spectral lagrangian methods for collisional models of non equilibrium statistical states we propose a new spectral lagrangian based deterministic solver for the non linear boltzmann transport equation bte in d dimensions for variable hard sphere vhs collision kernels with conservative or non conservative binary interactions the method is based on symmetries of the fourier transform of the collision integral where the complexity in its computation is reduced to a separate integral over the unit sphere s d 1 the conservation of moments is enforced by lagrangian constraints the resulting scheme implemented in free space is very versatile and adjusts in a very simple manner to several cases that involve energy dissipation due to local micro reversibility inelastic interactions or elastic models of slowing down process our simulations are benchmarked with available exact self similar solutions exact moment equations and analytical estimates for the homogeneous boltzmann equation both for elastic and inelastic vhs interactions benchmarking of the simulations involves the selection of a time self similar rescaling of the numerical distribution function which is performed using the continuous spectrum of the equation for maxwell molecules as studied first in bobylev et al a v bobylev c cercignani g toscani proof of an asymptotic property of self similar solutions of the boltzmann equation for granular materials journal of statistical physics 111 2003 403 417 and generalized to a wide range of related models in bobylev et al a v bobylev c cercignani i m gamba on the self similar asymptotics for generalized non linear kinetic maxwell models communication in mathematical physics in press url the method also produces accurate results in the case of inelastic diffusive boltzmann equations for hard spheres inelastic collisions under thermal bath where overpopulated non gaussian exponential tails have been conjectured in computations by stochastic methods t v noije m ernst velocity distributions in homogeneously cooling and heated granular fluids granular matter 1 57 1998 m h ernst r brito scaling solutions of inelastic boltzmann equations with over populated high energy tails journal of statistical physics 109 2002 407 432 s j moon m d shattuck j swift velocity distributions and correlations in homogeneously heated granular media physical review e 64 2001 031303 i m gamba s rjasanow w wagner direct simulation of the uniformly heated granular boltzmann equation mathematical and computer modelling 42 2005 683 700 and rigorously proven in gamba et al i m gamba v panferov c villani on the boltzmann equation for diffusively excited granular media communications in mathematical physics 246 2004 503 541 39 and a v bobylev i m gamba v panferov moment inequalities and high energy tails for boltzmann equations with inelastic interactions journal of statistical physics 116 2004 1651 1682

a hybridizable discontinuous galerkin method for stokes flow abstract in this paper we introduce a hybridizable discontinuous galerkin method for stokes flow the method is devised by using the discontinuous galerkin methodology to discretize a velocity pressure gradient formulation of the stokes system with appropriate choices of the numerical fluxes and by applying a hybridization technique to the resulting discretization one of the main features of this approach is that it reduces the globally coupled unknowns to the numerical trace of the velocity and the mean of the pressure on the element boundaries thereby leading to a significant reduction in the size of the resulting matrix moreover by using an augmented lagrangian method the globally coupled unknowns are further reduced to the numerical trace of the velocity only another important feature is that the approximations of the velocity pressure and gradient converge with the optimal order of k 1 in the l 2 norm when polynomials of degree k 0 are used to represent the approximate variables based on the optimal convergence of the hdg method we apply an element by element postprocessing scheme to obtain a new approximate velocity which converges with order k 2 in the l 2 norm for k 1 the postprocessing performed at the element level is less expensive than the solution procedure numerical results are provided to assess the performance of the method

a high order hybridizable discontinuous galerkin method with fast convergence to steady state solutions of the gas kinetic equation abstract the mass flow rate of poiseuille flow of rarefied gas through long ducts of two dimensional cross sections with arbitrary shape is critical in the pore network modeling of gas transport in porous media here for the first time the high order hybridizable discontinuous galerkin hdg method is used to find the steady state solution of the linearized bhatnagar gross krook equation on two dimensional triangular meshes the velocity distribution function and its traces are approximated in piecewise polynomial spaces of degree up to 4 on the triangular meshes and mesh skeletons respectively by employing a numerical flux that is derived from the first order upwind scheme and imposing its continuity weakly on the mesh skeletons global systems for unknown traces are obtained with fewer coupled degrees of freedom when compared to the original discontinuous galerkin formulation to achieve fast convergence to the steady state solution a diffusion like equation for flow velocity which is asymptotic preserving into the fluid dynamic limit is solved by the hdg simultaneously on the same meshes the proposed hdg synthetic iterative scheme is proved to be accurate and efficient specifically for flows in the near continuum regime numerical simulations have shown that to achieve the same level of accuracy our scheme could be faster than the conventional iterative scheme by two orders of magnitude also it is faster than the synthetic iterative scheme based on the finite difference discretization in the spatial space by one order of magnitude in addition the implicit hdg method is more efficient than an explicit discontinuous galerkin gas kinetic solver as well as the implicit discontinuous galerkin scheme when the degree of approximating polynomial is larger than 2 the hdg synthetic iterative scheme is ready to be extended to simulate rarefied gas mixtures and the boltzmann collision operator

a high order space momentum discontinuous galerkin method for the boltzmann equation in this paper we present a discontinuous galerkin method for the boltzmann equation the distribution function f is approximated by a shifted maxwellian times a polynomial in space and momentum while the test functions are chosen as polynomials the first property leads to consistency with the euler limit while the second property ensures conservation of mass momentum and energy the focus of the paper is on efficient algorithms for the boltzmann collision operator we transform between nodal hierarchical and polar polynomial bases to reduce the inner integral operator to diagonal form

unified hybridization of discontinuous galerkin mixed and continuous galerkin methods for second order elliptic problems we introduce a unifying framework for hybridization of finite element methods for second order elliptic problems the methods fitting in the framework are a general class of mixed dual finite element methods including hybridized mixed continuous galerkin nonconforming and a new wide class of hybridizable discontinuous galerkin methods the distinctive feature of the methods in this framework is that the only globally coupled degrees of freedom are those of an approximation of the solution defined only on the boundaries of the elements since the associated matrix is sparse symmetric and positive definite these methods can be efficiently implemented moreover the framework allows in a single implementation the use of different methods in different elements or subdomains of the computational domain which are then automatically coupled finally the framework brings about a new point of view thanks to which it is possible to see how to devise novel methods displaying very localized and simple mortaring techniques as well as methods permitting an even further reduction of the number of globally coupled degrees of freedom

review of options for structural design sensitivity analysis part 1 linear systems the paper reviews options for structural design sensitivity analysis including global finite differences continuum derivatives discrete derivatives and computational or automated differentiation the objective is to put these different approaches to design sensitivity analysis in the context of accuracy and consistency computational cost and implementation options and effort linear static analysis and transient dynamic analysis are reviewed in a separate appendix special attention is paid to the semi analytical method a future paper will address design sensitivity analysis in nonlinear structural problems

inverse sensitivity method for asymmetric multivariable nondefective systems an available parametric correction method for asymmetric multivariable nondefective systems is investigated it will be proved that the eigensolutions associated with the repeated eigenvalues are not differentiable although their partial derivatives exist a calculable generalized jacobian matrix is presented based on the first order taylor expansion of the repeated root eigenpairs as the case of symmetric systems which ensures the feasibility of the inverse sensitivity method for parametric correction the first order directional derivatives of the repeated root eigenpairs are also found two numerical asymmetric examples are given to verify the validity of the method by use of simulated data

