topology optimization with pressure load through a level set method abstract the topology optimization problem with pressure load is solved by using a level set method the free boundary and the pressure boundary of a structure are represented separately as two zero level sets of two level set functions and they are independently propagated during the optimization by solving two hamilton jacobi equations in order to prevent the two boundaries from touching or crossing each other the design velocities of the two boundaries that amount to the steepest descent directions are modified the optimization problem of minimum compliance with perimeter regularization is considered the shape derivatives of the two boundaries are derived by using the material derivative approach and the adjoint method the finite element analysis is done through an eulerian method by employing a fixed mesh and an artificial weak material that represents void numerical examples in two dimensions are investigated

minimum length scale control in structural topology optimization based on the moving morphable components mmc approach abstract a novel approach which can control the minimum length scale in topology optimization in a straightforward and explicit way is proposed in the present paper this approach is constructed under the so called moving morphable components mmc based solution framework where optimized structural topology can be found by changing the shapes and layout of a set of trapezoid shaped structural components on a fixed finite element mesh the extended finite element method xfem is employed for structural response analysis and shape sensitivity information is obtained by carrying out numerical integration along the structural boundary a precision definition of the minimum length scale of a structure is also suggested based on the proposed solution framework compared with existing approaches the proposed approach can achieve minimum length scale control by simply setting lower bounds on a set of geometric design variables only a small number of purely geometric constraints imposed on the sizes of intersection regions should be considered explicitly in order to get a complete minimum length scale control numerical examples demonstrate the effectiveness of the proposed method

color level sets a multi phase method for structural topology optimization with multiple materials in this paper we address the problem of structural shape and topology optimization in a multi material domain a level set method is employed as an alternative approach to the popular homogenization based methods of rule of mixtures for multi material modeling a multi phase level set model is adapted for material and topology representation this model eliminates the need for a material interpolation or phase mixing scheme it only requires m level set functions to represent a structure of n 2m different material phases in a principle similar to combining colors from the three primary colors therefore this multi phase model may be referred to as a color level set representation which has its unique benefits it is flexible to handle complex topologies it substantially reduces the number of model functions when n 3 it automatically avoids the problem of overlap between material phases of a conventional partitioning approach we describe numerical techniques for efficient and robust implementation of the method by embedding a rectilinear grid in a fixed finite element mesh defined on a reference design domain this would separate the issues of accuracy in numerical calculations of the physical equation and in the level set model propagation a gradient projection method is described for incorporating multiple constraints in the problem finally the benefits and the advantages of the developed method are illustrated with several 2d examples of mean compliance minimization of multi material structures

on the convergence of product formulas for the evaluation of certain two dimensional cauchy principal value integrals on etablit la convergence des regles de produits de type interpolatoire pour l evaluation numerique de certaines integrales bidimensionnelles a valeur principale de cauchy on obtient quelques estimations du reste pour plusieurs classes de fonctions

new method for deriving eigenvalue rate with respect to support location the authors present a new method to derive the formulas of eigenvalue rate with respect to in span support location using the generalized variational principle of the rayleigh quotient following the ideas of this note the eigenvalue rate with respect to such variables as location of discrete or continuous in span supports the location of concentrated mass location of elastic support and location of a substructure can be derived without any conceptual difficulties

on the convergence of an interpolatory product rule for evaluating cauchy principal value integrals etablissement des theoremes de convergence des regles de produits interpolatoires pour l evaluation d integrales singulieres de cauchy avec estimation asymptotique du reste amelioration et generalisation de resultats anterieurs

eigenvalue sensitivity analysis of planar frames with variable joint and support locations various sensitivity equations are developed in this study for eigenvalue sensitivity analysis of planar frames with variable joint and support locations the emphasis is placed on the derivation of the sensitivity equations by the continuum approach a variational form of an eigenvalue equation is first derived in which all of the quantities are expressed with respect to the local coordinate system the material derivative of this variational form is then sought to account for the changes in the member s length and orientation resulting from the perturbation of joint and support locations finally eigenvalue sensitivity equations are formulated in either domain quantities by the domain method or boundary quantities by the boundary method examples are presented to validate these derived sensitivity equations with analytical solutions as well as numerical results it is concluded that the sensitivity equation derived by the boundary method is computationally more efficient but less accurate than that of the domain method nevertheless both of them are superior to the conventional discrete analytical method in terms of computational efficiency nomenclature ait ei ij cross sectional area young s modulus and moment of inertia of member respectively b design variable j a line functional j and its total shape derivative k m global stiffness and mass matrices at m elementary stiffness and mass matrices dj pj length orientation angle and mass density of member respectively mit rij cosine and sine of member n total number of members n

