an optimization based approach for the design of pde solution algorithms we develop and analyze an optimization based approach for the robust and efficient solution of pde problems consisting of multiple physics operators with fundamentally different mathematical properties our approach relies on three essential steps decomposition of the original problem into subproblems for which robust solution algorithms are available integration of the subproblems into an equivalent pde constrained optimization problem and solution of the resulting optimization problem either directly as a fully coupled algebraic system or in the null space of the pde constraints this strategy gives rise to a general approach for synthesizing robust solvers for complex coupled problems from solvers for their simpler physics components

a cfar adaptive subspace detector based on a single observation in system dependent clutter background in this paper the problem of detecting target in system dependent clutter sdc background with a single observation from the test cell is researched classical detectors such as the generalized likelihood ratio detectors glrds and the adaptive matched filters amfs etc usually deal with the clutter and the noise as a whole the low rank detectors lrds make use of the low rank property of the clutter to improve the detection performance however the performance of lrds degrades when the signal is not orthogonal with respect to w r t the clutter in this paper an adaptive subspace detector for sdc sdc asd background which deals with the clutter and the noise separately is proposed the sdc asd designs the test statistic by replacing the signal and the clutter covariance matrix with their maximum likelihood estimations mles its theoretical false alarm probability and detection probability are analytically deduced analytical results show that the test statistic has the form of non central distribution besides it is shown that the sdc asd has constant false alarm rate cfar performance w r t the clutter and the noise numerical experiments are provided to validate the detection performance of the sdc asd in dealing with the target detection in sdc background less

an adaptive finite element method for transient compressible flows with moving boundaries a description is given of an adaptive finite element method for the simulation of two dimensional compressible flows with moving boundaries the method is implemented on an unstructured triangular grid and the mesh adaptation is achieved by local grid regeneration using an error estimation procedure coupled to an automatic triangular mesh generator two numerical examples are included to illustrate the numerical performance of the method

a new mesh generation scheme for arbitrary planar domains this paper describes a new algorithm to generate interior nodes within any arbitrary multi connected regions the boundary nodes and the interior nodes are then linked up to form the best possible triangular elements by a completely revised technique in an efficient and stable manner owing to the generality of the central generation program the global domain is allowed to be divided into as many irregular subdomains as desired in order to model closely the actual physical situation moreover the boundaries of the sub domains are updated from time to time when necessary to include the possibilities of progressive refinement around a sharp corner generating radiating mesh from a prescribed node generating mesh between two circular arcs etc despite its flexibility and capabilities data for triangulation have been kept to a minimum by a logical input module no connectivity information between subregions is needed and common boundaries are defined once only all these features have contributed to a powerful method to generate 3 node or 6 node triangular element meshes of great variety within the most irregular heterogeneous regions

the pressure corrected ice finite element method for compressible flows on unstructured meshes a new implicit continuous fluid eulerian ice scheme for simulating a wide range of transient and steady inviscid and viscous compressible flows on unstructured finite elements is presented this new computational fluid dynamics scheme termed the pressure corrected ice finite element method pcice fem represents an advancement in massmomentum coupled pressure based schemes the governing hydrodynamic equations for this scheme consist of the conservative forms of the momentum balance navier stokes mass conservation and total energy equations the pcice fem scheme is developed as a predictor corrector scheme by performing a fractional step splitting of the semi implicit temporal discretization of the governing equations into an explicit predictor phase and a semi implicit pressure correction phase coupled by a pressure poisson solution the result of this predictor corrector formulation is that the pressure poisson equation is provided with sufficient internal energy information to avoid iteration with the semi implicit pressure correction equations the pcice fem scheme combines a modified form of the two step taylor galerkin fem scheme as an explicit predictor for the fractional momentum equations and a time weighted fem method for the semi implicit form of the mass conservation and the total energy equations the pcice fem scheme employs flux corrected transport fct as a high resolution filter for shock capturing the ability of the pcice fem scheme to accurately and efficiently simulate a wide variety of flows from nearly incompressible to highly compressible is demonstrated

a rational function preconditioner for indefinite sparse linear systems this paper introduces a rational function preconditioner for linear systems with indefinite sparse matrices a by resorting to rational functions of a the algorithm decomposes the spectrum of a into two disjoint regions and approximates the restriction of a 1 on these regions separately we show a systematic way to construct these rational functions so that they can be applied stably and inexpensively an attractive feature of the proposed approach is that the construction and application of the preconditioner can exploit two levels of parallelism moreover the proposed preconditioner can be modified at a negligible cost into a preconditioner for a nearby matrix of the form a ci which can be useful in some applications the efficiency and robustness of the proposed preconditioner are demonstrated on a few tests with challenging model problems including problems arising from the helmholtz equation in three dimensions