efficient extraction of networks from three dimensional porous media 1 fluid flow through porous media and the thermal electrical and acoustic properties of these materials is largely controlled by the geometry and topology gt of the pore system which can be considered as a network network extraction techniques have been applied in many research fields including shape representation pattern recognition and artificial intelligence however the set of algorithms presented here significantly improves the efficiency of common thinning algorithms by introducing a sufficiency condition based on the idea of a simple set this paper describes an efficient and accurate algorithm for extracting the geometrical topological network that represents the pore structure of a porous medium referred to as the gt network the accurate medial axis and the specific gt description of the network are achieved by applying symmetrical and interval strategies during the erosion step in the image processing the gt network extraction algorithm presented here involves a number of steps including 1 calculation of the three dimensional euclidean distance map 2 clustering of voxels 3 extraction of the network of the pore space 4 partitioning of the pore space and 5 computation of shape factors the focus of this paper is mainly on the thinning method that underpins points 1 3 the paper is primarily a method description but we illustrate the functionality of the technique by extracting a pore scale gt network from micro computer tomography images of three sandstones

computation of eigenvector derivatives with repeated eigenvalues using a complete modal space this paper presents a complete modal space cms method that is an exact modal expansion method there is no modal truncation error existing in the derivation

application of the integro moment method to steady state two dimensional rarefied gas flows subject to boundary induced discontinuities the computational efficiency of the integro moment method for solving steady state two dimensional rarefied gas flows is investigated the two dimensional boundary driven flow of a single gas in a cavity is used as a model problem because the kinetic equations and the boundary conditions describing this flow contain most of the terms and features which might appear in problems modeled by kinetic equations following a detailed quantitative comparison with the discrete velocity method it is concluded that the integro moment method may be considered as a alternative reliable and efficient computational scheme for solving rarefied or non equilibrium flows in the whole range of the knudsen number even more it is shown that by implementing the integro moment method the propagation of any discontinuities which may exist at the boundaries inside the computational domain and the production of an unphysical oscillatory behavior in the macroscopic quantities are completely eliminated the proposed integro moment methodology is general and may be applied to any multidimensional non equilibrium flow described by linear kinetic model equations

an implicit high order hybridizable discontinuous galerkin method for the incompressible navier stokes equations we present an implicit high order hybridizable discontinuous galerkin method for the steady state and time dependent incompressible navier stokes equations the method is devised by using the discontinuous galerkin discretization for a velocity gradient pressure velocity formulation of the incompressible navier stokes equations with a special choice of the numerical traces the method possesses several unique features which distinguish itself from other discontinuous galerkin methods first it reduces the globally coupled unknowns to the approximate trace of the velocity and the mean of the pressure on element boundaries thereby leading to a significant reduction in the degrees of freedom moreover if the augmented lagrangian method is used to solve the linearized system the globally coupled unknowns become the approximate trace of the velocity only second it provides for smooth viscous dominated problems approximations of the velocity pressure and velocity gradient which converge with the optimal order of k 1 in the l2 norm when polynomials of degree k 0 are used for all components of the approximate solution and third it displays superconvergence properties that allow us to use the above mentioned optimal convergence properties to define an element by element postprocessing scheme to compute a new and better approximate velocity indeed this new approximation is exactly divergence free h div conforming and converges with order k 2 for k 1 and with order 1 for k 0 in the l2 norm moreover a novel and systematic way is proposed for imposing boundary conditions for the stress viscous stress vorticity and pressure which are not naturally associated with the weak formulation of the method this can be done on different parts of the boundary and does not result in the degradation of the optimal order of convergence properties of the method extensive numerical results are presented to demonstrate the convergence and accuracy properties of the method for a wide range of reynolds numbers and for various polynomial degrees

sensitivity analysis of smart structures abstract the simultaneous optimal design of adaptive structural systems has been formulated as a multi objective programming problem with the structural variables and controller parameters as design variables to construct a well behaved algorithm for the solution of a problem of such complexity accurate sensitivity information is essential the purpose of this paper is to systematically evaluate the analytical expressions for the design gradients of the various objectives and constraints with respect to the continuous design variables kleinman s lemma and bellman s expansion are employed in the derivation and as a result the gradient of quadratic performance criterion with respect to the open loop plant matrix is obtained this result provides along with previous results obtained by others a complete sensitivity package for smart structural control and optimisation with this sensitivity information a truly simultaneous optimisation of a smart structure could be possible numerical results are presented as verification of the analytical derivations

an asymptotic preserving monte carlo method for the multispecies boltzmann equation an asymptotic preserving ap scheme is efficient in solving multiscale kinetic equations with a wide range of the knudsen number in this paper we generalize the asymptotic preserving monte carlo method ap dsmc developed in 25 to the multispecies boltzmann equation this method is based on the successive penalty method 26 originated from the bgk penalization based ap scheme developed in 7 for the multispecies boltzmann equation the penalizing maxwellian should use the unified maxwellian as suggested in 12 we give the details of ap dsmc for multispecies boltzmann equation show its ap property and verify through several numerical examples that the scheme can allow time step much larger than the mean free time thus making it much more efficient for flows with possibly small knudsen numbers than the classical dsmc

effective mass sensitivities for systems with repeated eigenvalues a generalization for the calculation of effective mass sensitivities to the case of coincident eigenvalues has been proposed the results obtained with the exact approach and an approach based on a suitable perturbation introduced to eliminate the eigenvalue multiplicity are in excellent agreement the two approaches based on the finite dfference approximation are still in good agreement but as expected the elimination of significant digits does affect the precision

iterative computation of modal sensitivities the computation of frequency and mode shape sensitivities with respect to design parameters is essential to many structural optimization and finite element updating algorithms approximating the gradients may lead to poor estimates and loss of convergence but on the other hand the cost of exact methods such as nelson s nelson r simplified calculations of eigenvector derivatives a1aa journal vol 14 no 9 1976 pp 1201 1205 is often not acceptable for industrial size models the present study thus analyses existing approximation methods suggests a first order improvement of fox and kapoor s modal basis fox r and kapoor m rate of change of eigenvalues and eigenvectors a1aa journal vol 6 no 12 1968 pp 2426 242 9 and proposes a residual iteration technique allowing accurate computations of modeshape sensitivities an engine cover model and a model of the ariane 5 main cryogenic stage are used to analyze for models of realistic sizes the accuracy and computational costs of the proposed methods

how many hypersurfaces does it take to cut out a segre class abstract we prove an identity of segre classes for zero schemes of compatible sections of two vector bundles applications include bounds on the number of equations needed to cut out a scheme with the same segre class as a given subscheme of for example a projective variety and a segre bertini theorem controlling the behavior of segre classes of singularity subschemes of hypersurfaces under general hyperplane sections these results interpolate between an observation of samuel concerning multiplicities along components of a subscheme and facts concerning the integral closure of corresponding ideals the segre bertini theorem has applications to characteristic classes of singular varieties the main results are motivated by the problem of computing segre classes explicitly and applications of segre classes to enumerative geometry

