amge coarsening strategies and application to the oseen equations we provide some extensions to the algebraic multigrid method based on element interpolation amge concerning the agglomeration process the application to nonconforming elements and the application to the mixed finite element discretization of the oseen linearized navier stokes equations this last point using amge for mixed finite elements becomes straightforward because of the availability of coarse level topologies we show this exemplarily for the crouzeix raviart element including a stability result the numerical results show that it really pays off to take a closer look at the agglomeration strategy a wrong choice can lead to insufficient convergence or even divergence of the overall multigrid method

preference voting and project ranking using dea and cross evaluation cook and kress 1990 using data envelopment analysis dea as their starting point proposed a procedure to rank order the candidates in a preferential election notionally each candidate is permitted to choose the most favourable weights to be applied to his her standings first place second place etc votes in the usual dea manner with the additional assurance region restriction that the weight for a j place vote should be more than that for a j 1 amount we consider that this freedom to choose weights is essentially illusory when maximum discrimination between the candidates is sought in which case the weights used to evaluate and rank the candidates are as if imposed externally at the outset to avoid this we present an alternative procedure which retains cook and kress central idea but where as well as using each candidate s rating of him herself we now make use of each candidate s ratings of all the candidates we regard the so called cross evaluation matrix as the summary of a self and peer rating process in which the candidates seek to interpret the voters preferences as favourably for themselves relative to the other candidates as possible the problem then becomes one of establishing an overall rating for each candidate from these individual ratings for this for each candidate we use a weighted average of all the candidates ratings of that candidate where the weights themselves are in proportion to each candidate s overall rating the overall ratings are therefore proportional to the components of the principal left hand eigenvector of the cross evaluation matrix these ideas are then applied to the selection of r d projects to comprise an r d program thus indicating thier wider applicability

polyhedral cone ratio dea models with an illustrative application to large commercial banks abstract polyhedral cone ratio data envelopment analysis models generalizing the ccr ratio model are developed for situations with a finite number of dmus and employing polyhedral cones of virtual multipliers they provide improved definitions of efficiency over ccr models whose input output data and or numbers of dmus are inadequate to capture aspects or restrictions which should be involved the focus here is on the sum form for cones which easily provides for capturing exogenous expert opinion as well as mathematical reduction to the old form with its very powerful software transformation from the usual intersection form to it and vice versa is explicitly given thereby the advantages of either or both are available the theory is illustrated with two dimensional examples and by real banking examples for motivation

scalable parallel methods for monolithic coupling in fluid structure interaction with application to blood flow modeling we introduce and study numerically a scalable parallel finite element solver for the simulation of blood flow in compliant arteries the incompressible navier stokes equations are used to model the fluid and coupled to an incompressible linear elastic model for the blood vessel walls our method features an unstructured dynamic mesh capable of modeling complicated geometries an arbitrary lagrangian eulerian framework that allows for large displacements of the moving fluid domain monolithic coupling between the fluid and structure equations and fully implicit time discretization simulations based on blood vessel geometries derived from patient specific clinical data are performed on large supercomputers using scalable newton krylov algorithms preconditioned with an overlapping restricted additive schwarz method that preconditions the entire fluid structure system together the algorithm is shown to be robust and scalable for a variety of physical parameters scaling to hundreds of processors and millions of unknowns

robin robin preconditioned krylov methods for fluid structure interaction problems in this work we propose a robin robin preconditioner combined with krylov iterations for the solution of the interface system arising in fluid structure interaction fsi problems it can be seen as a partitioned fsi procedure and in this respect it generalizes the ideas introduced in s badia f nobile c vergara j comput phys 227 2008 7027 7051 we analyze the convergence of gmres iterations with the robin robin preconditioner on a model problem and compare its efficiency with some existing algorithms the method is shown to be very efficient for many challenging fluid structure interaction problems such as those characterized by a large added mass effect or by enclosed fluids in particular the possibility to solve balloon type problems without any special treatment makes this algorithm very appealing compared to the computationally intensive existing approaches c 2009 elsevier b v all rights reserved

