on the boundedness and compactness of operators of hankel type abstract boundedness and compactness results are obtained for commutators of multiplication operators with a general class of integral operators j of a critical homogeneity which are modeled on the bergman projection it is shown that the commutator m f j is bounded or compact on l p whenever the function is in an appropriately defined bmo or vmo space respectively special cases of the general results include commutators with the bergman projection in strictly pseudoconvex domains in c n and finite type domains in c 2 in addition it is shown that in the case of the bergman projection in a strictly pseudoconvex domain the sufficient condition is also necessary

shape sensitivity analysis and shape optimization in planar elasticity using the element free galerkin method abstract this paper demonstrates that the element free galerkin efg method can be successfully used in shape design sensitivity analysis and shape optimization for problems in 2d elasticity the continuum based variational equations for displacement sensitivities are derived and are subsequently discretized this approach allows one to avoid differentiating the efg shape functions the present formulation that employs a penalty method for imposing the essential boundary conditions can be easily extended to 3d and or non linear problems numerical examples are presented to show the capabilities of the current approach for calculating sensitivities the flexibility of the efg method that eliminates the element connectivity requirement of the finite element method fem permits solving shape optimization problems without re meshing the problem of shape optimization of a fillet is used to demonstrate this fact smoother stresses and better accuracy for points close to the boundary allow for a better efg solution compared to published results using the fem the boundary element method bem or the boundary contour method bcm furthermore for the efg approach grid optimization appears unnecessary

continuum approach for second order shape design sensitivity of three dimensional elastic solids a second order shape design sensitivity analysis method for three dimensional linear elastic solids is derived using a continuum approach with the material derivative to compute the second order shape design sensitivity a shape design acceleration field is defined which is similar to the shape design velocity field for the first order shape design sensitivity both direct differentiation and hybrid methods are presented in this paper the shape changes are assumed on the traction free boundary only a numerical method which can be implemented using established finite element analysis codes is developed to demonstrate feasibility and accuracy of the proposed second order shape design sensitivity analysis method

a boundedness criterion for generalized calderon zygmund operators in 1965 a p calderon showed the l2 boundedness of the so called first calderon commutator this is one of the first examples of a non convolution operator associated to a kernel which satisfies certain size and smoothness properties comparable to those of the kernel of the hilbert transform these properties together with the l2 boundedness imply the lp boundedness for all p s in 1 oo many operators in analysis such as certain classes of pseudo differential operators and the cauchy integral operator on a curve are associated with kernels having these properties for these operators one of the major questions is if they are bounded on l2 we are going to give necessary and sufficient conditions for such an operator to be bounded on l2 they are essentially that the images of the function 1 under the actions of the operator and its adjoint both lie in bmo in the case of the aforementioned first commutator this can be checked by an integration by parts in the first section we present some basic notions and state the theorem which is proved in sections 2 and 3 in section 4 we show how to recover some classical results in sections 5 and 6 we construct a functional calculus for small perturbations of a and in section 7 we show a connection between the theory of calderon zygmund operators and kato s conjecture it is a pleasure to express our thanks to r r coifman and y meyer for suggesting many elegant simplifications in our proofs and most of the applications we also wish to thank stephen semmes for several pertinent remarks

boundary integral equations for recovery of design sensitivities in shape optimization a new formulation for obtaining design sensitivities in shape optimization has been developed the formulation is based on a direct application of the material derivative concept to the appropriate boundary integral equations for displacements and stresses in an elastic solid as a check on accuracy the approach was applied to a uniformly loaded infinite plate containing an elliptical hole in this case the availability of an analytical solution made it possible to calculate errors exactly furthermore a wide range of stress states could be considered simply by varying the aspect ratio of the elliptical hole for convenience the design sensitivities were calculated with respect to changes in the major axis numerical convergence was established by comparing results based on four successive boundary meshes in general the predictions for both displacement and stress sensitivities were remarkably accurate

shape sensitivity analysis and optimal design of disks and plates with strong discontinuities of kinematic fields abstract disks plates or beams subjected to loading and initial strains or displacements are assumed to be composed of portions interconnected by hinge or slip and dilatancy lines admitting discontinuities in displacements or slopes the shape of such lines and their stiffness properties are subjected to variation the sensitivity analysis is first discussed for an arbitrary functional of generalized stress strain displacement and boundary traction the variation of complementary and potential energies is considered as a particular case of a general derivation for sensitivity the optimal design problem is then considered and the relevant optimally conditions are derived the general theory is illustrated by examples of sensitivity analysis and optimal design with respect to shape position and stiffness of discontinuity lines for disks plates and beams numerical aspects of sensitivity analysis are also discussed

finite analytic numerical method for two point boundary value problems of ordinary differential equations abstract the finite analytic numerical method is developed to solve two point boundary value problems of ordinary differential equations the basic idea of the finite analytic method is the incorporation of the local analytic solution of the governing equation in the numerical solution of the boundary value problem in this study the finite analytic solution is developed for both linear and nonlinear second order ordinary differential equations several examples are solved to demonstrate the application of the finite analytic method it is shown that the finite analytic method is simple accurate and well behaved in the presence of singularities it is also shown that the finite difference expression for the derivative is a particular simple case of the finite analytic expressions the finite analytic method can therefore be regarded as a desirable alternative to other numerical schemes for solving two point boundary value problems

carleson embedding theorem on convex finite type domains abstract this paper concerns certain geometric aspects of function theory on smoothly bounded convex domains of finite type in c n specifically we prove the carleson hormander inequality for this class of domains and provide examples of carleson measures improving a known result concerning such measures associated to bounded holomorphic functions