error estimator and adaptive moving grids for finite volumes schemes a new adaptation technique has been developed for two and three dimensional grids based on relocation of the mesh nodes the flow is governed by the euler equations expressed in an euler lagrange form and the discretization uses a first order finite volume scheme based on roe s approximate riemann solver the grid is unstructured and its motion and evolution obey the physical and geometrical conservation laws the error is evaluated by a reconstructed higher order solution which is used to derive a forcing term to drive the motion of the grid nodes this is formulated so as to uniformly distribute the error while keeping the same grid connectivity the development is made for two and three dimensional grids although results are presented only for two dimensional flows he adaptation of the grid to the flow characteristics is widely recognized as a method to improve the solution accuracy and the overall computing efficiency of numerical schemes the moti vation is that since the grid is normally generated before knowing the flow behavior it is possible that the nodes distribution does not correspond to the solution requirements the adaptivity process is made up of two key elements an error estimator and an adaptation procedure the simplest error estimator used for finite volume schemes 1 2 is based on the physical behavior of the flowfield more specifically on the gradient of the density or the mach number the adaptation consists in refining and coarsening the mesh in regions of higher or lower gradients respectively the projection method developed by zienkiewicz and zhu3 4 is based on the observation that for finite elements discretization the solution is continuous whereas the derivatives are discontinuous at the interface of two elements those derivatives are projected in a space of continuous functions and the norm of the difference be tween this projection and the derivatives is used as a measure of the computational error for some problems the fluxes instead of derivatives are physically continuous in all of the domain and con sequently more appropriate to be projected in a space of continuous functions 5 babuska and rheinboldt6 propose an error estimator based on the solution of a local variational problem where the unknowns are the approximation errors the advantage consists in the reduction of the size of the linear system to be solved in compressible flows with shock waves or contact discontinu ities the variables can no longer be considered continuous the computed errors based on the solution gradient increase unbound edly with the adaptation of the discontinuity this acts as permanent source for grid refinement and could produce wrong results 7 paillere et al 8 use a wave model to evaluate the error for com pressible flows the model combines the effects of the divergence and rotational of the velocity to reduce the influence of disconti nuities the error is multiplied by a power of a characteristic length of the grid cell the adaptation procedure also considers a minimal local grid size

a general explicit or semi explicit algorithm for compressible and incompressible flows this note presents a rational basis for a unified finite element algorithm capable of dealing with a wide range of fluid flow in both steady and transient cases it is hoped that empiricism inherent in many previous approaches can be avoided and a sound basis provided the algorithm permits the use of equal interpolation for all variables by avoiding the need for the babuska brezzi constraints in regions where the flow is nearly incompressible the success of the algorithm which here is written for the non conservative equation form is demonstrated on several examples ranging from nearly incompressible through transonic regions to supersonic flows up to mild shocks such as those occurring in the examples presented in this paper no artificial viscosity is added at any stage the algorithm extends some concepts introduced in an earlier paper

convergence conditions for splitting iteration methods for non hermitian linear systems abstract necessary and sufficient convergence conditions are studied for splitting iteration methods for non hermitian system of linear equations when the coefficient matrix is nonsingular when this theory is specialized to the generalized saddle point problem we obtain convergence theorem for a class of modified accelerated overrelaxation iteration methods which include the uzawa and the inexact uzawa methods as special cases moreover we apply this theory to the two stage iteration methods for non hermitian positive definite linear systems and obtain sufficient conditions for guaranteeing the convergence of these methods

the performance of a matched subspace detector that uses subspaces estimated from finite noisy training data we analyze the performance of a matched subspace detector msd where the test signal vector is assumed to reside in an unknown low rank k subspace that must be estimated from finite noisy signal bearing training data under both a stochastic and deterministic model for the test vector subspace estimation errors due to limited training data degrade the performance of the standard plug in detector relative to that of an oracle detector to avoid some of this performance loss we utilize and extend recent results from random matrix theory rmt that precisely quantify the quality of the subspace estimate as a function of the eigen snr dimensionality of the system and the number of training samples we exploit this knowledge of the subspace estimation accuracy to derive from first principles a new rmt detector and to characterize the associated roc performance curves of the rmt and plug in detectors using more than the a critical number of informative components which depends on the training sample size and eigen snr parameters of training data will result in a performance loss that our analysis quantifies in the large system limit we validate our asymptotic predictions with simulations on moderately sized systems

an adaptive finite element procedure for compressible high speed flows abstract a two step explicit finite element procedure for obtaining time accurate solutions to the compressible euler equations is described the method is coupled with an adaptive mesh refinement process which enables steady state solutions of improved quality to be obtained

locally optimum detection of signals in a generalized observation model the random signal case locally optimum detectors for weak random signals are derived for a generalized observation model incorporating signal dependent and multiplicative noise it is shown that the locally optimum random signal detectors in the generalized observation model are interesting generalizations of those that would be obtained in the purely additive noisy signal model examples of explicit results for the locally optimum detector test statistics are given for some typical cases both asymptotic and finite sample size performances of the locally optimum detectors are considered and compared with those of other standard detector structures

an implicit explicit scheme for compressible viscous high speed flows abstract an implicit explicit finite element based algorithm for the solution of 2d steady compressible viscous high speed flows is presented a structured grid is employed in the vicinity of solid walls and the implicit form of the algorithm is implemented in this region the explicit form of the algorithm is used in the remainder of the flow domain which is discretised with an unstructured assembly of triangles the quality of the computed solution is improved by the application of solution adaptive remeshing the computed results for two examples are compared with experimental observations to illustrate the performance of the proposed scheme

an approach to refining three dimensional tetrahedral meshes based on delaunay transformations a technique for refining three dimensional tetrahedral meshes is proposed in this paper the proposed technique is capable of treating arbitrary unstructured tetrahedral meshes convex or non convex with multiple regions resulting in high quality constrained delaunay triangulations the tetrahedra generated are of high quality nearly equilateral sliver tetrahedra which present a real problem to many algorithms are not produced with the new method the key to the generation of high quality tetrahedra is the iterative application of a set of topological transformations based on the voronoi delaunay theory and a reposition of nodes technique the computational requirements of the proposed technique are in linear relationship with the number of nodes and tetrahedra making it ideal for direct employment in a fully automatic finite element analysis system for 3 d adaptive mesh refinement application to some test problems is presented to show the effectiveness and applicability of the new method

