on the connectedness of optimum degeneracy graphs abstract so called optimum degeneracy graphs describe the structure of the set of primal and dual feasible bases associated with a degenerate vertex of the feasible solution set of a linear program the structural properties of these graphs play an important role in determining shadow prices or performing sensitivity analysis in linear programming under degeneracy we prove that general optimum degeneracy graphs are connected and that negative optimum degeneracy graphs are connected under certain conditions

an edge based method for the incompressible navier stokes equations on polygonal meshes abstract a pressure based method is presented for discretizing the unsteady incompressible navier stokes equations using hybrid unstructured meshes the edge based data structure and assembly procedure adopted lead naturally to a strictly conservative discretization which is valid for meshes composed of n sided polygons particular attention is given to the construction of a pressure velocity coupling procedure which is supported by edge data resulting in a relatively simple numerical method that is consistent with the boundary and initial conditions required by the incompressible navier stokes equations edge formulas are presented for assembling the momentum equations which are based on an upwind biased linear reconstruction of the velocity field similar formulas are presented for assembling the pressure equation the method is demonstrated to be second order accurate in space and time for two navier stokes problems admitting an exact solution results for several other well known problems are also presented including lid driven cavity flow impulsively started cylinder flow and unsteady vortex shedding from a circular cylinder although the method is by construction minimalist it is shown to be accurate and robust for the problems considered

a new indirect anisotropic quadrilateral mesh generation scheme with enhanced local mesh smoothing procedures an enhanced version of indirect advancing front technique is proposed for the construction of full quadrilateral anisotropic meshes on 3d surfaces the final quadrilateral mesh is constructed from a background triangular mesh and the merging procedure is carried out in the parametric space the proposed method employed the systemic merging technique for the formation of quadrilaterals and the metric specifications for controlling the anisotropic characteristics of the elements in order to generate well graded anisotropic quadrilaterals the selection criteria of base segment for merging are carefully defined furthermore in order to improve the shape quality of the final mesh a set of new local smoothing algorithms for anisotropic quadrilateral mesh quality enhancement has been proposed and tested in this study numerical examples obtained indicate that the proposed enhanced local smoothing schemes can effectively improve the quality of the quadrilateral meshes produced and increase the robustness of the mesh generation scheme copyright 2003 john wiley sons ltd

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

an adaptive strategy for elliptic problems including a posteriori controlled boundary approximation we derive a posteriori error estimates for the approximation of linear elliptic problems on domains with piecewise smooth boundary the numerical solution is assumed to be defined on a finite element mesh whose boundary vertices are located on the boundary of the continuous problem no assumption is made on a geometrically fitting shape a posteriori error estimates are given in the energy norm and the l 2 norm and efficiency of the adaptive algorithm is proved in the case of a saturated boundary approximation furthermore a strategy is presented to compute the effect of the non discretized part of the domain on the error starting from a coarse mesh this especially implies that parts of the domain where the measured error is small stay non discretized the presented algorithm includes a stable path following to supply a sufficient polygonal approximation of the boundary the reliable computation of the a posteriori estimates and a mesh adaptation based on delaunay techniques numerical examples illustrate that errors outside the initial discretization will be detected

generalized 3 d paving an automated quadrilateral surface mesh generation algorithm this paper discusses the extension of the paving algorithm for all quadrilateral mesh generation to arbitrary three dimensional trimmed surfaces methods of calculating angles projecting elements and detecting collisions between paving boundaries for general surfaces are presented extensions of the smoothing algorithms for three dimensions are set forth advances in the use of scalar sizing functions are presented these functions can be used to better approximate internal mesh density from boundary densities and surface characteristics

h morph an indirect approach to advancing front hex meshing h morph is a new automatic algorithm for the generation of a hexahedral dominant finite element mesh for arbitrary volumes the h morph method starts with an initial tetrahedral mesh and systematically transforms and combines tetrahedral into hexahedra it uses an advancing front technique where the initial front consists of a set of prescribed quadrilateral surface facets fronts are individually processed by recovering each of the six quadrilateral faces of a hexahedron from the tetrahedral mesh recovery techniques similar to those used in boundary constrained delaunay mesh generation are used tetrahedral internal to the six hexahedral faces are then removed and a hexahedron is formed at any time during the h morph procedure a valid mixed hexahedral tetrahedral mesh is in existence within the volume the procedure continues until no tetrahedral remain within the volume or tetrahedral remain which cannot be transformed or combined into valid hexahedral elements any remaining tetrahedral are typically towards the interior of the volume generally a less critical region for analysis transition from tetrahedral to hexahedra in the final mesh is accomplished through pyramid shaped elements advantages of the proposed method include its ability to conform to an existing quadrilateral surface mesh its ability to mesh without the need to decompose or recognize special classes of geometry and its characteristic well aligned layers of elements parallel to the boundary example test cases are presented on a variety of models