a monolithic geometric multigrid solver for fluid structure interactions in ale formulation summary we present a monolithic geometric multigrid solver for fluid structure interaction problems in arbitrary lagrangian eulerian coordinates the coupled dynamics of an incompressible fluid with nonlinear hyperelastic solids gives rise to very large and ill conditioned systems of algebraic equations direct solvers usually are out of question because of memory limitations and standard coupled iterative solvers are seriously affected by the bad condition number of the system matrices the use of partitioned preconditioners in krylov subspace iterations is an option but the convergence will be limited by the outer partitioning our proposed solver is based on a newton linearization of the fully monolithic system of equations discretized by a galerkin finite element method approximation of the linearized systems is based on a monolithic generalized minimal residual method iteration preconditioned by a geometric multigrid solver the special character of fluid structure interactions is accounted for by a partitioned scheme within the multigrid smoother only here fluid and solid field are segregated as dirichlet neumann coupling we demonstrate the efficiency of the multigrid iteration by analyzing 2d and 3d benchmark problems while 2d problems are well manageable with available direct solvers challenging 3d problems highly benefit from the resulting multigrid solver copyright 2015 john wiley sons ltd

a value efficiency approach to incorporating preference information in data envelopment analysis we develop a procedure and the requisite theory for incorporating preference information in a novel way in the efficiency analysis of decision making units the efficiency of deci sion making units is defined in the spirit of data envelopment analysis dea complemented with decision maker s preference information concerning the desirable structure of inputs and outputs our procedure begins by aiding the decision maker in searching for the most preferred combination of inputs and outputs of decision making units for short most preferred solution which are efficient in dea then assuming that the decision maker s most preferred solution maximizes his her underlying unknown value function we approximate the indifference contour of the value function at this point with its possible tangent hyperplanes value efficiency scores are then calculated for each decision making unit comparing the inefficient units to units having the same value as the most preferred solution the resulting value efficiency scores are optimistic approximations of the true scores the procedure and the resulting efficiency scores are immediately applicable to solving practical problems

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

performance analysis of music type high resolution estimators for direction finding in correlated and coherent scenes an asymptotic analysis is presented of a class of high resolution estimators for resolving correlated and coherent plane waves in noise these estimators are in turn constructed from certain eigenvectors associated with spatially smoothed or unsmoothed covariance matrices generated from a uniform array the analysis is first carried out for the smoothed case and from this the conventional i e unsmoothed multiple signal classification music scheme follows as a special case independent of the total number of sources present in the scene the variance of the conventional music estimator along the true arrival angles is shown to be zero within a first order approximation the bias expressions in the smoothed case are used to obtain a resolution threshold for two coherent equipowered plane waves in white noise and the result is compared to the one derived by kaveh et al 1986 for two uncorrelated equipowered plane waves

an efficient preconditioner for monolithically coupled large displacement fluid structure interaction problems with pseudo solid mesh updates we present a block preconditioner for the efficient solution of the linear systems that arise when employing newton s method to solve monolithically coupled large displacement fluid structure interaction problems in which the update of the moving fluid mesh is performed by the equations of large displacement elasticity following a theoretical analysis of the preconditioner we propose an efficient implementation that yields a solver with near optimal computational cost in the sense that the time for the solution of the linear systems scales approximately linearly with the number of unknowns we evaluate the performance of the preconditioner in selected two and three dimensional test problems

a note on preconditioning for indefinite linear systems preconditioners are often conceived as approximate inverses for nonsingular indefinite matrices of saddle point or kkt form we show how preconditioners incorporating an exact schur complement lead to preconditioned matrices with exactly two or exactly three distinct eigenvalues thus approximations of the schur complement lead to preconditioners which can be very effective even though they are in no sense approximate inverses

the cramer rao lower bound for directions of arrival of gaussian cyclostationary signals the cramer rao lower bound on the variance of estimates of directions of arrival signal strengths and carrier frequencies and phases of cyclostationary signals arriving at an array is considered numerical evaluations of the bound for the estimates of directions of arrival show that it can be orders of magnitude lower than the corresponding bound for stationary signals despite the great number of unknown parameters in the former case comparisons with the mean squared error of direction estimates obtained by the cyclic least squares algorithm show that the bound is not overly optimistic

partitioned solution algorithms for fluid structure interaction problems with hyperelastic models in this work we consider fluid structure interaction simulation with nonlinear hyperelastic models in the solid part we use a partitioned approach to deal with the coupled nonlinear fluid structure interaction problems we focus on handling the nonlinearity of the fluid and structure sub problems using adaptive newton s method the near incompressibility of materials the stabilization of employed finite element discretization and the robustness and efficiency of krylov subspace and algebraic multigrid methods for the linearized algebraic equations