a universal formulation of two equation models for adaptive computation of turbulent flows abstract this paper describes the application of a recently developed universal adaptive finite element algorithm to the simulation of several turbulent flows the objective of the present work is to show how the controlled accuracy of adaptive methods provides the means to perform careful quantitative comparisons of two equation models the formulation uses the logarithmic form of turbulence variables which naturally leads to a simple algorithm applicable to all two equation turbulence models the new methodology is free of ad hoc stability enhancement measures such as clipping and limiters which may often differ from one model to the other such techniques limit the predictive capability of a turbulence model and cloud the issues of a comparison study the present procedure results in one adaptive solver applicable to all two equation models the approach is demonstrated by comparing three popular turbulence models on a few non trivial compressible and incompressible flows we have chosen the following models the standard k model the k model of speziale and the k model of wilcox results show that accurate solutions can be obtained for all models and that systematic comparison of turbulence models can be made

a direct proof and a generalization for a kantorovich type inequality a direct proof for a kantorovich type inequality due to bauer and householder is presented a generalization of the inequality is also established by the theory of compound matrices

adaptive finite element method for turbulent flow near a propeller we present an adaptive finite element method based on remeshing to solve incompressible turbulent free shear flow near a propeller solutions are obtained in primitive variables using a highly accurate finite element approximation on unstructured grids turbulence is modeled by a mixing length formulation two general purpose error estimators which take into account swirl and the variation or the eddy viscosity are presented and applied to the turbulent wake or a propeller the proposed adaptive scheme is robust reliable and cost effective

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

matched subspace detection with hypothesis dependent noise power we consider the problem of detecting a subspace signal in white gaussian noise when the noise power may be different under the null hypothesis where it is assumed to be known and the alternative hypothesis this situation occurs when the presence of the signal of interest soi triggers an increase in the noise power accordingly it may be relevant in the case of a mismatch between the actual soi subspace and its presumed value resulting in a modelling error we derive the generalized likelihood ratio test glrt for the problem at hand and contrast it with the glrt which assumes known and equal noise power under the two hypotheses a performance analysis is carried out and the distributions of the two test statistics are derived from this analysis we discuss the differences between the two detectors and provide explanations for the improved performance of the new detector numerical simulations attest to the validity of the analysis

blockwise adaptivity for time dependent problems based on coarse scale adjoint solutions we describe and test an adaptive algorithm for evolution problems that employs a sequence of blocks consisting of fixed though nonuniform space meshes this approach offers the advantages of adaptive mesh refinement but with reduced overhead costs associated with load balancing remeshing matrix reassembly and the solution of adjoint problems used to estimate discretization error and the effects of mesh changes a major issue with a block adaptive approach is determining block discretizations from coarse scale solution information that achieve the desired accuracy we describe several strategies for achieving this goal using adjoint based a posteriori error estimates and we demonstrate the behavior of the proposed algorithms as well as several technical issues in a set of examples

comparisons between multiplicative and additive schwarz iterations in domain decomposition methods we consider the multiplicative and additive schwarz methods for solving linear systems of equations and we compare their asymptotic rate of convergence moreover we compare the multiplicative schwarz method with the weighted restricted additive schwarz method we prove that the multiplicative schwarz method is the fastest method among these three our comparisons can be done in the case of exact and inexact subspaces solves in addition we analyse two ways of adding a coarse grid correction multiplicatively or additively

analysis of the zienkiewicz zhu a posteriori error estimator in the finite element method an a posteriori error estimator for finite element analysis proposed by zienkiewicz and zhu is analysed and shown to be effective and convergent in addition we analyse wider classes of estimators of which the zienkiewicz zhu estimator is a special case it is shown that some of these estimators will be asymptotically exact numerical evidence is presented supporting the analysis

inexact preconditioned conjugate gradient method with inner outer iteration an important variation of preconditioned conjugate gradient algorithms is inexact preconditioner implemented with inner outer iterations g h golub and m l overton numerical analysis lecture notes in math 912 springer berlin new york 1982 where the preconditioner is solved by an inner iteration to a prescribed precision in this paper we formulate an inexact preconditioned conjugate gradient algorithm for a symmetric positive definite system and analyze its convergence property we establish a linear convergence result using a local relation of residual norms we also analyze the algorithm using a global equation and show that the algorithm may have the superlinear convergence property when the inner iteration is solved to high accuracy the analysis is in agreement with observed numerical behavior of the algorithm in particular it suggests a heuristic choice of the stopping threshold for the inner iteration numerical examples are given to show the effectiveness of this choice and to compare the convergence bound

weighted and flexible versions of block cmrh method for solving nonsymmetric linear systems with multiple right hand sides abstract block krylov subspace methods are the most popular algorithms for solving large nonsymmetric linear systems with multiple right hand sides one of them is the block cmrh method this method generates a non orthogonal basis of the krylov subspace through the block hessenberg process to accelerate the convergence of the block cmrh method we will introduce two new methods first we present the block cmrh method with weighting strategy in this method the block cmrh method uses a different product at each restart second we introduce a flexible version of the block cmrh algorithm that allows varying preconditioning at every step of the algorithm numerical experiments illustrate the benefits of the presented methods