an implementation of the boundary element method for zoned media with stress discontinuities the boundary element method as it applies to two dimensional elastostatic problems is implemented with quadratic variation in boundary variables and geometry additional parameters are associated with nodes at segment intersections to allow for discontinuous tractions supplementary equations consistent with linear elasticity are used to augment the regular boundary integral equations for certain mixed and displacement boundary conditions zoning or subregionalization capabilities are included to provide solutions to piecewise nonhomogeneous problems or problems on regions of irregular shape example problems are given to demonstrate the accuracy of the technique

adjoint sensitivity analysis for nonlinear dynamic thermoelastic systems an adjoint approach is presented to formulate explicit sensitivities for a general functional associated with a nonlinear dynamic thermoelastic system uncoupled thermoelastic response and small deformation behavior are assumed the formulation uses the lagrange multiplier method to define an adjoint system the convolution operator to incorporate transient effects and domain parameterization to describe shape variations variations of the functional are expressed in explicit form with respect to perturbations of the design fields structural shape material properties applied loads prescribed boundary conditions and initial conditions the functional is defined in terms of the design fields and the implicit response fields displacement temperature strain temperature gradient stress heat flux vector reaction force and reaction surface flux in an example problem the finite element method is used to evaluate the real and adjoint responses and the shape sensitivities for a tank design problem the tank is modeled as a nonlinear quasistatic uncoupled thermoelastic system

morrey boundedness and compactness characterizations of integral commutators with singular kernel on strictly pseudoconvex domains in cn abstract we prove the morrey boundedness and compactness characterization of integral commutators with singular kernel of calderon zygmund type on pseudo convex domains in c n our results extend some of the ones of krantz li in 16 17

shape sensitivity analysis and design optimization of linear thermoelastic solids in this study a numerical scheme is developed for shape sensitivity analysis and design optimization of linear quasistatic thermoelastic solids in this scheme the finite element method is used as the analyzer for analyzing stress temperature shape sensitivity and design velocity field based upon the method of material derivatives both the techniques of the direct differentiation method and the adjoint variable method are applied to derive the shape sensitivity equations the shape optimization formulations discussed here include boundary integrals of displacements and heat fluxes as well as domain integrals of stresses and areas numerical results show that the proposed scheme works well in terms of accuracy

commutators of singular integrals and fractional integral operators the commutators of integral and differential operators are very important tools in harmonic analysis and pde recently the third author of this paper gave a survey front math china 2011 6 5 821 833 on some late results and put forward a few problems on commutators of many important operators in harmonic analysis in this paper we present some results about the commutators of singular integrals and fractional integrals with rough or variable kernels which can be seen as a supplement of the aforementioned survey

optimal design of rib stiffeners in disks and plates abstract disks and plates subjected to stretching and flexure are stiffened by curvilinear ribstiffeners whose shape and cross sectional area are subject to optimization sensitivity analysis is first discussed for an arbitrary integral functional of generalized stress strain and displacement and boundary domains the optimality conditions are next derived the general theory is illustrated by three examples of optimal design of ring stiffeners in circular disks and plates and of rib stiffeners in a rectangular plate

3d multi region bem with corners and edges a novel set of auxiliary equations which supplement the fundamental boundary integral equations for the treatment of corners and edges arising in discontinuous traction problems and at zonal intersections is derived based on these equations an efficient linear 3d multi region bem algorithm is presented which can deal with arbitrarily many regions numerical examples demonstrate the effectiveness of this algorithm

variational approach by means of adjoint systems to structural optimization and sensitivity analysis ii structure shape variation abstract for a linear elastic structure the first variation of an arbitrary stress strain and displacement functionals corresponding to variation of shape of external boundaries or interfaces is derived by using the solutions for primary and adjoint systems the application to optimal design is next presented and the relevant optimally conditions are derived from general expressions the path independent integrals used in fracture mechanics are rederived as a particular case of general expressions

discrete shape sensitivity equations for aerodynamic problems intensive research and development in computational fluid dynamics cfd has recently produced many powerful cfd codes to simulate complex aerodynamic phenomena however in order to enhance the usefulness of these cfd codes for design practice development of design sensitivity equations compatible to these codes becomes very important this paper represents a part of such an effort to develop a sensitivity analysts methodology that enables the sensitivity equations to be implemented into existing cfd codes with minimal code modification the methodology is based upon a pre elimination procedure which accounts for consistently linearized boundary conditions formulations of both the direct differentiation and the adjoint variable methods will be presented in the paper

optimal topological design through insertion and configuration of finite sized heterogeneities in this paper we develop a procedure for optimal topological design by sequentially inserting finite sized non spherical inclusions or holes within a homogeneous domain we propose a new criterion for topology change that results in a trade off problem to achieve the greatest least change in the objective for the least greatest change in the size of the inclusion hole respectively we derive the material derivative of the proposed objective termed as the configurational derivative that describes sensitivity of arbitrary functionals to arbitrary motions of the inclusion hole as well as the domain boundaries we specifically utilize the sensitivity to position orientation and scaling of finite sized heterogeneities to effect topological design we simplify the configurational derivative to the special case of infinitesimally small spherical inclusions or holes and show that the developed derivative is a generalization of the classical topological derivative the computational implementation relies on b spline isogeometric approximations we demonstrate through a series of examples optimal topology achieved through sequential insertion of a heterogeneity of fixed shape and optimization of its configuration location orientation and scale