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

forward backward spatial smoothing techniques for coherent signal identification a spatial smoothing scheme is further investigated in the context of coherent signal classification it is shown that by making use of a set of forward and complex conjugated backward subarrays simultaneously it is always possible to estimate any k directions of arrival using at most 3k 2 sensor elements this is achieved by creating a smoothed array output covariance matrix that is structurally identical to a covariance matrix in some noncoherent situation by incorporating eigenstructure based techniques on this smoothed covariance matrix it then becomes possible to correctly identify all directions of arrival irrespective of their correlation

preconditioning for the steady state navier stokes equations with low viscosity we introduce a preconditioner for the linearized navier stokes equations that is effective when either the discretization mesh size or the viscosity approaches zero for constant coefficient problems with periodic boundary conditions we show that the preconditioning yields a system with a single eigenvalue equal to 1 so that performance is independent of both viscosity and mesh size for other boundary conditions we demonstrate empirically that convergence depends only mildly on these parameters and we give a partial analysis of this phenomenon we also show that some expensive subsidiary computations required by the new method can be replaced by inexpensive approximate versions of these tasks based on iteration with virtually no degradation of performance

algebraic multilevel preconditioning methods ii a recursive way of constructing preconditioning matrices for the stiffness matrix in the discretization of selfadjoint second order elliptic boundary value problems is proposed it is based on a sequence of nested finite element spaces with the usual nodal basis functions using a nodeordering corresponding to the nested meshes the finite element stiffness matrix is recursively split up into two level block structures and is factored approximately in such a way that any successive schur complement is replaced approximated by a matrix defined recursively and thereform only implicitely given to solve a system with this matrix we need to perform a fixed number v of iterations on the preceding level using as an iteration matrix the preconditioning matrix already defined on that level it is shown that by a proper choice of iteration parameters it suffices to use v left 1 gamma 2 right tfrac 1 2 iterations for the so constructedv foldv cycle wherev 2 corresponds to aw cycle preconditioning matrices to be spectrally equivalent to the stiffness matrix the conditions involve only the constant in the strengthened c b s inequality for the corresponding two level hierarchical basis function spaces and are therefore independent of the regularity of the solution for instance if we use successive uniform refinements of the meshes the method is of optimal order of computational complexity if gamma 2 tfrac 8 9 under reasonable assumptions of the finite element mesh the condition numbers turn out to be so small that there are in practice few reasons to use an accelerated iterative method like the conjugate gradient method for instance

efficient preconditioning of the linearized navier stokes equations for incompressible flow we outline a new class of robust and efficient methods for solving subproblems that arise in the linearization and operator splitting of navier stokes equations we describe a very general strategy for preconditioning that has two basic building blocks a multigrid v cycle for the scalar convection diffusion operator and a multigrid v cycle for a pressure poisson operator we present numerical experiments illustrating that a simple implementation of our approach leads to an effective and robust solver strategy in that the convergence rate is independent of the grid robust with respect to the time step and only deteriorates very slowly as the reynolds number is increased

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

structural comparison of data envelopment analysis and multiple objective linear programming the concept of efficiency as it applies to decision making units dmus solutions alternatives plays an important role both in data envelopment analysis dea and multiple objective linear programming molp despite this and other apparent similarities dea and molp research has developed separately we show that structurally the dea formulation to identify efficient units is quite similar to the molp model based on the reference point or the reference direction approach to generate efficient solutions dea and molp should not be seen as substitutes but rather as complements we show that they cross fertilize each other molp provides interesting extensions to dea and dea provides new areas of application to molp

a hybrid genetic algorithm for multiobjective problems with activity analysis based local search the objective of this research was the development of a method that integrated an activity analysis model of profits from production with a biophysical model and included the capacity for optimization over multiple objectives we specified a hybrid genetic algorithm using activity analysis as a local search method and nsga ii for calculation of the multiple objective pareto optimal set we describe a parallel computing approach to computation of the genetic algorithm and apply the algorithm to evaluation of an input tax to regulate pollution from agricultural production

an algebraic multigrid method for linear elasticity we present an algebraic multigrid amg method for the efficient solution of linear block systems stemming from a discretization of a system of partial differential equations pdes it generalizes the classical amg approach for scalar problems to systems of pdes in a natural blockwise fashion we apply this approach to linear elasticity and show that the block interpolation described in this paper reproduces the rigid body modes i e the kernel elements of the discrete linear elasticity operator it is well known from geometric multigrid methods that this reproduction of the kernel elements is an essential property to obtain convergence rates which are independent of the problem size we furthermore present results of various numerical experiments in two and three dimensions they confirm that the method is robust with respect to variations of the poisson ratio nu we obtain rates rho 0 4 for nu 0 4 these measured rates clearly show that the method provides fast convergence for a large variety of discretized elasticity problems

