dynamic response optimization using an active set rqp algorithm a recently developed recursive quadratic programming rqp algorithm is applied to dynamic response design problems the algorithm incorporates updated hessians of the lagrange function and uses an active set strategy in which only a subset of the constraints is included in the direction finding qp subproblem hessian updating with dynamic response constraints presents some difficulties the primary difficulty is that the total number of constraints and the location of time points where they have to be imposed can change from iteration to iteration this can cause inconsistencies in hessian updating if proper numerical procedures are not used a numerical procedure to handle the situation is developed implemented and evaluated automatic restarting procedures are necessary for proper convergence of the algorithm the new algorithm is robust as well as more efficient than the purely linear algorithm the active set strategy plays an important role for application to dynamic response problems the rqp algorithms that do not use such a strategy are not applicable to this class of problems

multipliers paramultipliers and weak strong uniqueness for the navier stokes equations abstract in this article we describe spaces p such that if u is a weak in the sense of leray j leray sur le mouvement d un fluide visqueux remplissant l espace acta math 63 1934 193 248 solution of the navier stokes system for some initial data u 0 and if u belongs to p then u is unique in the class of weak solutions we say then that weak strong uniqueness holds it turns out that the proof of such results relies on the boundedness of a trilinear functional f l 2 h l 2 h p r where belong to 0 1 in order to find optimal conditions for the boundedness of f we are led to describing spaces of multipliers and of paramultipliers that is functions which map by classical pointwise product or by paraproduct a given sobolev spaces in another given sobolev space the study of these spaces enables us to give conditions for weak strong uniqueness which generalise all previously known results from the famous serrin criterion j serrin the initial value problem for the navier stokes equations in r e langer ed nonlinear problems univ of wisconsin press 1963 pp 69 98 to the recent conditions formulated by lemarie rieusset p g lemarie rieusset recent developments in the navier stokes problem chapman and hall 2003

perturbations of elliptic operators in 1 sided chord arc domains part i small and large perturbation for symmetric operators the first and third authors acknowledge financial support from the spanish ministry of economy and competitiveness through the severo ochoa programme for centres of excellence in r d sev 2015 0554 they also acknowledge that the research leading to these results has received funding from the european research council under the european union s seventh framework programme fp7 2007 2013 erc agreement no 615112 hapdegmt the second author was supported by nsf grant dms 1664047

maximal l p regularity for the laplacian on lipschitz domains we consider the laplacian with dirichlet or neumann boundary conditions on bounded lipschitz domains both with the following two domains of definition d 1 delta u in w 1 p omega delta u in l p omega bu 0 or d 2 delta u in w 2 p omega bu 0 where b is the boundary operator we prove that under certain restrictions on the range of p these operators generate positive analytic contraction semigroups on lp which implies maximal regularity for the corresponding cauchy problems in particular if is bounded and convex and 1 p leq 2 the laplacian with domain d2 has the maximal regularity property as in the case of smooth domains in the last part we construct an example that proves that in general the dirichlet laplacian with domain d1 is not even a closed operator

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

the lp neumann problem for the heat equation in non cylindrical domains we consider the lp neumann problem for the heat equation when 1 p 2 in a time varying domain using a perturbation technique and previous l2 neumann results the authors obtain a generalization of earlier work in caloric cylinders

on the local boundedness of singular integral operators on etudie la classe des operateurs integraux singuliers dont les noyaux satisfont les conditions usuelles de regularite soit k un tel operateur on etablit des conditions necessaires qui impliquent que k a des inegalites en norme l p

a boundedness criterion for singular integral operators of convolution type on the fock space abstract we show that for an entire function belonging to the fock space f 2 c n on the complex euclidean space c n the integral operator s f z c n f w e z w z w d w z c n is bounded on f 2 c n if and only if there exists a function m l r n such that z r n m x e 2 x i 2 z 2 d x z c n here d w n e w 2 d w is the gaussian measure on c n with this characterization we are able to obtain some fundamental results of the operator s including the normality the c algebraic properties the spectrum and its compactness moreover we obtain the reducing subspaces of s in particular in the case n 1 we give a complete solution to an open problem proposed by k zhu for the fock space f 2 c on the complex plane c zhu 2015 30

