less

a comparative study of interactive tradeoff cutting plane methods for momp abstract in this paper four interactive cutting plane methods developed for multiple objective mathematical programming problems are compared to one another using randomly selected problems tradeoff cutting plane methods converge to the best compromise solution by iteratively reducing the objective space by cutting planes the cutting planes are constructed using partial preference information obtained from the decision maker the performance of the four methods is evaluated and compared to one another by solving the test problems under i four classes of preference functions in addition to the original preference functions to simulate the nonexisting decision maker ii different precision levels in the decision maker s comparative accuracy iii decision space expanded or contracted and iv inconsistent responses by the decision maker based on the comparative study some guidelines for performing a comparative study of multicriteria interactive methods are presented

cubic spline approximation techniques for parameter estimation in distributed systems approximation schemes employing cubic splines in the context of a linear semigroup framework are developed for both parabolic and and hyperbolic second order partial differential equation parameter estimation problems convergence results are established for problems with linear and nonlinear systems and a summary of numerical experiments with the techniques proposed is given

fracture initiation at sharp notches correlation using critical stress intensities abstract in the context of linear elasticity a stress singularity of the type k n r k n the magnitude of the intensity fully characterizes the stress state in the region of the corner a critical value of k n may be appropriate as a failure criterion in situations where the region around the corner dominated by the singular field is large compared to intrinsic flaw sizes inelastic zones and process zone sizes we determined k n for notched mode i three point flexure specimens using a combination of the williams williams m l 1952 stress singularities resulting from various boundary conditions in angular corners of plates in extension journal of applied mechanics 74 526 528 asymptotic method dimensional considerations and detailed finite element analysis we carried out an experimental study of the feasibility of using a critical value of k n to correlate failure with a series of notched polymethyl methacrylate pmma three point flexure specimens with notch angles of 60 90 and 120 using the measured failure loads and the finite element solutions for k n we infer the critical notch stress intensity k cr n for sharp notched pmma the data show that excellent failure correlation is obtained through the use of the single parameter k cr n furthermore simple estimates of the size of the inelastic zone for the notched pmma specimens show it to be small relative to the singularity dominated zone this supports the applicability of linear elastic notch mechanics lenm and the idea that a critical value of k n can be used to correlate fracture initiation

arbitrary branched and intersecting cracks with the extended finite element method summary extensions of a new technique for the nite element modelling of cracks with multiple branches multiple holes and cracks emanating from holes are presented this extended nite element method x fem allows the representation of crack discontinuities and voids independently of the mesh a standard displacementbased approximation is enriched by incorporating discontinuous elds through a partition of unity method a methodology that constructs the enriched approximation based on the interaction of the discontinuous geometric features with the mesh is developed computation of the stress intensity factors sif in dierent examples involving branched and intersecting cracks as well as cracks emanating from holes are presented to demonstrate the accuracy and the robustness of the proposed technique copyright 2000 john wiley sons ltd

the design and analysis of the generalized finite element method abstract in this paper we introduce the generalized finite element method gfem as a combination of the classical finite element method fem and the partition of unity method pum the standard finite element spaces are augmented by adding special functions which reflect the known information about the boundary value problem and the input data e g the singular functions obtained from the local asymptotic expansion of the exact solution in the neighborhood of a corner point etc the special functions are multiplied with the partition of unity corresponding to the standard linear vertex shape functions and pasted together with the existing finite element basis to construct an augmented conforming finite element space in this way the local approximability afforded by the special functions is included in the approximation while maintaining the existing infrastructure of finite element codes the major features of the gfem are 1 the essential boundary conditions can be imposed exactly as in the standard fem unlike other partition of unity based methods where this is a major issue 2 the accuracy of the numerical integration of the entries of the stiffness matrix and load vector is controlled adaptively so that the errors in integration of the special functions do not affect the accuracy of the constructed approximation this issue also has not been sufficiently addressed in other implementations of partition of unity or meshless methods and 3 linear dependencies in the system of equations are resolved by employing an easy modification of the direct linear solver the power of the gfem for solving problems in domains with complex geometry with less error and less computer resources than the standard fem is illustrated by numerical examples