modular vs non modular preconditioners for fluid structure systems with large added mass effect in this article we address the numerical simulation of fluid structure interaction fsi problems featuring large added mass effect we analyze different preconditioners for the coupled system matrix obtained after space time discretization and linearization of the fsi problem the classical dirichlet neumann preconditioner has the advantage of modularity because it allows to reuse existing fluid and structure codes with minimum effort simple interface communication unfortunately its performance is very poor in case of large added mass effects alternatively we consider two non modular approaches the first one consists in preconditioning the coupled system with a suitable diagonal scaling combined with an ilut preconditioner the system is then solved by a krylov method the drawback of this procedure is that the combination of fluid and structure codes to solve the coupled system is not straightforward the second non modular approach we consider is a splitting technique based on an inexact block lu factorization of the linear fsi system the resulting algorithm computes the fluid velocity separately from the coupled pressure structure system at each iteration reducing the computational cost independently of the preconditioner the efficiency of semi implicit algorithms i e those that treat geometric and fluid nonlinearities in an explicit way is highlighted and their performance compared to the one of implicit algorithms all the methods are tested on three dimensional blood vessel systems the algorithm combining the non modular ilut preconditioner with krylov methods proved to be the fastest

fluid structure algorithms based on steklov poincare operators in this paper we review some classical algorithms for fluid structure interaction problems and we propose an alternative viewpoint mutuated from the domain decomposition theory this approach yields preconditioned richardson iterations on the steklov poincare nonlinear equation at the fluid structure interface

direction finding methods for cyclostationary signals in the presence of coherent sources by exploiting the signal cyclostationarity conjugate cyclic music presented by gardner 1994 has been shown to be effective in performing signal selective direction finding however a direct application of conjugate cyclic music in the presence of coherent signals of interest sois will result in ambiguity to tackle the drawback of conjugate cyclic music we present a scheme called the hankel approximation method ham in conjunction with conjugate cyclic music to cope with the performance deterioration due to coherent sois for a uniform linear array theoretical analysis shows that at least 2k sensor elements are required to resolve k coherent sois making use of the forward backward f b technique presented by pillai and kwon 1989 f b ham is further developed which requires 3k 2 sensor elements to decorrelate k coherent sois where x represents the integer part of x several simulation examples are also presented for illustrating the effectiveness of the proposed methods

numerical simulation of fluid structure interaction problems on hybrid meshes with algebraic multigrid methods fluid structure interaction problems arise in many fields of application such as flows around elastic structures and blood flow in arteries the method presented in this paper for solving such a problem is based on a reduction to an equation at the interface involving the so called steklov poincare operators this interface equation is solved by a newton iteration for which directional derivatives involving shape derivatives with respect to the interface perturbation have to be evaluated appropriately one step of the newton iteration requires the solution of several decoupled linear sub problems in the structure and the fluid domains these sub problems are spatially discretized by a finite element method on hybrid meshes for the time discretization implicit first order methods are used for both sub problems the discretized equations are solved by algebraic multigrid methods

splitting methods based on algebraic factorization for fluid structure interaction we discuss in this paper the numerical approximation of fluid structure interaction fsi problems dealing with strong added mass effect we propose new semi implicit algorithms based on inexact block lu factorization of the linear system obtained after the space time discretization and linearization of the fsi problem as a result the fluid velocity is computed separately from the coupled pressure structure velocity system at each iteration reducing the computational cost we investigate explicit implicit decomposition through algebraic splitting techniques originally designed for the fsi problem this approach leads to two different families of methods which extend to fsi the algebraic pressure correction method and the yosida method two schemes that were previously adopted for pure fluid problems furthermore we have considered the inexact factorization of the fluid structure system as a preconditioner the numerical properties of these methods have been tested on a model problem representing a blood vessel system

analysis of iterative methods for saddle point problems a unified approach in this paper two classes of iterative methods for saddle point problems are considered inexact uzawa algorithms and a class of methods with symmetric preconditioners in both cases the iteration matrix can be transformed to a symmetric matrix by block diagonal matrices a simple but essential observation which allows one to estimate the convergence rate of both classes by studying associated eigenvalue problems the obtained estimates apply for a wider range of situations and are partially sharper than the known estimates in literature a few numerical tests are given which confirm the sharpness of the estimates