an approach to optimal design of structures with non linear response a commonly adopted procedure to solve a structural optimum design problem is to improve the design iteratively by solving a sequence of simpler problems where each of these is obtained as an approximation of the original problem considering structures with linear response this procedure works very well and can be implemented quite straightforwardly however considering structures with non linear response the situation is more sophisticated since structural stability properties have to be taken into account the paper presents an approach to optimal design of statically loaded structures with non linear response it is proposed to replace the original problem with a sequence of similar problems from which corresponding approximate problems can easily be obtained these similar problems additionally contain an estimation of the critical load constraint while other constraints are imposed at some properly chosen load level which is lower or at most equal to the critical load level by this approach the structural stability requirements are taken into account in an effective manner the efficiency is illustrated with several examples involving kinematic as well as material non linear effects

multi objective optimization of fuzzy structural systems it is recognized that there exists a vast amount of fuzzy information in both the objective and constraint functions of the optimum design of structures since most practical structural design problems involve several often conflicting objectives to be considered a multi objective fuzzy programming method is outlined in this work the fuzzy constraints define a fuzzy feasible domain in the design space and each of the fuzzy objective functions defines the optimum solution by a fuzzy set of points a method of solving a fuzzy multi objective structural optimization problem using ordinary single objective programming techniques is presented the computational approach is illustrated with two numerical examples

blow up problems for the heat equation with a local nonlinear neumann boundary condition abstract this paper estimates the blow up time for the heat equation u t u with a local nonlinear neumann boundary condition the normal derivative u n u q on 1 one piece of the boundary while on the rest part of the boundary u n 0 the motivation of the study is the partial damage to the insulation on the surface of space shuttles caused by high speed flying subjects we show the finite time blow up of the solution and estimate both upper and lower bounds of the blow up time in terms of the area of 1 in many other work they need the convexity of the domain and only consider the problem with 1 in this paper we remove the convexity condition and only require to be c 2 in addition we deal with the local nonlinearity namely 1 can be just part of

families of biorthogonal wavelets several families of biorthogonal wavelet bases are constructed with various properties in particular for a given filter fn of finite length 2n 1 a parametric family of dual filters fvn of length 2n 1 is constructed the parametric nature of the dual filters makes it possible to design the optimum dual filter fv0n corresponding to a fixed filter fn

localization of multi constrained optima and avoidance of local optima in structural optimization problems abstract this paper describes two new methods of structural optimization the first method is seen primarily in conjunction with optimality criteria algorithms it proposes a new procedure for the solution of multi constrained optimization problems based on the calculation of partial optima the partial optima refer to solutions of the optimization problem only for part of the constraints in the simplest case only for a single constraint and can be easily determined by already known procedures the second method is a new mathematical programming method designed to combine a high convergence speed together with a high reliability with respect to the avoidance of local minima

resolvent estimates in l p for the stokes operator in lipschitz domains we establish the l p resolvent estimates for the stokes operator in lipschitz domains in mathbb r d d geqq 3 for frac 1 p frac 1 2 frac 1 2d varepsilon the result implies that the stokes operator in a three dimensional lipschitz domain generates a bounded analytic semigroup in l p for 3 2 e p 3 e this gives an affirmative answer to a conjecture of m taylor progr nonlinear differential equations appl vol 42 pp 320 334

embedded function approach for turbulent flow prediction in conventional prediction methods for turbulent flow influence on surface properties very small mesh sizes and considerable computational effort is required to adequately resolve the intense velocity and temperature profile variations that occur in the wall layer region in this study an approach is described wherein an outer region numerical solution is smoothly matched to a set of embedded analytic profile functions in the near wall region these wall layer profile functions having been derived through consideration of the coherent structure of the time dependent near wall flow provide analytic expressions for the mean velocity and enthalpy profiles in the wall layer the concept is demonstrated through example applications to turbulent boundary layer flows in two dimensions the technique is shown to be very efficient and it is demonstrated that a reduction of approximately half the mesh points across the 2 d layer may be realized as compared to conventional methods with no degradation in accuracy

