development of a stabilised petrov galerkin formulation for conservation laws in lagrangian fast solid dynamics a stabilised second order finite element methodology is presented for the numerical simulation of a mixed conservation law formulation in fast solid dynamics the mixed formulation where the unknowns are linear momentum deformation gradient and total energy can be cast in the form of a system of first order hyperbolic equations the difficulty associated with locking effects commonly encountered in standard pure displacement formulations is addressed by treating the deformation gradient as one of the primary variables the formulation is first discretised in space by using a stabilised petrov galerkin pg methodology derived through the use of variational work conjugate principles the semi discretised system of equations is then evolved in time by employing a total variation diminishing runge kutta tvd rk time integrator the formulation achieves optimal convergence e g second order with linear interpolation with equal orders in velocity or displacement and stresses in contrast with the displacement based approach this paper defines a set of appropriate stabilising parameters suitable for this particular formulation where the results obtained avoid the appearance of non physical spurious zero energy modes in the solution over a long term response we also show that the proposed pg formulation is very similar and under certain conditions identical to the well known two step taylor galerkin 2tg a series of numerical examples are presented in order to assess the performance of the proposed algorithm the new formulation is proven to be very efficient in nearly incompressible and bending dominated scenarios

tetrahedral mesh generation based on node insertion in crystal lattice arrangements and advancing front delaunay triangulation a method of unstructured technical mesh generation for general three dimensional domains is presented a conventional boundary representation is adopted as the basis for the description of solids with evolving geometry and topology the geometry of the surfaces is represented either analytically or by piecewise polynominal interpolation a preliminary surface mesh is generated by an advancing front method with the nodes inserted by hard sphere packing in physical space in accordance with a prescribed mesh density interior nodes are inserted in a face centered cubic fcc crystal lattice arrangements coupled to octree spatial subdivision with the local lattice parameter determined by a prespecified nodal density function prior to triangulation of the volume the preliminary surface mesh is preprocessed by a combination of local transformations and subdivisions in order to guarantee that the surface triangulation be a subcomplex of the volume delaunay triangulation a joint delaunay triangulation of the interior and boundary nodes which preserves the modified surface mesh is then constructed via an advancing front approach the resulting mesh is finally improved upon by the application of local transformations the overall time complexity of the mesher is o n log n the robustness and versatility of the approach as well as the good quality of the resulting meshes is demostrated with the aid of selected examples

boundary recovery for three dimensional conforming delaunay triangulation we present an efficient boundary recovery method for conforming delaunay triangulation of three dimensional domains our method combines local transformations like edges faces swappings and modified constrained delaunay refinement like edges faces splittings to recover the missing boundary edges and faces its convergence is theoretically proved its effectiveness is also demonstrated through some meshing examples

parallel processing for the simulation of problems involving scattering of electromagnetic waves abstract the three dimensional simulation of the scattering of electromagnetic waves by obstacles of arbitrary geometrical shape is considered maxwell s curl equations are solved in the time domain on an unstructured mesh of linear tetrahedral elements the discrete equations are formed by a galerkin procedure with a lax wendroff consistent numerical flux function and explicit time stepping parallelisation of the procedure is achieved by mesh decomposition and the use of a single program multiple data model the approach is first validated and is then applied to problems involving the scattering of plane electromagnetic waves by a complete aircraft