a fast iterative scheme for the linearized boltzmann equation iterative schemes to find steady state solutions to the boltzmann equation is efficient for highly rarefied gas flows but can be very slow to converge in the near continuum flow regime in this paper a synthetic iterative scheme is developed to speed up the solution of the linearized boltzmann equation by penalizing the collision operator l into the form l l n delta h n delta h where delta is the gas rarefaction parameter h is the velocity distribution function and n is a tuning parameter controlling the convergence rate the velocity distribution function is first solved by the conventional iterative scheme then it is corrected such that the macroscopic flow velocity is governed by a diffusion type equation that is asymptotic preserving into the navier stokes limit the efficiency of this new scheme is assessed by calculating the eigenvalue of the iteration as well as solving for poiseuille and thermal transpiration flows we find that the fastest convergence of our synthetic scheme for the linearized boltzmann equation is achieved when n delta is close to the average collision frequency the synthetic iterative scheme is significantly faster than the conventional iterative scheme in both the transition and the near continuum gas flow regimes moreover due to its asymptotic preserving properties the synthetic iterative scheme does not need high spatial resolution in the near continuum flow regime which makes it even faster than the conventional iterative scheme using this synthetic scheme with the fast spectral approximation of the linearized boltzmann collision operator poiseuille and thermal transpiration flows between two parallel plates through channels of circular rectangular cross sections and various porous media are calculated over the whole range of gas rarefaction finally the flow of a ne ar gas mixture is solved based on the linearized boltzmann equation with the lennard jones intermolecular potential for the first time and the difference between these results and those using the hard sphere potential is discussed

eigenvalue and eigenvector approximate analysis for repeated eigenvalue problems the method developed for approximate analysis involves a reparamaterization of the multivariable structural eigenvalue problems in terms of a single positive valued parameter the resulting equations yield first order approximations of changes in both the eigenvalues and eigenvectors associated with the repeated eigenvalue problem

on simultaneous optimization of smart structures part ii algorithms and examples five algorithms for the simultaneous optimal design of smart structural systems are presented these algorithms are developed based on sequential mathematical programming and guided random search techniques being applied to multidisciplinary optimization in which both structural layout and controller parameters are involved a method to prevent singularities when updating the structural layout is suggested two adaptive trusses are optimised and comparison is made for the different optimal schemes on the basis of iteration histories and major results achieved all of the five algorithms are shown efficient in improving the truss s performance with respect to robustness and controllability the results show that the greatest improvement in all the performance indicators is achieved using a genetic algorithm whilst the most efficient scheme is seen to be a novel hybrid combining sequential linear programming with simulated annealing

eigensolutions sensitivity for nonsymmetric matrices with repeated eigenvalues a perturbation algorithm is developed for evaluating eigenvalue and eigenvector directional derivatives of nonsymmetric defective matrices some properties are recalled in particular chains of generalized right and left eigenvectors and their orthogonal properties are defined small perturbations of the matrix are then considered an asymptotic expansion of the eigensolutions of the perturbed problem is obtained in terms of noninteger powers of the perturbation parameter particular attention is devoted to the eigenvectors of the perturbed system and to the strong coupling that occurs between the chains

construction of discrete kinetic models with given invariants we consider the general problem of the construction of discrete kinetic models dkms with given conservation laws this problem was first stated by gatignol in connection with discrete models of the boltzmann equation be and it has been addressed in the last decade by several authors even though a practical criterion for the non existence of spurious conservation laws has been devised and a method for enlarging existing physical models by new velocity points without adding non physical invariants has been proposed a general algorithm for the construction of all normal physical discrete models with assigned conservation laws in any dimension and for any number of points is still lacking in the literature we introduce the most general class of discrete kinetic models and obtain a general method for the construction and classification of normal dkms in particular it is proved that for any given dimension d 2 and for any sufficiently large number n of velocities for example n 6 for the planar case d 2 there exists just a finite number of distinct classes of dkms we apply the general method in the particular cases of discrete velocity models dvms of the inelastic be and elastic be using our general approach to dkms and our results on normal dvms for a single gas we develop a method for the construction of the most natural from physical point of view subclass of normal dvms for binary gas mixtures we call such models supernormal models snms they have the property that by isolating the velocities of single gases involved in the mixture we also obtain normal dvms

natural frequency and mode shape sensitivities of damped systems part ii multiple natural frequencies abstract an efficient algorithm with proven numerical stability is derived for computation of eigenvalue and eigenvector derivatives of damped vibratory systems with multiple eigenvalues in the proposed method adjacent eigenvectors and orthonormal condition are used to compose an algebraic equation whose order is n m n m where n is the number of co ordinates and m the number of multiplicity of a multiple natural frequency the mode shape derivatives of the damped systems can be obtained by solving the algebraic equation the method can be consistently applied to both structural systems with structural design parameters and mechanical systems with lumped design parameters as an example of a structural system to demonstrate the theory of the proposed methods and its possibilities in the case of multiple eigenvalues the finite element model of the cantilever beam is considered and also a 5 dof mechanical system in the case of a non proportionally damped system the design parameter of the cantilever beam is its height and that of the 5 dof mechanical system is a spring

sensitivity analysis of flexible multibody systems using composite materials components in this paper a general formulation for the computation of the first order analytical sensitivities based on the direct method using automatic differentiation of flexible multibody systems is presented the direct method for sensitivity calculation is obtained by differentiating the equations that define the response of the flexible multibody systems of composite materials with respect to the design variables which are the ply orientations of the laminated in order to appraise the benefits of the approach suggested and to highlight the risks of the procedure the analytical sensitivities are compared with the numerical results obtained by using the finite difference method for the beam composite material elements the section properties and their sensitivities are found using an asymptotic procedure that involves a two dimensional 2 d finite element analysis of their cross section the equations of the sensitivities are obtained by automatic differentiation and integrated in time simultaneously with the equations of motion of the multibody systems the equations of motion and the sensitivities of the flexible multibody system are solved and the accelerations velocities and the sensitivities of accelerations and velocities are integrated in time using a multi step multi order integration algorithm through the application of the methodology to two simple flexible multibody systems the difficulties and benefits of the procedure with respect to finite difference approaches or to the direct implementation of the analytic sensitivities are discussed copyright 2008 john wiley sons ltd

discrete unified gas kinetic scheme for all knudsen number flows low speed isothermal case based on the boltzmann bgk bhatnagar gross krook equation in this paper a discrete unified gas kinetic scheme dugks is developed for low speed isothermal flows the dugks is a finite volume scheme with the discretization of particle velocity space after the introduction of two auxiliary distribution functions with the inclusion of collision effect the dugks becomes a fully explicit scheme for the update of distribution function furthermore the scheme is an asymptotic preserving method where the time step is only determined by the courant friedricks lewy condition in the continuum limit numerical results demonstrate that accurate solutions in both continuum and rarefied flow regimes can be obtained from the current dugks the comparison between the dugks and the well defined lattice boltzmann equation method d2q9 is presented as well

chern schwartz macpherson classes and the euler characteristic of degeneracy loci and special divisors this concept overlaps a large family of interesting varieties for example the varieties of special divisors studied in section 3 several authors have worked out explicit formulas for the euler characteristic of dr 9 in terms of different cohomological and numerical invariants under the assumption that x is nonsingular and v is appropriately general for instance if 0 is a section of a vector bundle then the formulas for the euler characteristic x do fp were given by hirzebruch h and navarro aznar n if dr is a curve or a surface in a nonsingular x some explicit formulas for x dr v were given by harris and tu h t in terms of the chern classes of e f and x but under the extra assumption dr 1 v 0 which implies that dr q is nonsingular in loc cit the authors also posed the problem of finding a general formula for x dr o if such exists under the assumption dr 1 0 or even stronger without this assumption the first problem was solved positively by the second named author prl proposition 5 7 by the use of polynomials universally supported on degeneracy

