weak efficiency for multiobjective variational problems abstract sometimes to locate efficient solutions for multiobjective variational problems mvps is quite costly so in this paper we tackle the study of weakly efficient solutions for mvps a new concept of weak vector critical point which generalizes other ones already existent and a new class of pseudoinvex functions are introduced we will apply a new approach to prove that the new class of pseudoinvex functions is equivalent to the class of functions whose weak vector critical points are weakly efficient solution for mvps

accurate projection methods for the incompressible navier stokes equations abstract this paper considers the accuracy of projection method approximations to the initial boundary value problem for the incompressible navier stokes equations the issue of how to correctly specify numerical boundary conditions for these methods has been outstanding since the birth of the second order methodology a decade and a half ago it has been observed that while the velocity can be reliably computed to second order accuracy in time and space the pressure is typically only first order accurate in the l norm this paper identifies the source of this problem in the interplay of the global pressure update formula with the numerical boundary conditions and presents an improved projection algorithm which is fully second order accurate as demonstrated by a normal mode analysis and numerical experiments in addition a numerical method based on a gauge variable formulation of the incompressible navier stokes equations which provides another option for obtaining fully second order convergence in both velocity and pressure is discussed the connection between the boundary conditions for projection methods and the gauge method is explained in detail

nonzero bound on fiedler eigenvalue causes exponential growth of h infinity norm of vehicular platoon we consider platoons composed of identical vehicles and controlled in a distributed way that is each vehicle has its own onboard controller the regulation errors in spacing to the immediately preceeding and following vehicles are weighted differently by the onboard controller which thus implements an asymmetric bidirectional control scheme the weights can vary along the platoon we prove that such platoons have a nonzero uniform bound on the second smallest eigenvalue of the graph laplacian matrix the fiedler eigenvalue furthermore it is shown that existence of this bound always signals undesirable scaling properties of the platoon namely the h infinity norm of the transfer function of the platoon grows exponentially with the number of vehicles regardless of the controllers used hence the benefits of a uniform gap in the spectrum of a laplacian with an asymetric distributed controller are paid for by poor scaling as the number of vehicles grows

a high order discontinuous galerkin method for wave propagation through coupled elastic acoustic media we introduce a high order discontinuous galerkin dg scheme for the numerical solution of three dimensional 3d wave propagation problems in coupled elastic acoustic media a velocity strain formulation is used which allows for the solution of the acoustic and elastic wave equations within the same unified framework careful attention is directed at the derivation of a numerical flux that preserves high order accuracy in the presence of material discontinuities including elastic acoustic interfaces explicit expressions for the 3d upwind numerical flux derived as an exact solution for the relevant riemann problem are provided the method supports h non conforming meshes which are particularly effective at allowing local adaptation of the mesh size to resolve strong contrasts in the local wavelength as well as dynamic adaptivity to track solution features the use of high order elements controls numerical dispersion enabling propagation over many wave periods we prove consistency and stability of the proposed dg scheme to study the numerical accuracy and convergence of the proposed method we compare against analytical solutions for wave propagation problems with interfaces including rayleigh lamb scholte and stoneley waves as well as plane waves impinging on an elastic acoustic interface spectral rates of convergence are demonstrated for these problems which include a non conforming mesh case finally we present scalability results for a parallel implementation of the proposed high order dg scheme for large scale seismic wave propagation in a simplified earth model demonstrating high parallel efficiency for strong scaling to the full size of the jaguar cray xt5 supercomputer

mistuning based control design to improve closed loop stability margin of vehicular platoons we consider a decentralized bidirectional control of a platoon of n identical vehicles moving in a straight line the control objective is for each vehicle to maintain a constant velocity and inter vehicular separation using only the local information from itself and its two nearest neighbors each vehicle is modeled as a double integrator to aid the analysis we use continuous approximation to derive a partial differential equation pde approximation of the discrete platoon dynamics the pde model is used to explain the progressive loss of closed loop stability with increasing number of vehicles and to devise ways to combat this loss of stability if every vehicle uses the same controller we show that the least stable closed loop eigenvalue approaches zero as o 1 n2 in the limit of a large number n of vehicles we then show how to ameliorate this loss of stability by small amounts of mistuning i e changing the controller gains from their nominal values we prove that with arbitrary small amounts of mistuning the asymptotic behavior of the least stable closed loop eigenvalue can be improved to o 1 n all the conclusions drawn from analysis of the pde model are corroborated via numerical calculations of the state space platoon model

distributed control of spatially invariant systems we consider distributed parameter systems where the underlying dynamics are spatially invariant and where the controls and measurements are spatially distributed these systems arise in many applications such as the control of vehicular platoons flow control microelectromechanical systems mems smart structures and systems described by partial differential equations with constant coefficients and distributed controls and measurements for fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator lqr h sub 2 and h sub spl infin optimal controllers can be obtained by solving a parameterized family of standard finite dimensional problems we show that optimal controllers have an inherent degree of decentralization and this provides a practical distributed controller architecture we also prove a general result that applies to partially distributed control and a variety of performance criteria stating that optimal controllers inherit the spatial invariance structure of the plant connections of this work to that on systems over rings and systems with dynamical symmetries are discussed