blossom quad a non uniform quadrilateral mesh generator using a minimum cost perfect matching algorithm a new indirect way of producing all quad meshes is presented the method takes advantage of a wellknown algorithm of the graph theory namely the blossom algorithm that computes the minimum cost perfect matching in a graph in polynomial time the new blossom quad algorithm is compared with standard indirect procedures meshes produced by the new approach are better both in terms of element shape and in terms of size eld ef ciency

numerical methods for partial differential equations based on power series stable difference schemes that approximate partial differential equations to any desired order are generated by means of power series the method is demonstrated on the one dimensional heat equation and the stability is studied in detail stability analyses are then presented for parabolic linear equations with constant coefficients a nonlinear example is presented which indicates the efficiency of the higher ordered schemes

automatic generation of anisotropic quadrilateral meshes on three dimensional surfaces using metric specifications a new algorithm for constructing full quadrilateral anisotropic meshes on 3d surfaces is proposed in this paper the proposed method is based on the advancing front and the systemic merging techniques full quadrilateral meshes are constructed by systemically converting triangular elements in the background meshes into quadrilateral elements by using the metric specifications to describe the element characteristics the proposed algorithm is applicable to convert both isotropic and anisotropic triangular meshes into full quadrilateral meshes special techniques for generating anisotropic quadrilaterals such as new selection criteria of base segment for merging new approaches for the modifications of the background mesh and construction of quadrilateral elements are investigated and proposed in this study since the final quadrilateral mesh is constructed from a background triangular mesh and the merging procedure is carried out in the parametric space the mesh generator is robust and no expensive geometrical computation that is commonly associated with direct quadrilateral mesh generation schemes is needed copyright 2002 john wiley sons ltd

nonlinear diffusion and discrete maximum principle for stabilized galerkin approximations of the convection diffusion reaction equation we investigate stabilized galerkin approximations of linear and nonlinear convectiondiffusion reaction equations we derive nonlinear streamline and cross wind diffusion methods that guarantee a discrete maximum principle for strictly acute meshes and first order polynomial interpolation for pure convectiondiffusion problems the discrete maximum principle is achieved using a nonlinear cross wind diffusion factor that depends on the angle between the discrete solution and the flow velocity for convectiondiffusion reaction problems two methods are considered residual based isotropic diffusion and the previous nonlinear cross wind diffusion factor supplemented by additional isotropic diffusion scaling as the square of the mesh size practical versions of the present methods suitable for numerical implementation are compared to previous discontinuity capturing schemes lacking theoretical justification numerical results are investigated in terms of both solution quality violation of maximum principle smearing of internal layers and computational costs

hybrid prismatic tetrahedral grid generation for viscous flow applications a method for the automatic generation of unstructured grids composed of tetrahedra and prisms is proposed the prismatic semistructured grid is generated around viscous boundary surfaces and covers viscous regions whereas the tetrahedral grid covers the rest of the computational domain the delaunay approach for tetrahedral grid generation is used the proposed prismatic grid is structured in directions normal to the boundary faces but the number of prisms generated from one boundary face is variable from face to face unlike conventional prismatic grid generators this technique works well even in regions of cavities and gaps the delaunay background grid generated for surface nodes serves as an efficient data structure to check possible intersections of prisms particular attention is given to the boundary constraining problem a robust algorithm for the boundary recovery by edge swapping followed by a direct subdivision of tetrahedra is used grid examples for internal and external flow problems of complex shapes demonstrate the efficiency of the method

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

construction of three dimensional improved quality triangulations using local transformations three dimensional delaunay triangulation are the most common form of three dimensional triangulation known but they are not very suitable for tetrahedral finite element meshes because they tend to contain poorly shaped sliver tetrahedra in this paper we present an algorithm for constructing improved quality triangulation with respect to a tetrahedron shape measure this algorithm uses combination of two or more local transformations to improve a given triangulation toward an optimal triangulation experimental results on finite element meshes show that this algorithm is much more effective than previous methods at removing slivers from delaunay triangulation and producing nearly optimal triangulation a variation of this algorithm for improving a pseudo locally optimal non delaunay triangulationn toward a delaunay triangulation is also presented

adjoint a posteriori error measures for anisotropic mesh optimisation in this paper an adjoint or sensitivity based error measure is formulated which measures the error contribution of each solution variable to an overall goal the goal is typically embodied in an integral functional e g the solution in a small region of the domain of interest the resulting a posteriori error measures involve the solution of both primal and adjoint problems a comparison of a number of important a posteriori error measures is made in this work there is a focus on developing relatively simple methods that refer to information from the discretised equation sets often readily accessible in simulation codes and do not explicitly use equation residuals this method is subsequently used to guide anisotropic mesh adaptivity of tetrahedral finite elements mesh adaptivity is achieved here with a series of optimisation heuristics of the landscape defined by mesh quality mesh quality is gauged with respect to a riemann metric tensor embodying an a posteriori error measure such that an ideal element has sides of unit length when measured with respect to this metric tensor this results in meshes in which each finite element node has approximately equal subject to certain boundary conforming constraints and the performance of the mesh optimisation heuristics error contribution to the functional goal