generation of tetrahedral mesh of variable element size by sphere packing over an unbounded 3d domain this paper describes an algorithm for the generation of tetrahedral mesh of specified element size over an unbounded three dimensional domain starting from an arbitrary point in space defined as the origin and guided by the concept of advancing front spheres of size compatible with the specified element size are packed tightly together one by one to form a cluster of spheres of different sizes the compactness of the cluster of spheres is achieved by packing spheres at a site closest to the origin in a densest manner with tangent but no overlapping with as many other spheres as possible in view of these criteria a rotational mechanism between spheres is innovated which allows the newly inserted sphere to follow the path by rotation between existing spheres until the lowest point is reached the centres of the packing spheres provide ideal locations for delaunay point insertion to form a triangulation of tetrahedral elements of size compatible with the specified value spheres of random size distribution or of size specified by a node spacing function are packed by the proposed algorithm in all test examples high quality tetrahedral elements of size consistent with the specified node spacing are generated the process is fast and robust and the time complexity for mesh generation is expected to be almost linear however in the present implementation a quasi linear time relationship is observed as a search for the nearest node on the front is proposed in the sphere packing process the memory requirement has been kept to a minimum as no additional data structure other than the adjacency relationship of the tetrahedral elements as required by the delaunay triangulation is stored the structure of the advancing frontal surface needs not be explicitly constructed nor updated as it is simply not required in the sphere packing process

fast and robust delaunay tessellation in periodic domains an algorithm is presented for constructing three dimensional delaunay tessellations in periodic domains applications include mesh generation for periodic transport problems and geometric decomposition for modelling particulate structures the algorithm is a point insertion technique and although the general framework is similar to point insertion in a convex hull a number of new issues are introduced by periodicity these issues are discussed in detail in the context of the computational algorithm examples are given for the tessellation of random points and random sphere packings performance data for the algorithm are also presented these data show an empirical scaling of the computation time with size of o n1 11 and tessellation rates of 7000 14000 tetrahedrons per second for the problems studied up to 105 points a breakdown of the performance is given which shows the computational load is shared most heavily by two specific parts of the point insertion procedure copyright 2002 john wiley sons ltd

three dimensional unstructured mesh generation part 1 fundamental aspects of triangulation and point creation abstract the present paper introduces an alternative approach for delaunay triangulation in which the triangulation is mapped from an equivalent convex hull in a higher dimension furthermore some fundamental aspects of a point creation algorithm for unstructured mesh generation have been addressed based on numerical experiments a point spacing tensor and point insertion criterion have been introduced aiming to deal with anisotropic meshes

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

random walk access times on partially disordered complex networks an effective medium theory an analytic effective medium theory is constructed to study the mean access times for random walks on hybrid disordered structures formed by embedding complex networks into regular lattices considering transition rates f that are different for steps across lattice bonds from the rates f across network shortcuts the theory is developed for structures with arbitrary shortcut distributions and applied to a class of partially disordered traversal enhanced networks in which shortcuts of fixed length are distributed randomly with finite probability numerical simulations are found to be in excellent agreement with predictions of the effective medium theory on all aspects addressed by the latter access times for random walks on these partially disordered structures are compared to those on small world networks which on average appear to provide the most effective means of decreasing access times uniformly across the network

grad div stablilization for stokes equations in this paper a stabilizing augmented lagrangian technique for the stokes equations is studied the method is consistent and hence does not change the continuous solution we show that this stabilization improves the well posedness of the continuous problem for small values of the viscosity coefficient we analyze the influence of this stabilization on the accuracy of the finite element solution and on the convergence properties of the inexact uzawa method

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

efficient surface reconstruction from contours based on two dimensional delaunay triangulation this paper introduces an efficient method for surface reconstruction from sectional contours the surface between neighbouring sections is reconstructed based on the consistent utilization of the two dimensional constrained delaunay triangulation the triangulation is used to extract the parametric domain and to solve the problems associated with correspondence tiling and branching in a general framework natural distance interpolations are performed in order to complete the mapping of the added intermediate points surface smoothing and remeshing are conducted to optimize the initial surface triangulations several examples are presented to demonstrate the effectiveness and efficiency of the proposed approach