an alternative approach to shape design sensitivity analysis a novel method is presented in this paper for calculating shape design sensitivity which is based on the finite difference method fdm by analysing the numerical procedure of the fdm the perturbation of the geometry is replaced by a perturbation load which can be calculated once the stress field of the initial problem and the design boundary perturbation are known the final shape design sensitivity is obtained by solving the perturbation problem which has the same geometry and the kinematical boundary condition as the initial problem but under the perturbation loads therefore the new method does not require the calculation of the matrices of the perturbed structure and is independent of the perturbation step a numerical implementation of the finite difference load method fdlm is described in which the boundary element method is used to evaluate the structural response the numerical examples demonstrate that this new method for shape design sensitivity analysis is very accurate

a new boundary element technique without domain integrals for elastoplastic solids summary a simple idea is proposed to solve boundary value problems for elastoplastic solids via boundary elements namely to use the green s functions corresponding to both the loading and unloading branches of the tangent constitutive operator to solve for plastic and elastic regions respectively in this way domain integrals are completely avoided in the boundary integral equations though a discretization of the region where plastic flow occurs still remains necessary to account for the inhomogeneity of plastic deformation the elastoplastic analysis reduces in essence to a straightforward adaptation of techniques valid for anisotropic linear elastic constitutive equations the loading branch of the elastoplastic constitutive operator may be viewed formally as a type of anisotropic elastic law numerical examples using j2 flow theory with linear hardening demonstrate that the proposed method retains all the advantages related to boundary element formulations is stable and performs well the method presented is for simplicity developed for the associative flow rule however a full derivation of green s function and boundary integral equations is also given for the general case of non associative flow rule it is shown that in the non associative case a domain integral unavoidably arises in the formulation copyright 2005 john wiley sons ltd

compactness for the commutators of singular integral operators with rough variable kernels abstract let t be the singular integral operator with variable kernel defined by t f x p v r n x x y x y n f y d y where x y is homogeneous of degree zero in the second variable y and s n 1 x z d z 0 for any x r n in this paper the authors prove that if l r n l q s n 1 for some q 2 n 1 n then the commutator generated by a cmo r n function and t and the associated lacunary maximal operator are compact on l 2 r n the associated continuous maximal commutator is also considered

design sensitivity metric for structural dynamic response an approach to study the sensitivity of dynamic responses for structural systems with respect to a set of design parameters is presented the sensitivity is evaluated by considering the behavior of the system response when the design parameters vary within a given region of the design space the sensitivity is computed by means of approximate responses which are evaluated using approximation concepts the approximation is based on modal analysis and it is valid for general underdamped linear systems intermediate design variable and intermediate response quantity concepts are used to enhance the accuracy of the approximation in this approach modal energies and mode shapes are chosen as intermediate response quantities and they are approximated in terms of selected intermediate system parameters the approximation of these quantities requires a standard eigenvalue and eigenvector sensitivity analysis numerical results that illustrate the usefulness and effectiveness of the method are presented great insight into the behavior of the system can be gained using this methodology

a continuous lagrangian sensitivity equation method for incompressible flow a continuous lagrangian sensitivity equation method clsem is presented as a cost effective alternative to the continuous eulerian sensitivity equation method cesem in the case of shape parameters boundary conditions for the clsem are simpler than those of the cesem however a mapping must be introduced to relate the undeformed and deformed configurations thus making the pdes more complicated we propose the use of pseudo elasticity equations to provide a general framework to generate this mapping for unstructured meshes on complex geometries the methodology is presented in details for the incompressible navier stokes and sensitivity equations in variational form the pdes are solved with an adaptive fem sensitivity data obtained with both approaches for a flow around a naca 4512 are used to obtain estimates of flows around nearby geometries results indicate that the clsem produces significant improvements in terms of both accuracy and cpu time

nonlinear structural design sensivitity analysis for path dependent problems part 1 general theory abstract two procedures direct differentiation and adjoint structure for design sensitivity analysis of nonlinear structural systems with path dependent effects are described in this paper continuum formulation is used and both geometric and material nonlinearities are included in the derivations incremental nonlinear analysis based on the total lagrangian concept is adopted the reference volume concept is used to unify the shape and nonshape design problems to show the generality of the theory the derived expressions are reduced to some special cases that have been treated previously in the literature in part 2 of the paper a few analytical example problems will be solved to demonstrate the use of the design sensitivity analysis theory the theory has also beendiscretized elsewhere using finite element approximations for implementation into structural analysis programs these developments offer a firm foundation for design optimization of complex structural systems

an interpretation for min max structural design problems including a method for relaxing constraints alas ret min max type problems arise in structural design when the objective is to minimize the maximum value ol some local measure of system response e g design to minimize the maximum stress or displacement a method is described whereby the min max problem is interpreted as a simple min problem governing equations for the adjoint structure are derived directly from the lagrangian for this min problem by using the generalized multiplier rule on the original state equations also certain advantages are demonstrated for a modified form of the min max problem a form obtained by introducing a relaxation on the local constraints the analysis is applied for examples of structural design with stress and displacement criteria and for the design of an elastic foundation to minim support pressure practical rcquircmcnts as constraints in structural optimization problems often lead to mathematical statement in the form of min max problems minimization with respect to the design of the maximum value of stress or displacement over the structure are simple examples of this type of problem a general method is provided in this paper for the formulation of min max structural design problems directly via a formal procedure the method is substantiated on the basis of generalized kuhn tucker theory the existence of solutions for such design problems is treated as well it is common to interpret some of the necessary conditions associated with the cited min max problems in terms of an adjoint structural analysis problem the term represent ing load in the adjoint problem may be singular e g whenever the constraint on local measure of structural response is tight only at points in the domain of the structure this load is identified as a dirac function in certain prior treatments of the latter of the examples cited above e g i 21 the support in analysis for this form of the adjoint load and for the evaluation of the design derivative as well is provided in haug s paptr 2 a compre hensive and well documented discussion of optimal design relative to displacement con straints is presented in this paper the singularity is avoided via the introduction of a p norm measure of displacement in the paper by banichuk et al 3 on plate design in related developments presented by mroz and mironov rl where a broader treatment is given for problems of design within mechanical state constraints the singularity issue does not arise since only global measures of the constraints are considered in the development presented in the next section the min max problem is recast as a simple min problem governing equations for the adjoint problem are produced here as certain of the necessary conditions associated with the lagrangian for this min problem in a separate part of the development it is established that with the introduction of a function that comprises a relaxation of the local constraint the entire problem may be analyzed in terms of ordinary functions i e the singularities mentioned above are avoided also it is demonstrated that solutions of the relaxed problem converge to the solution of the original one as the relaxation approaches zero two specific example problems are treated in order to demonstrate the method of formulation and various other applications are discussed as well