a finite element formulation of compressible flows using various sets of independent variables abstract this paper presents a finite element method for the simulation of compressible flows the navier stokes and euler equations are solved in the conservation form using various sets of independent variables a variational formulation is developed based upon a variant of the petrov galerkin method and uses a shock capturing operator an adaptive algorithm based on a particular residual norm is proposed several numerical examples are presented to demonstrate the performances of each set of variables in solving compressible high speed flows

flexible global generalized hessenberg methods for linear systems with multiple right hand sides a variant of the global generalized hessenberg method is presented which allows varying preconditioning at each restart theoretical results that relate the residual norm of this new method with its original version are developed as two special variants the flexible global gmres method and the flexible global cmrh method are investigated both theoretically and experimentally numerical examples are conducted to illustrate the performance of these two flexible global methods in comparison with both the original global methods and weighted global methods

preconditioning techniques for large linear systems a survey this article surveys preconditioning techniques for the iterative solution of large linear systems with a focus on algebraic methods suitable for general sparse matrices covered topics include progress in incomplete factorization methods sparse approximate inverses reorderings parallelization issues and block and multilevel extensions some of the challenges ahead are also discussed an extensive bibliography completes the paper

finite element method for computing turbulent propeller flow a numerical procedure based on the primitive variable navier stokes equations is applied to the simulation of the three dimensional axisymmetric flow near a propeller in a uniform flow the time averaged navier stokes equations are solved using both a mixed and a penalty function finite element method a new model is developed to compute axisymmetric viscous throughflow past propellers this is achieved by forcing the flow to be tangent to the mean stream surface between the blades this condition is enforced by introducing a lagrange multiplier that can be interpreted as the force applied by the blades on the fluid turbulence is modelled by a simple mixing length equation detailed comparison with wind tunnel measurements shows good prediction of velocity and pressure the present approach represents a first step toward the development of a viscous quasi three dimensional capability

robust detection of signals a large deviations approach robust detection of a signal is considered for the case of independent and identically distributed observations following an asymptotic but nonlocal approach the exponential rates of decrease of the error probabilities are considered as measure of performance under this measure a robust detection structure for the symmetric density case is derived this detection structure is a generalization of an existing result for the local case and is reduced to it when the signal magnitude tends to zero

analysis of the finite precision bi conjugate gradient algorithm for nonsymmetric linear systems in this paper we analyze the bi conjugate gradient algorithm in finite precision arithmetic and suggest reasons for its often observed robustness by using a tridiagonal structure which is preserved by the finite precision bi conjugate gradient iteration we are able to bound its residual norm by a minimum polynomial of a perturbed matrix i e the residual norm of the exact gmres applied to a perturbed matrix multiplied by an amplification factor this shows that occurrence of near breakdowns or loss of biorthogonality does not necessarily deter convergence of the residuals provided that the amplification factor remains bounded numerical examples are given to gain insights into these bounds

surface mesh sizing control a method is presented for controlling element sizes on the interior of areas during surface meshing a delaunay background mesh is defined over which natural neighbour interpolation a neighbourhood based interpolation scheme is used to generate a sizing function the sizing function may be used to interpolate element sizes anisotropic stretching parameters or other surface characteristics required during meshing a brief description of natural neighbour interpolation is included and the sizing results obtained from this interpolation method are compared to those obtained using linear interpolation three specific applications are presented that utilize the sizing function namely boundary layer meshing surface curvature refinement and anisotropic mesh generation for these applications criteria used for augmenting the sizing function based on insertion of additional interior vertices into the background mesh are discussed copyright 2000 john wiley sons ltd

scaling to the stars a linearly scaling elliptic solver for p multigrid abstract high order methods gain increased attention in computational fluid dynamics however due to the time step restrictions arising from the semi implicit time stepping for the incompressible case the potential advantage of these methods depends critically on efficient elliptic solvers due to the operation counts of operators scaling with the polynomial degree p times the number of degrees of freedom n dof the runtime of the best available multigrid solvers scales with o p n dof this scaling with p significantly lowers the applicability of high order methods to high orders while the operators for residual evaluation can be linearized when using static condensation schwarz type smoothers require their inverses on fixed subdomains no explicit inverse is known in the condensed case and matrix matrix multiplications scale with p n dof this paper derives a matrix free explicit inverse for the static condensed operator in a cuboidal cartesian subdomain it scales with p 3 per element i e n dof globally and allows for a linearly scaling additive schwarz smoother yielding a p multigrid cycle with an operation count of o n dof the resulting solver uses fewer than four iterations for all polynomial degrees to reduce the residual by ten orders and has a runtime scaling linearly with n dof for polynomial degrees at least up to 48 furthermore the runtime is less than one microsecond per unknown over wide parameter ranges when using one core of a cpu leading to time stepping for the incompressible navier stokes equations using as much time for explicitly treated convection terms as for the elliptic solvers

flexible bicg and flexible bi cgstab for nonsymmetric linear systems flexible versions of the bicg and bi cgstab algorithms are presented which allow for the use of a different preconditioner at each step of the algorithm in particular inexact solutions of the preconditioned equations are allowed as well as the use of some inner iterative method as a preconditioner flexible bicg is investigated theoretically and a theorem is presented comparing the residual norms of flexible bicg and flexible qmr that generalizes a well known relation between the residual norms of bicg and qmr numerical experiments are conducted for flexible bi cgstab for several matrices including some indefinite and highly nonsymmetric matrices these experiments illustrate the applicability of the flexible method