a multiple criteria approach to data envelopment analysis in this paper we present a multiple criteria data envelopment analysis mcdea model which can be used to improve discriminating power of dea methods and also effectively yield more reasonable input and output weights without a priori information about the weights in the proposed model several different efficiency measures including classical dea efficiency are defined under the same constraints each measure serves as a criterion to be optimized efficiencies are then evaluated under the framework of multiple objective linear programming molp the method is illustrated through three examples in which data sets are taken from previous research on dea s discriminating power and weight restriction

truly monolithic algebraic multigrid for fluid structure interaction the coupling of flexible structures to incompressible fluids draws a lot attention during the last decade many different solution schemes have been proposed in this contribution we concentrate on strong coupling fluid structure interaction by means of monolithic solution schemes therein a newton krylov method is applied to the monolithic set of nonlinear equations such schemes require good preconditioning to be efficient we propose two preconditioners that apply algebraic multigrid techniques to the entire fluid structure interaction system of equations the first is based on a standard block gauss seidel approach where approximate inverses of the individual field blocks are based on a algebraic multigrid hierarchy tailored for the type of the underlying physical problem the second is based on a monolithic coarsening scheme for the coupled system that makes use of prolongation and restriction projections constructed for the individual fields the resulting nonsymmetric monolithic algebraic multigrid method therefore involves coupling of the fields on coarse approximations to the problem yielding significantly enhanced performance

algebraic multilevel preconditioning methods i a recursive way of constructing preconditioning matrices for the stiffness matrix in the discretization of selfadjoint second order elliptic boundary value problems is proposed it is based on a sequence of nested finite element spaces with the usual nodal basis functions using a nodeordering corresponding to the nested meshes the finite element stiffness matrix is recursively split up into two level block structures and is factored approximately in such a way that any successive schur complement is replaced approximated by a matrix defined recursively and thereform only implicitely given to solve a system with this matrix we need to perform a fixed number v of iterations on the preceding level using as an iteration matrix the preconditioning matrix already defined on that level it is shown that by a proper choice of iteration parameters it suffices to use v left 1 gamma 2 right tfrac 1 2 iterations for the so constructedv foldv cycle wherev 2 corresponds to aw cycle preconditioning matrices to be spectrally equivalent to the stiffness matrix the conditions involve only the constant in the strengthened c b s inequality for the corresponding two level hierarchical basis function spaces and are therefore independent of the regularity of the solution for instance if we use successive uniform refinements of the meshes the method is of optimal order of computational complexity if gamma 2 tfrac 8 9 under reasonable assumptions of the finite element mesh the condition numbers turn out to be so small that there are in practice few reasons to use an accelerated iterative method like the conjugate gradient method for instance

performance analysis of the cyclic music method of direction estimation for cyclostationary signals the cyclic music algorithm exploits the cyclostationarity exhibited by most man made communication signals to perform signal selective estimation of directions of arrival at an array of sensors in the paper the bias and mean squared error of these direction estimates are derived under the assumption that the signals are complex possibly non gaussian and cyclostationary the analytical results are shown to be excellent predictors of empirical results obtained from computer simulation of the cyclic music algorithm and are also compared with the cramer rao bound which in certain cases can be orders of magnitude less than the cramer rao bound for the directions of arrival of stationary signals

a multiplier bound approach to assess relative efficiency in dea without slacks abstract in this paper we propose a new approach to deal with the non zero slacks in data envelopment analysis dea assessments that is based on restricting the multipliers in the dual multiplier formulation of the used dea model it guarantees strictly positive weights which ensures reference points on the pareto efficient frontier and consequently zero slacks we follow a two step procedure which after specifying some weight bounds results in an assurance region type model that will be used in the assessment of the efficiency the specification of these bounds is based on a selection criterion among the optimal solutions for the multipliers of the unbounded dea models that tries to avoid the extreme dissimilarity between the weights that is often found in dea applications the models developed do not have infeasibility problems and we do not have problems with the alternate optima in the choice of weights that is made to use our multiplier bound approach we do not need a priori information about substitutions between inputs and outputs and it is not required the existence of full dimensional efficient facets on the frontier either as is the case of other existing approaches that address this problem

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100