interpolation of characteristic classes of singular hypersurfaces abstract we show that the chern schwartz macpherson class of a hypersurface x in a nonsingular variety m interpolates between two other notions of characteristic classes for singular varieties provided that the singular locus of x is smooth and that certain numerical invariants of x are constant along this locus this allows us to define a lift of the chern schwartz macpherson class of such nice hypersurfaces to intersection homology as another application the interpolation result leads to an explicit formula for the chern schwartz macpherson class of x in terms of its polar classes

a gaussian quadrature procedure for use in the solution of the boltzmann equation and related problems abstract a new gaussian quadrature procedure is developed for integrals of the form 0 e y 2 y p y dy for p 0 1 and 2 recursion relations are derived for the coefficients in the general three term recurrence relation for the polynomials whose roots are the quadrature abscissae a comparison with the gauss laguerre quadrature procedure is presented solutions of the chemical kinetic boltzmann equation are obtained with a discrete ordinate method based on this gaussian quadrature procedure the results are compared with previous solutions obtained with a polynomial expansion method

the segre zeta function of an ideal abstract we define a power series associated with a homogeneous ideal in a polynomial ring encoding information on the segre classes defined by extensions of the ideal in projective spaces of arbitrarily high dimension we prove that this power series is rational with poles corresponding to generators of the ideal and with numerator of bounded degree and with nonnegative coefficients we also prove that this segre zeta function only depends on the integral closure of the ideal the results follow from good functoriality properties of the shadows of rational equivalence classes of projective bundles more precise results can be given if all homogeneous generators have the same degree and for monomial ideals in certain cases the general description of the segre zeta function given here leads to substantial improvements in the speed of algorithms for the computation of segre classes we also compute the projective ranks of a nonsingular variety in terms of the corresponding zeta function and we discuss the segre zeta function of a local complete intersection of low codimension in projective space

a class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources in this paper we propose a general time discrete framework to design asymptotic preserving schemes for initial value problem of the boltzmann kinetic and related equations numerically solving these equations are challenging due to the nonlinear stiff collision source terms induced by small mean free or relaxation time we propose to penalize the nonlinear collision term by a bgk type relaxation term which can be solved explicitly even if discretized implicitly in time moreover the bgk type relaxation operator helps to drive the density distribution toward the local maxwellian thus naturally imposes an asymptotic preserving scheme in the euler limit the scheme so designed does not need any nonlinear iterative solver or the use of wild sum it is uniformly stable in terms of the possibly small knudsen number and can capture the macroscopic fluid dynamic euler limit even if the small scale determined by the knudsen number is not numerically resolved it is also consistent to the compressible navier stokes equations if the viscosity and heat conductivity are numerically resolved the method is applicable to many other related problems such as hyperbolic systems with stiff relaxation and high order parabolic equations

mode tracking issues in structural optimization within the context of optimization of the structural dynamics properties of finite element models methodology is developed for the tracking of eigenpairs through changes in the structural eigenvalue problem the goal is to eliminate difficulties caused by mode switching i e frequency crossing out of several candidate methods two methods for mode tracking are successful the first method the higher order eigenpair perturbation algorithm is based on a perturbation expansion of the eigenproblem it iteratively computes changes in the eigenpairs due to parameter perturbations with the important feature of maintaining the correspondence between the baseline and perturbed eigenpairs the second method is a cross orthogonality check method which uses mass orthogonality to reestablish correspondence after a standard reanalysis modified eigenpair extraction routines lanczos subspace iteration inverse power were unsuccessful in tracking modes applications of mode tracking technology that are presented are frequency constrained optimization and optimization with mode shape constraints each application procedure is outlined and examples are given recommendations are made based on method efficiency and robustness in the example problems

discrete velocity models for mixtures without nonphysical collision invariants an important aspect of constructing discrete velocity models dvms for the boltzmann equation is to obtain the right number of collision invariants it is a well known fact that dvms can also have extra collision invariants so called spurious collision invariants in plus to the physical ones a dvm with only physical collision invariants and so without spurious ones is called normal for binary mixtures also the concept of supernormal dvms was introduced meaning that in addition to the dvm being normal the restriction of the dvm to any single species also is normal here we introduce generalizations of this concept to dvms for multicomponent mixtures we also present some general algorithms for constructing such models and give some concrete examples of such constructions one of our main results is that for any given number of species and any given rational mass ratios we can construct a supernormal dvm the dvms are constructed in such a way that for half space problems as the milne and kramers problems but also nonlinear ones we obtain similar structures as for the classical discrete boltzmann equation for one species and therefore we can apply obtained results for the classical boltzmann equation

rates of change of closed loop eigenvalues and eigenvectors of actively controlled structures the sensitivity of the closed loop eigenvalues and eigenvectors of actively controlled flexible structures with distinct eigenvalues is considered the sensitivity information is essential in the optimization of large space structures with stability performance robustness closed loop eigenvalues or damping ratios treated as objective or constraint functions

discrete unified gas kinetic scheme for all knudsen number flows ii thermal compressible case this paper is a continuation of our work on the development of multiscale numerical scheme from low speed isothermal flow to compressible flows at high mach numbers in our earlier work z l guo et al phys rev e 88 033305 2013 a discrete unified gas kinetic scheme dugks was developed for low speed flows in which the mach number is small so that the flow is nearly incompressible in the current work we extend the scheme to compressible flows with the inclusion of thermal effect and shock discontinuity based on the gas kinetic shakhov model this method is an explicit finite volume scheme with the coupling of particle transport and collision in the flux evaluation at a cell interface as a result the time step of the method is not limited by the particle collision time with the variation of the ratio between the time step and particle collision time the scheme is an asymptotic preserving ap method where both the chapman enskog expansion for the navier stokes solution in the continuum regime and the free transport mechanism in the rarefied limit can be precisely recovered with a second order accuracy in both space and time the dugks is an idealized multiscale method for all knudsen number flow simulations a number of numerical tests including the shock structure problem the sod tube problem in a whole range of degree of rarefaction and the two dimensional riemann problem in both continuum and rarefied regimes are performed to validate the scheme comparisons with the results of direct simulation monte carlo dsmc and other benchmark data demonstrate that the dugks is a reliable and efficient method for multiscale flow problems

modal expansion method for eigensensitivity with repeated roots extensions are made to the modal expansion eigensensitivity procedure for self adjoint systems originally formulated by fox and kapoor these allow the computation of sensitivity information for mode shapes associated with repeated roots and repeated root derivatives the extensions follow a similar line to additions to nelson s direct method proposed first by ojalvo and later generalized independently by mills curran and dailey the formulation based on modal expansion is simpler and more computationally efficient than the direct method although some accuracy is sacrificed by modal truncation the method generally yields acceptable results for the primary application in optimization

normal high order discrete velocity models of the boltzmann equation abstract this paper aims at approximations of the collision operator in the boltzmann equation the developed framework guarantees the normality of the approximation which means correct collision invariants h theorem and equilibrium solutions it fits into the discrete velocity model framework is given in such a way that it is understandable with undergraduate level mathematics and can be used to construct approximations with arbitrary high convergence orders at last we give an example alongside a numerical verification here the convergence orders range up to 3 2 and the time complexity is given by 3 1 2 4 2 3 in 2 3 dimensions

