multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

a characteristic finite element algorithm for time dependent 3 d advection dominated transport using unstructured grids abstract an algorithm based on operator splitting has been successfully implemented for solving unsteady advection dominated transport problems in 3 d specifically the general operator integration factor splitting method of maday et al is applied to the unsteady advection diffusion equation with source sink terms the algorithm incorporates a 3 d characteristic galerkin scheme to treat advection and a standard galerkin treatment of the diffusion and source sink terms up to third order operator splitting was implemented and validated against several analytical solutions the algorithm showed the expected error behaviour and good performance in modeling advection dominated transport problems the practical utility and effectiveness of the proposed numerical scheme was further demonstrated by solving the graetz nusselt problem i e high peclet number mass heat transport in a fully developed pipe flow

finite element computation of unsteady viscous compressible flows in this article we present our results for computation of unsteady viscous transonic flows past cylinders and airfoils stabilized finite element methods are employed to solve the compressible navier stokes equations in their conservation law form the nonlinear equations resulting from the finite element discretizations are solved using gmres technique to test the accuracy of the formulation mach 2 flow past a circular cylinder is computed with a mesh that is fine enough to resolve the shock structure for reynolds number 50 the computational results agree quite well with the analytical and theoretical results the methodology is applied to compute unsteady transonic flows past cylinders and airfoils several cases involving flows past a naca0012 airfoil are computed and compared with numerical results from other researchers interesting flow patterns are observed for all the cases it is observed that flow past an airfoil in a channel of width 8 5 chord lengths at mach 0 85 and re 10 000 is unsteady when it is placed at zero incidence to the flow while it reaches a steady state when the angle of attack of the airfoil is 10

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

the characteristic based split cbs scheme a unified approach to fluid dynamics this paper presents a comprehensive overview of the characteristic based methods and characteristic based split cbs scheme the practical difficulties of employing the original characteristic schemes are discussed the important features of the cbs scheme are brought out by studying several problems of compressible and incompressible flows all special consideration necessary for solving these problems are thoroughly discussed the cbs scheme is presented in such a way that any interested researcher should be able to develop a code using the information provided several invicid and viscous flow examples are also provided to demonstrate the unified cbs approach for sample two dimensional codes input files and instructions the readers are referred to www nithiarasu co uk copyright 2006 john wiley sons ltd

fast algorithm for computing discrete cosine transform an efficient method for computing the discrete cosine transform dct is proposed based on direct decomposition of the dct the recursive properties of the dct for an even length input sequence is derived which is a generalization of the radix 2 dct algorithm based on the recursive property a new dct algorithm for an even length sequence is obtained the proposed algorithm is very structural and requires fewer computations when compared with others the regular structure of the proposed algorithm is suitable for fast parallel algorithm and vlsi implementation

a fast recursive algorithm for computing the discrete cosine transform the discrete cosine transform dct is widely applied in various fields including image data compression because it operates like the karhunen loeve transform for stationary random data this paper presents a recursive algorithm for dct with a structure that allows the generation of the next higher order dct from two identical lower order dct s as a result the method for implementing this recursive dct requires fewer multipliers and adders than other dct algorithms

restructured recursive dct and dst algorithms the discrete cosine transform dct and the discrete sine transform dst have found wide applications in speech and image processing as well as telecommunication signal processing for the purpose of data compression feature extraction image reconstruction and filtering in this paper we present new recursive algorithms for the dct and the dst the proposed method is based on certain recursive properties of the dct coefficient matrix and can be generalized to design recursive algorithms for the 2 d dct and the 2 d dst these new structured recursive algorithms are able to decompose the dct and the dst into two balanced lower order subproblems in comparison to previous research works therefore when converting our algorithms into hardware implementations we require fewer hardware components than other recursive algorithms finally we propose two parallel algorithms for accelerating the computation

polylog time and near linear work approximation scheme for undirected shortest paths shortest paths computations constitute one of the most fundamental network problems nonetheless known parallel shortest paths algorithms are generally inefficient they perform significantly more work product of time and processors than their sequential counterparts this gap known in the literature as the transitive closure bottleneck poses a long standing open problem our main result is an o mn e 0 s m n1 e 0 work polylog time randomized algorithm that computes paths within 1 o 1 polylog n of shortest from s source nodes to all other nodes in weighted undirected networks with n nodes and m edges for any fixed e 0 0 this work bound nearly matches the o d sm sequential time in contrast previous polylog time algorithms required nearly min o d n3 o d m2 work even when s 1 and previous near linear work algorithms required near o n time we also present faster sequential algorithms that provide good approximate distances only between distant vertices we obtain an o m sn n e 0 time algorithm that computes paths of weight 1 o 1 polylog n dist o w max polylog n where dist is the corresponding distance and w max is the maximum edge weight our chief instrument which is of independent interest are efficient constructions of sparse hop sets a d e hop set of a network g v e is a set e of new weighted edges such that mimimum weight d edge paths in v e e have weight within 1 e of the respective distances in g we construct hop sets of size o n1 e 0 where e o 1 polylog n and d o polylog n