elastic wave propagation in heterogeneous anisotropic media using the lumped finite element method a numerical technique for wave propagation simulation in 2 d heterogeneous anisotropic structures is presented the scheme is flexible in incorporating arbitrary surface topography inner openings liquid solid boundaries and irregular interfaces and it naturally satisfies the free surface conditions of complex geometrical boundaries the algorithm based on a discretization mesh of triangles and quadrilaterals solves the problem using integral equilibrium around each node instead of satisfying elastodynamic differential equations at each node as in the finite difference method this study is an extension of previous work for the elastic isotropic case besides accounting for anisotropy a simplified quadrilateral grid cell with low computational cost is introduced the transversely isotropic medium with a symmetry axis on the horizontal or vertical plane as typically caused by a system of parallel cracks or fine layers is discussed in detail a 2 d algorithm is presented that can handle the situatio

unstructured grid generation using iterative point insertion and local reconnection a procedure is presented for efficient generation of high quality two or three dimensional unstructured grids of triangular or tetrahedral elements the present procedure uses an iterative point creation and insertion scheme wherein points are created using advancing front type point placement initially the connectivity for these generated points is obtained by directly subdividing the elements which contain them without regard to quality this connectivity is then improved by iteratively using local reconnection subject to a quality criterion for two dimensions a min max criterion is used and for three dimensions a delaunay in sphere criterion followed by a min max type criterion is used the overall procedure is applied repetitively until a complete field grid is generated with a desired point distribution grid quality and performance statistics are presented for a variety of two and three dimensional configurations the combined quality and efficiency attributes of this procedure appear to be a substantial improvement over existing methods

a genetic based framework for solving multi criteria weighted matching problems abstract the purpose of this paper is to present a flexible genetic based framework for solving the multi criteria weighted matching problem mc wmp in the first part of this paper we design a genetic based framework for solving the ordinary weighted matching problem we present an extensive analysis of the quality of the results and introduce a methodology for tuning its parameters in the second part we develop a modified genetic based algorithm for solving the mc wmp the algorithm generates a significant and representative portion of the pareto optimal set to assess the performance of the algorithm we conduct computational experiments with two and three criteria the potential of the proposed algorithm is demonstrated by comparing to a multi objective simulated annealing algorithm

the paradox of parrondo s games we introduce parrondo s paradox that involves games of chance we consider two fair games a and b both of which can be made to lose by changing a biasing parameter an apparently paradoxical situ

an adaptive finite element method with crosswind diffusion for low mach steady laminar combustion we investigate adaptive finite element methods for low mach steady laminar combustion the finite element discretization of the flame equations involves least squares control of streamline derivatives and pressure velocity coupling as well as a new shock capturing term based on nonlinear crosswind diffusion yielding a suitable discrete maximum principle for the discrete solution a posteriori error estimates derived from the dual weighted residual method are used to refine the mesh adaptively numerical results are presented for a bunsen flame with simple chemistry on locally refined as well as fully unstructured delaunay meshes solution quality is evaluated in terms of overall flame characteristics including length lift off and width as well as undershoots in species and temperature profiles

efficient unstructured mesh generation by means of delaunay triangulation and bowyer watson algorithm this work is devoted to the description of an efficient unstructured mesh generation method entirely based on the delaunay triangulation the distinctive characteristic of the proposed method is that point positions and connections are computed simultaneously this result is achieved by taking advantage of the sequential way in which the bowyer watson algorithm computes the delaunay triangulation two methods are proposed which have great geometrical flexibility in that they allow us to treat domains of arbitrary shape and topology and to generate arbitrarily nonuniform meshes the methods are computationally efficient and are applicable both in two and three dimensions

on curvature element size control in metric surface mesh generation summary a new procedure is suggested for controlling the element size distribution of surface meshes during automatic adaptive surface mesh generation in order to ensure that the geometry of the surface can be accurately captured the curvature properties of the surface are first analyzed based on the principal curvatures and principal directions of the surface the curvature element size requirement is defined in form of a metric tensor field this element size controlling metric tensor field which can either be isotopic or anisotopic depends on the user requirement is then employed to control the element size distribution during mesh generation the suggested procedure is local adaptive and can be easily used with many parametric surface mesh generators as the proposed scheme defines the curvature element size requirement in an implicit manner it can be combined with any other user defined element size specification using the standard metric intersection procedure this eventually leads to a simple implementation procedure and a high computational efficiency numerical examples indicate that the new procedure can effectively control the element size of surface meshes in the cost of very little additional computational effort