simultaneous material load shape variations of thermoelastic structures a continuous approach is adopted in order to find the total variation of a general performance criterion the present analysis may find important physical applications in the simultaneous shape optimization and control of large space structures in time by applied thermal and or mechanical loads the adjoint variable method and the material derivative concept are used to find the sensitivity expressions

optimal design for polymer extrusion part ii sensitivity analysis for weakly coupled nonlinear steady state systems the die design methodology presented in part i is extended to include performance measures that are functions of material residence time we solve a hyperbolic differential equation using the velocity field computed from the hele shaw pressure analysis to evaluate the material residence time in polymer melts the residence time governing equation lacks natural diffusion therefore we employ the streamline upwind petrov galerkin supg finite element method to compute a spatially stable residence time field in the design problem we derive design sensitivities for steady state nonlinear weakly coupled systems and include design variables that parameterize essential boundary conditions design sensitivities are derived via the direct differentiation and adjoint methods special consideration is given to the supg weighting function since it is a function of the design to demonstrate the methodology sheet extrusion dies are designed to simultaneously minimize the exit velocity variation and the exit residence time variation

estimates for the bergman and szego kernels in mathbf c 2 the purpose of this paper some of whose conclusions were announced in nrsw is to study the bergman and szegd projection operators on pseudoconvex domains q of finite type in c2 the results we obtain are of three kinds i the size estimates of the bergman and szeg6 kernels and their derivatives ii the cancellation properties of those kernels expressed in terms of the actions of these operators on suitable bump functions these properties have an interest in their own right but are also crucial in iii below iii the sharp mapping properties of these operators on functions spaces such as lp the nonisotropic sobolev spaces and the nonisotropic lipschitz spaces which are naturally attached to the geometry of the boundary this also leads ultimately to sharp results in the regularity properties of solutions of the equation du f in q and 9bu f on the boundary let us describe these matters in more detail our starting points are certain basic geometric constructs associated to q a metric p defined in terms of the vector fields x1 and x2 which are the real and imaginary parts of the tangential levi vector field on d 2 and a function a p 8 a polynomial in 8 for p e d 2 which represents the higher levi invariant attached to d 9 the significance of these to the geometry of d q can be understood from the following facts the ball b p 8 c d q centered at p of radius 8 in the metric p when viewed in the appropriate coordinates has width 8 in the complex tangential directions but its width is a p 8 in the complementary direction thus the volume of the ball is 82a p 8 among other crucial properties

improvements on objective and constraint functions in domain optimization in this paper a sequential quadratic programming algorithm is efficiently coupled with the finite element package msc nastran in order to optimize the shape of two dimensional parts with piecewise constant thickness where linearized elasticity is used three different methods for gradient calculation with respect to the changing of the shape are also coupled to msc nastran the aim of this article is to give a study on difficulties in the convergence of the shape using usual objective and constraint functions and improvements on them to avoid these difficulties two examples are presented to illustrate the improvements made and to give numerical results

isogeometric shape optimization for quasi static processes summary a framework to solve shape optimization problems for quasi static processes is developed and implemented numerically within the context of isogeometric analysis iga recent contributions in shape optimization within iga have been limited to static or steady state loading conditions in the present contribution the formulation of shape optimization is extended to include time dependent loads and responses a general objective functional is used to accommodate both structural shape optimization and passive control for mechanical problems an adjoint sensitivity analysis is performed at the continuous level and subsequently discretized within the context of iga the methodology and its numerical implementation are tested using benchmark static problems of optimal shapes of orifices in plates under remote bi axial tension and pure shear under quasi static loading conditions the method is validated using a passive control approach with an a priori known solution several applications of time dependent mechanical problems are shown to illustrate the capabilities of this approach in particular a problem is considered where an external load is allowed to move along the surface of a structure the shape of the structure is modified in order to control the time dependent displacement of the point where the load is applied according to a pre specified target copyright 2015 john wiley sons ltd

compactness of riesz transform commutator on stratified lie groups abstract let g be a stratified lie group and x j 1 j n a basis for the left invariant vector fields of degree one on g let j 1 n x j 2 be the sub laplacian on g the jth riesz transform on g is defined by r j x j 1 2 1 j n in this paper we provide a concrete construction of the twisted truncated sector which is related to the pointwise lower bound of the kernel of r j on g then we obtain the characterisation of compactness of the commutators of r j with a function b vmo g the space of functions with vanishing mean oscillation on g