performance and design of cycles in consensus networks abstract this work explores the role of cycles in consensus seeking networks for analysis and synthesis purposes cycles are critical for many reasons including improving the convergence rate of the system resilience to link failures and the overall performance of the system the focus of this work examines how cycles impact the h 2 performance of consensus networks a first contribution shows that the addition of cycles always improves the performance of the system we provide an analytic characterization of how the addition of edges improves the performance and show that it is related to the inverse of the cycle lengths and the number of shared edges between independent cycles these results are then used to consider the design of consensus networks in this direction we present an l 1 relaxation method that leads to a convex program for adding a fixed number of edges to a consensus networks we also demonstrate how this relaxation can be used to embed additional performance criteria such as maximization of the algebraic connectivity of the graph

sparse solution of the lyapunov equation for large scale interconnected systems we consider the problem of computing an approximate banded solution of the continuous time lyapunov equation a x x a t p where the coefficient matrices a and p are large symmetric banded matrices the sparsity pattern of a describes the interconnection structure of a large scale interconnected system recently it has been shown that the entries of the solution x are spatially localized or decaying away from a banded pattern we show that the decay of the entries of x is faster if the condition number of a is smaller by exploiting the decay of entries of x we develop two computationally efficient methods for approximating x by a banded matrix for a well conditioned and sparse banded a the computational and memory complexities of the methods scale linearly with the state dimension we perform extensive numerical experiments that confirm this and that demonstrate the effectiveness of the developed methods the methods proposed in this paper can be generalized to sparsity patterns of a and p that are more general than banded matrices the results of this paper open the possibility for developing computationally efficient methods for approximating the solution of the large scale riccati equation by a sparse matrix

approximate projection methods part i inviscid analysis the use of approximate projection methods for modeling low mach number flows avoids many of the numerical complications associated with exact projection methods but introduces additional design choices in developing a robust algorithm in this paper we first explore these design choices in the setting of inviscid incompressible flow using several computational examples we then develop a framework for analyzing the behavior of the different design variations and use that analysis to explain the features observed in the computations as part of this work we introduce a new variation of the approximate projection algorithm that combines the advantages of several of the previous versions

a cartesian grid finite volume method for the advection diffusion equation in irregular geometries we present a fully conservative high resolution finite volume algorithm for advection diffusion equations in irregular geometries the algorithm uses a cartesian grid in which some cells are cut by the embedded boundary a novel feature is the use of a capacity function to model the fact that some cells are only partially available to the fluid the advection portion then uses the explicit wave propagation methods implemented in clawpack and is stable for courant numbers up to 1 diffusion is modelled with an implicit finite volume algorithm results are shown for several geometries convergence is verified and the 1 norm order of accuracy is found to between 1 2 and 2 depending on the geometry and peclet number software is available on the web

duality for multiobjective variational problems abstract wolfe and mond weir type duals for multiobjective variational problems are formulated under convexity assumptions on the functions involved weak and converse duality theorems are proved to relate properly efficient solutions of the primal and dual problems a close relationship between these variational problems and nonlinear multiobjective programming problems is also indicated

a numerical method for the incompressible navier stokes equations based on an approximate projection in this method we present a fractional step discretization of the time dependent incompressible navier stokes equations the method is based on a projection formulation in which we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields our treatment of the diffusion convection step uses a specialized second order upwind method for differencing the nonlinear convective terms that provides a robust treatment of these terms at a high reynolds number in contrast to conventional projection type discretizations that impose a discrete form of the divergence free constraint we only approximately impose the constraint i e the velocity field we compute is not exactly divergence free the approximate projection is computed using a conventional discretization of the laplacian and the resulting linear system is solved using conventional multigrid methods numerical examples are presented to validate the second order convergence of the method for euler finite reynolds number and stokes flow a second example illustrating the behavior of the algorithm on an unstable shear layer is also presented

augmented lagrangian approach to design of structured optimal state feedback gains we consider the design of optimal state feedback gains subject to structural constraints on the distributed controllers these constraints are in the form of sparsity requirements for the feedback matrix implying that each controller has access to information from only a limited number of subsystems the minimizer of this constrained optimal control problem is sought using the augmented lagrangian method notably this approach does not require a stabilizing structured gain to initialize the optimization algorithm motivated by the structure of the necessary conditions for optimality of the augmented lagrangian we develop an alternating descent method to determine the structured optimal gain we also utilize the sensitivity interpretation of the lagrange multiplier to identify favorable communication architectures for structured optimal design examples are provided to illustrate the effectiveness of the developed method

