krylov based uzawa algorithms for the solution of the stokes equations using discontinuous pressure tetrahedral finite elements the objective of this work is to develop an efficient and robust krylov based uzawa algorithm for the solution of the 3d steady state and unsteady state stokes equations with discontinuous pressure tetrahedral finite elements to this end a class of preconditioned conjugate gradient uzawa algorithms are presented and compared to those of the literature for other finite element types a comparison is also made with an inexact uzawa algorithm for the steady state case an analysis of the results obtained for various problems leads to an iterative scheme that is well adapted to the solution of stokes problems of all sizes and complexities such as those found in industrial applications

preconditioned conjugate gradient methods for three dimensional linear elasticity finite element modelling of three dimensional elasticity problems give rise to large sparse matrices various preconditioning methods are developed for use in preconditioned conjugate gradient iterative solution techniques incomplete factorizations based on levels of fill drop tolerance and a two level hierarchical basis are developed various techniques for ensuring that the incomplete factors have positive pivots are presented computational tests are carried out for problems generated using unstructured tetrahedral meshes quadratic basis functions are used the performance of the iterative methods is compared to a standard direct sparse matrix solver problems with up to 70 000 degrees of freedom and small 1 element aspect ratio are considered

a hybrid element formulation for the three dimensional penalty finite element analysis of incompressible fluids this work presents a hybrid element formulation for the three dimensional penalty finite element analysis of incompressible newtonian fluids the formulation is based on a mixed variational statement in which velocity and stresses are treated as independent field variables the main advantage of this formulation is that it bypasses the use of ad hoc techniques such as selective reduced integration that are commonly used in penalty based finite element formulations and directly yields high accuracy for the velocity and stress fields without the need to carry out smoothing in addition since the stress degrees of freedom are condensed out at an element level the cost of solving for the global degrees of freedom is the same as in a standard penalty finite element method although the gain in accuracy for both the velocity and stress including the pressure fields is quite significant

assumed strain stabilization of the eight node hexahedral element an accurate and robust stabilization based on the assumed strain method and an operator orthogonal to constant strain fields is presented for an eight node hexahedral element with uniform reduced integration the stabilization forces depend only on the element geometry and material properties user specified parameters are not needed yet the assumed strain stabilization is nearly as fast as perturbation type hourglass control in an explicit code it has excellent coarse mesh accuracy for linear elastic bending and is easily incorporated into a nonlinear program the assumed strain field is also used with four point integration which does not require stabilization in addition two forms of the b matrix are studied and it is shown that the mean form is more efficient since it passes the patch test in a simplified form

spectral hp least squares finite element formulation for the navier stokes equations we consider the application of least squares finite element models combined with spectral hp methods for the numerical solution of viscous flow problems the paper presents the formulation validation and application of a spectral hp algorithm to the numerical solution of the navier stokes equations governing two and three dimensional stationary incompressible and low speed compressible flows the navier stokes equations are expressed as an equivalent set of first order equations by introducing vorticity or velocity gradients as additional independent variables and the least squares method is used to develop the finite element model high order element expansions are used to construct the discrete model the discrete model thus obtained is linearized by newton s method resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method spectral convergence of the l2 least squares functional and l2 error norms is verified using smooth solutions to the two dimensional stationary poisson and incompressible navier stokes equations numerical results for flow over a backward facing step steady flow past a circular cylinder three dimensional lid driven cavity flow and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation

multigrid methods to accelerate convergence of element by element solution algorithms for viscous incompressible flows abstract the use of iterative solvers for large systems of equations results in a slow convergence rate after the small wave length error components are resolved for a fixed convergence tolerance limit the error resolution capability of an iterative solver is a function of the mesh density two iterative solvers gmres and orthomin which utilize the element by element ebe data structure of the finite element mesh are studied to demonstrate this behavior a significant improvement in the accuracy of the solution and the rate of convergence is achieved for these iterative solvers by using a successive mesh refinement scheme like in a multigrid method this approach is found to better resolve both the large and the small scale flow phenomenon for a fine mesh while satisfying the convergence criterion in a fraction of the cpu time required by the standard iterative methods an iterative penalty finite element model is used to solve the governing equations for laminar incompressible isothermal fluid flows the solution accuracy and cpu time savings are demonstrated for two sample problems