boundary recovery after 3d delaunay tetrahedralization without adding extra nodes in this paper we investigate boundary recovery the problem that has troubled researchers ever since delaunay based methods were applied to generate mesh there are a number of algorithms for boundary recovery already and most of them depend heavily on adding extra nodes in this paper we make an effort to seek a method to recover boundaries without using extra nodes it was noted that some previous algorithms imposed artificial boundary constraints on a meshing problem at the recovering stage we first try to discard these artificial constraints and thus make things easier then a new method is proposed by which the boundaries can be recovered by means of two operations 1 creating a segment in the mesh and 2 removing a segment from the mesh both operations are special cases of a general local transformation called small polyhedron reconnection operation the method works well when coupled with the sphere packing method proposed by the first author if the mesh sizing function is suitable a good configuration of nodes will be created accordingly by the sphere packing method and the boundary can be recovered by the local transformation presented here without inserting extra nodes

reduced order mesh optimisation using proper orthogonal decomposition and a modified cuckoo search summary a new mesh optimisation scheme reduced order mesh optimisation is introduced the technique uses proper orthogonal decomposition to reduce the number of dimensions in a mesh optimisation problem this reduction in dimensionality allows the expression of the optimisation problem globally rather than the more traditional local mesh optimisation or smoothing algorithms to perform the optimisation the recently developed gradient free technique modified cuckoo search is applied the effectiveness of the algorithm is shown by considering the problem of optimising meshes for use in co volume techniques co volume techniques require the existence of two mutually orthogonal meshes this is achieved by utilising the delaunay voronoi dual a combination of considering the problem globally and the use of a gradient free technique results in a scheme that significantly outperforms previous methods in solving this particular problem although the examples presented in this paper are specific to optimising dual meshes the technique is general and can be simply modified to any mesh optimisation problem copyright 2012 john wiley sons ltd

effective medium approximation for lattice random walks with long range jumps we consider the random walk on a lattice with random transition rates and arbitrarily long range jumps we employ bruggeman s effective medium approximation ema to find the disorder averaged coarse grained dynamics the ema procedure replaces the disordered system with a cleverly guessed reference system in a self consistent manner we give necessary conditions on the reference system and discuss possible physical mechanisms of anomalous diffusion in the case of a power law scaling between transition rates and distance lattice variants of l evy flights emerge as the effective medium and the problem is solved analytically bearing the effective anomalous diffusivity finally we discuss several example distributions and demonstrate very good agreement with numerical simulations

extensions of effective medium theory of transport in disordered systems the effective medium theory of transport in disordered systems whose basis is the replacement of spatial disorder by temporal memory is extended in several practical directions restricting attention to a one dimensional system with bond disorder for specificity a transformation procedure is developed to deduce explicit expressions for the memory functions from given distribution functions characterizing the system disorder it is shown how to use the memory functions in the laplace domain forms in which they first appear and in the time domain forms which are obtained via numerical inversion algorithms to address time evolution of the system beyond the asymptotic domain of large times normally treated an analytic but approximate procedure is provided to obtain the memories in addition to the inversion algorithm good agreement of effective medium theory predictions with numerically computed exact results is found for all time ranges for the distributions used except near the percolation limit as expected the use of ensemble averages is studied for normal as well as correlation observables the effect of size on effective medium theory is explored and it is shown that even in the asymptotic limit finite size corrections develop to the well known harmonic mean prescription for finding the effective rate a percolation threshold is shown to arise even in one dimension for finite but not infinite systems at a concentration of broken bonds related to the system size spatially long range transfer rates are shown to emerge naturally as a consequence of the replacement of spatial disorder by temporal memories in spite of the fact that the original rates possess nearest neighbor character pausing time distributions in continuous time random walks corresponding to the effective medium memories are calculated

weak subordination breaking for the quenched trap model we map the problem of diffusion in the quenched trap model onto a different stochastic process brownian motion that is terminated at the coverage time s nx with nx being the number of visits to site x here 0 t t g 1 is a measure of the disorder in the original model this mapping allows us to treat the intricate correlations in the underlying random walk in the random environment the operational time s is changed to laboratory time t with a l evy time transformation investigation of brownian motion stopped at time s yields the diffusion front of the quenched trap model which is favorably compared with numerical simulations in the zero temperature limit of 0 we recover the renormalization group solution obtained by monthus phys rev e 68 036114 2003 our theory surmounts the critical slowing down that is found when 1 above the critical dimension 2 mapping the problem to a continuous time random walk becomes feasible though still not trivial