eigenvector derivatives with repeated eigenvalues in this paper an algorithm is derived for computing the derivatives of eigenvalues and eigenvectors for real symmetric matrices in the case of repeated eigenvalues where the matrices are functions of real parameters such as mass density or moment of inertia the algorithm is an extension of recent work by i u ojalvo the key step in this extended derivation is to differentiate the eigenvalue equation twice the algorithm preserves the symmetry and band structure of the matrices allowing efficient computer storage and solution techniques applications include sensitivity analysis and optimization of the normal modes of finite element modeled structures such as large space structures a cantilever beam finite element example is included

optimal selection of weighting matrices in integrated design of structures controls a methodology is developed for the optimal selection of state and input weighting matrices q and r respectively of the linear quadratic regulator lqr method in the integrated design of structures controls an optimal control problem is set up in such a way that design variables are the diagonal entries of q and r the objective function is the trace of the solution matrix to the algebraic riccati equation of the lqr method p matrix and constraints are imposed on the closed loop eigenvalues to satisfy minimum stability conditions for the control system the procedure finds the optimal diagonal q and i that enables the actively controlled system to meet the prespecified stability and performance bounds furthermore the resulting q and r yield the minimum possible performance index and hence the control effort is substantially reduced the proposed method is integrated with a substructure decomposition scheme which results in substantial savings on the numerical computations with very little loss in the accuracy of the original system response it is found that for trusslike space structures the proposed optimization scheme is mostly affected by the changes in the diagonal terms of r and the changes in the velocity diagonal terms of q of the controlled system the method is expected to be very useful for large scale systems and is illustrated with the help of two example problems

a comparative study of an asymptotic preserving scheme and unified gas kinetic scheme in continuum flow limit asymptotic preserving ap schemes target to simulate both continuum and rarefied flows many existing ap schemes are capable of recovering the euler limit in the continuum regime however to get accurate navier stokes solutions is still challenging in order to distinguish physical mechanism underlining different ap schemes an implicit explicit imex ap method and the unified gas kinetic scheme ugks are employed to solve the bhatnagar gross krook bgk kinetic equation in both transition and continuum flow regimes as a benchmark test case the lid driven cavity flow is used for evaluating numerical performance of these two ap schemes the numerical results show that the ugks captures the viscous solution accurately the velocity profiles converge to the classical benchmark solutions in continuum regime with the mesh size being much larger than the local particle mean free path however the imex ap scheme seems to have difficulty to get these solutions in the corresponding limit the analysis demonstrates that the dissipation of ap schemes has to be properly controlled in the continuum flow regime through a delicate numerical treatment of collision and convection of the kinetic equation physically it becomes necessary to couple both the convection and collision terms in the flux evaluation in order to recover correct navier stokes limit

a robust numerical method for the r13 equations of rarefied gas dynamics application to lid driven cavity in this work we present a finite difference scheme to compute steady state solutions of the regularized 13 moment r13 equations of rarefied gas dynamics the scheme allows fast solutions for 2d and 3d boundary value problems bvps with velocity slip and temperature jump boundary conditions the scheme is applied to the lid driven cavity problem for knudsen numbers up to 0 7 the results compare well with those obtained from more costly solvers for rarefied gas dynamics such as the integro moment method imm and the direct simulation monte carlo dsmc method the r13 equations yield better results than the classical navier stokes fourier equations for this boundary value problem since they give an approximate description of knudsen boundary layers at moderate knudsen numbers the r13 based numerical solutions are computationally economical and may be considered as a reliable alternative mathematical model for complex industrial problems at moderate knudsen numbers

genetic algorithm development for multiobjective optimization of structures genetic algorithms gas have the characteristic of maintaining a population of solutions and can search in a parallel manner for many nondominated solutions these features coincide with the requirement of seeking a pareto optimal set in a multiobjective multicriteria vector optimization problem the rationale for multiobjective optimization via gas is that at each generation the fitness of each individual is defined according to its nondominated property because nondominated individuals are assigned the highest fitness values the convergence of a population will go to the nondominated zone the pareto optimal set based on this concept a pareto ga whose goal is to locate the pareto optimal set of a multiobjective optimization problem is developed in this ga to avoid missing pareto optimal points during evolutionary processes a new concept called pareto set filter is adopted at each generation the points of rank 1 are put into the filter and undergo a nondominated check in addition a niche technique is provided to prevent genetic drift in population evolution this technique sets a replacement rule for reproduction procedures for a constrained optimization problem a revised penalty function method is introduced to transfer a constrained problem into a nonconstralned one the transferred function of a point contains information on a point s status feasible or infeasible position in a search region and distance to the pareto optimal set two multiobjective optimization examples a 25 bar space truss optimal design objectives structural weight and virtual work constraints stresses and a four bar pyramid truss with control system objectives structural weight and control effort constraints closed loop frequencies are provided to demonstrate analysis procedures of the proposed pareto ga

fast algorithms for computing the boltzmann collision operator the development of accurate and fast numerical schemes for the five fold boltzmann collision integral represents a challenging problem in scientific computing for a particular class of interactions including the so called hard spheres model in dimension three we are able to derive spectral methods that can be evaluated through fast algorithms these algorithms are based on a suitable representation and approximation of the collision operator explicit expressions for the errors in the schemes are given and spectral accuracy is proved parallelization properties and adaptivity of the algorithms are also discussed

pareto optima of isostatic trusses abstract multicriterion optimization of elastic stress limited isostatic trusses is considered and a numerical method for determining the pareto optimal set of the problem is developed the weight of the structure and some chosen nodal displacements are taken as design criteria and member areas are used as design variables the corresponding bicriterion problem with weight and one displacement in the objective function is solved exactly and this result is used as a basis of the proposed method by introducing certain parameters each joined with one displacement criterion the pareto optimal solutions of the general problem may be obtained with any accuracy two examples are given to illustrate the method

chern classes and characteristic cycles of determinantal varieties abstract let k be an algebraically closed field of characteristic 0 for m n we define m n k to be the set of m n matrices over k with kernel dimension k this is a projective subvariety of p m n 1 and is called the generic determinantal variety in most cases m n k is singular with singular locus m n k 1 in this paper we give explicit formulas computing the chern mather class c m and the chern schwartz macpherson class c s m of m n k as classes in the projective space we also obtain formulas for the conormal cycles and the characteristic cycles of these varieties and for their generic euclidean distance degree further when k c we prove that the characteristic cycle of the intersection cohomology sheaf of a determinantal variety agrees with its conormal cycle and hence is irreducible our formulas are based on calculations of degrees of certain chern classes of the universal bundles over the grassmannian for some small values of m n k we use macaulay2 to exhibit examples of the chern mather classes the chern schwartz macpherson classes and the classes of characteristic cycles of m n k on the basis of explicit computations in low dimensions we formulate conjectures concerning the effectivity of the classes and the vanishing of specific terms in the chern schwartz macpherson classes of the largest strata m n k m n k 1 the irreducibility of the characteristic cycle of the intersection cohomology sheaf follows from the kashiwara dubson s microlocal index theorem a study of the tjurina transform of m n k and the recent computation of the local euler obstruction of m n k