an implicit algorithm within the arbitrary lagrangian eulerian formulation for solving incompressible fluid flow with large boundary motions abstract the objective of the paper is to present an implicit algorithm for incompressible fluid flow solution using the arbitrary lagrangian eulerian ale formulation and to investigate solution accuracy and stability of the algorithm the governing equations of the implicit procedure are derived using isoparametric interpolations for the fluid velocities and pressure the details suitable for general use are presented in our derivations of the fundamental equations and of the basic finite element balance equations the penalty method is utilized to eliminate the pressure on the element level accuracy and stability of the solutions are demonstrated in three examples for which the analytical solutions are known in the first example the burger s equation analogue to 1 d fluid flows is solved without and with fe mesh motion to show that the mesh motion practically does not affect the solutions in the second example the solitary wave motion with large displacements of the free boundary is solved as a benchmark problem in the third example the fluid flow in an infinite contractible and expandable pipe with prescribed large radial wall motion is solved this example is specifically attractive for biological flows as in blood vessels and lung airways all solutions presented show that the proposed algorithm is sufficiently accurate and stable since the algorithm is implicit high accuracy of results can be achieved with a relatively large time step

a combined parametric quadratic programming and iteration method for 3 d elastic plastic frictional contact problem analysis abstract this paper is concerned with the formulation and numerical realization of elastic plastic frictional contact problems comparing with two dimensional elastic plastic contact problems three dimensional elastic plastic contact problems with friction are more difficult to deal with because of the unknown slip direction of the tangential force and exhausting computing time when the double nonlinear problems are considered in order to avoid these difficulties a combined pqp parametric quadratic programming and iteration method is constructed in this paper the stiffness matrix of a 3 d contact element is introduced by means of a penalty function expression of the contact pressure and frictional force the contact condition and the flow rule are expressed by the same form as in a non associated plastic flow problem and the penalty factors can be eliminated by using a definite numerical technique the iteration algorithm whose functions are to give a precise discretization of space coulomb s friction law is used along with the pqp method and alleviates the difficulty of unknown slip direction and cuts down computing costs also the additional complementary conditions are discussed here so that the non physical ray solutions caused by original mathematical model can be eliminated numerical examples are given to demonstrate the validity of the present method

fifteen node tetrahedral elements for explicit methods in nonlinear solid dynamics abstract despite the ease in meshing and benefits for modeling flexure curved shapes etc second order tetrahedral elements are not contained in typical explicit solid dynamic programs this is primarily due to the lack of both a satisfactory consistent nodal loading distribution and mass lumping technique row summation lumping for instance produces negative vertex node masses for the popular ten node serendipity tetrahedron which also has zero vertex node loads resulting from a constant pressure on an element face this has led to piecewise composites of four node tetrahedrons to represent a ten node one in explicit codes in this paper truly second order fifteen node formulations for compressible and for nearly incompressible materials are presented and evaluated in addition to producing all positive nodal loads from a uniform traction row summation mass lumping for the fifteen node element is shown to produce all positive nodal masses performance is assessed in standard benchmark problems and practical applications using various elastic and elastic plastic material models and involving very large strains deformations severe distortions and contact impact comparisons are also made with several first order elements and second order hexahedral formulations the offered elements performed satisfactorily in all examples as recently found for second order hexahedral elements it is shown that the inclusion of face and centroidal nodes is vital for robust performance with row summation lumping and high order quadrature rules are crucial with explicit methods these second order elements are shown to be viable for practical applications especially using today s parallel computers whereas the reliable performance is generally attained at significant computational expense compared with first order and brick types these elements can be more computationally competitive in flexure and have the desirable trait that they are amenable to automatic tetrahedral meshing software