interactive relaxation method for a broad class of integer and continuous nonlinear multiple criteria problems an interactive decomposition algorithm for solving a broad class of multiple criteria mc problems is presented in this paper on the one hand the method is designed to solve a broad class of mc problems including complex ones i e problems with nonlinear objective functions and nonlinear constraints with continuous and or integer valued decision variables and with an unknown underlying nonlinear preference function on the other hand the method is intended to reduce the assessment burden on the decision maker dm by simplifying and facilitating the task of making preference assessments and tradeoffs the method is efficient from a computational standpoint since the only program that needs to be solved at each iteration is linear in the decision variables also the algorithm is capable of producing lower and upper bounds lb and ub on the optimal objective value of the mc problem at each iteration although the dm s preference function is not assumed to be known explicitly lb and ub can be used to terminate the search prematurely at a satisfactory good enough solution and consequently to reduce the computational time as well as the number of preference assessments that the dm must make finally all the tradeoffs that the dm is required to make are of the form of ordinal paired comparisons most of which are particularly simple since they involve changes in only two criteria at a time also all the preference assessments are made in the context of feasible solutions only

a numerical model of stress driven grain boundary diffusion the stress driven grain boundary diffusion problem is a continuum model of mass transport phenomena in microelectronic circuits due to high current densities electromigration and gradients in normal stress along grain boundaries the model involves coupling many different equations and phenomena and difficulties such as nonlocality stiffness complex geometry and singularities in the stress tensor near corners and junctions make the problem difficult to analyze rigorously and simulate numerically we present a new numerical approach to this problem using techniques from semigroup theory to represent the solution the generator of this semigroup is the composition of a type of dirichlet to neumann map on the grain boundary network with the laplace operator on the network to compute the former we solve the equations of linear elasticity several times once for each basis function on the grain boundary we resolve singularities in the stress field near corners and junctions by adjoining special singular basis functions to both finite element spaces 2d for elasticity 1d for grain boundary functions we develop data structures to handle jump discontinuities in displacement across grain boundaries singularities in the stress field complicated boundary conditions at junctions and interfaces and the lack of a natural ordering for the nodes on a branching grain boundary network the method is used to study grain boundary diffusion for several geometries

an approximation theory for nonlinear partial differential equations with applications to identification and control approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations these ideas are used to establish theoretical convergence results for parameter identification using modal eigenfunction approximation techniques results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given

on the numerical evaluation of stress intensity factors for an interface crack of a general shape a numerical algorithm is presented for the problem of a crack along the interface of an elastic inclusion embedded in an elastic plane subjected to uniform stress at infinity the algorithm is based on a fredholm integral equation of the second kind and allows for fast and accurate solutions to geometries of great complexity in an example crack opening displacement and stress intensity factors are computed for a crack in the interface of an inclusion with nineteen protruding arms

multiple crack analysis in finite plates in this study interactions of multiple cracks in finite rectangular plates are analyzed a finite plate is treated as a polygon shaped plate which can be created by contiguous crack segments embedded in an infinite plate forming an enclosed region so there are no true crack tips remaining around the plate the problem is formulated in terms of integral equations expressed by edge dislocation distributions representing opening displacement profiles for the cracks with both normal and tangential components to solve this boundary value problem we employ the superposition approach based on the dislocation distributions requiring the determination of crack opening displacement profiles that satisfy the traction free condition on interior crack faces and the given boundary tractions on four exterior cracks defining the rectangular plate applying the method with a new point allocation scheme reducing the number of evaluation points leads to a set of linear algebraic equations in terms of unknown weighting coefficients of opening displacement profiles these opening displacement profile components are categorized in terms of polynomial terms which are integers and wedge terms which are rational numbers approximated from irrational wedge eigenvalues to evaluate integrals in closed forms once the coefficients of opening displacement profile components are obtained stress and displacement fields on the entire body as well as stress intensity factors at the crack tips and kinks are calculated after the accuracy of the method is shown by comparing the results for different sample problems the strong interactions of multiple cracks in a rectangular plate under various loading conditions are demonstrated with figures and tables