some convergence results in perimeter controlled topology optimization abstract the computation of optimal topologies of elastic continuum structures using a constraint on the perimeter is investigated predicting macroscopic black white topologies without the use of homogenization techniques this approach is presently one of the most attractive approaches in topology optimization mathematical justifications are given for both the relaxation of the discrete value constraint on the design variable and for the finite element discretizations it turns out that the way in which the perimeter has been calculated to date the numerical results will not approximate the intended original problem but one with a taxi cab perimeter which measures lengths of structural edges after projection onto the coordinate axes

functional equations of weng s zeta functions for g p q it is shown that weng s zeta functions associated with arbitrary semisimple algebraic groups defined over the rational number field and their maximal parabolic subgroups satisfy the functional equations 1 introduction recently lin weng introduced a new class of abelian zeta functions associated to a pair of reductive algebraic group g and its maximal parabolic subgroup p which are related with constant terms of eisenstein series in this paper we simply refer to these zeta functions as weng s zeta functions these are motivated by and closely related to non abelian zeta functions called high rank zeta functions associated with algebraic number fields which were also introduced by weng himself from a viewpoint of arakelov geometry based on iwasawa s interpretation and tate s fourier analysis on adeles high rank zeta functions are generalizations of the dedekind zeta functions and in fact rank one zeta functions coincide with the dedekind zeta functions up to constant multiples hence the study of weng s zeta functions is not only interesting itself but also sug gestive for the study of the dedekind zeta functions the profound background the path to the discovery and the development of weng s zeta functions are detailed in his elaborated papers 13 14 15 16 one of the most significant properties for weng s zeta functions is the behav ior of their zeros weng conjectured that for any pair g p weng s zeta functions satisfy certain functional equations and the riemann hypothesis as is expected or shown for various kinds of zeta functions as for the functional equations initially weng proved them in the cases sl n n 2 3 4 5 sp 4 s o 8 and g2 a nd successively h kim weng in the cases sl n p n 1 1 for arbitrary n 2 un published as for the riemann hypothesis its validity was shown in the cases sl n n 2 3 4 5 sp 4 and g2 with their arbitrary maximal parabolic sub groups see 6 8 10 11 12 for the details in this paper we establish the functional equations in arbitrary semisimple cases in a unified way we will see that the functional equations are governed by the involutions on the weyl groups see the last paragraph of section 3 and lemma 5 3 furthermore we give the explicit forms of weng s zeta functions and

cbs based topology optimization including design dependent body loads abstract in this paper the inherent problem of the so called parasitic effect of low density region caused by design dependent loads is investigated for topology optimization a cbs closed b splines based method is developed to solve efficiently the problem in the way of shape optimization compared to the standard density method design variables are unattached to the finite element model and defined by control parameters dominating the parametric equation of the cbs as a result design dependent loads associated with the material layout of a structure are made change indirectly by the boundary variation of the structure to favour structural reanalyses and sensitivity analysis the implicit form of the cbs i e level set function lsf is used in conjunction with the fixed computing grid of finite cell method fcm a variety of design dependent body loads is considered for the mathematical formulation of the cbs based method typical examples are given to illustrate that the cbs based method is free of low density regions in the optimized topology owing to the proper definitions of design variables

approximation of the hilbert transform on the real line using hermite zeros the authors study the hilbert transform on the real line they introduce some polynomial approximations and some algorithms for its numerical evaluation error estimates in uniform norm are given

topology optimization of compliant mechanism and its support through a level set method abstract in the present paper the task of designing a compliant mechanism is accomplished by solving a multi objective topology optimization problem the objective function includes a target displacement at the output port and compliances of two load cases the design variables include two types of boundaries i e the traction free boundary and the dirichlet boundary the topology optimization of compliant mechanism and its support is solved by using a level set method two level set functions are used to represent a compliant mechanism and the two types of boundaries each of the two boundaries is represented by a part of the zero level set of one level set function evolution of the two boundaries is modeled by two independent hamilton jacobi equations thus the shape and topology of the two boundaries change independently the shape derivatives are derived by using a lagrangian function and the adjoint method the finite element analysis is done by modifying a fixed background mesh and the artificial weak material is not used numerical examples in two dimensions are investigated