penalty finite element analysis of 3 d navier stokes equations abstract the steady state navier stokes equations in three dimensions are solved by a penalty finite element method for the problems of wall driven cavity flow in a cubical box and natural convection in a cubical cavity subjected to differential side heating the present solutions are compared with recent finite difference solutions of the wall driven cavity problem for reynolds numbersre 100 and 400 the agreement is found to be very good

a note on three dimensional pursuit evasion game with bounded curvature the system of kinematic equations which describes isaacs game of two cars has been extended to the case of a three dimensional pursuit evasion game between players with bounded curvature it is shown that in the three dimensional version of the homicidal chauffeur game both players when playing optimally strive to steer the system into a common plane and will remain on this plane until game termination the situation is somewhat different for the three dimensional version of the game of two cars where it is not always advantageous to steer an initially three dimensional dynamic system into a plane nevertheless if at any instant the velocity vectors and the line of sight between players are coplanar both players strive to remain on this plane

an analysis of 3d particle path integration algorithms several techniques for the numerical integration of particle paths in steady and unsteady vector velocity fields are analyzed most of the analysis applies to unsteady vector fields however some results apply to steady vector field integration multistep multistage and some hybrid schemes are considered it is shown that due to initialization errors many unsteady particle path integration schemes are limited to third order accuracy in time multistage schemes require at least three times more internal data storage than multistep schemes of equal order however for timesteps within the stability bounds multistage schemes are generally more accurate a linearized analysis shows that the stability of these integration algorithms are determined by the eigenvalues of the local velocity tensor thus the accuracy and stability of the methods are interpreted with concepts typically used in critical point theory this paper shows how integration schemes can lead to erroneous classification of critical points when the timestep is finite and fixed for steady velocity fields we demonstrate that timesteps outside of the relative stability region can lead to similar integration errors from this analysis guidelines for accurate timestep sizing are suggested for both steady and unsteady flows in particular using simulation data for the unsteady flow around a tapered cylinder we show that accurate particle path integration requires timesteps which are at most on the order of the physical timescale of the flow

an unbiased parametric imaging algorithm for nonuniformly sampled biomedical system parameter estimation an unbiased algorithm of generalized linear least squares glls for parameter estimation of nonuniformly sampled biomedical systems is proposed the basic theory and detailed derivation of the algorithm are given this algorithm removes the initial values required and computational burden of nonlinear least regression and achieves a comparable estimation quality in terms of the estimates bias and standard deviation therefore this algorithm is particular useful in image wide pixel by pixel based parameter estimation e g to generate parametric images from tracer dynamic studies with positron emission tomography an example is presented to demonstrate the performance of this new technique this algorithm is also generally applicable to other continuous system parameter estimation

a particle tracking technique for the lagrangian eulerian finite element method in multi dimensions summary this paper presents a multi dimensional particle tracking technique for applying the lagrangian eulerian finite element method to solve transport equations in transient state simulations in the lagrangianeulerian approach the advection term is handled in the lagrangian step so that the associated numerical errors can be considerably reduced it is important to have an adequate particle tracking technique for computing advection accurately in the lagrangian step the particle tracking technique presented here is designed to trace fictitious particles in the real world flow field where the flow velocity is either measured or computed at a limited number of locations the technique named in element particle tracking traces fictitious particles on an element by element basis given a velocity field a fictitious particle is traced one element by one element until either a boundary is encountered or the available time is completely consumed for the tracking within an element the element is divided into a desired number of subelements with the interpolated velocity computed at all nodes of the subelements a fictitious particle thus is traced one subelement by one subelement within the element the desired number of subelements can be determined based on the complexity of the flow field being considered the more complicated the flow field is the more subelements are needed to achieve accurate particle tracking results a single velocity approach can be used to efficiently perform particle tracking in a smooth flow field while an average velocity approach can be employed to increase the tracking accuracy for more complex flow fields

finite element navier stokes calculation of three dimensional turbulent flow near a propeller les equations de navier stokes sont resolues par une methode d elements finis a fonction de penalite l helice est modelisee par un disque actuateur et le transport turbulent par une equation d energie cinetique turbulente