an adaptive remeshing strategy for flows with moving boundaries and fluid structure interaction the primary objective of this work is to extend the capability of the arbitrary lagrangian eulerian ale based strategy for solving fluid structure interaction problems this is driven by the fact that the ale mesh movement techniques will not be able to treat problems in which fluid structure interface experiences large motion in addition for certain problems the need arises to capture accurately flow features such as a region with high gradients of the solution variables this can be achieved by incorporating an adaptive remeshing procedure into the solution strategy as in our previous works comput methods appl mech eng 2006 195 1633 1666 comput methods appl mech eng 2006 195 5754 5779 here the fluid flow is governed by the incompressible navier stokes equations and modelled by using stabilized low order velocity pressure finite elements the motion of the fluid domain is accounted for by an arbitrary lagrangian eulerian ale strategy the flexible structure is represented by means of appropriate standard finite element formulations while the motion of the rigid body is described by rigid body dynamics for temporal discretization of both fluid and solid bodies the discrete implicit generalized method is employed the resulting strongly coupled set of non linear equations is then solved by means of a novel partitioned solution procedure which is based on the newton raphson methodology and incorporates full linearization of the overall incremental problem within the adaptive solution strategy the quality of fluid mesh and the solution quality indicator are evaluated regularly and compared against the appropriate remeshing criteria to decide whether a remeshing step is required the adaptive remeshing procedure follows closely the standard computational procedure in which the adaptive remeshing process produces a mesh that can capture salient features of the flow field for the problems under consideration in this work the motion of the fluid boundary very often results in boundaries with very high curvatures and a fluid domain that contain areas with small cross sections to be able to generate meshes that give result with acceptable accuracy these local geometrical features need to be included in determining the element density distribution the numerical examples demonstrate the robustness and efficiency of the methodology copyright 2007 john wiley sons ltd

a taylor galerkin method for convective transport problems a method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions to produce accurate temporal differencing the method employs forward time taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation this yields a generalized time discretized equation which is successively discretized in space by means of the standard bubnov galerkin finite element method the technique is illustrated first in one space dimension with linear elements and euler leap frog and crank nicolson time stepping several interesting relations with standard galerkin and recently developed petrov galerkin methods emerge and the new taylor galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping the method is successively extended to deal with variable coefficient problems and multi dimensional situations

an algebraic convergence theory for restricted additive schwarz methods using weighted max norms convergence results for the restrictive additive schwarz ras method of cai and sarkis siam j sci comput 21 1999 pp 792 797 for the solution of linear systems of the form ax b are provided using an algebraic view of additive schwarz methods and the theory of multisplittings the linear systems studied are usually discretizations of partial differential equations in two or three dimensions it is shown that in the case of a symmetric positive definite the projections defined by the methods are not orthogonal with respect to the inner product defined by a and therefore the standard analysis cannot be used here the convergence results presented are for the class of m matrices and more generally for h matrices using weighted max norms comparison between different versions of the ras method are given in terms of these norms a comparison theorem with respect to the classical additive schwarz method makes it possible to indirectly get quantitative results on rates of convergence which otherwise cannot be obtained by the theory several ras variants are considered including new ones and two level schemes

adaptive remeshing for three dimensional compressible flow computations an adaptive mesh procedure for computing steady state solutions of the compressible euler equations in three dimensions is presented the method is an extension of previous work in two dimensions the approach requires the coupling of a surface triangulator an automatic tetrahedral mesh generator a finite element flow solver and an error estimation procedure an example involving flow at high mach number is included to demonstrate the numerical performance of the proposed approach the example shows that the use of this form of adaptivity in three dimensions offers the potential of even greater computational savings than those attained in the corresponding two dimensional implementation

adaptative remeshing for viscous incompressible flows this paper presents an adaptive finite element procedure for solving viscous incompressible flows the methodology is based on adaptive remeshing for steady state problems the navier stokes equations for an incompressible fluid are solved in primitive variables by an uzawa algorithm using a highly accurate element the efficiency and convergence rate of the adaptive strategy are evaluated by solving problems with known analytical solutions finally the methodology is applied to the flow over a backward facing step and predictions are compared with experimental measurements the use of the proposed adaptive procedure is shown to lead to improved accuracy of the finite element predictions nomenclature c a constant e error in the solution h element size dissipation energy n number of elements in the mesh p pressure 5 step and fence height u velocity vector u v velocity components x y coordinates v gradient operator 6 element size predicted by adaptation module e strain rate tensor 1a v u v ut a stress tensor 2 e similarity variable in a boundary layer t relative error on a mesh h absolute viscosity of the fluid v kinematic viscosity of the fluid

flexible inner outer krylov subspace methods flexible krylov methods refers to a class of methods which accept preconditioning that can change from one step to the next given a krylov subspace method such as cg gmres qmr etc for the solution of a linear system ax b instead of having a fixed preconditioner m and the right preconditioned equation am 1 y b mx y one may have a different matrix say mk at each step in this paper the case where the preconditioner itself is a krylov subspace method is studied there are several papers in the literature where such a situation is presented and numerical examples given a general theory is provided encompassing many of these cases including truncated methods the overall space where the solution is approximated is no longer a krylov subspace but a subspace of a larger krylov space we show how this subspace keeps growing as the outer iteration progresses thus providing a convergence theory for these inner outer methods numerical tests illustrate some important implementation aspects that make the discussed inner outer methods very appealing in practical circumstances