optimization of support positions to maximize the fundamental frequency of structures in this paper the position optimization of simple supports is implemented to maximize the fundamental frequency of a beam or plate structure both elastic and rigid supports are taken into account first the frequency sensitivity with respect to the movement of a simple support is derived using the discrete method by means of the shape functions of the finite element method closed form sensitivity formulations are developed straightforwardly then a heuristic approach called evolutionary shift method is presented for optimizing support positions with a fixed grid mesh scheme based on the design sensitivity analysis the support with the highest efficiency is shifted in priority along the elementary edges with the interval step of the elementary size to facilitate the convergence of the process the interpolation technique is employed to evaluate the solution more accurately finally three numerical examples are presented to demonstrate the validity of the sensitivity analysis and the effectiveness of the optimization method copyright 2004 john wiley sons ltd

numerical methods for some special fredholm integral equations on the real line the authors propose a simple numerical method to approximate the solution of csie the convergence and the stability of the procedure are proved and some numerical examples are shown

velocity extension for the level set method and multiple eigenvalues in shape optimization in the context of structural optimization by the level set method we propose an extension of the velocity of the underlying hamilton jacobi equation the gradient method is endowed with a hilbertian structure based on the h1 sobolev space numerical results for compliance minimization and mechanism design show a strong improvement of the rate of convergence of the level set method another important application is the optimization of multiple eigenvalues

approximation of the hilbert transform on the real semiaxis using laguerre zeros the authors propose two new algorithms for the computation of cauchy principal value integrals on the real semiaxis the proposed quadrature rules use zeros of laguerre polynomials theoretical error estimates are proved and some numerical examples are showed

constraints of distance from boundary to skeleton for the control of length scale in level set based structural topology optimization abstract a method is proposed for the control of minimum maximum length scale in the level set based structural topology optimization the minimum maximum length scale of structure is characterized by using the concept of smallest biggest maximal inscribable ball in order to prevent trivial zero minimum length scale the skeleton of structure is utilized and trimmed the control of length scale is realized by constraining the distance from boundary to skeleton and the distance is explicitly constructed by using the highly efficient fast marching method numerical examples in two dimensions are investigated

the topological asymptotic for pde systems the elasticity case the aim of the topological sensitivity analysis is to obtain an asymptotic expansion of a design functional with respect to the creation of a small hole in this paper such an expansion is obtained and analyzed in the context of linear elasticity for general functionals and arbitrary shaped holes by using an adaptation of the adjoint method and a domain truncation technique the method is general and can be easily adapted to other linear pdes and other types of boundary conditions

higher rank zeta functions for elliptic curves in earlier work by l w a nonabelian zeta function was defined for any smooth curve x over a finite field f q and any integer n 1 bywhere the sum is over isomorphism classes of f q rational semistable vector bundles v of rank n on x with degree divisible by n this function which agrees with the usual artin zeta function of x f q if n 1 is a rational function of q s with denominator 1 q n s 1 q n n s and conjecturally satisfies the riemann hypothesis in this paper we study the case of genus 1 curves in detail we show that in that case the dirichlet serieswhere the sum is now over isomorphism classes of f q rational semistable vector bundles v of degree 0 on x is equal to k 1 x f q s k and use this fact to prove the riemann hypothesis for x n s for all n

a level set method for structural topology optimization this paper presents a new approach to structural topology optimization we represent the structural boundary by a level set model that is embedded in a scalar function of a higher dimension such level set models are flexible in handling complex topological changes and are concise in describing the boundary shape of the structure furthermore a well founded mathematical procedure leads to a numerical algorithm that describes a structural optimization as a sequence of motions of the implicit boundaries converging to an optimum solution and satisfying specified constraints the result is a 3d topology optimization technique that demonstrates outstanding flexibility of handling topological changes fidelity of boundary representation and degree of automation we have implemented the algorithm with the use of several robust and efficient numerical techniques of level set methods the benefit and the advantages of the proposed method are illustrated with several 2d examples that are widely used in the recent literature of topology optimization especially in the homogenization based methods

stress based shape and topology optimization with the level set method abstract this paper proposes a level set method to solve minimum stress and stress constrained shape and topology optimization problems the method solves a sub optimization problem every iteration to obtain optimal boundary velocities a p norm stress functional is used to aggregate stresses in a single constraint the shape sensitivity function is derived and a computational procedure based on a least squares interpolation approach is devised in order to compute sensitivities at the boundaries adaptive constraint scaling is used to enforce exact control of stress limits numerical results show that the method is able to solve the problem efficiently for single and multiple load cases obtaining solutions with smooth boundaries