numerical modeling of the mixing flow of second order fluids with helical ribbon impellers rheology is known to have a strong impact on the flow behavior and the power consumption of mechanically agitated tanks in the case of viscoelastic fluids the role of elasticity on power draw has yet to be elucidated though recent studies with helical ribbon impellers indicate that elasticity increases torque the objective of this paper is to show that in the case of second order fluids the use of a simple constitutive equation derived from a second order retarded motion expansion succeeds in predicting a rise in power draw owing to elasticity the equations of change governing fluid flow are solved using a finite element method combined with an augmented lagrangian method for the treatment of the non linear constitutive equation we show in particular how the underlying non linear tensor equations can be solved directly using a spectral decomposition of the related matrix operator first the numerical methodology is explained next simulation results are presented in the case of a tank provided with a helical ribbon these results are then compared with experimental data a rise of power draw similar in shape but smaller than that measured experimentally may be noted when elasticity is increased

a least squares approach for uniform strain triangular and tetrahedral finite elements a least squares approach is presented for implementing uniform strain triangular and tetrahedral finite elements the basis for the method is a weighted least squares formulation in which a linear displacement field is fit to an element s nodal displacements by including a greater number of nodes on the element boundary than is required to define the linear displacement field it is possible to eliminate volumetric locking common to fully integrated lower order elements such results can also be obtained using selective or reduced integration schemes but the present approach is fundamentally different from those the method is computationally efficient and can be used to distribute surface loads on an element edge or face in a continuously varying manner between vertex mid edge and mid face nodes example problems in two and three dimensional linear elasticity are presented element types considered in the examples include a six node triangle eight node tetrahedron and ten node tetrahedron 1998 john wiley sons ltd

generalized linear least squares method for fast generation of myocardial blood flow parametric images with n 13 ammonia pet in this paper the authors developed and tested strategies for estimating myocardial blood flow mbf and generating mbf parametric images using positron emission tomography pet n 13 ammonia and the generalized linear least square glls method glls was generalized to the general linear compartment model modified for the correction of spillover validated using simulated n 13 ammonia data and examined using pet data from several patient studies in comparison to the standard model fitting procedure the glls method provided similar accuracy and superior computational speed

large deformation triangular and tetrahedral element formulations for unstructured meshes abstract the increasing use of automatic mesh generators and remeshers has spurred the need for accurate and efficient triangular and tetrahedral elements in unstructured meshes in large deformation analysis of solids accuracy and efficiency require the treatment of volumetric locking and element distortions respectively in this paper a mixed formulations is proposed to treat these issues and applied to triangular and tetrahedral elements the formulations enforces in the weak sense the expression for the volumetric strain in terms of the deformation gradient the mixed formulation is combined with an irreducible formulation to provide a balance between the treatment of volumetric locking and the maintenance of an adequate critical timestep three techniques are proposed to determine such a balance at the local element level example computations in two and three dimensions of an iron cylinder impacting a rigid surface are used to demonstrate the formulations and to compare them to the irreducible displacement based formulation

finite element solution of three dimensional incompressible fluid flow problems by a preconditioned conjugate residual method a new algorithm for the solution of the three dimensional navier stokes equation using the mixed formulation and an incomplete factorization technique is presented the linear system obtained at each modified newton raphson iteration is solved by the preconditioned conjugate residual method pcr using an out of core incomplete lu factorization as preconditioning this factorization is performed on a matrix stored by a new static storage method called the packed skyline method the performance of the proposed algorithm is assessed for the wall driven cubic cavity problem using the q p1 enriched element

a comparison of gmres and cgstab accelerations for incompressible navier stokes problems abstract chin p and p a forsyth a comparison of gmres and cgstab accelerations for incompressible navier stokes problems journal of computational and applied mathematics 46 1993 415 426 recently incomplete lu preconditioned conjugate gradient type matrix solvers have been used in conjunction with newton or newton like methods to solve the fully coupled incompressible navier stokes equations a number of acceleration methods can be used for the large sparse nonsymmetric linear systems that arise from such situations in this work we compare gmres and cgstab a stabilized variant of cgs by observing the effect of various factors e g grid size preconditioning we attempt to determine the classes of problems to which each acceleration method is best suited numerical results obtained with several two dimensional geometries are provided