centroidal voronoi tessellation based finite element superconvergence in this article a finding on finite element superconvergence is reported the laplacian operator with dirichlet boundary condition is considered the linear finite element solutions have an o h2 0 5 superconvergence in l2 norm at nodes on an almost equilateral triangular mesh generated based on centroidal voronoi tessellation for an arbitrary 2d bounded domain extensive numerical examples are presented to demonstrate the superconvergence property copyright 2008 john wiley sons ltd

adaptivity techniques for compressible inviscid flows abstract to enhance the resolution of numerically simulated flowfields grid adaptivity is vitally important further to afford complete flexibility in the spatial discretisation of the flow domain both structured unstructured and combinations of grid types are likely to be required hence the development of grid adaptivity techniques for general grids is important this paper discusses adaptivity achieved through point enrichment point derefinement and point movement applied on general grids a flexible data structure is described together with suitable strategies for adaptively refining a computational grid applications are presented of adaptive grid refinement for two dimensional compressible flow simulation

3d delaunay mesh generation coupled with an advancing front approach abstract this paper describes a fully automatic mesh generation method suitable for domains of any shape in r 3 initially a so called boundary mesh is generated wherein internal points are created using advancing front point placement and inserted using a delaunay method the algorithm combines the advantages of efficiency and nice mathematical properties of a delaunay approach with advancing front high quality point placement strategy several three dimensional examples are presented to demonstrate the overall efficiency and the relevance of the combined procedure the present method can be extended to isotropic or anisotropic adaptive mesh generation

enhanced error estimator for adaptive finite element analysis of 3d incompressible flow abstract this paper describes an enhanced error estimator for adaptive finite element analysis of three dimensional incompressible viscous flow the estimator uses a modified form of the recovery functional employed in the well known l 2 local patch recovery technique lpr originally proposed by zienkiewicz and zhu the modified recovery functional is obtained by penalizing the conventional recovery functional using the residual of the continuity equation for the constraint the enhanced estimator which we denote as lprc is tested on unstructured second order tetrahedral meshes using an analytical solution to the three dimensional incompressible navier stokes equations we report significant improvements in the effectiveness of the resulting error estimate both for interior and boundary nodes at virtually no additional computational cost the lprc estimator is particularly useful for flows in which stresses at the boundary of the computational domain play an important role such as in blood flow modeling although in this paper the lprc error estimator is tested exclusively on the 10 noded tetrahedral taylor hood element we expect that when applied to incompressible flows the lprc estimator will perform more effectively than the lpr estimator when used with other types of elements as well

filling space with tetrahedra in the context of 3d finite element meshes various options for filling an indefinite space such as would be approached within a fine mesh with tetrahedra are considered this problem is not trivial as it is in 2 d since unlike equilateral triangles regular tetrahedra cannot be fitted together to fill space various groupings or assemblies which can be repeated indefinitely to fill space are considered by altering the shape of the tetrahedra in one of these to minimize a suitable function a unique shape of tetrahedron is obtained which optimizes the conditioning the mesh thus produced is shown to be better conditioned than alternatives based on assemblies of different shaped tetrahedra a number of conditioning measures are used to confirm this finally actual meshes which fit boundaries are briefly considered copyright 1999 john wiley sons ltd

matched subspace detectors we formulate a general class of problems for detecting subspace signals in subspace interference and broadband noise we derive the generalized likelihood ratio glr for each problem in the class we then establish the invariances for the glr and argue that these are the natural invariances for the problem in each case the glr is a maximal invariant statistic and the distribution of the maximal invariant statistic is monotone this means that the glr test glrt is the uniformly most powerful invariant detector we illustrate the utility of this finding by solving a number of problems for detecting subspace signals in subspace interference and broadband noise in each case we give the distribution for the detector and compute performance curves

electromagnetic induction in a generalized 3d anisotropic earth part 2 the lin preconditioner a practical limitation in the use of generalized 3d forward modeling algorithms for inversion of electromagnetic data is the high computational cost of solving large ill conditioned systems of linear equations arising from the discretization of the governing maxwell equations to address this problem a new class of preconditioners has recently been proposed which is based on a helmholtz decomposition of the electric field in the low induction number lin regime this paper further develops that idea and introduces a lin preconditioner which can be applied to problems characterized by a fully generalized anisotropic medium included are sample calculations demonstrating a reduction by two orders of magnitude in the number of quasi minimal residual iterates and a speedup by a factor of approximately four in the solution time for one forward calculation also included are results previously unobtainable by standard jacobi preconditioning for simulating multicomponent induction sonde response in a horizo

the effect of non optimal bases on the convergence of krylov subspace methods there are many examples where non orthogonality of a basis for krylov subspace methods arises naturally these methods usually require less storage or computational effort per iteration than methods using an orthonormal basis optimal methods but the convergence may be delayed truncated krylov subspace methods and other examples of non optimal methods have been shown to converge in many situations often with small delay but not in others we explore the question of what is the effect of having a non optimal basis we prove certain identities for the relative residual gap i e the relative difference between the residuals of the optimal and non optimal methods these identities and related bounds provide insight into when the delay is small and convergence is achieved further understanding is gained by using a general theory of superlinear convergence recently developed our analysis confirms the observed fact that in exact arithmetic the orthogonality of the basis is not important only the need to maintain linear independence is numerical examples illustrate our theoretical results

compressible flowfield solutions with unstructured grids generated by delaunay triangulation a method is described that constructs three dimensional unstructured tetrahedral meshes using the delaunay triangulation criterion the approach includes an automatic point creation technique and ensures that given an initial surface triangulation which bounds a domain a valid boundary conforming assembly of tetrahedra is produced the efficiency of the proposed procedure reduces the computer time for the generation of realistic unstructured tetrahedral grids to the order of minutes on workstations of modest computational capabilities the grids generated are used with two finite element algorithms to simulate inviscid transonic compressible flows flow solutions for aerospace configurations are presented and computed results compared with experimental data