an interior penalty galerkin method for the mhd equations in heterogeneous domains the maxwell equations in the magnetohydrodynamic mhd limit in heterogeneous domains composed of conducting and non conducting regions are solved by using lagrange finite elements and by enforcing continuities across interfaces using an interior penalty technique a la baker finite element methods for elliptic equations using non conforming elements math comp 31 137 1977 45 59 the method is shown to be stable and convergent and is validated by convergence tests it is used to compute ohmic decay in various compact conducting domains and to simulate the kinematic dynamo action in two different geometries

faster scaling algorithms for general graph matching problems an algorithm for minimum cost matching on a general graph with integral edge costs is presented the algorithm runs in time close to the fastest known bound for maximum cardinality matching specifically let n m and n denote the number of vertices number of edges and largest magnitude of a cost respectively the best known time bound for maximum cardinal ity matching m 0 am the new algorithm for minimum cost matching has time bound 0 in a m n iog n m log nn a slight modification of the new algorithm finds a maximum cardinality matching in 0 fire time other applications of the new algorlthm are given mchrding an efficient implementa tion of christofides traveling salesman approximation algorithm and efficient solutions to update problems that require the linear programming duals for matching

anisotropic centroidal voronoi tessellations and their applications in this paper we introduce a novel definition of the anisotropic centroidal voronoi tessellation acvt corresponding to a given riemann metric tensor a directional distance function is used in the definition to simplify the computation we provide algorithms to approximate the acvt using the lloyd iteration and the construction of anisotropic delaunay triangulation under the given riemannian metric the acvt is applied to the optimization of two dimensional anisotropic delaunay triangulation to the generation of surface cvt and high quality triangular mesh on general surfaces various numerical examples demonstrating the effectiveness of the proposed method are presented

linear time approximation for maximum weight matching the maximum cardinality and maximum weight matching problems can be solved in o m n time a bound that has resisted improvement despite decades of research here m and n are the number of edges and vertices in this article we demonstrate that this m n barrier can be bypassed by approximation for any e 0 we give an algorithm that computes a 1 e approximate maximum weight matching in o me 1 log e 1 time that is optimal linear time for any fixed e our algorithm is dramatically simpler than the best exact maximum weight matching algorithms on general graphs and should be appealing in all applications that can tolerate a negligible relative error

stochastic dynamics and parrondo s paradox abstract the spanish physicist juan parrondo has provided two stochastic losing games such that for certain stochastic combinations one may obtain a winning game if a large number of players are involved and if they try to play such that their gain in the next round is maximized one arrives at the problem of investigating a random walk on a certain space of measures the appropriate abstract setting is as follows there is given a compact metric space m d and m is written as the union of certain closed subsets a 1 a r for every 1 r there is prescribed a strict contraction a m a random walk x m m n 0 on m is then defined as follows the starting position is x 0 x 0 where x 0 m is fixed and if the walk at the m th step is at position x m m then one chooses a among the with x m a with equal probability say and defines x m 1 as x m associated with the walk is a gain x m in every round where m r is a continuous function the aim of the present investigations is the study of the expectation g m of x m as a function of m our main result states that the sequence g m is eventually approximately periodic provided that all a are not only closed but also open in m for every e there is an l 0 n such that g m is l 0 periodic up to an error of at most e for sufficiently large m in fact it turns out that the behaviour of our process can be described well with a finite markov chain in the general case however the process might behave rather chaotically we give an example where m is the unit interval m is written as the union of two closed subsets a 1 a 2 the contractions 1 2 are rather simple but the expectations of the gains are not even cesaro convergent

quality estimates and stretched meshes based on delaunay triangulations any other vertex is exploited for the automation of the grid generation process moreover delaunay grids have many interesting properties an extensive documentation of which can be found in ref 10 in the following we will first describe the different elements of frod the derivation of the background mesh as well as the vertex generation for the viscous and inviscid regions the latter half of this paper presents the quality measures that can be derived for the isotropic vertex generation part

an indirect approach for automatic generation of quadrilateral meshes with arbitrary line constraints a new approach to the automatic generation of a quadrilateral mesh with arbitrary line constraints is proposed in this paper it is an indirect all quad mesh generation and presented in the following steps 1 discretizing the constrained lines within the domain 2 converting the above domain to a triangular mesh together with the line constraints 3 transforming the generated triangular mesh with line constraints to an all quad mesh through performing an advancing front algorithm from the line constraints which enables the construction of quadrilaterals layer by layer and roughly keeps the feature of the initial triangular mesh 4 optimizing the topology of the quadrilateral mesh to reduce the number of irregular nodes 5 smoothing the generated mesh toward high quality all quad mesh generation finally a few application examples are given to demonstrate the reliability and usefulness of the proposed algorithm copyright c 2011 john wiley sons ltd