parallel finite element simulations of incompressible viscous fluid flow by domain decomposition with lagrange multipliers a parallel approach to solve three dimensional viscous incompressible fluid flow problems using discontinuous pressure finite elements and a lagrange multiplier technique is presented the strategy is based on non overlapping domain decomposition methods and lagrange multipliers are used to enforce continuity at the boundaries between subdomains the novelty of the work is the coupled approach for solving the velocity pressure lagrange multiplier algebraic system of the discrete navier stokes equations by a distributed memory parallel ilu 0 preconditioned krylov method a penalty function on the interface constraints equations is introduced to avoid the failure of the ilu factorization algorithm to ensure portability of the code a message based memory distributed model with mpi is employed the method has been tested over different benchmark cases such as the lid driven cavity and pipe flow with unstructured tetrahedral grids it is found that the partition algorithm and the order of the physical variables are central to parallelization performance a speed up in the range of 5 13 is obtained with 16 processors finally the algorithm is tested over an industrial case using up to 128 processors in considering the literature the obtained speed ups on distributed and shared memory computers are found very competitive

a two target game analysis in line of sight coordinates abstract the engagement between two aggressively operating similar aircraft armed with boresight limited all aspect missiles is modelled as a two target differential game between two identical cars by using a line of sight coordinate system the symmetry of the problem can be exploited leading to a reduced complexity in the game of kind analysis the barrier trajectories are obtained in a closed form allowing us to generate closed barrier surfaces with a reasonable computational effort these barrier surfaces enclose the winning zone of each player and the region of mutual kill the analysis reveals several new features not encountered in previous studies

the game of two cars with a containment probability as a cost function the case of variable speed abstract a stochastic version of isaacs s 1 game of two cars is dealt with here in this version the pursuer has a variable speed owing to thrust and drag forces whereas the evader s speed is constant also the pursuer can manuever as long as his speed is bounded by some lower and upper bounds by using a containment probability as a cost functional for the game saddle point feedback strategies are computed and it is shown for a range of values of some parameters that a proportional navigation guidance law is a suboptimal feedback pursuit strategy

identification of continuous time multivariable systems from sampled data abstract several approaches to estimating the parameters of a continuous time model of a multivariable system from samples of input and output observations arc discussed these include indirect methods where a discrete time model is first obtained from the input output data and then transformed into a continuous time model as well as direct methods where the continuous time model is obtained straight from the samples of the observations an example is used to compare the methods

a finite element method for elasto plastic structures and contact problems by parametric quadratic programming in this paper the stiffness matrix of a contact element is introduced by means of a penalty function expression of the contact pressure and frictional force the contact condition and the flow rule are expressed by the same form as in a non associated plastic flow problem a unified pqp parametric quadratic programming model related to contact problems as well as to elasto plastic structures is constructed a series of pqp formulae for contact problems and elastic plastic structures is derived in the text and some numerical examples are illustrated as well

finite element analysis of oscillatory flow with heat transfer inside a square cavity in this work a semi implicit projection type finite element method is applied to solve the incompressible oscillatory cavity flow with heat transfer the two dimensional time dependent navier stokes and energy equations are numerically integrated by a time split galerkin finite element method using direct matrix solvers the time accuracy of the method was tested by calculating the transient buoyancy driven flow in a square cavity with differentially heated vertical walls the oscillatory cavity flow is then studied considering the effects of heat transfer reynolds number and oscillatory stokes number to measure the stability of the scheme for such a high singularity phenomenon the proposed scheme is found to be stable and convergent for high rayleigh numbers and will be applicable to general problems involving flow and heat transfer especially in three dimensions