outflow boundary conditions for three dimensional finite element modeling of blood flow and pressure in arteries flow and pressure waves emanate from the heart and travel through the major arteries where they are damped dispersed and reflected due to changes in vessel caliber tissue properties and branch points as a consequence solutions to the governing equations of blood flow in the large arteries are highly dependent on the outflow boundary conditions imposed to represent the vascular bed downstream of the modeled domain the most common outflow boundary conditions for three dimensional simulations of blood flow are prescribed constant pressure or traction and prescribed velocity profiles however in many simulations the flow distribution and pressure field in the modeled domain are unknown and cannot be prescribed at the outflow boundaries an alternative approach is to couple the solution at the outflow boundaries of the modeled domain with lumped parameter or one dimensional models of the downstream domain we previously described a new approach to prescribe outflow boundary conditions for simulations of blood flow based on the dirichlet to neumann and variational multiscale methods this approach termed the coupled multidomain method was successfully applied to solve the non linear one dimensional equations of blood flow with a variety of models of the downstream domain this paper describes the extension of this method to three dimensional finite element modeling of blood flow and pressure in the major arteries outflow boundary conditions are derived for any downstream domain where an explicit relationship of pressure as a function of flow rate or velocities can be obtained at the coupling interface we developed this method in the context of a stabilized semi discrete finite element method flow rate and pressure distributions are shown for different boundary conditions to illustrate the dramatic influence of alternative boundary conditions on these quantities

coherence in large scale networks dimension dependent limitations of local feedback we consider distributed consensus and vehicular formation control problems specifically we address the question of whether local feedback is sufficient to maintain coherence in large scale networks subject to stochastic disturbances we define macroscopic performance measures which are global quantities that capture the notion of coherence a notion of global order that quantifies how closely the formation resembles a solid object we consider how these measures scale asymptotically with network size in the topologies of regular lattices in 1 2 and higher dimensions with vehicular platoons corresponding to the 1 d case a common phenomenon appears where a higher spatial dimension implies a more favorable scaling of coherence measures with a dimensions of 3 being necessary to achieve coherence in consensus and vehicular formations under certain conditions in particular we show that it is impossible to have large coherent 1 d vehicular platoons with only local feedback we analyze these effects in terms of the underlying energetic modes of motion showing that they take the form of large temporal and spatial scales resulting in an accordion like motion of formations a conclusion can be drawn that in low spatial dimensions local feedback is unable to regulate large scale disturbances but it can in higher spatial dimensions this phenomenon is distinct from and unrelated to string instability issues which are commonly encountered in control problems for automated highways

a second order projection method for the incompressible navier stokes equations in this paper we describe a second order projection method for the time dependent incom pressible navier stokes equations as in the original projection method developed by chorin we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields by introducing more coupling between the diffusion onvection step and the projection step we obtain a temporal discretiza tion that is second order accurate our treatment of the diffusion convection step uses a specialized higher order godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high reynolds number the godunov procedure is second order accurate for smooth flow and remains stable for discontinuous initial data even in the zero viscosity limit we approximate the projection directly using a galerkin procedure that uses a local basis for discretely divergence free vector fields numerical results are presented validating the convergence properties of the method we also apply the method to doubly periodic shear layers to assess the performance of the method on more difficult

estimation from relative measurements electrical analogy and large graphs we examine the problem of estimating vector valued variables from noisy measurements of the difference between certain pairs of them this problem which is naturally posed in terms of a measurement graph arises in applications such as sensor network localization time synchronization and motion consensus we obtain a characterization on the minimum possible covariance of the estimation error when an arbitrarily large number of measurements are available this covariance is shown to be equal to a matrix valued effective resistance in an infinite electrical network covariance in large finite graphs converges to this effective resistance as the size of the graphs increases this convergence result provides the formal justification for regarding large finite graphs as infinite graphs which can be exploited to determine scaling laws for the estimation error in large finite graphs furthermore these results indicate that in large networks estimation algorithms that use small subsets of all the available measurements can still obtain accurate estimates

mean square stability analysis of stochastic continuous time linear networked systems in this technical note we study the mean square stability based analysis of stochastic continuous time linear networked systems the stochastic uncertainty is assumed to enter multiplicatively in system dynamics through input and output channels of the plant necessary and sufficient conditions for mean square exponential stability are expressed in terms of the input output property of deterministic or nominal system dynamics captured by the mean square system norm and variance of channel uncertainty the stability results can also be interpreted as a small gain theorem for continuous time stochastic systems linear matrix inequalities based optimization formulation is provided for the computation of mean square system norm for the stability analysis for a special case of single input channel uncertainty we also prove a fundamental limitation result that arises in the mean square exponential stabilization of the continuous time linear system overall the contributions in this technical note generalize the existing results on stability analysis from discrete time linear systems to continuous time linear systems with multiplicative uncertainty simulation results are presented for western system coordinating council 9 bus power system to demonstrate the application of the developed framework

leader selection problem for stochastically forced consensus networks based on matrix differentiation abstract the leader selection problem refers to determining a predefined number of agents as leaders in order to minimize the mean square deviation from consensus in stochastically forced networks the original leader selection problem is formulated as a non convex optimization problem where matrix variables are involved by relaxing the constraints a convex optimization model can be obtained by introducing a chain rule of matrix differentiation we can obtain the gradient of the cost function which consists matrix variables we develop a revisited projected gradient method rpgm and a probabilistic projected gradient method ppgm to solve the two formulated convex and non convex optimization problems respectively the convergence property of both methods is established for convex optimization model the global optimal solution can be achieved by rpgm while for the original non convex optimization model a suboptimal solution is achieved by ppgm simulation results ranging from the synthetic to real life networks are provided to show the effectiveness of rpgm and ppgm this works will deepen the understanding of leader selection problems and enable applications in various real life distributed control problems