finite element transport modeling using analytic element flow solutions 1 finite element methods for solute transport simulation typically use a discrete representation of the flow domain obtained from a finite element solution of the associated groundwater flow problem velocity saturated thickness and components of the dispersion coefficient tensor are represented as a set of nodal and or element averaged values in contrast the analytic element method aem provides continuous mesh independent solutions for these variables in this paper a set of techniques for using two dimensional aem flow solutions as the basis of finite element solute transport models is introduced first a general aem based discretization approach is presented that addresses the existence of curved boundaries singularities and discontinuities in vertically averaged concentration second residual integration methods that handle continuous parameters with internal and boundary singularities are developed and evaluated third an approach is introduced for handling internal discontinuities in concentration across certain analytic elements this new approach uses a nonstandard mesh topology and a new formulation for internal coupled boundary conditions the aem based transport simulation methods introduced in this paper are demonstrated to be robust and accurate for a variety of test problems

algorithmic applications of baur strassen s theorem shortest cycles diameter and matchings consider a directed or an undirected graph with integral edge weights from the set w w that does not contain negative weight cycles in this article we introduce a general framework for solving problems on such graphs using matrix multiplication the framework is based on the usage of baur strassen s theorem and of strojohann s determinant algorithm it allows us to give new and simple solutions to the following problems finding shortest cycles we give a simple o wn time algorithm for finding shortest cycles in undirected and directed graphs for directed graphs and undirected graphs with nonnegative weights this matches the time bounds obtained in 2011 by roditty and williams on the other hand no algorithm working in o wn time was previously known for undirected graphs with negative weights furthermore our algorithm for a given directed or undirected graph detects whether it contains a negative weight cycle within the same running time computing diameter and radius we give a simple o wn time algorithm for computing a diameter and radius of an undirected or directed graphs to the best of our knowledge no algorithm with this running time was known for undirected graphs with negative weights finding minimum weight perfect matchings we present an o wn time algorithm for finding minimum weight perfect matchings in undirected graphs this resolves an open problem posted by sankowski 2009 who presented such an algorithm but only in the case of bipartite graphs these three problems that are solved in the full generality demonstrate the utility of this framework hence we believe that it can find applications for solving larger spectra of related problems as an illustrative example we apply it to the problem of computing a set of vertices that lie on cycles of length at most t for some given t we give a simple o wn time algorithm for this problem that improves over the o wn t time algorithm given by yuster in 2011 besides giving this flexible framework the other main contribution of this article is the development of a novel combinatorial interpretation of the dual solution for the minimum weight perfect matching problem despite the long history of the matching problem such a combinatorial interpretation was not known previously this result sheds a new light on the problem as there exist many structural theorems about unweighted matchings but almost no results that could cope with the weighted case

robust geometrically based automatic two dimensional mesh generation a technical description of the algorithms employed in the modified quadtree mesh generator is given although the basis of the mesh generator is the same as the original version developed by yerry and shephard 1 2 the actual algorithms on which it is built have been entirely changed for the purpose of ensuring the robustness of the technique as demonstrated in the paper the algorithmic changes made do ensure the robustness of the approach but introduce additional algorithmic difficulties the solutions of which are also presented in addition to examples showing the capability of the mesh generator the linear computational growth rate of the mesh generator is demonstrated

quantum models of parrondo s games abstract a parrondo s paradox is an effect where two losing games when combined can produce a net winning result we provide a short introduction to quantum versions of parrondo s games and review the current status of the work

are bilinear quadrilaterals better than linear triangles this paper compares the theoretical effectiveness of bilinear approximation over quadrilaterals with linear approximation over triangles anisotropic mesh transformation is used to generate asymptotically optimally efficient meshes for piecewise linear interpolation over triangles and bilinear interpolation over quadrilaterals for approximating a convex function although bilinear quadrilaterals are more efficient linear triangles are more accurate and may be preferred in finite element computations whereas for saddle shaped functions quadrilaterals may offer a higher order approximation on a well designed mesh a surprising finding is different grid orientations may yield an order of magnitude improvement in approximation accuracy

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

automatic adaptive grid refinement for the euler equations a method of adaptive grid refinement for the solution of the steady euler equations for transonic flow is presented the algorithm automatically decides where the coarse grid accuracy is insufficient and creates locally uniform refined grids in these regions this typically occurs at the leading and trailing edges the solution is then integrated to steady state using the same integrator flo52 in the interior of each grid the boundary conditions needed on the fine grids are examined and the importance of treating the fine coarse grid interface conservatively is discussed numerical results indicate substantial computational savings for the same solution accuracy can be achieved

entropy viscosity method for nonlinear conservation laws a new class of high order numerical methods for approximating nonlinear conservation laws is described entropy viscosity method the novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand this new approach does not use any flux or slope limiters applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation various benchmark problems are solved with finite elements spectral elements and fourier series to illustrate the capability of the proposed method