proportional navigation and the game of two cars the case of a pursuer with variable speed a stochastic version of the game of two cars is considered in this version the pursuer has a variable speed owing to thrust and drag forces whereas the evader s speed is constant also the pursuer can maneuver as long as his speed is bounded by some lower and upper bounds the motion of the players is confined to the pursuer s effective operation zone dp and the cost function of the game is the probability of the event before the evader enters his safe zone the evader enters the pursuer s killing zone kp at some t 0 t t or the evader stays at the domain dp kp for all t 0 t0 for some t0 t by numerically solving a nonlinear parabolic boundary value problem on a generalized torus in r4 it is shown that for a range of values of some parameters a proportional navigation guidance law is a suboptimal feedback pursuit strategy

fast and reliable estimation of multiple parametric images using an integrated method for dynamic spect dynamic single photon emission computed tomography spect has demonstrated the potential to quantitatively estimate physiological parameters in the brain and the heart the generalized linear least square glls method is a well established method for solving linear compartment models with fast computational speed however the high level of noise intrinsic in the spect data leads to reliability and instability problems of glls for generating parametric images an integrated method is proposed to restrict the noise in both the temporal and spatial domains to estimate multiple parametric images for dynamic spect this method comprises three steps which are optimum image sampling schedule in the projection space cluster analysis applied postreconstruction and parametric image generation with glls the simulation and experimental studies for the neuronal nicotine acetylcholine receptor tracer of 5 123i iodo a 85380 were employed to evaluate the performance of the proposed method the results of influx rate of k1 and volume of distribution of vd demonstrated that the integrated method was successful in generating low noise parametric images for high noise spect data without enhancing the partial volume effect furthermore the integrated method is computationally efficient for potential clinical applications

pursuit evasion in medium range air combat scenarios abstract strategies for unmanned air combat simulation are usually constructed by synthesizing control laws derived from pilot behaviour analysis typical maneuver sequences are pre launch maneuvering for favourable missile launch conditions post launch maneuvering for deterioration of anticipated counterfire missile avoidance reattack an alternate procedure for developing such strategies consists of modelling the air combat scenario as a differential game problem or a series of such problems and applying differential game theory in this paper full order modelling of 1 vs 1 engagements with medium range missiles is discussed including constraints in dynamic pressure radar visibility and load factors as an example the open loop solution of a characteristic pursuit evasion problem is presented and compared to a simulation result using a typical air combat simulation computer program

symmetric gaussian quadrature formulae for tetrahedronal regions abstract quadrature formulae of degrees 2 to 6 are presented for the numerical integration of a function over tetrahedronal regions the formulae presented are of gaussian type and fully symmetric with respect to the four vertices of the tetrahedron

hourglass control in linear and nonlinear problems abstract mesh stabilization techniques for controlling the hourglass modes in under integrated hexahedral and quadrilateral elements are described it is shown that the orthogonal hourglass techniques previously developed can be obtained from simple requirements that insure the consistency of the finite element equations in the sense that the gradients of linear fields are evaluated correctly it is also shown that this leads to an hourglass control that satisfies the patch test the nature of the parameters which relate the generalized stresses and strains for controlling hourglass modes is examined by means of a mixed variational principle and some guidelines for their selection are discussed finally effective means of implementing these hourglass procedure in computer codes are described applications to both the laplace equation and the equations of solid mechanics in 2 and 3 dimensions are considered

a new computational framework for electro activation in cardiac mechanics abstract this paper presents a novel computational framework for the numerical simulation of the electromechanical response of the myocardium during the cardiac cycle the paper presents the following main novelties 1 two new mixed formulations tailor made for active stress and active strain coupling approaches have been developed and used in conjunction with two different ionic models namely bueno orovio et al 2008 and ten tusscher et al 2004 taking as a reference the mixed formulations introduced by bonet et al 2015 in the context of nonlinear elasticity the proposed formulations include as unknown fields the geometry and the transmembrane potential and possibly a lagrange multiplier enforcing weakly the incompressibility constraint as well as the deformation gradient tensor its cofactor its determinant the gradient of the transmembrane potential and their respective work conjugates the finite element implementation of these formulations is shown in this paper where a static condensation procedure is presented in order to yield an extremely competitive computational approach 2 a comprehensive and rigorous study of different ionic models i e bueno orovio and ten tusscher and electromechanical activation couplings i e active strain and active stress has been carried out 3 an analytical and numerical analysis of the possible loss of ellipticity and polyconvexity of one of the most widely used constitutive models in the context of cardiac mechanics is carried out in this paper putting forward possible polyconvexifications of the existing model 4 in addition an invariant representation of guccione s constitutive model is proposed finally a series of numerical examples are included in order to demonstrate the applicability and robustness of the proposed formulations