shape optimization of dirichlet boundaries based on weighted b spline finite cell method and level set function abstract this paper addresses extended shape optimization problems where structural supports i e dirichlet boundaries and free boundaries are simultaneously optimized unlike traditional fem the weighted b spline finite cell method fcm is applied as structural analysis tool and combined with the level set function lsf to take into account dirichlet boundary condition dbc automatically through penalization of the displacement field the proposed shape optimization method achieves a comprehensive integration of fixed grid b spline shape function and level set function as both the structure and dirichlet boundaries are described in the form of lsf any modification of dirichlet boundaries can be made in a straightforward way as easily as free boundaries by changing continuous design variables meanwhile the computing accuracy is ensured within the framework of fixed grid owing to the quadtree refinements of boundary cells stress related shape optimization problems are finally solved to demonstrate the merit and validity of the proposed optimization method in dealing with shape optimization of dirichlet boundaries

incorporating topological derivatives into shape derivatives based level set methods shape derivatives and topological derivatives have been incorporated into level set methods to investigate shape optimization problems the shape derivative measures the sensitivity of boundary perturbations while the topological derivative measures the sensitivity of creating a small hole in the interior domain the combination of these two derivatives yields an efficient algorithm which has more flexibility in shape changing and may escape from a local optimal examples on finding the optimal shapes for maximal band gaps in photonic crystal and acoustic drum problems are demonstrated

non abelian zeta functions for function fields in this paper we initiate a geometrically oriented construction of non abelian zeta functions for curves defined over finite fields more precisely we first introduce new yet genuine non abelian zeta functions for curves defined over finite fields by a weighted count on rational points over the corresponding moduli spaces of semi stable vector bundles using moduli interpretation of these points then we define non abelian l functions for curves over finite fields using integrations of eisenstein series associated to l2 automorphic forms over certain generalized moduli spaces introduction in this paper we initiate a geometrically oriented construction of non abelian zeta functions for curves defined over finite fields it consists of two chapters more precisely in chapter i we first introduce new yet genuine non abelian zeta functions for curves defined over finite fields this is achieved by a weighted count on rational points over the corresponding moduli spaces of semi stable vector bundles using moduli interpretation of these points we justify our con struction by establishing basic properties for these new zetas such as functional equation and rationality and show that if only line bundles are involved our newly defined zetas coincide with artin s zeta all this in particular the ratio nality then leads naturally to our definition of global non abelian zeta functions for curves defined over number fields which themselves are justified by a con vergence result we end this chapter with a detailed study on rank two non abelian zeta functions for genus two curves based on what we call infinitesimal structures of brill noether loci and weierstrass points in chapter ii we begin with a similar construction for the field of rationals to motivate what follows in particular we show that there is an intrinsic relation between our non abelian zeta functions and eisenstein series due to this instead of introducing general non abelian l functions for curves defined over finite fields with more general test functions as what tate did in his thesis for abelian l functions we then define non abelian l functions for curves over finite fields as integrations of eisenstein series associated to l2 automorphic forms over certain generalized moduli spaces here geometric truncations play a key role basic properties for these non abelian l functions such as meromorphic continuation

regular article a pde based fast local level set method we develop a fast method to localize the level set method of osher and sethian 1988 j comput phys 79 12 and address two important issues that are intrinsic to the level set method a how to extend a quantity that is given only on the interface to a neighborhood of the interface b how to reset the level set function to be a signed distance function to the interface efficiently without appreciably moving the interface this fast local level set method reduces the computational effort by one order of magnitude works in as much generality as the original one and is conceptually simple and easy to implement our approach differs from previous related works in that we extract all the information needed from the level set function or functions in multiphase flow and do not need to find explicitly the location of the interface in the space domain the complexity of our method to do tasks such as extension and distance reinitialization is o n where n is the number of points in space not o n log n as in works by sethian 1996 proc nat acad sci 93 1591 and helmsen and co workers 1996 spie microlithography ix p 253 this complexity estimation is also valid for quite general geometrically based front motion for our localized method