nearly weakly orthonormal sequences singular value estimates and calderon zygmund operators abstract the direct way to estimate the singular values of a compact operator is to decompose it as a sum of orthogonal rank one pieces however such decompositions can generally not be found in practice we give a variation of the decomposition using nearly weakly orthonormal nwo sequences the nwo decomposition is easier to do in examples but is still strong enough to give good singular value estimates we illustrate this by giving sharp trace ideal estimates for the double layer potential and for the first and higher commutators of multiplication operators and calderon zygmund operators in particular nwo sequences seem well suited for dealing with operators which depend nonlinearly on their symbol we also show that the class of operators which admit nwo expansions is well behaved under composition under conjugation by weights and under conjugation by changes of variable

design sensitivity analysis and optimization of dynamic response abstract the paper presents methods of design sensitivity analysis and optimization of dynamic response of mechanical and structural systems a key feature of the paper is the development of procedures to handle point wise state variable constraints difficulties with a previous treatment where such constraints were transformed to equivalent integral constraints are noted and explained from theoretical as well as engineering standpoints an alternate treatment of such constraints is proposed developed and evaluated in this treatment each point wise state variable constraint is replaced by several constraints that are imposed at all the local max points for the original constraint function the differential equations of motion are formulated in the first order form so as to handle more general problems the direct differentiation and adjoint variable methods of design sensitivity analysis to deal with the point wise constraints are presented with the adjoint variable methods there are two ways of calculating design sensitivity coefficients the first approach uses an impulse load and the second approach uses a step load for the corresponding adjoint equation since the adjoint variable methods are better for a large class of problems an efficient computational algorithm with these methods is presented in detail optimum results for several problems are obtained and compared with those available in the literature the new formulation works extremely well as precise optimum designs are obtained

defect stream function law of the wall wake method for turbulent boundary layers a law of the wall law of the wake formulation for the inner part of the boundary layer is presented that greatly simplifies the computational task near the wall and eliminates the need for an eddy viscosity model in this region the eddy viscosity model in the outer part of the boundary layer is arbitrary formulations for both equilibrium and nonequilibrium boundary layers are presented and results are compared with previous methods for equilibrium boundary layers

the generalization of paraproducts and the full t1 theorem for sobolev and triebel lizorkin spaces abstract we study the boundedness of generalized calderon zygmund operators acting on sobolev and more generally triebel lizorkin spaces of arbitrary order of smoothness we are able to relax the assumptionst x 0 and ort x 0 which have been required in earlier results by other authors to do this we consider generalized paraproduct operators we obtain the sharpness of our assumptions for some special cases using the same technique we also obtain some sharper results for norming and molecular families

multilinear littlewood paley estimates with applications to partial differential equations abstract we obtain a collection of multilinear littlewood paley estimates which we then apply to two problems in partial differential equations the first problem is the estimation of the square root of an elliptic operator in divergence form and the second is the estimation of solutions to the cauchy problem for nondivergence form parabolic equations

an adaptive fast gauss transform in two dimensions a variety of problems in computational physics and engineering require the convolution of the heat kernel a gaussian with either discrete sources densities supported on boundaries or continuous

boundedness criterion of journeʼs class of singular integrals on multiparameter hardy spaces abstract this article concerns nonconvolutional type operators also known as journe s type operators associated with a multiparameter family of dilations given by x 1 x 2 x m 1 x 1 2 x 2 m x m where x 1 r n 1 x 2 r n 2 x m r n m and m 3 we are especially interested in the boundedness of such operators on the multiparameter hardy spaces this work is motivated by pipher s result on the boundedness of these operators from the multiparameter h p spaces to l p spaces for 0 p 1 and journe s counter example which shows that the number of parameter plays a crucial role in boundedness of singular integral operators on multiparameter hardy spaces journe s work shows that there is a sharp difference between the situations for two and three or more parameters we establish in this paper the necessary and sufficient conditions under which the singular integral operators in journe s class are bounded on multiparameter h p spaces 0 p 1 with arbitrary number of parameters

area integral estimates for caloric functions we study the relationship between the area integral and the para bolic maximal function of solutions to the heat equation in domains whose boundary satisfies a 5 1 mixed lipschitz condition our main result states that the area integral and the parabolic maximal function are equivalent in lp p 0 p oo the measure p must satisfy muckenhoupt s loo condition with respect to caloric measure we also give a fatou theorem which shows that the existence of parabolic limits is a e with respect to caloric measure equivalent to the finiteness of the area integral