gradient projection and local region search for multiobjective optimisation this paper presents a new method for multiobjective optimisation based on gradient projection and local region search the gradient projection is conducted through the identification of normal vectors of an efficient frontier the projection of the gradient of a nonlinear utility function onto the tangent plane of the efficient frontier at a given efficient solution leads to the definition of a feasible local region in a neighbourhood of the solution within this local region a better efficient solution may be sought to implement such a gradient based local region search scheme a new auxiliary problem is developed if the utility function is given explicitly this search scheme results in an iterative optimisation algorithm capable of general nonseparable multiobjective optimisation otherwise an interactive decision making algorithm is developed where the decision maker dm is expected to provide local preference information in order to determine trade off directions and step sizes optimality conditions for the algorithms are established and the convergence of the algorithms is proven a multiobjective linear programming molp problem is taken for example to demonstrate this method both graphically and analytically a nonlinear multiobjective water quality management problem is finally examined to show the potential application of the method to real world decision problems

a domain independent integral for computation of stress intensity factors along three dimensional crack fronts and edges by bem the present work deals with an evaluation of stress intensity factors sifs along straight crack fronts and edges in three dimensional isotropic elastic solids a new numerical approach is developed for extraction from a solution obtained by the boundary element method bem of those sifs which are relevant for a failure assessment of mechanical components in particular the generalized sifs associated to eigensolutions characterized by unbounded stresses at a neighbourhood of the crack front or a reentrant edge and also that associated to t stress at the crack front can be extracted the method introduced is based on a conservation integral called h integral which leads to a new domain independent integral represented by a scalar product of the sif times some element shape function defined along the crack front or edge for sufficiently small element lengths these weighted averages of sifs give reasonable pointwise estimation of the sifs a proof of the domain integral independency based on the bi orthogonality of the classical two dimensional eigensolutions associated to a corner problem is presented numerical solutions of two three dimensional problems a crack problem and a reentrant edge problem are presented the accuracy and convergence of the new approach for sif extraction being analysed

efficient boundary element analysis of sharp notched plates the present paper further develops the boundary element singularity subtraction technique to provide an efficient and accurate method of analysing the general mixed mode deformation of two dimensional linear elastic structures containing sharp notches the elastic field around sharp notches is singular because of the convergence difficulties that arise in numerical modelling of elastostatic problems with singular fields these singularities are subtracted out of the original elastic field using the first term of the williams series expansion this regularization procedure introduces the stress intensity factors as additional unknowns in the problem hence extra conditions are required to obtain a solution extra conditions are defined such that the local solution in the neighbourhood of the notch tip is identical to the williams solution the procedure can take into account any number of terms of the series expansion the standard boundary element method is modified to handle additional unknowns and extra boundary conditions analysis of plates with symmetry boundary conditions is shown to be straightforward with the modified boundary element method in the case of non symmetrical plates the singular tip tractions are not primary boundary element unknowns the boundary element method must be further modified to introduce the boundary integral stress equations of an internal point approaching the notch tip as primary unknowns in the formulation the accuracy and efficiency of the method is demonstrated with some benchmark tests of mixed mode problems new results are presented for the mixed mode analysis of a non symmetrical configuration of a single edge notched plate

on the computation of stress fields on polygonal domains with v notches the interior stress problem is solved numerically for a single edge notched specimen under uniaxial load the algorithm is based on a modification of a fredholm second kind integral equation with compact operators due to muskhelishvili several singular basis functions for each of the seven corners in the geometry enable high uniform resolution of the stress field with a modest number of discretization points as a consequence notch stress intensity factors can be computed directly from the solution this is an improvement over other procedures where the stress field is not resolved in the corners and where notch stress intensity factors are computed in a roundabout way via a path independent integral numerical examples illustrate the superior stability and economy of the new scheme less

path independent integrals for computing stress intensity factors at sharp notches in elastic plates a set of path independent integrals is constructed for the calculation of the generalized stress intensity factors occurring in elastic plates having sharp re entrant corners or notches with stress free faces and subjected to mode i ii or iii type loading the mode i integral is then demonstrated to enjoy a reasonable degree of numerical path independence in a finite element analysis of a test problem having an exact solution finally this integral is used on the same problem in conjunction with a regularizing finite element procedure or superposition method the results indicate that sufficiently accurate estimates of these stress intensity factors for engineering purposes can be achieved with little computational effort

optimum choice of moving sensor trajectories for distributed parameter system identification the problem is considered of the optimal choice of moving sensor trajectories from the viewpoint of distributed parameter system identification accuracy the determinant of the information matrix of parameter estimates is taken as a measure of identification accuracy necessary and sufficient conditions for the trajectories to be optimal are derived it is shown that the optimum trajectories can be found by solving a sequence of optimal sensor allocation problems a number of examples illustrates the proposed approach