rarefied flow computations using nonlinear model boltzmann equations high resolution finite difference schemes for solving the nonlinear model boltzmann equations are presented for the computations of rarefied gas flows the discrete ordinate method is first applied to remove the velocity space dependency of the distribution function which renders the model boltzmann equation in phase space to a set of hyperbolic conservation laws with source terms in physical space then a high order essentially nonoscillatory method due to harten et al j comput phys 71 231 1987 is adapted and extended to solve them explicit methods using operator splitting and implicit methods using the lower upper factorization are described to treat multidimensional problems the methods are tested for both steady and unsteady rarefied gas flows to illustrate its potential use the computed results using model boltzmann equations are found to compare well both with those using the direct simulation monte carlo results in the transitional regime flows and those with the continuum navier stokes calculations in near continuum regime flows

a unified gas kinetic scheme for continuum and rarefied flows iv fluid dynamic equations are valid in their respective modeling scales such as the particle mean free path scale of the boltzmann equation and the hydrodynamic scale of the navier stokes ns equations with a variation of the modeling scales theoretically there should have a continuous spectrum of fluid dynamic equations even though the boltzmann equation is claimed to be valid in all scales many boltzmann solvers including direct simulation monte carlo method require the cell resolution to the order of particle mean free path scale therefore they are still single scale methods in order to study multiscale flow evolution efficiently the dynamics in the computational fluid has to be changed with the scales a direct modeling of flow physics with a changeable scale may become an appropriate approach the unified gas kinetic scheme ugks is a direct modeling method in the mesh size scale and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path the cell size of ugks is not limited by the particle mean free path with the variation of the ratio between the numerical cell size and local particle mean free path the ugks recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale the previous ugks is mostly constructed from the evolution solution of kinetic model equations even though the ugks is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time it still has space to develop more accurate flow solver in the region where the time step is comparable with the local particle mean free time in such a scale there is dynamic difference from the full boltzmann collision term and the model equations this work is about the further development of the ugks with the implementation of the full boltzmann collision term in the region where it is needed the central ingredient of the ugks is the coupled treatment of particle transport and collision in the flux evaluation across a cell interface where a continuous flow dynamics from kinetic to hydrodynamic scales is modeled the newly developed ugks has the asymptotic preserving ap property of recovering the ns solutions in the continuum flow regime and the full boltzmann solution in the rarefied regime in the mostly unexplored transition regime the ugks itself provides a valuable tool for the non equilibrium flow study the mathematical properties of the scheme such as stability accuracy and the asymptotic preserving will be analyzed in this paper as well

a fast iterative model for discrete velocity calculations on triangular grids a fast synthetic type iterative model is proposed to speed up the slow convergence of discrete velocity algorithms for solving linear kinetic equations on triangular lattices the efficiency of the scheme is verified both theoretically by a discrete fourier stability analysis and computationally by solving a rarefied gas flow problem the stability analysis of the discrete kinetic equations yields the spectral radius of the typical and the proposed iterative algorithms and reveal the drastically improved performance of the latter one for any grid resolution this is the first time that stability analysis of the full discrete kinetic equations related to rarefied gas theory is formulated providing the detailed dependency of the iteration scheme on the discretization parameters in the phase space the corresponding characteristics of the model deduced by solving numerically the rarefied gas flow through a duct with triangular cross section are in complete agreement with the theoretical findings the proposed approach may open a way for fast computation of rarefied gas flows on complex geometries in the whole range of gas rarefaction including the hydrodynamic regime

time relaxed monte carlo methods for the boltzmann equation a new family of monte carlo schemes is introduced for the numerical solution of the boltzmann equation of rarefied gas dynamics the schemes are inspired by the wild sum expansion of the solution of the boltzmann equation for maxwellian molecules and consist of a novel time discretization of the equation in particular high order terms in the expansion are replaced by the equilibrium maxwellian distribution the two main features of the schemes are high order accuracy in time and asymptotic preservation the first property allows to recover accurate solutions with time steps larger than those required by direct simulation monte carlo dsmc while the latter guarantees that for the vanishing knudsen number the numerical solution relaxes to the local maxwellian conservation of mass momentum and energy are preserved by the scheme numerical results on several space homogeneous problems show the improvement of the new schemes over standard dsmc applications to a one dimensional shock wave problem are also presented

segre classes on smooth projective toric varieties we provide a generalization of the algorithm of eklund jost and peterson for computing segre classes of closed subschemes of projective k space the algorithm is here generalized to computing the segre classes of closed subschemes of smooth projective toric varieties

integrated design of structural and control systems with a homotopy like iterative method we consider an integrated design problem of structural and control systems it is well known that even the simplest formulation of this problem results in a kind of a bmi problem in this paper homotopy like iterative design method based on lmis is proposed to obtain an optimal plant and a controller simultaneously for a full order output feedback problem we can deal with a multiobjective problem e g control problem etc in the proposed design method we can also optimize structural design parameters appearing non linearly in the coefficient matrices of the plant state space form using the first order approximation of the non linear dependence in the proposed algorithm several design examples show that the proposed algorithm works quite effectively for various integrated design problems

half space problems for a linearized discrete quantum kinetic equation we study typical half space problems of rarefied gas dynamics including the problems of milne and kramer for a general discrete model of a quantum kinetic equation for excitations in a bose gas in the discrete case the plane stationary quantum kinetic equation reduces to a system of ordinary differential equations these systems are studied close to equilibrium and are proved to have the same structure as corresponding systems for the discrete boltzmann equation then a classification of well posed half space problems for the homogeneous as well as the inhomogeneous linearized discrete kinetic equation can be made the number of additional conditions that need to be imposed for well posedness is given by some characteristic numbers these characteristic numbers are calculated for discrete models axially symmetric with respect to the x axis when the characteristic numbers change is found in the discrete as well as the continuous case as an illustration explicit solutions are found for a small sized model

calculation of eigenpair derivatives for asymmetric damped systems with distinct and repeated eigenvalues summary an algorithm is derived for the computation of eigenpair derivatives of asymmetric quadratic eigenvalue problem with distinct and repeated eigenvalues in the proposed method the eigenvector derivatives of the damped systems are divided into a particular solution and a homogeneous solution by introducing an additional normalization condition we construct two extended systems of linear equations with nonsingular coefficient matrices to calculate the particular solution the method is numerically stable and the homogeneous solutions are computed by the second order derivatives of the eigenequations two numerical examples are used to illustrate the validity of the proposed method copyright 2015 john wiley sons ltd

discrete velocity models without nonphysical invariants models for mixtures of discrete velocity gases have been recently introduced by the authors and have produced unexpected results particularly with regard to the possible existence of nonphysical collision invariants here we discuss a method to construct models without spurious invariants the method can be extended to very general models including polyatomic gases chemical reactions etc

eigenmode computation of cavities with perturbed geometry using matrix perturbation methods applied on generalized eigenvalue problems abstract generalized eigenvalue problems are standard problems in computational sciences they may arise in electromagnetic fields from the discretization of the helmholtz equation by for example the finite element method fem geometrical perturbations of the structure under concern lead to a new generalized eigenvalue problems with different system matrices geometrical perturbations may arise by manufacturing tolerances harsh operating conditions or during shape optimization directly solving the eigenvalue problem for each perturbation is computationally costly the perturbed eigenpairs can be approximated using eigenpair derivatives two common approaches for the calculation of eigenpair derivatives namely modal superposition method and direct algebraic methods are discussed in this paper based on the direct algebraic methods an iterative algorithm is developed for efficiently calculating the eigenvalues and eigenvectors of the perturbed geometry from the eigenvalues and eigenvectors of the unperturbed geometry

unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement this paper describes a unified flow solver ufs for rarefied and continuum gas flows the ufs separates the rarefied and continuum flow domains and selects appropriate solvers to combine the efficiency of continuum models with the accuracy of kinetic models the direct numerical solution of the boltzmann transport equation is used in rarefied regions while kinetic schemes of continuum fluid dynamics are used elsewhere using similar computational techniques for the kinetic and continuum solvers and employing intelligent domain decomposition algorithms attain the efficiency and numerical stability of the ufs solutions of test problems are presented to illustrate the capabilities of the ufs for high and low speed flows it is shown that the ufs can dynamically adapt the computational mesh and automatically introduce and remove kinetic patches to provide significant savings by limiting molecular scale solutions only to the regions where they are needed

implicit unified gas kinetic scheme for steady state solutions in all flow regimes this paper presents an implicit unified gas kinetic scheme ugks for non equilibrium steady state flow computation the ugks is a direct modeling method for flow simulation in all regimes with the updates of both macroscopic flow variables and microscopic gas distribution function by solving the macroscopic equations implicitly a predicted equilibrium state can be obtained first through iterations with the newly predicted equilibrium state the evolution equation of the gas distribution function and the corresponding collision term can be discretized in a fully implicit way for fast convergence through iterations as well the lower upper symmetric gauss seidel lu sgs factorization method is implemented to solve both macroscopic and microscopic equations which improves the efficiency of the scheme since the ugks is a direct modeling method and its physical solution depends on the mesh resolution and the local time step a physical time step needs to be fixed before using an implicit iterative technique with a pseudo time marching step therefore the physical time step in the current implicit scheme is determined by the same way as that in the explicit ugks for capturing the physical solution in all flow regimes but the convergence to a steady state speeds up through the adoption of a numerical time step with large cfl number many numerical test cases in different flow regimes from low speed to hypersonic ones such as the couette flow cavity flow and the flow passing over a cylinder are computed to validate the current implicit method the overall efficiency of the implicit ugks can be improved by one or two orders of magnitude in comparison with the explicit one

deterministic solution of the spatially homogeneous boltzmann equation using discontinuous galerkin discretizations in the velocity space abstract we present a new deterministic approach for the solution of the spatially homogeneous boltzmann kinetic equation based on nodal discontinuous galerkin dg discretizations in the velocity space in the new approach the collision operator has the form of a bilinear operator with a pre computed kernel its evaluation requires o n 5 operations at every point of the phase space where n is the number of degrees of freedom in one velocity dimension the method is generalized to any molecular potential results of numerical simulations are presented for the problem of spatially homogeneous relaxation for the hard spheres potential comparison with the method of direct simulation monte carlo showed excellent agreement

game theory approach for the integrated design of structures and controls the problem of design of actively controlled structures subject to constraints on the damping parameters of the closed loop system is formulated as a multiobjeetive optimization problem the structural weight and the controlled system energy are considered as objective functions for minimization with cross sectional areas of members as design variables a computational procedure is developed for solving the multiobjeetive optimization problem using cooperative game theory the feasibility of the procedure is demonstrated through the design of two truss structures

an improved iterative hdg approach for partial differential equations abstract we propose and analyze an iterative high order hybridized discontinuous galerkin ihdg discretization for linear partial differential equations we improve our previous work 45 in several directions 1 the improved ihdg approach converges in a finite number of iterations for the scalar transport equation 2 it is unconditionally convergent for both the linearized shallow water system and the convection diffusion equation 3 it has improved stability and convergence rates 4 we uncover a relationship between the number of iterations and time stepsize solution order meshsize and the equation parameters this allows us to choose the time stepsize such that the number of iterations is approximately independent of the solution order and the meshsize and 5 we provide both strong and weak scalings of the improved ihdg approach up to 16 384 cores a connection between ihdg and time integration methods such as parareal and implicit explicit methods are discussed extensive numerical results for linear and nonlinear pdes are presented to verify the theoretical findings

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

locally refined discrete velocity grids for stationary rarefied flow simulations most of deterministic solvers for rarefied gas dynamics use discrete velocity or discrete ordinate approximations of the distribution function on a cartesian grid this grid must be sufficiently large and fine to describe the distribution functions at every space position in the computational domain for 3 dimensional hypersonic flows like in re entry problems this induces much too dense velocity grids that cannot be practically used for memory storage requirements in this article we present an approach to generate automatically a locally refined velocity grid adapted to a given simulation this grid contains much less points than a standard cartesian grid and allows us to make realistic 3 dimensional simulations at a reduced cost with a comparable accuracy

exact calculation of the multiloop stability margin a mapping theorem by l a zadeh and c a desoer 1963 serves as the basis for an algorithm that computes the stability margin k sub m of diagonally perturbed multivariable feedback systems without conservatism the stability margin determination not only verifies system stability but also quantifies how much further the plan uncertainties can be extended before instability occurs the essence of the computational approach is the realization that the true image of a given domain can be approximated with arbitrary accuracy by first subdividing the domain into the requisite number of subdomains and then forming the union of the convex hulls of their images the technique is illustrated in an example with a plant model having three uncertainties in general the method is applicable to either siso or mimo lti systems whose uncertainties can be modeled with noninteracting coefficients in the open loop transfer function representations

robustness improvement of actively controlled structures through structural modifications the parameter variations introduced by the analysis model uncertain material properties or optimization may adversely influence the stability and performance characteristics of a closed loop controlled structure the improvement of robustness of actively controlled structures through structural modifications is considered in this work the stability and performance robustness indices are defined as measures of robustness of actively controlled structures the integrated structural control design problem is considered as a multiobjective optimization problem in which three objectives structural weight stability robustness index and performance robustness index are considered for minimization the utility function lexicographic and goal programming methods are applied to solve the multiobjective nonlinear programming problem two examples a two bar truss and two bay truss are considered to demonstrate the procedure here has been a dramatic increase in the past decade in the use of active control systems to improve structural performance 1 2 the major challenge in the field of active control of structures is in the design of control systems for very large space structures these structures are by nature distributed parameter systems with multiple inputs controls and a continuum of outputs displacements the finite ele ment method is commonly used for the description of these structures this is a source of parameter errors and truncated or reduced order models in the system in addition the structural properties of large space structures cannot be tested before they are put into orbit and hence sizeable uncertain ties exist in modal parameters a great deal of research is currently in progress on develop ing methods for the simultaneous integrated design of the structure and the control system the weight of the structure was minimized with constraints on the distribution of the eigenvalues and or damping ratio of the closed loop system by khot et al 3 miller and shim4 considered the simultaneous minimization in structural and control variables of the sum of structural weight and the infinite horizon linear regulator quadratic control cost the structure control system optimiza tion problem was formulated by khot et al 5 with constraints on the closed loop eigenvalue distribution and the minimum frobenious norm of the control gains it can be seen that in all the above works the consideration of robustness of the control system has been ignored the parameter variations introduced by the analysis model uncertain material properties or optimization may adversely influence the stability and performance characteristics of the control system the robustness is an extremely important feature of a feedback control design a robust control design is one that satisfactorily meets the system specifications even in the presence of parameter uncertainties and other modeling errors since the system specifications could be in terms of