robust shape optimization of continuous structures via the level set method abstract this work proposes a stochastic shape optimization method for continuous structures using the level set method such a method aims to minimize the expected compliance and its variance as measures of the structural robustness the behavior of continuous structures is modeled by linear elasticity equations with uncertain loading and material this uncertainty can be modeled using random variables with different probability distributions as well as random fields the proper problem formulation is ensured by the proof of the existence colorrev of solution under certain geometrical constraints on the set of admissible shapes the proposed method addresses the stochastic linear elasticity problem in its weak form obtaining the explicit expressions for the continuous shape derivatives some numerical examples are presented to show the effectiveness of the proposed approach

numerical approximation of weakly singular integrals on the half line this paper deals with the numerical approximation of a weakly singular integral transform by means of laguerre nodes error estimates in a weighted uniform norm and some numerical tests are given

incorporating topological derivatives into level set methods the aim of this paper is to investigate the use of topological derivatives in combination with the level set method for shape reconstruction and optimization problems we propose a new approach generalizing the standard speed method which is obtained by using a source term in the level set equation that depends on the topological derivative of the objective functional the resulting approach can be interpreted as a generalized fixed point iteration for the optimality system with respect to topological and shape variations moreover we apply the new approach for a simple model problem in shape reconstruction where the topological derivative can be computed without additional effort finally we present numerical tests related to this model problem which demonstrate that the new method based on shape and topological derivative successfully reconstructs obstacles in situations where the standard level set approach fails

a level set method for shape and topology optimization of both structure and support of continuum structures abstract we present a level set method for the shape and topology optimization of both structure and support two level set functions are used to implicitly represent a structure the traction free boundary and the dirichlet boundary are represented separately and are allowed to be continuously changed during the optimization the optimization problem of minimum compliance is considered the shape derivatives of both boundaries are derived by using a lagrangian function and the adjoint method the finite element analysis is done by modifying a fixed background mesh and we do not use the artificial weak material numerical examples in two dimensions are investigated

level set topology optimization for mechanical metamaterials under hybrid uncertainties abstract this paper proposes a level set based robust topology optimization rto method for computational design of metamaterials under hybrid uncertainties e g auxetics with negative poisson s ratio where the young s modulus of the solid is described as a random variable while the poisson s ratio is regarded as an interval variable firstly the robust objective function is formulated by a combination of interval mean and interval variance of the deterministic objective function secondly the interval mean and interval variance are computed by a hybrid uncertain analysis approach termed as polynomial chaos chebyshev interval pcci method thirdly the design sensitivities of the robust objective function are obtained after the implementation of the pcci method finally a powerful parametric level set method plsm in conjunction with the numerical homogenization method is applied to achieve the robust topological design for the auxetic microstructure several numerical cases are used to demonstrate the effectiveness of the proposed method for the robust topology optimization problems this method is non intrusive and general and can be easily extended to a range of design problems of micro structured metamaterials

convergence of product formulas for the numerical evaluation of certain two dimensional cauchy principal value integrals we consider product rules of interpolatory type for the numerical approximation of certain two dimensional cauchy principal value integrals we present convergence results which generalize those known in the one dimensional case

where best to hold a drum fast if we are allowed to fasten say one half of a drum s boundary which half produces the lowest or highest bass note the answer is a natural limit of solutions to a family of extremal robin problems for the least eigenvalue of the laplacian we produce explicit extremizers when the drum is a disk while for general shapes we establish existence and necessary conditions and we build and test a pair of numerical methods

level set methods for optimization problems involving geometry and constraints i frequencies of a two density inhomogeneous drum many problems in engineering design involve optimizing the geometry to maximize a certain design objective geometrical constraints are often imposed in this paper we use the level set method devised in osher and sethian j comput phys 79 12 1988 the variational level set calculus presented in zhao et al j comput phys 127 179 1996 and the projected gradient method as in rudin et al physica d 60 259 1992 to construct a simple numerical approach for problems of this type we apply this technique to a model problem involving a vibrating system whose resonant frequency or whose spectral gap is to be optimized subject to constraints on geometry our numerical results are quite promising we expect to use this approach to deal with a wide class of optimal design problems in the future

on the topological derivative in shape optimization in this paper the topological derivative for an arbitrary shape functional is defined examples are provided for elliptic equations and the elasticity system in the plane the topological derivative can be used for solving shape optimization problems in structural mechanics