weight minimisation of displacement constrained truss structures using a strain energy criterion this paper discusses a new method for the solution of the general truss weight minimisation problem under simultaneous stress and displacement constraints the method introduces a novel strain energy density criterion that refers to the ratio of the virtual strain energy per unit volume in each structural member to its average value on the whole structure the virtual strain energy comes from the unit load theorem and it is proportional to the product of the axial member forces due to both the actual loads and a virtual unit load that is applied at the node with the maximum displacement a simple recursive formula for updating the cross sectional areas based on displacement constraints is presented a general subsequent algorithm applicable to both single and multiple load cases follows this formula the results are encouraging since in all test cases the method was found to be robust and generally led to the same weight level as the literature in both small and large structures

trust region methods for structural optimization using exact second order sensitivity the performance of multiplier algorithms for structural optimization has been significantly improved by using trust regions the trust regions are constructed using analytical second order sensitivity and within this region the augmented lagrangian is minimized subject to bounds evaluation of first and second derivatives of by the adjoint method does not require derivations of individual implicit constraint functions which makes the method economical eight test problems are considered and a vast improvement over previously used multiplier algorithms has been noted also the algorithm is robust with respect to scaling input parameters and starting designs

the method of layer potentials for the heat equation in lipschitz cylinders pour l equation de la chaleur dans des cylindres de lipschitz on etudie des problemes aux valeurs limites d initiales avec conditions de neumann et de dirichlet

discrete decompositions for bilinear operators and almost diagonal conditions this is the published version also available here http dx doi org 10 1090 s0002 9947 01 02912 9 first published in transaction of american mathematical society in 2002 published by the american mathematical society

weak 1 1 bounds for oscillatory singular integrals pour un polynome p r n r n r et un noyau de calderon zygmund k l operateur t f x pv exp ip x y k x y f y dy est de type faible sur l 1 avec une borne dependant seulement de k cz et le degre de p

the trace of the heat kernel in lipschitz domains we establish the existence of an asymptotic expansion as t 0 for the trace of the heat kernel for the neumann laplacian in a bounded lip schitz domain the proof of an asymptotic expansion for the heat kernel for the dirichlet laplacian is also sketched the treatment of the dirichlet lapla cian extends work of brossard and carmona who obtained the same result in c1 domains a classical question in analysis asks what is the relationship between the spectrum of the laplacian on a domain and the geometry of the domain this question has been studied by many authors including 1 3 7 11 12 14 15 17 19 one approach to this problem proceeds by considering the trace of the heat semigroup on d tr 0 i g t x x dx te jd where g is the heat kernel on d and 0 ai a2 a3 is the sequence of eigenvalues for a on d one attempts to give an asymptotic expansion for tx g near t 0 whose coefficients are quantities associated with the geometry of d thus one can deduce geometrical information about d from knowledge of the spectrum in this paper we will address this question under minimal smoothness as sumptions on the boundary of d in particular we will obtain asymptotic ex pansions for tx g when the order of smoothness of the boundary corresponds exactly to the order of accuracy of the asymptotic expansion in order to state our main theorem we need one definition by a lipschitz domain we mean a bounded connected open set whose boundary may be locally described as the graph of a lipschitz function our main result is main theorem suppose that d c r is a lipschitz domain then the heat kernel for the laplacian with dirichlet boundary conditions on 3d satisfies tx g t 4ntyn 2 d n x dd o txl2

a recursive quadratic programming method with active set strategy for optimal design recursive quadratic programming methods have become popular in the field of mathematical programming owing to their excellent convergence characteristics there are two recursive quadratic programming methods that have been published in the literature one is by han and the other is by pshenichny published in 1977 and 1970 respectively the algorithm of pshenichny had been undiscovered until now and is examined here for the first time it is found that the proof of global convergence by han requires computing sensitivity coefficients derivatives of all constraint functions of the problem at every iteration this is prohibitively expensive for large scale applications in optimal design in contrast pshenichny has proved global convergence of his algorithm using only an active set strategy this is clearly preferable for large scale applications the method of pshenichny has been coded into a fortran program applications of this method to four example problems are presented the method is found to be very reliable however the method is found to be very sensitive to local minima i e it converges to a local minimum nearest to the starting design thus for optimal design problems which usually possess multiple local minima it is suggested that pshenichny s method be used as part of a hybrid method