bilinear operators on herz type hardy spaces the authors prove that bilinear operators given by finite sums of products of calderon zygmund operators on rn are bounded from hk11 q1 hk22 q2 into hk p q if and only if they have vanishing moments up to a certain order dictated by the target space herehk q are homogeneous herztype hardy spaces with 1 p 1 p1 1 p2 0 pi 1 q 1 q1 1 q2 1 q1 q2 1 q 1 2 and n qi i as an application they obtain that the commutator of a calderon zygmund operator with a bmo function maps a herz space into itself

variational approach by means of adjoint systems to structural optimization and sensitivity analysis i variation of material parameters within fixed domain abstract for a linear elastic structure the first variation of an arbitrary stress strain and displacement functionals corresponding to variation of material parameters within specified domain is derived by using the solution for primary and adjoint systems this variation is of fundamental importance in sensitivity analysis optimal design and identification problems simple examples of optimal stiffness design and identification of stiffness parameters in beams are presented

tropical geometry of statistical models this article presents a unified mathematical framework for inference in graphical models building on the observation that graphical models are algebraic varieties from this geometric viewpoint observations generated from a model are coordinates of a point in the variety and the sum product algorithm is an efficient tool for evaluating specific coordinates here we address the question of how the solutions to various inference problems depend on the model parameters the proposed answer is expressed in terms of tropical algebraic geometry the newton polytope of a statistical model plays a key role our results are applied to the hidden markov model and the general markov model on a binary tree

shape design sensitivity analysis via material derivative adjoint variable technique for 3 d and 2 d curved boundary elements a general approach to shape design sensitivity analysis of three and two dimensional elastic solid objects is developed using the material derivative adjoint variable technique and boundary element method the formulation of the problem is general and first order sensitivities in the form of boundary integrals for the effect of boundary shape variations are derived for an arbitrary performance functional second order quadrilateral surface elements for 3 d problems and quadratic boundary elements for 2 d problems are employed in the solution of primary and adjoint systems and discretization of the boundary integral expressions for sensitivities the accuracy of sensitivity information is studied for selected global performance functionals and also for boundary state fields at discrete points numerical results are presented to demonstrate the accuracy and efficiency of this approach

a gradient based shape optimization scheme using an interface enriched generalized fem abstract a gradient based shape optimization scheme using an interface enriched generalized finite element method igfem is presented wherein the design geometry is projected onto a fixed mesh and the igfem is used for analysis this approach eliminates the mesh distortion present in conventional lagrangian shape optimization methods as well as the need for remeshing an analytical sensitivity analysis using both the adjoint or direct approaches is presented to compute derivatives of the objective and constraint functions due to the fixed nature of the mesh the so called design velocity field only needs to be computed on the structure boundary interface a comparison between igfem and conventional fem based shape optimization schemes is presented showing an improved precision for the igfem approach finally we solve various numerical examples to demonstrate the capability of the method including the computational design of particulate and microvascular composites

numerical methods for second order shape sensitivity analysis with applications to heat conduction problems in this paper two finite element based schemes for second order shape sensitivity analysis are presented in the first formulation the av dd method the first order shape sensitivity equation is derived and expressed in terms of state and adjoint variables the resultant equation is then directly differentiated to obtain the second order shape sensitivity equation in the second formulation the dd av method the functional of concern is differentiated twice to yield the second order sensitivity equation in which the second order shape derivatives can be eliminated by introducing a proper adjoint equation a thermal fin problem and a thermal insulation layer problem have been studied to validate the proposed schemes it is shown that both methods yield identical results though the dd av method is computationally more efficient

the collapsed gibbs sampler in bayesian computations with applications to a gene regulation problem abstract this article describes a method of grouping and collapsing in using the gibbs sampler and proves from an operator theory viewpoint that the method is in general beneficial the norms of the forward operators associated with the corresponding nonreversible markov chains are used to discriminate among different simulation schemes when applied to bayesian missing data problems the idea of collapsing suggests skipping the steps of sampling parameter s values in standard data augmentation by doing this we obtain a predictive update version of the gibbs sampler a procedure of calculating the posterior odds ratio via the collapsed gibbs sampler when incomplete observations are involved is presented as an illustration of possible applications three examples along with a bayesian treatment for identifying common protein binding sites in unaligned dna sequences are provided

optimal design for polymer extrusion part i sensitivity analysis for nonlinear steady state systems we present a general framework to obtain analytical design sensitivities for steady state nonlinear systems where special emphasis is given to design variables that define prescribed boundary conditions the sensitivities are derived for a general response functional using both the direct and adjoint methods and are compared to show that the two sensitivity analysis methods yield identical expressions both adjoint and direct sensitivities for the generalized hele shaw system which models the flow of purely viscous non newtonian fluids through thin cavities are obtained using weak formulations and then discretized for the finite element analysis these sensitivities are used with numerical optimization to design polymer sheeting dies with minimum pressure drop and reduced velocity variation across the die exit

domain sensitivity analysis of the elastic far field patterns in scattering from nonsmooth obstacles we consider elastic scattering problems described by the dirichlet or the neumann boundary value problem for the elastodynamic equation in the exterior of a 2d bounded domain or in the exterior of a crack the boundary of the domain is assumed to have a finite set of corner points where the scattered wave may have singular behaviour the paper is concerned with the sensitivity of the far scattered field with respect to small perturbations of the shape of the scatterer using a modification of the method of adjoint problems k dems z mroz internat j solids structures 20 1984 527 552 we obtain a representation for the shape derivative which is well suited for a numerical realization with boundary element methods and which shows in some cases directly the influence of the singularities of the solution on the sensitivity of the far field patterns