an approach for maximizing the smallest eigenfrequency of structure vibration based on piecewise constant level set method abstract maximization of the smallest eigenfrequency of the linearized elasticity system with area constraint is investigated the elasticity system is extended into a large background domain but the void is vacuum and not filled with ersatz material the piecewise constant level set pcls method is applied to present two regions the original material region and the void region a quadratic pcls function is proposed to represent the characteristic function consequently the functional derivative of the smallest eigenfrequency with respect to pcls function takes nonzero value in the original material region and zero in the void region a penalty gradient algorithm is proposed which initializes the whole background domain with the original material and decreases the area of original material region till the area constraint is satisfied 2 d and 3 d numerical examples are presented illustrating the validity of the proposed algorithm

structural optimization using sensitivity analysis and a level set method in the context of structural optimization we propose a new numerical method based on a combination of the classical shape derivative and of the level set method for front propagation we implement this method in two and three space dimensions for a model of linear or nonlinear elasticity we consider various objective functions with weight and perimeter constraints the shape derivative is computed by an adjoint method the cost of our numerical algorithm is moderate since the shape is captured on a fixed eulerian mesh although this method is not specifically designed for topology optimization it can easily handle topology changes however the resulting optimal shape is strongly dependent on the initial guess

functions of the second kind for freud weights and series expansions of hilbert transforms abstract let w e q where q r r is even continuous and of smooth polynomial growth at infinity then we call w 2 e 2 q a freud weight the most typical examples being w 2 x exp x 1 corresponding to the weight w 2 we can form the sequence of orthonormal polynomials p j w 2 x j 0 the functions of the second kind are q j w 2 x h p j w 2 x j 0 where h denotes the hilbert transform that is for g l r h g x p v g t t x dt here p v denotes principal value for a large class of freud weights we obtain bounds on q j j 0 in the l and l p norms we also estimate the generalized function of the second kind q j w 2 v x h p j w v x for a fixed function v we then apply these estimates to investigate the convergence of series of the second kind which form the basis of henrici s method of approximating cauchy principal value integrals

optimization of the shape of regions supporting boundary conditions this article deals with the optimization of the shape of the regions assigned to different types of boundary conditions in the definition of a physical partial differential equation at first we analyze a model situation involving the solution u varomega to a laplace equation in a domain varomega the boundary partial varomega is divided into three parts vargamma d vargamma and vargamma n supporting respectively homogeneous dirichlet homogeneous neumann and inhomogeneous neumann boundary conditions the shape derivative j prime varomega theta of a general objective function j varomega of the domain is calculated in the framework of hadamard s method when the considered deformations theta are allowed to modify the geometry of vargamma d vargamma and vargamma n i e theta does not vanish on the boundary of these regions the structure of this shape derivative turns out to depend very much on the regularity of u varomega near the boundaries of the regions vargamma d vargamma and vargamma n for this reason in particular j prime varomega is difficult to calculate and to evaluate numerically when the transition overline vargamma d cap overline vargamma between homogeneous dirichlet and homogeneous neumann boundary conditions is subject to optimization to overcome this difficulty an approximation method is proposed in which the considered exact laplace equation with mixed boundary conditions is replaced with a smoothed version featuring robin boundary conditions on the whole boundary partial varomega with coefficients depending on a small parameter varepsilon we prove the consistency of this approach in our model context the approximate objective function j varepsilon varomega and its shape derivative converge to their exact counterparts as varepsilon vanishes although it is rigorously justified only in a model problem this approximation methodology may be adapted to many more complex situations for example in three space dimensions or in the context of the linearized elasticity system various numerical examples are eventually presented in order to appraise the efficiency of the proposed approximation process

the shape and topological optimizations connection abstract in 1973 jean cea introduced a topological shape optimization algorithm based on a fixed point method the recent topological gradient concept provides a mathematical justification of cea s powerful method the aim of the topological gradient is to compute the sensitivity of a cost function when we drill a little hole in the domain some optimality conditions are derived when classical shape gradient and topological gradient are used simultaneously and numerical results are shown both in mechanics and electromagnetics

truncated quadrature rules over 0 infty and nystrom type methods we propose replacing the classical gauss laguerre quadrature formula by a truncated version of it obtained by ignoring the last part of its nodes this has the effect of obtaining optimal orders of convergence corresponding quadrature rules with kernels are then considered and optimal error estimates are derived also for them these rules are finally used to define stable nystrom type interpolants for a second kind of integral equation on the real semiaxis whose solutions decay exponentially at infty