a fast and stable solver for singular integral equations on piecewise smooth curves a scheme for the numerical solution of singular integral equations on piecewise smooth curves is presented it relies on several techniques reduction nystrom discretization composite quadrature recursive compressed inverse preconditioning and multipole acceleration the scheme is fast and stable its computational cost grows roughly logarithmically with the precision sought and linearly with overall system size when the integral equation models a boundary value problem the achievable accuracy may be close to the condition number of that problem times machine epsilon this is illustrated by application to elastostatic problems involving zigzag shaped cracks with up to twenty thousand corners and branched cracks with hundreds of triple junctions

treatment of singularities in helmholtz type equations using the boundary element method abstract in many engineering problems boundaries with sharp corners or abrupt changes in the boundary conditions and or the material properties give rise to singularities of various types which tend to slow down the rate of convergence with respect to decreasing the mesh size of any standard numerical method used for obtaining the solution in this paper in order to develop a method which overcomes this difficulty the singular solutions of isotropic and anisotropic helmholtz type equations with homogeneous dirichlet and or neumann boundary conditions in the neighbourhood of a singular point are derived the standard boundary element method bem is then modified to take account of the form of singularity without an appreciable increase in the computational effort and at the same time keeping a uniform discretization three examples are carefully investigated and the numerical results presented show an excellent performance of the approach developed

a convergent interactive cutting plane algorithm for multiobjective optimization this paper presents an interactive cutting plane algorithm for determining a best compromise solution to a multiobjective optimization problem in situations with an implicitly defined utility function we derive cutting planes that are based on suitable pairwise trade offs between the objective functions as prescribed by the decision maker at each iterate generated by the algorithm the proposed algorithm requires no line searches and generates iterates that are all contained in the efficient frontier this feature facilitates the preference judgment of the decision maker and permits an analyst to terminate short of optimality with an efficient near optimal solution a convergence analysis establishes that any accumulation point generated by the algorithm is a best compromise solution we also conduct an error analysis to point out the effect of inconsistencies in trade off information provided by the decision maker the algorithm may be extended to situations involving nonconvex feasible regions as well as nonconcave for a max problem objective functions we offer remarks for such cases and describe an application to an urban runoff control design problem

the generalized finite element method an example of its implementation and illustration of its performance the generalized finite element method gfem was introduced in reference 1 as a combination of the standard fem and the partition of unity method the standard mapped polynomial finite element spaces are augmented by adding special functions which reflect the known information about the boundary value problem and the input data the geometry of the domain the loads and the boundary conditions the special functions are multiplied with the partition of unity corresponding to the standard linear vertex shape functions and are pasted to the existing finite element basis to construct a conforming approximation the essential boundary conditions can be imposed exactly as in the standard fem adaptive numerical quadrature is used to ensure that the errors in integration do not affect the accuracy of the approximation this paper gives an example of how the gfem can be developed for the laplacian in domains with multiple elliptical voids and illustrates implementation issues and the superior accuracy of the gfem versus the standard fem copyright 2000 john wiley sons ltd

an overview of techniques for solving multiobjective mathematical programs multiobjective mathematical programming has been one of the fastest growing areas of or ms during the last 15 years this paper presents some reasons for the rapidly growing increase in interest in multiobjective mathematical programming a discussion of the advantages and disadvantages of the three general approaches articulation of the decision maker s preference structure over the multiple objectives prior to during or after the optimization towards multiobjective mathematical programming a nontechnical overview of many of the specific solution techniques for multiobjective mathematical programming and a discussion of important areas for further research the overview concentrates on those techniques which require an articulation of the decision maker s preference structure either during or after the optimization since these are the areas where most of the recent research has been conducted it differs from previous overviews in that in addition to the timing of the elicited preference informa

reduction of distributed system identification complexity using intelligent sensors abstract the identification problems of distributed parameter systems dps is dealt with a special method of data collection by using moving sensors is proposed the sensors are intelligent in the sense that they are able to track the positions of the exiremum values of a system state at each time instant it is shown how to reduce the identification problem for dps to that of identifying a certain system described by ordinary differential equations ode the proposed approach is applicable to the dps described by quasi linear partial differential equations of the hyperbolic type attention is focused on the problem of reduction while the identification of the resulting ode is not considered in detail since it is an easier task