sensitivity analysis for coupled thermoelastic systems abstract this paper presents an adjoint approach derived from the reciprocal theorem for the sensitivity analysis of linear dynamic thermoelastic systems the variation of a general response functional is expressed in explicit form with respect to variations of the design fields which consist of the material properties applied loads prescribed boundary initial conditions and the structural shape the functional is dependent on these design quantities as well as the following implicity defined response fields displacement temperature stress strain heat flux temperature gradient reaction forces and reaction surface flux the formulation incorporates the reciprocal relation between variations of the real system design and response fields and an adjoint state here convolution is employed in lieu of time mappings used in other transient adjoint sensitivity derivations specializations of the formulation to uncoupled combined quasi static uncoupled and steady state thermoelasticity are also presented the finite element method is used to demonstrate the application of the formulation to a problem in automobile engine design

computational geometry an introduction from the reviews this book offers a coherent treatment at the graduate textbook level of the field that has come to be known in the last decade or so as computational geometry the book is well organized and lucidly written a timely contribution by two founders of the field it clearly demonstrates that computational geometry in the plane is now a fairly well understood branch of computer science and mathematics it also points the way to the solution of the more challenging problems in dimensions higher than two

a cascade optimization methodology for automatic parameter identification and shape process optimization in metal forming simulation computer simulations of metal forming processes using the finite element method fem are today well established this form of simulation uses an increasing number of sophisticated geometrical and material models relying on a certain number of input data which are not always readily available the aim of inverse problems which will be considered here is to determine one or more of the input data relating to these forming process simulations thereby leading to a desired result in this paper we will focus on two categories of such inverse problems the first category consists of parameter identification inverse problems these involve evaluating the material parameters for material constitutive models that would lead to the most accurate results with respect to physical experiments i e minimizing the difference between experimental results and fem simulations the second category consists of shape process optimization inverse problems these involve determining the initial geometry of the specimen and or the shape of the forming tools as well as some parameters of the process itself in order to provide the desired final geometry after the forming process these two categories of inverse problems can be formulated as optimization problems in a similar way i e by using identical optimization algorithms in this paper we intend firstly to solve these two types of optimization problems by using different non linear gradient based optimization methods and secondly to compare their efficiency and robustness in a variety of numerical applications

variational principle for shape design sensitivity analysis in this paper the adjoint method of design sensitivity analysis is stated as a general variational principle that is applicable to a wide range of problems the principle gives a very simple and straightforward method of obtaining the design sensitivity expression for a functional dependent on the state fields the sensitivity expression involves certain adjoint fields and explicit design variations of the functional and the governing equations for the primary state fields the principle is stated in terms of an augmented functional that is defined by adding to the response functional whose sensitivity is desired the equilibrium equation of the primary problem then explicit design variation of the augmented functional gives the total design variation of the response functional stationarity of the augmented functional with respect to the state fields defines the adjoint problem for the response functional the principle is proved and applied to several classes of linear and nonlinear problems such as field problems structural problems and dynamic response problems it is shown that the design sensitivity expressions derived in the literature using long procedures are obtained quite routinely by use of the principle

sensitivity analysis of linear elastic systems using domain parameterization and a mixed mutual energy principle abstract a unified approach for explicit structural design sensitivity analysis of linear elastic systems is presented first order sensitivity expression involving the complete set of design variable including shape design parameters are derived for general response functional both direct differentiation and adjoint variable methods are developed in a general variational context a domain parameterization method related to the mixed eulerian lagrangian kinematic description is introduced for the treatment of shape variation problems this approach is an alternative to the material derivative methods presented elsewhere in the literature the adjoint variable derivation is based on a mixed energy principle the mutual hu washizu energy principle which is formally stated and proved the design sensitivity derivation based on this principle unifies and extends several of the adjoint variable methods found in the literature the derivations presented here are extended to nonlinear systems in a subsequent paper the sensitivity expressions are valid for use with force displacement or mixed approximate solutions of the elasticity equations other formulations are generally only consistent with displacement solution methods numerical implementation of the design sensitivity methods is discussed and illustrative examples are included

design sensitivity analysis for shape optimization based on the lie derivative abstract the paper presents a theoretical framework for the shape sensitivity analysis of systems governed by partial differential equations the proposed approach based on geometrical concepts borrowed from differential geometry shows that sensitivity of a performance function i e any function of the solution of the problem with respect to a given design variable can be represented mathematically as a lie derivative i e the derivative of that performance function along a flow representing the continuous shape modification of the geometrical model induced by the variation of the considered design variable theoretical formulae to express sensitivity analytically are demonstrated in detail in the paper and applied to a nonlinear magnetostatic and a linear elastic problem following both the direct and the adjoint approaches following the analytical approach one linear system of which only the right hand side needs be evaluated the system matrix being known already has to be solved for each of the design variables in the direct approach or for each performance functions in the adjoint approach a substantial gain in computation time is obtained this way compared to a finite difference evaluation of sensitivity which requires solving a second nonlinear system for each design variable this is the main motivation of the analytical approach there is some freedom in the definition of the auxiliary flow that represents the shape modification we present a method that makes benefit of this freedom to express sensitivity locally as a volume integral over a single layer of finite elements connected to both sides of the surfaces undergoing shape modification all sensitivity calculations are checked with a finite difference in order to validate the analytic approach convergence is analyzed in 2d and 3d with first and second order finite elements