a new element by element method for trajectory calculations with tetrahedral finite element meshes a new method to track massless particles in a three dimensional flow field is presented the method is based on an element by element approach coupled with a predictor corrector shooting scheme and does not use any time step by analogy with time dependent schemes the number of shootings is related to an equivalent number of time steps the method has been implemented in a finite element framework using unstructured tetrahedral finite element meshes however it is general enough so that it can be implemented in finite difference and finite volume frameworks as well it has been tested on a variety of flow systems namely the poiseuille flow in an empty circular pipe the rotating flow in a stirred tank the shear flow in a square tank and the flow through a static mixer accuracy has been found to depend on the accuracy of the velocity computation the number of points per element and the level of mesh refinement copyright 2006 john wiley sons ltd

a study on statistically reliable and computationally efficient algorithms for generating local cerebral blood flow parametric images with positron emission tomography with the advent of positron emission tomography pet a variety of techniques have been developed to measure local cerebral blood flow lcbf noninvasively in humans a potential class of techniques which includes linear least squares ls linear weighted least squares wls linear generalized least squares gls and linear generalized weighted least squares gwls is proposed the statistical characteristics of these methods are examined by computer simulation the authors present a comparison of these four methods with two other rapid estimation techniques developed by huang et al 1982 and alpert 1984 and two classical methods the unweighted and weighted nonlinear least squares regression the results show that these methods can take full advantage of the contribution from the fine temporal sampling data of modern tomographs and thus provide statistically reliable estimates that are comparable to those obtained from nonlinear ls regression these methods also have high computational efficiency and the parameters can be estimated directly from operational equations in one single step therefore they can potentially be used in image wide estimation of local cerebral blood flow and distribution volume with pet

on the roles of minimization and linearization in least squares finite element models of nonlinear boundary value problems in this paper we examine the roles of minimization and linearization in the least squares finite element formulations of nonlinear boundary values problems the least squares principle is based upon the minimization of the least squares functional constructed via the sum of the squares of appropriate norms of the residuals of the partial differential equations in the present case we consider l 2 norms since the least squares method is independent of the discretization procedure and the solution scheme the least squares principle suggests that minimization should be performed prior to linearization where linearization is employed in the context of either the picard or newton iterative solution procedures however in the least squares finite element analysis of nonlinear boundary value problems it has become common practice in the literature to exchange the sequence of application of the minimization and linearization operations the main purpose of this study is to provide a detailed assessment on how the finite element solution is affected when the order of application of these operators is interchanged the assessment is performed mathematically through an examination of the variational setting for the least squares formulation of an abstract nonlinear boundary value problem and also computationally through the numerical simulation of the least squares finite element solutions of both a nonlinear form of the poisson equation and also the incompressible navier stokes equations the assessment suggests that although the least squares principle indicates that minimization should be performed prior to linearization such an approach is often impractical and not necessary

adaptive domain decomposition for the bound method application to the incompressible navier stokes and energy equations in three space dimensions abstract large scale numerical simulations of the flow and associated transport phenomena governed by the navier stokes and energy equations are routinely calculated in engineering practice nevertheless the uncertainty due to spatial discretization limits the confidence of practitioners in numerical solutions an approach to provide information about the accuracy of the quantity of interest is proposed here in the novel a posteriori error estimation technique the bound method is based on relaxing lagrange multipliers that enforces continuity between sub domains the method provides fast efficient asymptotic but reliable lower and upper bounds to the output of underlying partial differential equations pdes herein we highlight the method when applied to outputs of the steady incompressible navier stokes and energy equations the bound method in this paper follows the directly equilibrated hybrid flux approach for the flux calculation between sub domains and uses the crouzeix raviart p 2 p 1 approximation spaces to improve the effectiveness of the bound method an adaptive sub domain refinement strategy leading to sharper bounds is adopted a convective heat transfer problem in a series of electronic chip devices is investigated the novelty of this paper is to present bounds using adaptive domain decomposition for outputs associated to a complex three dimensional field solution of the navier stokes and energy equations