an introduction to finite element methods for transient advection problems abstract an introduction is presented to time accurate finite element methods recently developed for solving unsteady problems governed by linear and nonlinear advection equations this includes methods making an explicit use of the characteristic curves methods based on the taylor series in time and least squares methods

computation of an odd length dct from a real valued dft of the same length the discrete cosine transform dct is often computed from a discrete fourier transform dft of twice or four times the dct length dct algorithms based on identical length dft algorithms generally require additional arithmetic operations to shift the phase of the dct coefficients it is shown that a dct of odd length can be computed by an identical length dft algorithm by simply permuting the input and output sequences using this relation odd length dct modules for a prime factor dct are derived from corresponding dft modules the multiplicative complexity of the dct is then derived in terms of dft complexities

derivation of stabilized equations for numerical solution of advective diffusive transport and fluid flow problems abstract the concept of the so called artificial or balancing diffusion used to stabilize the numerical solution of advective diffusive transport and fluid flow problems is revised in this paper it is shown that the standard forms of the balancing diffusion terms usually chosen in a heuristic manner can be naturally found by introducing higher order approximations in the derivation of the governing differential equations via standard conservation or equilibrium principles this allows us to reinterpret many stabilization algorithms and concepts used in every day practice by numerical analysts and also provides an expression for computing the stabilization parameter

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

a new algorithm to compute the dct and its inverse a novel algorithm to convert the discrete cosine transform dct to skew circular convolutions is presented the motivation for developing such an algorithm is the fact that vlsi implementation of distributed arithmetic is very efficient for computing convolutions it is also shown that the inverse dct idct can be computed using the same building blocks which are used for computing the dct a dct idct processor can be designed to compute either the dct or the idct depending on a 1 b control signal

on computing the discrete hartley transform the discrete hartley transform dht is a real valued transform closely related to the dft of a real valued sequence bracewell has recently demonstrated a radix 2 decimation in time fast hartley transform fht algorithm in this paper a complete set of fast algorithms for computing the dht is developed including decimation in frequency radix 4 split radix prime factor and winograd transform algorithms the philosophies of all common fft algorithms are shown to be equally applicable to the computation of the dht and the fht algorithms closely resemble their fft counterparts the operation counts for the fht algorithms are determined and compared to the counts for corresponding real valued fft algorithms the fht algorithms are shown to always require the same number of multiplications the same storage and a few more additions than the real valued fft algorithms even though computation of the fht takes more operations in some situations the inherently real valued nature of the discrete hartley transform may justify this extra cost

steady and unsteady incompressible flow in a double driven cavity using the artificial compressibility ac based characteristic based split cbs scheme in this paper the explicit characteristic based split cbs scheme has been employed to solve both steady and unsteady flows inside a non rectangular double driven cavity this problem is recently suggested as a benchmark problem for incompressible flows both unstructured and structured meshes have been employed in the present study to make sure that the predicted results are as close to reality as possible the results obtained show the existence of steady state at lower reynolds numbers 1000 and transient states at higher reynolds numbers the flow approaches a turbulent state as the reynolds number is increased to 10 000 copyright 2005 john wiley sons ltd

systolic architectures for the computation of the discrete hartley and the discrete cosine transforms based on prime factor decomposition two dimensional systolic array implementations for computing the discrete hartley transform dht and the discrete cosine transform dct when the transform size n is decomposable into mutually prime factors are proposed the existing two dimensional formulations for dht and dct are modified and the corresponding algorithms are mapped into two dimensional systolic arrays the resulting architecture is fully pipelined with no control units the hardware design is based on bit serial left to right msb most significant bit to lsb least significant bit binary arithmetic

on boundary conditions of the characteristic based split cbs algorithm for fluid dynamics this paper discusses alternative procedures which can be used in the application of boundary conditions for the cbs algorithm attention is focused on the problem of application of prescribed velocity and traction conditions the paper is illustrated with some incompressible flow problems although previously logical and correct boundary condition specifications were introduced the procedures outlined in this paper simplify calculations and generally make it more accurate copyright 2002 john wiley sons ltd