higher rank zeta functions and sln zeta functions for curves in earlier papers l w introduced two sequences of higher rank zeta functions associated to a smooth projective curve over a finite field both of them generalizing the artin zeta function of the curve one of these zeta functions is defined geometrically in terms of semistable vector bundles of rank n over the curve and the other one group theoretically in terms of certain periods associated to the curve and to a split reductive group g and its maximal parabolic subgroup p it was conjectured that these two zeta functions coincide in the special case when formula see text and p is the parabolic subgroup consisting of matrices whose final row vanishes except for its last entry in this paper we prove this equality by giving an explicit inductive calculation of the group theoretically defined zeta functions in terms of the original artin zeta function corresponding to formula see text and then verifying that the result obtained agrees with the inductive determination of the geometrically defined zeta functions found by sergey mozgovoy and markus reineke in 2014

optimization of boundary conditions for maximum fundamental frequency of vibrating structures a sensitivity formula of eigenvalues with respect to the change of boundary conditions is derived using the material derivative concept based on a variational formulation the change of boundary conditions is described with the introduction of the tangential component of the design velocity field used in shape design simply supported and partially welded plates are taken as numerical examples to check the accuracy of the sensitivity formula the sensitivites of the distinct and multiple eigenvalues calculated by the formulas are compared with those calculated by finite differences optimal support locations are then determined by use of a gradient based optimization method it is shown that a crossing of eigenvalues can occur in the solution process

product integration over infinite intervals i rules based on the zeros of hermite polynomials the paper discusses both theoretical properties and practical implementation of product integration rules of the form n j k x f x dx wnlj xnj o i l where f is continuous k is absolutely integrable the nodes xn are roots of the hermite polynomials hn x and the weights wn are chosen so that the rule is exact if f is any polynomial of degree n convergence of the rule to the exact integral as n oo is proved for a wide class of functions f and k including singular or oscillatory functions k and rates of convergence are estimated the rules are shown to have the property of asymptotic positivity and as a consequence exhibit good numerical stability numerical calculations for some practical cases are presented which show the method to be computationally effective for integrands including highly oscillatory ones that decay suitably at infinity applications of the method to integration over 0 oo are also discussed

structural boundary design via level set and immersed interface methods we develop and test an algorithmic approach to the boundary design of elastic structures the goal of our approach is two fold first to develop a method which allows one to rapidly solve the two dimensional lam equations in arbitrary domains and compute for example the stresses and second to develop a systematic way of modifying the design to optimize chosen properties at the core our approach relies on two distinct steps given a design we first apply an explicit jump immersed interface method to compute the stresses for a given design shape we then use a narrow band level set method to perturb this shape and progress towards an improved design the equations of 2d linear elastostatics in the displacement formulation on arbitrary domains are solved quickly by domain embedding and the use of fast elastostatic solvers this effectively reduces the dimensionality of the problem by one once the stresses are found the level set method which represents the design structure through an embedded implicit function is used in the second step to alter the shape with velocities depending on the stresses in the current design criteria are provided for advancing the shape in an appropriate direction and for correcting the evolving shape when given constraints are violated

optimization of structures with thin layer functional device on its surface through a level set based multiple type boundary method abstract functional structure i e native base structure equipped with thin layer functional devices on its surface is important in many engineering applications the performance of such a functional structure is seriously affected by the configuration of the base structure and the surface functional devices and the optimization of configuration is a simultaneous topology optimization of the boundaries that belong to different types in the present study load cell is taken as an example of the functional structure and strain gauge is taken as an example of the functional device the task of designing a load cell is accomplished by solving a multi objective topology optimization problem whose objective makes a compromise between stiffness and flexibility of the base structure the design variables include two types of boundaries functional boundary where a strain gauge is installed the free boundary where there does not exist any connection to the environment the optimization problem is solved by using a level set based multiple type boundary method two level set functions are used to represent a functional structure and the two types of boundaries evolution of the two boundaries is modeled by two independent hamilton jacobi equations re meshing is conducted in each iteration of optimization quadrilateral body fitted mesh is used for the finite element analysis and the artificial weak material is not used numerical examples in two dimensions are investigated

on the numerical solution of fredholm integral equations on unbounded intervals the authors propose some numerical methods to solve fredholm integral equations of the second kind on unbounded intervals the proposed procedure includes projection methods and their discretized versions special attention is turned to the conditioning of the linear system corresponding to the finite dimensional equation