controlling unstructured mesh partitions for massively parallel simulations parallel simulations at extreme scale require that the mesh is distributed across a large number of processors with equal work load and minimum interpart communications a number of algorithms have been developed to meet these goals e g graph hypergraph and coordinate based methods however the global implementation of current approaches can fail on very large core counts which is resolved by combining global and local partitioning using multiple parts per processor the other limitation of graph hypergraph based partitioning is that it uses one type of mesh entity as graph nodes thus the balance of other mesh entities may not be optimal in the case of three dimensional 3 d linear finite element analysis it is common to select mesh regions elements as partition objects in current examples the regions are well balanced up to 163 840 parts for a 1 07 billion element mesh while the vertices have an imbalance which is as high as 19 52 two methods are developed that work in conjunction with graph hypergraph based procedures to provide improved partitions example computations executed on an ibm blue gene p system using up to 163 840 cores demonstrate the usefulness of the procedures particularly for time critical calculations where individual cores may be lightly loaded in terms of the number of mesh entities per core the algorithms presented in this paper reduced the vertex imbalance from 17 8 to 4 97 for a partition with 131 072 parts and accelerated the equation solution phase of the finite element analysis by 10 4

recursive algorithms for distributed forests of octrees the forest of octrees approach to parallel adaptive mesh refinement and coarsening has recently been demonstrated in the context of a number of large scale pde based applications efficient reference software has been made freely available to the public both in the form of the standalone tt p4est library and more indirectly by the general purpose finite element library tt deal ii which has been equipped with a tt p4est backend although linear octrees which store only leaf octants have an underlying tree structure by definition it is not fully exploited in previously published mesh related algorithms this is because tree branches are not explicitly stored and because the topological relationships in meshes such as the adjacency between cells introduce dependencies that do not respect the octree hierarchy in this work we combine hierarchical and topological relationships between octants to design efficient recursive algorithms that operate on distributed forests of octrees we present three imp

a second order projection method for variable density flows this paper describes a second order projection method for variabledensity incompressible flows the method is suitable for both finite amplitude density variations and for fluids that are modeled using a boussinesq approximation it is based on a second order fractional step scheme in which diffusion convection terms are advanced without enforcing the incompressibility condition and the resulting intermediate velocity field is then projected onto the space of discretely divergencefree vector fields the nonlinear convection terms are treated using a godunov type procedure that is second order for smooth flow and remain stable and non oscillatory for nonsmooth flows with low fluid viscosities the method is described for finite amplitude density variation and the simplifications for a boussinesq approximation are sketched numerical results are presented that validate the convergence properties of the method and demonstrate its performance on more realistic problems

optimality conditions and duality for multiobjective variational problems with generalized b invexity we extend the concepts of b type i and generalized b type i functions to the continuous case and we use these concepts to establish sufficient optimality conditions and duality results for multiobjective variational programming problems

necessary and sufficient conditions in constrained optimization additional conditions are attached to the kuhn tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization under appropriate constraint qualifications necessary and sufficient conditions are also given for optimality of the dual problem duality and converse duality are treated accordingly

new spectral bounds on h2 norm of linear dynamical networks abstract in this paper we obtain new lower and upper bounds for the h 2 norm of a class of linear time invariant systems subject to exogenous noise inputs we show that the h 2 norm as a performance measure can be tightly bounded from below and above by some spectral functions of state and output matrices of the system in order to show the usefulness of our results we calculate bounds for the h 2 norm of some network models with specific coupling or graph structures e g systems with normal state matrices linear consensus networks with directed graphs and cyclic linear networks as a specific example the h 2 norm of a linear consensus network over a directed cycle graph is computed and shown how its performance scales with the network size our proposed spectral bounds reveal the important role and contribution of fast and slow dynamic modes of a system in the best and worst achievable performance bounds under white noise excitation finally we use several numerical simulations to show the superiority of our bounds over the existing bounds in the literature

distributed control of networked dynamical systems static feedback integral action and consensus this paper analyzes distributed control protocols for first and second order networked dynamical systems we propose a class of nonlinear consensus controllers where the input of each agent can be written as a product of a nonlinear gain and a sum of nonlinear interaction functions by using integral lyapunov functions we prove the stability of the proposed control protocols and explicitly characterize the equilibrium set we also propose a distributed proportional integral pi controller for networked dynamical systems the pi controllers successfully attenuate constant disturbances in the network we prove that agents with single integrator dynamics are stable for any integral gain and give an explicit tight upper bound on the integral gain for when the system is stable for agents with double integrator dynamics throughout the paper we highlight some possible applications of the proposed controllers by realistic simulations of autonomous satellites power systems and building temperature control