tetrahedral composite finite elements we develop and analyse a composite ct3d tetrahedral element consisting of an ensemble of 12 four node linear tetrahedral elements coupled to a linear assumed deformation defined over the entire domain of the composite element the element is designed to have well defined lumped masses and contact tractions in dynamic contact problems while at the same time minimizing the number of volume constraints per element the relation between displacements and deformations is enforced weakly by recourse to the hu washizu principle the element arrays are formulated in accordance with the assumed strain prescription the formulation of the element accounts for fully non linear kinematics integrals over the domain of the element are computed by a five point quadrature rule the element passes the patch test in arbitrarily distorted configurations our numerical tests demonstrate that ct element has been found to possess a convergence rate comparable to those of linear simplicial elements and that these convergence rates are maintained as the near incompressible limit is approached we have also verified that the element satisfies the babuska brezzi condition for a regular mesh configuration these tests suggest that the ct3d element can indeed be used reliably in calculations involving near incompressible behaviour which arises e g in the presence of unconfined plastic flow

improved signal to noise ratio in parametric images by cluster analysis abstract parametric images are formed by analyzing the concentration history of every voxel in pet data sets because pet concentration data at the voxel level are rather noisy noise propagation into the parametric image is often quite noticeable to address this problem a model based clustering method has been developed to generate parametric images the basic idea of the clustering method is to average over voxels whose concentration histories have the same shape we applied the method to a two parameter k 1 k 2 compartment model of local cerebral blood flow the statistic r tc t dt c t dt te k 2 t c a t dt e k 2 t c a t dt classifies curves in terms of k 2 where c t and c a t denote the tissue and blood concentration histories respectively and is the convolution operator simulation studies of noise propagation in the clustering statistic showed that 30 voxel noise yielded a 2 standard deviation in r parametric images of blood flow and partition coefficient were computed for an o 15 study with and without clustering cluster size affected bias statistical precision and computation time with clusters of 400 voxels the variance of the flow parameter was around 1 50 smaller with clustering with negligible bias and a computation time of 30 s on a 64 mhz workstation for 15 128 128 images with matlab 5 1

triangles and tetrahedra in explicit dynamic codes for solids explicit dynamic codes which are used currently for the study of plastic deformations in impact or with some modification for metal forming suffer two serious limitations first only quadrilateral or hexahedral linear elements can be used thus limiting the possibilities of adaptive refinement and adaptive meshing second even with the use of such elements special devices such as reduced integration must be introduced to avoid locking and reduce costs these necessitate complex hour glass control mending type procedures the main difficulties are those due to the need of treatment of almost incompressible deformation modes recently similar difficulties have been overcome in the context of fluid dynamics soil dynamics and we show here how the processes introduced there can be adopted effectively to the present problem thus allowing an almost unrestricted choice of element interpolations 1998 john wiley sons ltd

an evaluation of the algorithms for determining local cerebral metabolic rates of glucose using positron emission tomography dynamic data measurement of the local cerebral metabolic rate of glucose lcmrglc and the individual rate constant parameters of the sup 18 f 2 fluoro 2 deoxy d glucose fdg model can provide a clearer understanding and insight to the physiological processes in the human brain and a quicker and more accurate means of diagnosis in clinical applications a systematic study using simulated and clinical tissue time activity data is presented to evaluate several existing and newly developed major algorithms used for determining lcmrglc and the individual rate constants from positron emission tomography dynamic data the computational and statistical properties of the autoradiographic approach weighted and unweighted nonlinear least squares methods patlak graphic approach weighted integration method linear least squares and generalized linear least squares methods are investigated and discussed in this paper