discrete adjoint formulation for continuum sensitivity analysis continuum sensitivity analysis csa is an approach for calculating analytic derivatives a direct csa formulation is advantageous for computing derivatives of many state variables or performance functions an adjoint formulation of csa is beneficial for computing derivatives with respect to many design variables although adjoint csa boundary conditions are often problematic for the proposed continuum discrete hybrid adjoint approach the adjoint variable is introduced after discretization which simplifies boundary conditions the sensitivity boundary conditions for the hybrid csa are posed in terms of the continuum state variables thus the hybrid adjoint formulation of csa results in design derivatives that are as accurate as those obtained from direct csa in addition to making the analysis efficient for the case of large number of design variables two test cases first of an axial bar and second of a cantilever beam modeled with solid elements illustrate how the hybrid adjoint formulation inherits the benefits of the direct and adjoint csa formulations this is also the first application of csa to obtain design derivatives nonintrusively using three dimensional 3 d spatial gradient reconstruction sgr method for 3 d solid elements

first order design sensitivities for transient conduction problems by an adjoint method an adjoint approach is presented for the design sensitivity analysis of transient conduction problems variations of a general design functional are expressed in explicit form with respect to all design quantities i e material properties shape applied thermal loads including convection and initial conditions the methodology incorporates the mutual energy between the real and adjoint thermal problems and a geometric mapping to describe shape variations finite element implementation of the method is discussed and an example is provided some potential difficulties that might be encountered when using the adjoint method with the finite element method are addressed these involve the application of impulse loadings and dirac temperature fields in the adjoint loadings

variational approach to first and second order sensitivity analysis of elastic structures for a linear elastic structure the first variations of arbitrary stress strain and displacement functionals were explicitly expressed in terms of variations of material stiffness parameters within specified domain in references 1 and 2 by using the solutions for primary and adjoint systems in this paper explicit expressions for second variations are derived for the case when the material stiffness or compliance variations depend on a set of parameters these expressions arc obtained in terms of variations of stiffness or compliance parameters by using the solutions of two additional sets of adjoint systems furthermore the variation of local stress strain or displacement is considered several illustrative examples are provided for the first and second order sensitivity analysis of beams

design sensitivity coefficients for linear elastic bodies with zones and corners by the derivative boundary element method abstract the subject of this paper is the efficient and accurate determination of design sensitivity coefficients dscs in an elastic solid with zones and corners direct differentiation of the relevant derivative boundary element method dbem formulation of the problem is carried out here corners and zones in a body are treated carefully with conforming elements a numerical implementation of the method is carried out with isoparametric quadratic boundary elements the power of this approach is demonstrated through several numerical examples it is shown that the dscs of the various mechanical quantities of interest are obtained accurately and efficiently in one example even the dsc of the stress at a corner with respect to the corner angle is obtained very accurately by this method

a systematic approach to shape sensitivity analysis abstract a fully detailed development of the domain parameterization method is presented for shape sensitivity analysis it is shown that equivalent results are obtained from the material derivative method in fact the material derivative method may be viewed as a special case of the domain parameterization method which occurs when the reference configuration coincides with the body configuration the method is illustrated for the laplace problem in which explicit shape sensitivities are derived by the adjoint and direct differentiation methods both finite element and boundary element applications are discussed the similarities between this approach and the isoparametric finite boundary element method are transparent in the finite element approach it is shown that the sensitivity integrals may be transformed to the boundary as is commonly done in the material derivative method for the adjoint method however this does not seem possible for the direct differentiation method finally in the boundary element approach the sensitivities do not require the differentiation of the fundamental solutions

shape optimization in elasticity and elasto viscoplasticity by the boundary element method abstract this paper is concerned with the optimal shape design of solids undergoing small strain small rotation elasto viscoplastic deformation shape sensitivities for this class of problems are determined by using a direct differentiation approach dda to the governing boundary element method bem equations of the problem the standard bem and the sensitivity equations are discretized and solved numerically shape optimization is carried out by coupling the standard and sensitivity analyses with an optimizer the optimization algorithm chosen here uses sequential quadratic programming to obtain the desired optimal shape of a body in an iterative manner numerical solutions for optimal shapes of cutouts in plates two dimensional plane stress are presented the difference between optimal shapes of solids undergoing purely elastic and elasto viscoplastic deformation is shown clearly in these examples

comparison of shape design sensitivity analysis formulations via material derivative adjoint variable and implicit differentiation techniques for 3 d and 2 d curved boundary element this paper reviews and compares two different approaches to continuum structural shape design sensitivity analysis the material derivative adjoint variable method and the implicit differentiation method using 3 d and 2 d bem employing identical bea models curved element technology numerical integration and equation solving techniques the similarities and differences of both methods are highlighted significant theoretical and computational aspects associated with both methods are presented and accuracy and computational efficiency characteristics are demonstrated advantages and disadvantages of both techniques are identified the characterization provided can aid in the prudent selection between these sensitivity analysis techniques based on the characteristics of the proposed application

a gradient based parameter free approach to shape optimization in shape optimization the independent node movement approach wherein finite element node coordinates are used directly as design variables allows the most freedom for shape change and avoids the time consuming parameterization preprocess however this approach lacks a length scale control that is necessary to ensure a well posed shape optimization problem and avoid numerical instability motivated by the success of filtering techniques that impose minimum length scales in topology optimization we propose a scheme with consistent filtering to introduce a length scale and thereby ensure smoothness in shape optimization while preserving the advantages of the independent node movement approach