resistance based performance analysis of the consensus algorithm over geometric graphs the performance of the linear consensus algorithm is studied by using a linear quadratic lq cost the objective is to understand how the communication topology influences this algorithm this is achieved by exploiting the analogy between markov chains and electrical resistive networks indeed this allows us to uncover the relation between the lq performance cost and the average effective resistance of a suitable electrical network and moreover to show that if the communication graph fulfills some local properties then its behavior can be approximated by that of a grid which is a graph whose associated lq cost is well known

a necessary and sufficient condition for duality in multiobjective variational problems abstract in this paper we move forward in the study of duality and efficiency in multiobjective variational problems we introduce new classes of pseudoinvex functions and prove that not only it is a sufficient condition to establish duality results but it is also necessary moreover these functions are characterized in order that all kuhn tucker or fritz john points are efficient solutions recent papers are improved we provide an example to show this improvement and illustrate these classes of functions and results

efficient anisotropic adaptive discretization of the cardiovascular system we present an anisotropic adaptive discretization method and demonstrate how computational efficiency can be increased when applying it to the simulation of cardiovascular flow we further propose a new adaptive approach which controls the mesh adaptation procedure to maintain structured and graded elements near the wall resulting in a more accurate wall shear stress computation to perform mesh adaptation for hemodynamic flows a single mesh metric field is constructed for the whole cardiac cycle two alternative approaches are applied one in which a metric field is constructed based on the average flow whereas in the other approach the metric field is obtained by intersecting metric fields computed at specified instants in the cycle we apply the method to the case of a 3d branching vessel model the efficiency of our approach is measured by analyzing the wall shear stress a challenging but important quantity in the understanding of cardiovascular disease the general anisotropic adaptivity based on metric intersection achieves over an order of magnitude reduction in terms of degrees of freedom when compared to uniform refinement for a given level of accuracy

numerical simulation of a cylinder in uniform flow in this study a virtual boundary technique is applied to the numerical simulation of stationary and moving cylinders in uniform flow this approach readily allows the imposition of a no slip boundary within the flow field by a feedback forcing term added to the momentum equations in the present work this technique is used with a high order finite difference method effectively eliminating spurious oscillations caused by the feedback forcing when used with spectrally discretized flow solvers very good agreement is found between the present calculations and previous computational and experimental results for steady and time dependent flow at low reynolds numbers

volume of fluid interface tracking with smoothed surface stress methods for three dimensional flows motivated by the need for three dimensional methods for interface calculations that can deal with topology changes we describe a numerical scheme built from a volume of fluid interface tracking technique that uses a piecewise linear interface calculation in each cell momentum balance is computed using explicit finite volume finite differences on a regular cubic grid surface tension is implemented by the continuous surface stress or continuous surface force method examples and verifications of the method are given by comparing simulations to analytical results and experiments for sedimenting droplet arrays and capillary waves at finite reynolds number in the case of a pinching pendant drop both three dimensional and axisymmetric simulations are compared to experiments agreement is found both before and after the reconnections

a cartesian grid embedded boundary method for poisson s equation on irregular domains we present a numerical method for solving poisson s equation with variable coefficients and dirichlet boundary conditions on two dimensional regions the approach uses a finite volume discretization which embeds the domain in a regular cartesian grid we treat the solution as a cell centered quantity even when those centers are outside the domain cells that contain a portion of the domain boundary use conservative differencing of second order accurate fluxes on each cell volume the calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes this allows us to use multigrid iterations with a simple point relaxation strategy we have combined this with an adaptive mesh refinement amr procedure we provide evidence that the algorithm is second order accurate on various exact solutions and compare the adaptive and nonadaptive calculations

an adaptive mesh projection method for viscous incompressible flow many fluid flow problems of practical interest particularly at high reynolds number are characterized by small regions of complex and rapidly varying fluid motion surrounded by larger regions of relatively smooth flow efficient solution of such problems requires an adaptive mesh refinement capability to concentrate computational effort where it is most needed we present in this paper a fractional step version of chorin s projection method for incompressible flow with adaptive mesh refinement which is second order accurate in both space and time convection terms are handled by a high resolution upwind method which provides excellent resolution of small scale features of the flow while a multilevel iterative scheme efficiently solves the parabolic and elliptic equations associated with viscosity and the projection numerical examples demonstrate the performance of the method on two dimensional problems involving vortex spindown with viscosity and inviscid vortex merger

sparsity promoting optimal control of systems with symmetries consensus and synchronization networks abstract optimal control problems in systems with symmetries and consensus synchronization networks are characterized by structural constraints that arise either from the underlying group structure or the lack of absolute measurements for part of the state vector our objective is to design controller structures and resulting control strategies that utilize limited information exchange between subsystems in large scale networks to obtain controllers with low communication requirements we seek solutions to regularized versions of the h 2 optimal control problem non smooth regularization terms are introduced to tradeoff network performance with sparsity of the feedback gain matrix in contrast to earlier results our framework allows the state space representations that are used to quantify the system s performance and sparsity of the static output feedback controller to be expressed in different sets of coordinates we show how alternating direction method of multipliers can be leveraged to exploit the underlying structure and compute sparsity promoting controllers in particular for spatially invariant systems the computational complexity of our algorithm scales linearly with the number of subsystems we also identify a class of optimal control problems that can be cast as semidefinite programs and provide an example to illustrate our developments