on prime factor mapping for the discrete hartley transform the authors propose a new prime factor mapping scheme which requires no extra arithmetic operations for the realization of prime factor mapping for the computation of the discrete hartley transform dht it is achieved by embedding all the extra arithmetic operations into the subsequent short length computations with the computational complexities of these embedded short lengths remaining unchanged consequently the present approach significantly eliminates the burden which is introduced by the extra arithmetic operations with this mapping scheme it is further demonstrated that a prime factor mapped dht would have superb performance compared with other fast dht algorithms

input and output index mappings for a prime factor decomposed computation of discrete cosine transform a formal direct derivation of the prime factor decomposed computation algorithm is presented the derivation is direct in the sense that it is based on the real cosine function without resort to the discrete fourier transform expressions or the complex functions based on the equations obtained from the derivation input and output index mappings are introduced in the form of tables this tabulation enables any prime factor decomposable discrete cosine transform dct to be implemented in a straight forward manner the use of the index mapping tables is demonstrated for the 12 point dct

comparison of some finite element methods for solving the diffusion convection reaction equation abstract in this paper we describe several finite element methods for solving the diffusion convection reaction equation none of them is new although the presentation is non standard in an effort to emphasize the similarities and differences between them in particular it is shown that the classical supg method is very similar to an explicit version of the characteristic galerkin method whereas the taylor galerkin method has a stabilization effect similar to a sub grid scale model which is in turn related to the introduction of bubble functions

a fully explicit characteristic based split cbs scheme for viscoelastic flow calculations in this paper an explicit characteristic based split cbs scheme is proposed for the numerical solution of incompressible viscoelastic flow equations the scheme proposed is free from simultaneous solution to the matrices arising from the finite element discretization of the governing equations the experience gained from the solution of newtonian fluid dynamics problems has been applied to the solution of viscoelastic flows the oldroyd b model has been employed to solve two benchmark problems of viscoelastic flow they are viscoelastic flow past a circular cylinder and viscoelastic flow through planar contraction geometry the results show that the solutions obtained are stable for the weissenberg or deborah number range studied in this paper the solutions obtained at lower weissenberg or deborah numbers are accurate and agree excellently with the majority of available numerical data however at higher weissenberg or deborah numbers results show some sign of negative influence of the artificial dissipation added to the discrete constitutive equations

a new algorithm to compute the discrete cosine transform a new algorithm is introduced for the 2m point discrete cosine transform this algorithm reduces the number of multiplications to about half of those required by the existing efficient algorithms and it makes the system simpler

an efficient prime factor algorithm for the discrete cosine transform and its hardware implementations the prime factor decomposition is a fast computational technique for many important digital signal processing operations such as the convolution the discrete fourier transform the discrete hartley transform and the discrete cosine transform dct the authors present a new prime factor algorithm for the dct they also design a prime factor algorithm for the discrete sine transform based on the prime factor dct algorithm hardware implementations for the prime factor dct are also studied they are especially interested in the hardware designs which are suitable for the vlsi implementations they show three hardware designs for the prime factor dct including a vlsi circuit fabricated directly according to the signal flow graph a linear systolic array and a mesh connected systolic array these three designs show the trade off between cost and performance the methodology which deals with general n sub 1 spl times n sub 2 point dcts where n sub 1 and n sub 2 are mutually prime is illustrated by converting a 15 point dct problem into a 3 spl times 5 point 2d dct problem

prime factor algorithm for multidimensional discrete cosine transform a prime factor fast algorithm is proposed for the computation of the multidimensional forward and inverse discrete cosine transform dct by using an example of a two dimensional 2 d dct it shows that an r dimensional dct can be obtained from a 2r dimensional dct with a post processing stage efficient method for input output mapping is reported to substantially reduce the computational overhead associated with the prime factor algorithm

an efficient characteristic galerkin scheme for the advection equation in 3 d conventional galerkin based finite element algorithms perform poorly when modeling advective transport here we develop and test a characteristic galerkin scheme to solve the unsteady three dimensional advective transport equation the algorithm uses tracking of the gaussian quadrature points to project the information from the eulerian background grid to the lagrangian grid numerical experiments were carried out to investigate the performance of this scheme despite speculations to the contrary in the literature this scheme does not suffer from instability problems further it is conservative and shows good phase characteristics with slight numerical diffusion we conclude that the characteristic galerkin method is a viable and efficient scheme for solving advection problems in three dimensions

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

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