tetrahedral mesh optimisation and adaptivity for steady state and transient finite element calculations abstract a method for optimising a pre existing mesh of tetrahedral finite elements is described it is based on a series of mesh connectivity and node position searches of the landscape defining mesh quality a riemannian metric reflecting the a posteriori error measure is used to calculate element size and shape a functional is defined which embodies both shape and size quality of an element with respect to the metric and is used to gauge mesh quality a heuristic based local search strategy is adopted local in the sense that it has no hill climbing abilities the paper presents applications of the method to complex steady state and time dependent problems which highlight its anisotropic feature capturing abilities numerical evidence is provided which suggests that the computational complexity time of the proposed algorithm varies linearly with the number of elements or nodes of the finite element mesh

discrete time ratchets the fokker planck equation and parrondo s paradox parrondo s games manifest the apparent paradox where losing strategies can be combined to win and have generated significant multidisciplinary interest in the literature here we review two recent approaches based on the fokker planck equation that rigorously establish the connection between parrondo s games and a physical model known as the flashing brownian ratchet this gives rise to a new set of parrondo s games of which the original games are a special case for the first time we perform a complete analysis of the new games via a discrete time markov chain analysis producing winning rate equations and an exploration of the parameter space where the paradoxical behaviour occurs

algebraic grid generation on trimmed parametric surface using non self overlapping planar coons patch using a coons patch mapping to generate a structured grid in the parametric region of a trimmed surface can avoid the singularity of elliptic pde methods when only c1 continuous boundary is given the error of converting generic parametric c1 boundary curves into a specified representation form is also avoided however overlap may happen on some portions of the algebraically generated grid when a linear or naive cubic blending function is used in the mapping this severely limits its usage in most of engineering and scientific applications where a grid system of non self overlapping is strictly required to solve the problem non trivial blending functions in a coons patch mapping should be determined adaptively by the given boundary so that self overlapping can be averted we address the adaptive determination problem by a functional optimization method the governing equation of the optimization is derived by adding a virtual dimension in the parametric space of the given trimmed surface both one and two parameter blending functions are studied to resolve the difficulty of guessing good initial blending functions for the conjugate gradient method used a progressive optimization algorithm is then proposed which has been shown to be very effective in a variety of practical examples also an extension is added to the objective function to control the element shape finally experiment results are shown to illustrate the usefulness and effectiveness of the presented method copyright 2004 john wiley sons ltd

weighting the edge stabilization a modification of the edge stabilization technique is proposed to improve the behavior of the method when solving conservation equations with nonsmooth data or nonsmooth solutions the key ingredient is tempering the edge stabilization in regions of large gradients through appropriate weights the new method is shown to preserve the convergence properties of the original method on smooth solutions and numerical tests indicate that it performs better on nonsmooth solutions

development of an automatic two dimensional finite element mesh generator using quadrilateral elements and bezier curve boundary definition this paper describes the development of an automatic two dimensional quadrilateral element mesh generator the methodology is based on the looping algorithm developed in part by dr m l c sluiter bezier curves are used to define the boundaries of the parts to be meshed the required interaction by the user is reduced to specifying the boundary geometry the preferred element size and the refinement coefficient transition elements are automatically generated between regions of varying element sizes the ability to offset specified boundary curves insures well conditioned elements along the boundary meshes for several sample geometries are presented to illustrate the versatility of the mesh generator

calculation of incompressible viscous flows by an unconditionally stable projection fem this paper investigates the numerical performance of a finite element implementation of a new incremental fractional step method to compute steady and unsteady incompressible viscous flows under general boundary conditions and using unstructured meshes a variational framework is adopted which accommodates two different spaces for representing and approximating the velocity fields calculated respectively in the viscous and inviscid phases of the method but which leads to a very simple numerical scheme in terms of only one discrete velocity field an unconditionally stable semi implicit approximation of the nonlinear term is used to eliminate any time step restriction as far as the numerical stability is concerned numerical results for five test problems in two dimensions are reported to illustrate the flexibility of the proposed method

efficient three dimensional delaunay triangulation with automatic point creation and imposed boundary constraints a method is described which constructs three dimensional unstructured tetrahedral meshes using the delaunay triangulation criterion several automatic point creation techniques will be highlighted and an algorithm will be presented which can ensure that given an initial surface triangulation which bounds a domain a valid boundary conforming assembly of tetrahedra will be produced statistics of measures of grid quality are presented for several grids 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

a new approach to the development of automatic quadrilateral mesh generation a methodology for the automatic mesh generation of quadrilateral elements is proposed the methodology is based on the facts that i a region can always be subdivided entirely into quadrilaterals if the polygon which forms the boundary of the region has an even number of sides ii a quadrilateral can be formed by two triangles which share a common side by taking advantage of the techniques developed in an existing automatic triangular mesh generator quadrilateral meshes can be generated according to the distribution of user specified element size over the domain of interest in particular an automatic quadrilateral mesh generator based on the advancing front technique for triangular mesh generation1 is described techniques to improve the quality of the generated quadrilateral meshes are introduced the robustness and versatility of the mesh generator are demonstrated by a variety of examples