fully parallel mesh i o using petsc dmplex with an application to waveform modeling large scale pde simulations using high order finite element methods on unstructured meshes are an indispensable tool in science and engineering the widely used open source petsc library offers an

string stability of interconnected systems introduces the notion of string stability of a countably infinite interconnection of a class of nonlinear systems intuitively string stability implies uniform boundedness of all the states of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded it is well known that the input output gain of all the subsystems less than unity guarantees that the interconnected system is input output stable the authors derive sufficient weak coupling conditions which guarantee the asymptotic string stability of a class of interconnected systems under the same weak coupling conditions string stable interconnected systems remain string stable in the presence of small structural singular perturbations in the presence of parameter mismatch these weak coupling conditions ensure that the states of all the subsystems are all uniformly bounded when a gradient based parameter adaptation law is used and that the states of all the systems go to zero asymptotically

tight bound for deciding convergence of consensus systems abstract we analyze the asymptotic convergence of all infinite products of matrices taken in a given finite set by looking only at finite or periodic products it is known that when the matrices of the set have a common nonincreasing polyhedral norm all infinite products converge to zero if and only if all infinite periodic products with period smaller than a certain value converge to zero moreover bounds on that value are available lagarias and wang 1995 we provide a stronger bound that holds for both polyhedral norms and polyhedral seminorms in the latter case the matrix products do not necessarily converge to zero but all trajectories of the associated system converge to a common invariant subspace we prove that our bound is tight for all seminorms our work is motivated by problems in consensus systems where the matrices are stochastic nonnegative with rows summing to one and hence always share a same common nonincreasing polyhedral seminorm in that case we also improve existing results

a generalized α method for integrating the filtered navier stokes equations with a stabilized finite element method abstract a generalized method is developed and analyzed for linear first order systems the method is then extended to the filtered navier stokes equations within the context of a stabilized finite element method the formulation is studied through the application to laminar flow past a circular cylinder and turbulent flow past a long transverse groove the method is formulated to obtain a second order accurate family of time integrators whose high frequency amplification factor is the sole free parameter such an approach allows the replication of midpoint rule zero damping gear s method maximal damping or anything in between

a cell centered adaptive projection method for the incompressible euler equations we present an algorithm to compute adaptive solutions for incompressible flows using block structured local refinement in both space and time this method uses a projection formulation based on a cell centered approximate projection which allows the use of a single set of cell centered solvers because of refinement in time additional steps are taken to accurately discretize the advection and projection operators at grid refinement boundaries using composite operators which span the coarse and refined grids this ensures that the method is approximately freestream preserving and satisfies an appropriate form of the divergence constraint

a cartesian grid projection method for the incompressible euler equations in complex geometries many problems in fluid dynamics require the representation of complicated internal or external boundaries of the flow here we present a method for calculating time dependent incompressible inviscid flow which combines a projection method with a cartesian grid approach for representing geometry in this approach the body is represented as an interface embedded in a regular cartesian mesh the advection step is based on a cartesian grid algorithm for compressible flow in which the discretization of the body near the flow uses a volume of fluid representation a redistribution procedure is used to eliminate time step restrictions due to small cells where the boundary intersects the mesh the projection step uses an approximate projection based on a cartesian grid method for potential flow the method incorporates knowledge of the body through volume and area fractions along with certain other integrals over the mixed cells convergence results are given for the projection itself and for the time dependent algorithm in two dimensions the method is also demonstrated on flow past a half cylinder with vortex shedding

average resistance of toroidal graphs abstract the average effective resistance of a graph is a relevant performance index in many applications including distributed estimation and control of network systems in this paper we study how the average resistance depends on the graph topology and specifically on the dimension of the graph we concentrate on d dimensional toroidal grids and we exploit the connection between resistance and laplacian eigenvalues our analysis provides tight estimates of the average resistance which are key to study its asymptotic behavior when the number of nodes grows to infinity in dimension two the average resistance diverges in this case we are able to capture its rate of growth when the sides of the grid grow at different rates in higher dimensions the average resistance is bounded uniformly in the number of nodes in this case we conjecture that its value is of order 1 d for large d we prove this fact for hypercubes and when the side lengths go to infinity

distributed estimation from relative and absolute measurements this note defines the problem of least squares distributed estimation from relative and absolute measurements by encoding the set of measurements in a weighted undirected graph the role of its topology is studied by an electrical interpretation which easily allows distinguishing between topologies that lead to small or large estimation errors the least squares problem is solved by a distributed gradient algorithm the computed solution is approximately optimal after a number of steps that does not depend on the size of the problem or on the graph theoretic properties of its encoding this fact indicates that only a limited cooperation between the sensors is necessary