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

adaptive finite element method for thermal flow problems this paper presents an adaptive finite element method based on remeshing to solve incompressible viscous flow problems including heat transfer effects by forced or free convection conjugate heat transfer problems are also considered solutions are obtained in primitive variables by an uzawa algorithm using a highly accurate finite element approximation on unstructured grids two error estimators are presented and compared on problems with known analytical solutions the methodology is then applied to a problem of practical interest and predictions are compared with experimental measurements and show very good agreement

finite element navier stokes solver for unstructured grids a three dimensional finite element navier stokes solver has been developed for calculating transonic viscous flow on unstructured grids about complex aerodynamic configurations the solver employs a second orderaccurate space discretization of the navier stokes equations obtained from a galerkin weighted residual approximation time discretization is obtained using either an explicit two step lax wendroff scheme or an explicit multistep runge kutta scheme boundary conditions are implemented using a procedure based on the method of characteristi cs the overall solution procedure has been initially validated by calculating two and three dimensional inviscid and viscous transonic flows

finite element euler computations in three dimensions an explicit finite element solution procedure for the three dimensional euler equations is presented the solution domain is automatically meshed using a tetrahedral mesh generator which is an extension of our previous two dimensional work several examples are included to illustrate the performance of the generator and solver an adaptive mesh regeneration procedure is used for the first time in three dimensions

generation of oriented three dimensional delaunay grids suitable for the control volume integration method a fully automatic algorithm for three dimensional mesh generation is presented the algorithm preserves the robustness and time efficiency of the finite octree technique replacing octrees by more general 2 4 8 trees it is capable of generating oriented meshes in a post processing step meshes are transformed in order to satisfy the delaunay criterion and so that non overlapping closed control volumes can be defined for each mesh point through edge bisectors the method is shown to be appropriate for modelling semiconductor devices where the control volume scheme is the method of choice due to the peculiarities of the partial differential equations involved and where locally refined and oriented meshes are essential to describe the relevant internal physical quantities adequately while keeping the number of mesh points practical

fast adaptive finite element scheme for viscous incompressible flows this paper presents an adaptive finite element procedure for solving viscous incompressible flows the methodology is based on adaptive remeshing for the solution of the steady state navier stokes equations for an incompressible fluid solutions are obtained in primitive variables by an uzawa algorithm using a highly accurate element two error estimators are presented and compared for a problem with a known analytical solution the methodology is then applied to a problem of practical interest and predictions are compared with experimental measurements the proposed adaptive scheme is shown to lead to improved accuracy of the finite element predictions c e e h l n p q q 5 u u v x y 6 v a v v nomenclature constant velocity error error in the solution element size dissipation energy plate length number of elements in the mesh pressure pressure error test function for pressure error step and fence height velocity vector velocity components test function for velocity error coordinates element size predicted by adaptation module strain rate tension vi vu vf 7 relative error on a mesh similarity variable in a boundary layer absolute viscosity of the fluid kinematic viscosity of the fluid deviatoric stress sensor 2pe gradient operator

an automatic adaptive meshing technique for delaunay triangulations abstract a new algorithm is described for adaptivity of delaunay triangulations it distinguishes between regions of mesh according to whether they are to be refined unaltered or coarsened the method automatically identifies nodes of the mesh which are candidates for deletion for a region to be coarsened a node deletion process is proposed and it is proved that the resulting triangulation is delaunay after coarsening the mesh retains a high quality for two reasons the first is because a set of nodes have been used to obtain the coarse mesh which are equi distant apart in some sense defined by the original mesh the second is because the triangulation is delaunay the mesh refinement procedure sub divides elements into a number of similar elements in the regions to be refined two dimensional examples demonstrate the quality of the mesh after coarsening refinement

adaptive remeshing for the k epsilon model of turbulence an adaptive nite element method for solving incompressible turbulentows using the k model of turbulence is presented solutions are obtained in primitive variables using a highly accurate quadratic nite element on unstructured grids turbulence is modeled using the k model of turbulence two error estimators are presented that take into account in a rigorous way the relative importance of the errors in velocity pressure turbulence variables and eddy viscosity the ef ciency and convergence rate of the methodology are evaluated by solving problemswith known analytical solutions themethod isthen applied to turbulent free shearowsand predictions are compared to measurements nomenclature cl c1 c2 k model constants e error f body force h element size k element in the mesh k turbulent kinetic energy n outward unit vector p u production of turbulence p pressure u velocity vector