weak ψ ω formulation for unsteady flows in 2d multiply connected domains abstract this paper describes a variational formulation for solving the time dependent navier stokes equations expressed in terms of the stream function and vorticity around multiple airfoils this approach is an extension to the case of multiply connected domains of the weak formulation based on explicit viscous diffusion recently proposed by guermond and quartapelle in their method the momentum equation was interpreted as a dynamical equation governing the evolution of the weak laplacian of the stream function while the poisson equation for the latter was used as an expression to evaluate the distribution of the vorticity time discretizations with the viscous term made explicit were used leading to the viscosity being split from the incompressibility similarly to the primitive variable fractional step method in the present work the multiconnectedness is addressed by introducing an influence matrix to determine the constant values of the stream function on the airfoils in a noniterative fashion the explicit treatment of the viscous term leads to an influence matrix rooted in the harmonic problem instead of in the biharmonic problem occurring in methods enforcing integral conditions on the vorticity such as the glowinski pironneau method the influence matrix changes at each time step or is constant depending on whether a semi implicit or fully explicit treatment is adopted for the nonlinear term the resulting split method is implemented using a first order euler backward difference or a second order bdf scheme and linear finite elements numerical results are given and compared with the solutions obtained by means of the biharmonic formulation for multiply connected domains

efficient implementation of graph algorithms using contraction the component merging problem is a new graph problem versions of this problem appear as bottlenecks in various graph algorithms a new data structure solves this problem efficiently and two special cases of the problem have even more efficient solutions based on other data structures the performance of the data structures is sped up by introducing a new algorithmic tool called packets the algorithms that use these solutions to the component merging problem also exploit new properties of two existing data structures specifically trees can be used simultaneously as a priority queue and a concatenable queue similarly f heaps support some kinds of split operations with no loss of efficiency an immediate application of the solution to the simplest version of the merging problem is an o t m n algorithm for finding minimum spanning trees in undirected graphs without using f heaps where t m n m log 2 log 2 log d n the graph has n vertices and m edges and d max m n 2 packets also improve the f heap minimum spanning tree algorithm giving the fastest algorithm currently known for this problem the efficient solutions to the merging problem and the new observation about f heaps lead to an o n t m n n log n algorithm for finding a maximum weighted matching in general graphs this settles an open problem posed by tarjan 15 p 123 where the weaker bound of o nm log n 2 m was conjectured

on the np completeness of the perfect matching free subgraph problem given a bipartite graph g u v e such that u v and every edge is labelled true or false or both the perfect matching free subgraph problem is to determine whether or not there exists a subgraph of g containing for each node u of u either all the edges labelled true or all the edges labelled false incident to u and which does not contain a perfect matching this problem arises in the structural analysis of differential algebraic systems the purpose of this paper is to show that this problem is np complete we show that the problem is equivalent to the stable set problem in a restricted case of tripartite graphs then we show that the latter remains np complete in that case we also prove the np completeness of the related minimum blocker problem in bipartite graphs with perfect matching

survey of solved and open problems in the degeneracy phenomenon degeneracy is a phenomenon that may arise e g in linear programming lp for short bottleneck lp multiparametric lp linear vectormaximization etc if it does arise then it certainly influences any vertex searching method for mathematical models based on a system of linear inequalities and in some cases it leads to misinterpretation of optimal solutions

an o ev log v algorithm for finding a maximal weighted matching in general graphs we define two generalized types of a priority queue by allowing some forms of changing the priorities of the elements in the queue we show that they can be implemented efficiently consequently each operation takes o log n time we use these generalized priority queues to construct an o ev log v algorithm for finding a maximal weighted matching in general graphs

an overlapping domain decomposition preconditioning method for monolithic solution of shear bands metals subjected to high strain rate impact often exhibit a sudden and profound drop in the material s load bearing capability a ductile failure phenomenon known as shear banding shear bands characterized as material instabilities are driven by shear heating and described as narrow regions that have sustained intense plastic deformation and high temperature rise this coupled thermo mechanical localization problem can be formulated as a nonlinear system with two balance equations momentum and energy and two constitutive laws for elasticity and plasticity in our formulation mixed finite elements are used to discretize the equations in space and an implicit finite difference scheme is used to advance the system in time where at every time step a newton type method is used to solve the system monolithically to that end a block jacobian matrix is formed analytically using g teaux derivatives the resulting jacobian is sparse nonsymmetric and its sparsity pattern and eigenvalue content vary with the different stages of shear bands formation consequently posing a significant challenge to iterative solvers to address this issue an overlapping domain decomposition preconditioner that takes into account the physics of shear bands and the domain in which it forms is proposed the key idea is to resolve the shear band domain accurately while only solving the remaining domain approximately with selective updates when necessary the preconditioner is formed on the basis of an additive schwartz method that is applied to a schur complement partition of the system the proposed preconditioner is implemented in parallel and tested on three different benchmark problems as compared against off the shelf solvers we study the effect of hh and kk refinement that are obtained from isogeometric discretizations of the system the overlapping strategy and its parallel performance excellent performance is demonstrated in serial and parallel on all benchmark examples