spectral element formulations on non conforming grids a comparative study of pointwise matching and integral projection methods pointwise matching pm and integral projection ip methods are two widely used techniques to extend the classical weak formulations to include non conforming grids we present spectral element formulations on polynomial p type and geometric h type non conforming grids using both the pm also known as the constrained approximation and ip also known as the mortar element methods we systematically compare the convergence characteristics of pm and ip methods for diffusion convection and convection diffusion equations consistency errors due to the non conforming formulations of the diffusion equation result in convergence problems for the pm method using the maximum rule both non conforming formulations for the unsteady convection operator result in eigenvalue spectrum with positive real values causing convergence problems due to the consistency errors however small physical diffusion in the convection diffusion equation eliminates these problems resulting in spectral convergence for both methods encouraged by this we present spectral element formulations for incompressible navier stokes equations using pm and ip methods on p type and h type non conforming grids and demonstrate spectral convergence for unsteady and steady test cases results for two dimensional lid driven cavity flow at re 1000 are also presented

transients of platoons with asymmetric and different laplacians abstract we consider an asymmetric control of platoons of identical vehicles with nearest neighbor interaction recent results show that if the vehicle uses different asymmetries for position and velocity errors the platoon has a short transient and low overshoots in this paper we investigate the properties of vehicles with friction to achieve consensus an integral part is added to the controller making the vehicle a third order system we show that the parameters can be chosen so that the platoon behaves as a wave equation with different wave velocities simulations suggest that our system has a better performance than other nearest neighbor scenarios moreover an optimization based procedure is used to find the controller properties

gerris a tree based adaptive solver for the incompressible euler equations in complex geometries an adaptive mesh projection method for the time dependent incompressible euler equations is presented the domain is spatially discretised using quad octrees and a multilevel poisson solver is used to obtain the pressure complex solid boundaries are represented using a volume of fluid approach second order convergence in space and time is demonstrated on regular statically and dynamically refined grids the quad octree discretisation proves to be very flexible and allows accurate and efficient tracking of flow features the source code of the method implementation is freely available

regular article an accurate cartesian grid method for viscous incompressible flows with complex immersed boundaries a cartesian grid method has been developed for simulating two dimensional unsteady viscous incompressible flows with complex immersed boundaries a finite volume method based on a second order accurate central difference scheme is used in conjunction with a two step fractional step procedure the key aspects that need to be considered in developing such a solver are imposition of boundary conditions on the immersed boundaries and accurate discretization of the governing equation in cells that are cut by these boundaries a new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the second order spatial accuracy of the underlying solver the presence of immersed boundaries alters the conditioning of the linear operators and this can slow down the iterative solution of these equations the convergence is accelerated by using a preconditioned conjugate gradient method where the preconditioner takes advantage of the structured nature of the underlying mesh the accuracy and fidelity of the solver is validated by simulating a number of canonical flows and the ability of the solver to simulate flows with very complicated immersed boundaries is demonstrated

enclave tasking for dg methods on dynamically adaptive meshes high order discontinuous galerkin dg methods promise to be an excellent discretization paradigm for hyperbolic differential equation solvers running on supercomputers since they combine high arithmetic intensity with localized data access since they straightforwardly translate into nonoverlapping domain decomposition and since they facilitate dynamic adaptivity without the need for conformal meshes an efficient parallel evaluation of dg weak formulation in an mpi x setting however remains nontrivial as dependency graphs over dynamically adaptive meshes change with each mesh refinement or coarsening as resolution transitions yield nontrivial data flow dependencies and as data sent along domain boundaries through message passing mpi have to be triggered in the correct order domain decomposition with mpi alone starts to become insufficient if the mesh changes very frequently if mesh changes cannot be predicted and if limiters and nonlinear per cell solves yield unpredictable costs per cell we introduce enclave tasking as a task invocation technique for shared memory and mpi x it does not assemble any task graph instead the mesh traversal spawns ready tasks directly a marker and cell approach ensures that tasks feeding into mpi or triggering mesh modifications as well as latency sensitive or bandwidth demanding tasks are processed with high priority the remaining cell tasks form enclaves i e groups of tasks that can be processed in the background enclave tasking introduces high concurrency which is homogeneously distributed over the mesh traversal it mixes memory intensive volumetric dg calculations with compute bound riemann solves and it helps to overlap communication with computations our work focuses on ader dg and patch based finite volumes yet we discuss how the paradigm can be generalized to the whole dg family and finite volume stand alone solvers

algorithms for leader selection in stochastically forced consensus networks we are interested in assigning a pre specified number of nodes as leaders in order to minimize the mean square deviation from consensus in stochastically forced networks this problem arises in several applications including control of vehicular formations and localization in sensor networks for networks with leaders subject to noise we show that the boolean constraints which indicate whether a node is a leader are the only source of nonconvexity by relaxing these constraints to their convex hull we obtain a lower bound on the global optimal value we also use a simple but efficient greedy algorithm to identify leaders and to compute an upper bound for networks with leaders that perfectly follow their desired trajectories we identify an additional source of nonconvexity in the form of a rank constraint removal of the rank constraint and relaxation of the boolean constraints yields a semidefinite program for which we develop a customized algorithm well suited for large networks several examples ranging from regular lattices to random graphs are provided to illustrate the effectiveness of the developed algorithms