fast iterative solution of elliptic control problems in wavelet discretization we investigate wavelet methods for the efficient numerical solution of a class of control problems constrained by a linear elliptic boundary value problem where the cost functional may contain fractional sobolev norms of the control and the state starting point is the formulation of the infinite dimensional control problem in terms of boundary adapted biorthogonal spline wavelets involving only l2 norms of wavelet expansion coefficients where different norms are realized by a diagonal scaling together with a riesz map and constraints in form of an l2 isomorphism the coupled system of equations resulting from optimization is solved by an inexact conjugate gradient cg method for the control which involves the approximate inversion of the primal and the adjoint operator using again cg iterations starting from a coarse discretization level we use nested iteration to solve the coupled system on successively finer uniform discretizations up to discretization error accuracy on each level the resulting inexact cg scheme is a fast solver it is of asymptotic optimal complexity in the sense that the overall computational effort to compute the solution up to discretization error on the finest grid is proportional to the number of unknowns on that grid a consequence of grid independent condition numbers of the linear operators in wavelet coordinates in the numerical examples we study the choice of different norms and the regularization parameter in the cost functional and their effect on the solution moreover for different situations the performance of the fully iterative inexact cg scheme is investigated confirming the theoretical results

robust multigrid for high order discontinuous galerkin methods we present a polynomial multigrid method for nodal interior penalty and local discontinuous galerkin formulations of the poisson equation on cartesian grids for smoothing we propose two classes of overlapping schwarz methods the first class comprises element centered and the second face centered methods within both classes we identify methods that achieve superior convergence rates prove robust with respect to the mesh spacing and the polynomial order at least up to p 32 consequent structure exploitation yields a computational complexity of o pn where n is the number of unknowns further we demonstrate the suitability of the face centered method for element aspect ratios up to 32 p multigrid for discontinuous formulations of poisson problems on cartesian grids robust with respect to the mesh size and polynomial order at least up to p 32 convergence rates between 0 02 and 0 003 improving with increasing p computational complexity of pn for n unknowns linear complexity in runtime excellent performance up to aspect ratios of 1 16

ccd noise removal in digital images in this work we propose a denoising scheme to restore images degraded by ccd noise the ccd noise model measured in the space of incident light values light space is a combination of signal independent and signal dependent noise terms this model becomes more complex in image brightness space normal camera output due to the nonlinearity of the camera response function that transforms incoming data from light space to image space we develop two adaptive restoration techniques both accounting for this nonlinearity one operates in light space where the relationship between the incident light and light space values is linear while the second method uses the transformed noise model to operate in image space both techniques apply multiple adaptive filters and merge their outputs to give the final restored image experimental results suggest that light space denoising is more efficient since it enables the design of a simpler filter implementation results are given for real images with synthetic noise added and for images with real noise

incompressibility without tears how to avoid restrictions of mixed formulation the severe restrictions of the babuska brezzi stability criteria permit only a limited number of interpolations for velocities displacements and pressure to be used for incompressible behaviour these restrictions preclude the use of many useful elements we show in this paper how such difficulties can be side stepped by seeking the steady state solution through the use of various time marching schemes this permits a simple iterative approach to incompressible or nearly incompressible problems of fluid mechanics or solid mechanics and provides a stimulus for the use of such procedures in metal forming flow etc

a stabilized finite point method for analysis of fluid mechanics problems in this paper a meshless procedure termed the finite point method for solving convection diffusion and fluid flow type problems is presented the method is based on the use of a weighted least square interpolation procedure together with point collocation for evaluating the approximation integrals special emphasis is given to the stabilization of the convective terms and the neumann boundary condition which has been found to be essential to obtain accurate results some examples of application to diffusive and convective transport and compressible flow problems using quadratic fp interpolations are presented

a robust matched detector we address the matched detector problem in the case the signal to be detected is imperfectly known while in the standard detector the signal is known to lie along a particular direction we consider the case where this direction is known up to additive white gaussian noise this somehow amounts to assuming that the signal lies in a cone the aperture of which depends upon the level of uncertainty we build the associated generalized likelihood ratio glr analyze its statistical properties indicate how to set the threshold to achieve a given false alarm rate and how to predict the associated probability of detection the so obtained detector reduces to the conventional one when the uncertainty vanishes and we analyze its behavior when the level of uncertainty which has to be known a priori is mis evaluated it appears that the sensitivity of the detector is quite low with respect to this kind of errors more importantly several realistic examples are presented that indicate that the proposed detector remains quite efficient when the true signals are far from being of the assumed model and whatever the model of the uncertainty actually is it is this robustness that makes the detector valuable

adaptive mesh generation for fluid mechanics problems in this study we give an in depth investigation of the adaptive procedures for compressible and incompressible flow problems many tests have been carried out with different error indicators for different problems these refinement procedures show that the interpolation error indicators are adequate to predict an accurate solution comparison between the gradient and curvature based error indicators show that the former yields better performance in most situations however we found that the latter indicators predict better motion in the recirculatory and unstable regions than the gradient based method many test cases have been presented for both compressible and incompressible flow problems in the later part of the paper we suggest a simple way of combining the curvature gradient indicators of different key variables and present an appropriate problem where it is applicable a wide coverage of relevant literature has also been presented in this paper copyright 2000 john wiley sons ltd

adaptive remeshing for compressible flow computations an adaptive mesh procedure for improving the quality of steady state solutions of the euler equations in two dimensions is described the procedure is implemented in conjunction with a finite element solution algorithm using linear triangular elements and an explicit time stepping scheme the mesh adaptation is accomplished by regeneration using information provided by the computed solution on the current mesh the meshes produced are characterised by the appearance of stretched elements in the vicinity of one dimensional flow features and can exhibit a large variation in element size this allows solutions of enhanced quality to be produced in a computationally efficient manner