finite difference outer layer analytic inner layer method for turbulent boundary layers a new turbulent boundary layer method is developed which models the inner region with the law of the wall whereas the outer region uses clauser s eddy viscosity in matsuno s finite difference method the match point between the inner and outer regions as well as the wall shear stress is determined at each marching step during the computation results obtained for incompressible two dimensional flow over flat plates and ellipses are compared with solutions from a baseline method that uses a finite difference method for the entire boundary layer since the present method used the finite difference method in the outer region only the number of grid points required was about half that needed for the baseline method accurate displacement and momentum thicknesses were predicted for all cases skin friction was predicted well for the flat plate but the accuracy decreased significantly for the ellipses adding a wake function to the law of the wall allows some of the pressure gradient effect to be taken into account thereby increasing the accuracy of the method

a refined convergence result in homogenization of second order parabolic systems abstract we derive the sharp o e convergence rate in l 2 0 t l q 0 q 0 2 d d 1 in periodic homogenization of second order parabolic systems with bounded measurable coefficients in lipschitz cylinders this extends the corresponding result for elliptic systems established in 20 to parabolic systems and improves the corresponding result in l 2 settings derived in 7 28 for second order parabolic systems with time dependent coefficients

the solution of the kato square root problem for second order elliptic operators on rn we prove the kato conjecture for elliptic operators on jfin more precisely we establish that the domain of the square root of a uniformly complex elliptic operator l div av with bounded measurable coefficients in ietn is the

l2 solvability of boundary value problems for divergence form parabolic equations with complex coefficients abstract we consider parabolic operators of the form t l l div a x t in r n 2 x t x x n 1 t r n r r x n 1 0 n 1 we assume that a is a n 1 n 1 dimensional matrix which is bounded measurable uniformly elliptic and complex and we assume in addition that the entries of a are independent of the spatial coordinate x n 1 as well as of the time coordinate t for such operators we prove that the boundedness and invertibility of the corresponding layer potential operators are stable on l 2 r n 1 c l 2 r n 2 c under complex l perturbations of the coefficient matrix subsequently using this general result we establish solvability of the dirichlet neumann and regularity problems for t l by way of layer potentials and with data in l 2 assuming that the coefficient matrix is a small complex perturbation of either a constant matrix or of a real and symmetric matrix

new integral estimates for deformations in terms of their nonlinear strains if u is a bi lipschitzian deformation of a bounded lipschitz domain in ln n 2 we show that the lp norm p 1 p n of a certain nonlinear strain function e u associated with u dominates the distance in lq q np n p if p n from u to a suitably chosen rigid motion of n this work extends that of f john who proved corresponding estimates for p 1 under the hypothesis that u has uniformly small strain we also obtain a bound for the oscillation of du in l2 these estimates are apparently the first to apply with no a priori pointwise hypotheses upon the strain of u in 3 the integral int limits omega e u 2d 3 is dominated by typical hyperelastic energy functionals proposed in the literature for modeling the behavior of rubber thus the case n 3 p 2 gives the first general bound for the deformations of such materials in terms of the associated nonlinear elastic work

stability results on interpolation scales of quasi banach spaces and applications we investigate the stability of fredholm properties on interpolation scales of quasi banach spaces this analysis is motivated by problems arising in pde s and several applications are presented

parabolic regularity and dirichlet boundary value problems abstract we study the relationship between the regularity and dirichlet boundary value problems for parabolic equations of the form l u div a u u t 0 in lip 1 1 2 time varying cylinders where the coefficient matrix a a i j x t is uniformly elliptic and bounded we show that if the regularity problem r p for the equation l u 0 is solvable for some 1 p then the dirichlet problem d p for the adjoint equation l v 0 is also solvable where p p p 1 this result is an analogue of the result established in the elliptic case by kenig and pipher 1993 in the parabolic settings in the special case of the heat equation in slightly smoother domains this has been established by hofmann and lewis 1996 and nystrom 2006 for scalar parabolic systems in comparison our result is abstract with no assumption on the coefficients beyond the ellipticity condition and is valid in more general class of domains