a conservative adaptive projection method for the variable density incompressible navier stokes equations in this paper we present a method for solving the equations governing time dependent variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids the method is based on a projection formulation in which we first solve advection diffusion equations to predict intermediate velocities and then project these velocities onto a space of approximately divergence free vector fields our treatment of the first step uses a specialized second order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high reynolds number flow density and other scalars are advected in such a way as to maintain conservation if appropriate and free stream preservation our approach to adaptive refinement uses a nested hierarchy of logically rectangular girds with simultaneous refinement of the girds in both space and time the integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized the single grid algorithm is described briefly but the emphasis here is on the time stepping procedure for the adaptive hierarchy numerical examples are presented to demonstrate the algorithms s accuracy and convergence properties and illustrate the behavior of the method an additional example demonstrates the performance of the method on a more realistic problem namely a three dimensional variable density shear layer

bottom up construction and 2 1 balance refinement of linear octrees in parallel in this article we propose new parallel algorithms for the construction and 2 1 balance refinement of large linear octrees on distributed memory machines such octrees are used in many problems in computational science and engineering e g object representation image analysis unstructured meshing finite elements adaptive mesh refinement and n body simulations fixed size scalability and isogranular analysis of the algorithms using an mpi based parallel implementation was performed on a variety of input data and demonstrated good scalability for different processor counts 1 to 1024 processors on the pittsburgh supercomputing center s tcs 1 alphaserver the results are consistent for different data distributions octrees with over a billion octants were constructed and balanced in less than a minute on 1024 processors like other existing algorithms for constructing and balancing octrees our algorithms have mathcal o n log n work and mathcal o n storage complexity under reasonable assumptions on the distribution of octants and the work per octant the parallel time complexity is mathcal o frac n n p log frac n n p n p log n p where n is the size of the final linear octree and n p is the number of processors

combined immersed boundary finite difference methods for three dimensional complex flow simulations a second order accurate highly efficient method is developed for simulating unsteady three dimensional incompressible flows in complex geometries this is achieved by using boundary body forces that allow the imposition of the boundary conditions on a given surface not coinciding with the computational grid the governing equations therefore can be discretized and solved on a regular mesh thus retaining the advantages and the efficiency of the standard solution procedures two different forcings are tested showing that while the quality of the results is essentially the same in both cases the efficiency of the calculation strongly depends on the particular expression a major issue is the interpolation of the forcing over the grid that determines the accuracy of the scheme this ranges from zeroth order for the most commonly used interpolations up to second order for an ad hoc velocity interpolation the present scheme has been used to simulate several flows whose results have been validated by experiments and other results available in the literature finally in the last example we show the flow inside an ic piston cylinder assembly at high reynolds number to our knowledge this is the first example in which the immersed boundary technique is applied to a full three dimensional complex flow with moving boundaries and with a reynolds number high enough to require a subgrid scale turbulence model

a projection method for locally refined grids a numerical method for the solution of the two dimensional euler equatons for incompressible flow on locally refined grids is presented the method is a second order godunov projection method adapted from bell colella and glaz second order accuracy of the numerical method in time and space is established through numerical experiments the main contributions of this work concern the formulation and implementation of a projection for refined grids a discussion of the adjointness relation between gradient and divergence operators for a refined grid mac projection is presented and a refined grid approximate projection is developed an efficient multigrid method which exactly solves the projection is developed and a method for casting certain approximate projections as mac projections on refined grids is presented

duality with bf type i functions for a class of nondifferentiable multiobjective variational problems a class of bf type i functions and its extensions are introduced in the continuous case an example is presented in support utilizing these new concepts sufficient optimality conditions and duality results are presented for multiobjective variational problems involving arbitrary norms

second order duality for the variational problems under ρ η θ invexity in this paper we introduce the concept of second order duality for the variational problems using r h q invexity type conditions weak strong and converse duality results of mangasarian and mond weir type of variational problems are established under r h q invexity assumptions many examples and counterexamples are illustrated to justify our work

information centrality and ordering of nodes for accuracy in noisy decision making networks this technical note considers a network of stochastic evidence accumulators each represented by a drift diffusion model accruing evidence towards a decision in continuous time by observing a noisy signal and by exchanging information with other units according to a fixed communication graph these network dynamics model distributed sequential hypothesis testing as well as collective decision making we prove the relationship between the location of each unit in the graph and its certainty as measured by the inverse of the variance of its state under mild connectivity assumptions we show that only in balanced directed graphs do the node variances remain within a bounded constant from the minimum possible variance we then prove that for these digraphs node ranking based on certainty is governed by information centrality which depends on the notion of effective resistance suitably generalized to directed graphs our results which describe the certainty of each unit as a function of the structural properties of the graph can guide the selection of leaders in problems that involve the observation of noisy external signals by a cooperative multi agent network

regular article generation of short and long range temporal correlated noises we present the implementation of an algorithm to generate gaussian random noises with prescribed time correlations that can be either long or short ranged examples of langevin dynamics with short and long range noises are presented and discussed