an exposition of the material derivative approach for structural shape sensitivity analysis abstract the material derivative approach for structural shape design sensitivity analysis is described in a unified manner using the continuum formulation both the direct differentiation and adjoint methods are derived and computer implementation aspects are discussed the basic purpose of the paper is to present the shape design sensitivity analysis as an application of the material derivative concept of continuum mechanics and the calculus of variation procedures for taking variations of integrals over the variable domains it is also shown that the use of a recently developed variational principle for design sensitivity analysis greatly simplifies derivation of the adjoint method the indicial notation is used and expressions derived by different authors are related to each other a basic understanding of the material derivative approach of shape sensitivity analysis has been gained which can lead to insights for computer implementations of the method

sensitivity analysis of discrete structural systems methods for calculating sensitivity derivatives for discrete structural systems are surveyed primarily covering literature published during the past two decades methods are described for calculating derivatives of static displacements and stresses eigenvalues and eigenvectors transient structural response and derivatives of optimum structural designs with respect to problem parameters the survey is focused on publications developed in nonstructural fields such as electronics controls and physical chemistry which are directly applicable to structural problems most notable among the nonstructural based methods are the adjoint variable technique from control theory and the green s function and fast methods from physical chemistry

variational method for design sensitivity analysis in nonlinear structural mechanics this paper describes a unified variational theory of design sensitivity analysis of linear and nonlinear structures for shape nonshape and material selection problems the concepts of reference volume and adjoint structure are used to develop the unified viewpoint a general formula for design sensitivity analysis is derived several analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use such analytical examples give insight into the application of the general formula to more complex problems that must be treated numerically adjoint state fields are also interpreted as sensitivities for the functional related to the primary structure

boundary integral equation method for shape optimization of elastic structures a general method for shape design sensitivity analysis as applied to plane elasticity problems is developed with a direct boundary integral equation formulation using the material derivative concept and adjoint variable method the problem formulation is very general and a complete consideration is given to describing the boundary variation by including the tangential component of the velocity field the method is then applied to obtain the sensitivity formula for a general stress constraint imposed over a small part of the boundary the accuracy of the design sensitivity analysis is studied with a fillet and an elastic ring design problem among the several numerical implementations tested the second order boundary elements with a cubic spline representation of the moving boundary have shown the best accuracy a smooth characteristic function is found to be better than a plateau function for localization of the stress constraint optimal shapes for the two problems are presented to show numerical applications

on a class of conservation rules associated with sensitivity analysis in linear elasticity abstract considering arbitrary stress strain or displacement functionals specified over a domain of an elastic homogeneous and isotropic body their invariance is proved for the case of translation rotation and scale change of an arbitrary domain within the body the assosciated class of path independent integrals is derived it is shown that sensitivity analysis with respect to translation rotation or expansion of defects can be performed by using these path independent integrals

incremental finite element sensitivity analysis for non linear mechanics applications finite element formulations for structural sensitivity analysis of non linear systems with fixed overall shape are discussed both the direct differentiation and adjoint variable methods are employed the resulting sensitivity algorithms are consistent with time integration scheme adopted for solving equilibrium problem effectiveness and computational aspects of the procedures are discussed and compared numerical algorithms are shown to be readily implemented in existing finite element codes large scale examples illustrate the paper

parametric inference for biological sequence analysis one of the major successes in computational biology has been the unification by using the graphical model formalism of a multitude of algorithms for annotating and comparing biological sequences graphical models that have been applied to these problems include hidden markov models for annotation tree models for phylogenetics and pair hidden markov models for alignment a single algorithm the sum product algorithm solves many of the inference problems that are associated with different statistical models this article introduces the polytope propagation algorithm for computing the newton polytope of an observation from a graphical model this algorithm is a geometric version of the sum product algorithm and is used to analyze the parametric behavior of maximum a posteriori inference calculations for graphical models

optimal design of nonlinear parabolic systems part ii variable spatial domain with applications to casting optimization abstract in part i design sensitivity expressions for nonlinear parabolic systems were derived and then specialized for the analysis for thermal systems which govern many processing operations however that presentation did not account for shape variations here we present the shape sensitivity analysis for the thermal system the sensitivities are derived via the domain parameterization method and computed with the finite element method various means for parameterizing the shape are also discussed finally the sensitivity analysis is coupled with nonlinear programming to optimize the design of a sand casting

sensitivity and optimization for shape and non linear boundary conditions in thermal boundary elements this paper is concerned with the minimization of functionals of the form b f h t b h d b where variation of the vector b modifies the shape of the domain on which the potential problem 2t 0 is defined the vector h is dependent on non linear boundary conditions that are defined on the boundary the method proposed is founded on the material derivative adjoint variable method traditionally used for shape optimization attention is restricted to problems where the shape of is described by a boundary element mesh where nodal co ordinates are used in the definition of b propositions are presented to show how design sensitivities for the modified functional b f h t b h d b b b h 2t b h d b can be derived more readily with knowledge of the form of the adjoint function determined via non shape variations the methods developed in the paper are applied to a problem in pressure die casting where the objective is the determination of cooling channel shapes for optimum cooling the results of the method are shown to be highly convergent copyright 2002 john wiley sons ltd

boundary element implicit differentiation equations for design sensitivities of axisymmetric structures abstract design sensitivity analysis of axisymmetric elastic media is formulated using boundary elements the kernels for sensitivity matrices are obtained through implicit differentiation of the corresponding boundary element elasticity kernels the singular terms are obtained by applying the boundary displacements and tractions and their respective sensitivities for the rigid body motion mode and the inflation mode the equations for the recovery of sensitivities of axisymmetric boundary stresses are presented as a check on accuracy the approach is applied to a series of examples for which analytical elasticity solutions are available the predictions for both displacement and stress sensitivities are accurate additional examples are provided to demonstrate the versatility of the present approach