accounting for curved domains in mesh adaptation this paper presents a procedure to project vertices created by refining straight sided tetrahedra to appropriate locations on curved model boundaries although many of the vertices introduced by refinement of mesh edges and faces on the boundary of the model can easily be projected to the model geometry there are situations where this projection creates invalid elements to ensure the ability to place those vertices on the model boundary an efficient two step procedure has been developed the first step applies local mesh modification operations such as collapse and swap to incrementally project vertices it is shown that the effective application of mesh modifications that will yield a mesh in which the vertex in question can be projected to the boundary must focus on ensuring the vertex in question moves at least as far as the plane on which the mesh would have element shapes degrade to zero volume the second step applies a generalized local cavity triangulation algorithm to ensure the success of the process when the set of local mesh modifications considered is unable to project the vertex to the boundary copyright 2003 john wiley sons ltd

adaptive mesh generation for viscous flows using delaunay triangulation abstract a method for generating an unstructured triangular mesh in two dimensions suitable for computing high reynolds number flows over arbitrary configurations is presented the method is based on a delaunay triangulation which is perfored in a locally stretched space in order to obtain very high aspect ratio tiangles in the boundary layer and wake regions it is shown how the method can be coupled with an unstructured navier stokes solver to produce a solution adaptive mesh generation procedure for viscous 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

can two chaotic systems give rise to order abstract the recently discovered parrondo s paradox claims that two losing games can result under random or periodic alternation of their dynamics in a winning game losing losing winning in this paper we follow parrondo s philosophy of combining different dynamics and we apply it to the case of one dimensional quadratic maps we prove that the periodic mixing of two chaotic dynamics originates an ordered dynamics in certain cases this provides an explicit example theoretically and numerically tested of a different parrondian paradoxical phenomenon chaos chaos order

adaptive triangular quadrilateral mesh generation in this paper we begin by recalling an adaptive mesh generation method governed by isotropic and anisotropic discrete metric maps by means of the generation of a unit mesh with respect to a riemannian structure we propose then an automatic triangular to quadrilateral mesh conversion scheme which generalizes the standard case to the anisotropic context in addition we introduce an optimal vertex smoothing procedure application test examples in particular a cfd test are given to demonstrate the eciency of the proposed method 1998 john wiley sons ltd int j numer meth engng 41 915 934 1998

an adaptive method with rigorous error control for the hamilton jacobi equations part ii the two dimensional steady state case in this paper we devise and study an adaptive method for finding approximations to the viscosity solution of hamilton jacobi equations the method which is an extension to two space dimensions of a similar method previously proposed for one space dimension is studied in the framework of steady state hamilton jacobi equations with periodic boundary conditions it seeks numerical approximations whose l distance to the viscosity solution is no bigger than a prescribed tolerance a thorough numerical study is carried out which shows that a strict error control is achieved and that the method exhibits an optimal computational complexity which does not depend on the value of the tolerance or on the type of hamiltonian

a frontal delaunay quad mesh generator using the l norm a new indirect way of producing all quad meshes is presented the method takes advantage of a well known algorithm of the graph theory namely the blossom algorithm that computes the minimum cost perfect matching in a graph in polynomial time then the triangulation itself is taylored with the aim of producing right triangles in the domain this is done using the infinity norm to compute distances in the meshing process the alignement of the triangles is controlled by a cross field that is defined on the domain meshes constructed this way have their points aligned with the cross field direction and their triangles are almost right everywhere then recombination with our blossom based approach yields quadrilateral meshes of excellent quality

sensitivity analysis of the optimal assignment abstract this paper concentrates on sensitivity analysis of the optimal solution for the assignment problem ap due to the high degeneracy of the ap traditional sensitivity analysis which determines the range in which the current optimal basis remains optimal is impractical thus changing the optimal basis does not ensure that the optimal assignment will be changed herein we investigate the properties of the ap and then propose several lemmas to determine two other types of sensitivity range the first type is used to determine the range in which the current optimal assignment remains optimal we further discuss what is the new optimal assignment when the changes surpass the range the second type of sensitivity range is to determine those values of assignment model parameters for which the rate of change of optimal value function remains constant an example is presented in order to demonstrate that the approaches are useful in practice

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

parrondo s paradox and complementary parrondo processes abstract parrondo s paradox has gained a fair amount of attention due to it being counter intuitive given two stochastic processes both of which are losing in nature it is possible to have an overall net increase in capital by periodically or randomly alternating between the two processes in this paper we analyze the paradox with a different approach in which we start with one process and seek to derive its complementary process we will also state the conditions required for this to occur possible applications of our results include the development of future models based on the paradox