nash equilibrium seeking in noncooperative games we introduce a non model based approach for locally stable convergence to nash equilibria in static noncooperative games with n players in classical game theory algorithms each player employs the knowledge of the functional form of his payoff and the knowledge of the other players actions whereas in the proposed algorithm the players need to measure only their own payoff values this strategy is based on the extremum seeking approach which has previously been developed for standard optimization problems and employs sinusoidal perturbations to estimate the gradient we consider static games with quadratic payoff functions before generalizing our results to games with non quadratic payoff functions that are the output of a dynamic system specifically we consider general nonlinear differential equations with n inputs and n outputs where in the steady state the output signals represent the payoff functions of a noncooperative game played by the steady state values of the input signals we employ the standard local averaging theory and obtain local convergence results for both quadratic payoffs where the actual convergence is semi global and non quadratic payoffs where the potential existence of multiple nash equilibria precludes semi global convergence our convergence conditions coincide with conditions that arise in model based nash equilibrium seeking however in our framework the user is not meant to check these conditions because the payoff functions are presumed to be unknown for non quadratic payoffs convergence to a nash equilibrium is not perfect but is biased in proportion to the perturbation amplitudes and the higher derivatives of the payoff functions we quantify the size of these residual biases and confirm their existence numerically in an example noncooperative game in this example we present the first application of extremum seeking with projection to ensure that the players actions remain in a given closed and bounded action set

acceleration schemes of the discrete velocity method gaseous flows in rectangular microchannels the convergence rate of the discrete velocity method dvm which has been applied extensively in the area of rarefied gas dynamics is studied via a fourier stability analysis the spectral radius of the continuum form of the iteration map is found to be equal to one which justifies the slow convergence rate of the method next the efficiency of the dvm is improved by introducing various acceleration schemes the new synthetic type schemes speed up significantly the iterative convergence rate the spectral radius of the acceleration schemes is also studied and the so called h1 acceleration method is found to be the optimum one finally the two dimensional flow problem of a gas through a rectangular microchannel is solved using the new fast iterative dvm the number of required iterations and the overall computational time are significantly reduced providing experimental evidence of the analytic formulation the whole approach is demonstrated using the bgk and s kinetic models

multiobjective optimization of large scale structures this paper presents a multiobjective optimization algorithm based on generalized compound scaling techniques the algorithm handles any number of objective functions similar to handling behavior constraints this technique generates a partial pareto set while solving the optimization problem a reliability ba sed decision criterion is used for selecting the best compromise design the example cases considered in this work include various disciplines in airframe structures such as stress displacement and frequency with hundreds of design variables and constraints this paper also discusses the concept of pareto optima l solutions in the context of a multiobjective structural optimization problem and the commonly used methods of generating pareto optimal solutions

conservative evaluation of boltzmann collision integral in discrete ordinates approximation abstract within the framework of a discrete ordinates approximation two conservative methods of evaluation of a boltzmann collision integral are proposed the first method that is partially conservative preserves density and kinetic momentum and is based on a decomposition of the velocity subspace on equal cubic cells centered around discrete velocity nodes the second method is completely conservative and needs for its construction the more elaborate projection technique described in the article both methods are tested on a numerical example and compared with other known methods it is demonstrated that a completely conservative method possesses better convergence properties with respect to numbers of discrete ordinates and integration nodes and is more efficient in a computational aspect

efficiency of high order elements for continuous and discontinuous galerkin methods summary to evaluate the computational performance of high order elements a comparison based on operation count is proposed instead of runtime comparisons more specifically linear versus high order approximations are analyzed for implicit solver under a standard set of hypotheses for the mesh and the solution continuous and discontinuous galerkin methods are considered in two dimensional and three dimensional domains for simplices and parallelotopes moreover both element wise and global operations arising from different galerkin approaches are studied the operation count estimates show that for implicit solvers high order methods are more efficient than linear ones copyright 2013 john wiley sons ltd

structural eigenderivative analysis using practical and simplified dynamic flexibility method a practical and simplified technique for computing a large number of eigenvector derivatives of a complex structural system has been developed this technique uses the dynamic flexibility method and is based on the practical complete modal space approach the practical complete modal space technique is an exact modal method there is no modal truncation error existing in the derivation the dynamic flexibility method requires only the solving of the system governing equation once regardless of the number of eigenvector derivatives needed to be computed using this method the computer time required to obtain more than one eigenvector derivative can be dramatically reduced this method gives the mathematical expression of the solution for eigenvector derivatives and is easier for engineers to use to perform theoretical formulation this method can be applied to systems with and without repeated eigenvalues this method gives better numerical precision and may be a very good tool for engineers to compute many eigenvector derivatives

a new method for calculating derivatives of eigenvalues and eigenvectors for discrete structural systems abstract a new method is presented for calculating the derivatives of eigenvalues and eigenvectors for discrete structural systems in the cases of distinctive eigenvalues proportional damping is assumed and the exact eigen pair derivatives of arbitrary order are calculated for a repeated eigenvalue its first order derivatives are calculated by solving a reduced eigenvalue problem of order equal to the eigenvalue s geometric multiplicity the new method is computationally efficient and numerically robust examples are presented to illustrate the use and effectiveness of the new method

asymptotic preserving implicit explicit runge kutta methods for nonlinear kinetic equations we discuss implicit explicit imex runge kutta methods which are particularly adapted to stiff kinetic equations of boltzmann type we consider both the case of easy invertible collision operators and the challenging case of boltzmann collision operators we give sufficient conditions in order that such methods are asymptotic preserving and asymptotically accurate their monotonicity properties are also studied in the case of the boltzmann operator the methods are based on the introduction of a penalization technique for the collision integral this reformulation of the collision operator permits us to construct penalized imex schemes which work uniformly for a wide range of relaxation times avoiding the expensive implicit resolution of the collision operator finally we show some numerical results which confirm the theoretical analysis

discrete velocity models and numerical schemes for the boltzmann bgk equation in plane and axisymmetric geometries we present new numerical models for computing transitional or rarefied gas flows as described by the boltzmann bgk and bgk es equations we first propose a new discrete velocity model based on the entropy minimization principle this model satisfies the conservation laws and the entropy dissipation moreover the problem of conservation and entropy for axisymmetric flows is investigated we find algebraic relations that must be satisfied by the discretization of the velocity derivative appearing in the transport operator then we propose some models that satisfy these constraints owing to these properties we obtain numerical schemes that are economic in terms of discretization and robust in particular we develop a linearized implicit scheme for computing stationary solutions of the discrete velocity bgk and bgk es models this scheme is the basis of a code which can compute high altitude hypersonic flows in 2d plane and axisymmetric geometries our results are analyzed and compared to other methods

eigenvector sensitivity when tracking modes with repeated eigenvalues abstract while eigenvalue optimization problems have been widely studied during the last three decades particularly for structural and topology optimization problems there are very few examples of problems involving mode shapes either in the cost or the constraints in this paper we propose a general framework for computing eigenvector sensitivity whenever tracking specific mode shapes selected beforehand of course the approach is valid for either non repeated or repeated eigenvalues but here the emphasis is placed on the multiple eigenvalues case both mathematical validity of the algorithm and numerical corroboration through several examples are included