regularity properties of commutators and layer potentials associated to the heat equation in recent years there has been renewed interest in the solution of parabolic boundary value problems by the method of layer potentials in this paper we consider graph domains d x t x f t in 9j2 where the boundary function f is in i112 bmo this class of domains would appear to be the minimal smoothness class for the solvability of the dirichlet problem for the heat equation by the method of layer potentials we show that for 1 p oo the boundary single layer potential operator for d maps lp into the homogeneous sobolev space i1i2 lp this regularity result is obtained by studying the regularity properties of a related family of commutators along the way we prove lp estimates for a class of singular integral operators to which the t 1 theorem of david and journe does not apply the necessary estimates are obtained by a variety of real variable methods

fourier analysis on starlike lipschitz surfaces a theory of a class of singular integrals on starlike lipschitz surfaces in rn is established the class of singular integrals forms an operator algebra identical to the class of bounded holomorphic fourier multipliers as well as to the cauchy dunford bounded holomorphic functional calculus of the spherical dirac operator the study proposes a new method inducing clifford holomorphic functions from holomorphic functions of one complex variable by means of which problems on the sphere are reduced to those on the unit circle

efficient approximation concepts using second order information the primary goal of this paper is to show how second derivative information can be used in an effective way in structural optimization problems the basic idea is to generate such an information at the expense of only one more virtual load case in the sensitivity analysis part of the finite element code to achieve this goal a primal dual approach is employed that can also be interpreted as a sequential quadratic programming method another objective is to relate the proposed method to the well known family of approximation concepts techniques where the primary optimization problem is transformed into a sequence of non linear explicit subproblems when restricted to diagonal second derivatives the new approach can be viewed as a recursive convex programming method similar to the convex linearization method conlin and to its recent generalization the method of moving asymptotes mma this new method has been successfully tested on simple problems that can be solved in closed form as well as on sizing optimization of trusses in all cases the method converges faster than conlin mma or other approximation techniques based on reciprocal variables

a liouville theorem for stationary and ergodic ensembles of parabolic systems a first order liouville theorem is obtained for random ensembles of uniformly parabolic systems under the mere qualitative assumptions of stationarity and ergodicity furthermore the paper establishes almost surely an intrinsic large scale mathcal c 1 alpha regularity estimate for caloric functions

on the waterbag continuum the aim of this paper is to study the existence of a classical solution for the waterbag model with a continuum of waterbags which can been viewed as an infinite dimensional system of first order conservation laws the waterbag model which constitutes a special class of exact weak solution of the vlasov equation is well known in plasma physics and its applications in gyrokinetic theory and laser plasma interaction are very promising the proof of the existence of a continuum of regular waterbags relies on a generalized definition of hyperbolicity for an integrodifferential hyperbolic system of equations some results in singular integral operators theory and harmonic analysis riemann hilbert boundary value problems and energy estimates

representation of bi parameter singular integrals by dyadic operators abstract we prove a dyadic representation theorem for bi parameter singular integrals that is we represent certain bi parameter operators as averages of rapidly decaying sums of what we call bi parameter shifts a new version of the product space t 1 theorem is established as a consequence

hardy spaces and the neumann problem in l p for laplace s equation in lipschitz domains on donne des resultats optimaux pour la resolubilite du probleme de neumann dans des domaines de lipschitz a donnees dans l p on obtient des resultats du point extreme correspondant pour des espaces de hardy

a basis change strategy for the reduced gradient method and the optimum design of large structures this paper proposes a basis change strategy within the reduced gradient method for optimization under linear constraints it ensures a non singular basis matrix at every iteration the same strategy can reliably be used within the generalized reduced gradient method for optimization under non linear constraints this method is applied to the minimum weight design of large structures under displacement and stress constraints exploiting the sparsity of the constraint jacobian matrix

an efficient galerkin boundary element method for the transient heat equation we present boundary integral representations of several initial boundary value problems related to the heat equation a galerkin discretization with piecewise constant functions in time and piecewise linear functions in space leads to optimal a priori error estimates provided that the meshwidths in space and time satisfy h t mathcal o h x 2 each time step involves the solution of a linear system whose spectral condition number is independent of the refinement under the same assumption on the mesh we show that if the parabolic multipole method is used to apply parabolic boundary integral operators the overall complexity of the scheme is log linear while preserving the convergence of the galerkin discretization method the theoretical estimates are confirmed numerically at the end of the paper