tensor methods for the boltzmann bgk equation abstract we present a tensor decomposition method to solve the boltzmann transport equation bte in the bhatnagar gross krook approximation the method represents the six dimensional bte as a set of six one dimensional problems which are solved with the alternating least squares algorithm and the discrete fourier transform at n collocation points we use this method to predict the equilibrium distribution steady state simulation and a non equilibrium distribution returning to the equilibrium transient simulation our numerical experiments demonstrate n log n scaling unlike many bte specific numerical techniques the numerical tensor decomposition method we propose is a general technique that can be applied to other high dimensional systems

traversal times for random walks on small world networks we study the mean traversal time for a class of random walks on newman watts small world networks in which steps around the edge of the network occur with a transition rate that is different from the rate for steps across small world connections when f f the mean time to traverse the network exhibits a transition associated with percolation of the random graph i e small world part of the network and a collapse of the data onto a universal curve this transition was not observed in earlier studies in which equal transition rates were assumed for all allowed steps we develop a simple self consistent effective medium theory and show that it gives a quantitatively correct description of the traversal time in all parameter regimes except the immediate neighborhood of the transition as is characteristic of most effective medium theories

a time domain unstructured grid approach to the simulation of electromagnetic scattering in piecewise homogeneous media abstract the simulation of the scattering of plane electromagnetic waves by obstacles constructed from piecewise homogeneous material media is considered the governing equations are maxwell s equations which are expressed in a conservation form the solution is obtained on a grid consisting of an unstructured assembly of linear triangular elements in 2d by modifying a technique developed originally for the solution of the compressible euler equations the computed solution is used to determine the radar scattering width of the obstacle

variational delaunay approach to the generation of tetrahedral finite element meshes we describe an algorithm which generates tetrahedral decomposition of a general solid body whose surface is given as a collection of triangular facets the principal idea is to modify the constraints in such a way as to make them appear in an unconstrained triangulation of the vertex set apriori the vertex set positions are randomized to guarantee existence of a unique triangulation which satisfies the delaunay empty sphere property algorithms for robust parallelized construction of such triangulations are available in order to make the boundary of the solid appear as a collection of tetrahedral faces we iterate two operations edge flip and edge split with the insertion of additional vertex until all of the boundary facets are present in the tetrahedral mesh the outcome of the vertex insertion is another triangulation of the input surfaces but one which is represented as a subset of the tetrahedral faces to determine if a constraining facet is present in the unconstrained delaunay triangulation of the current vertex set we use the results of rajan which re formulate delaunay triangulation as a linear programming problem

on the quasistatic approximation in the stokes darcy model of groundwater surface water flows abstract we study the validity of the quasistatic approximation in the fully evolutionary stokes darcy problem for the coupling of groundwater and surface water flows as well as the dependence of the problem on the specific storage parameter in the coupled equations that describe the groundwater and surface water flows for an incompressible fluid the specific storage s 0 represents the volume of water that a fully saturated porous medium will expel or absorb per unit volume per unit change in hydraulic head in confined aquifers s 0 takes values ranging from 1 0 6 or smaller to 1 0 2 in this work we analyze the validity of the previously studied quasistatic approximation setting s 0 0 in the stokes darcy equations by proving that the weak solution of the fully evolutionary stokes darcy problem approaches the weak solution of the quasistatic problem as s 0 0 we also estimate the rate of convergence

shape reconstruction and volume meshing for complex solids the reconstruction of a solid surface from a series of cross sections and the generation of a volume mesh that conforms with a prescribed surface are issues that arise in numerous applications we describe an approach to both these problems that is based on the generation of a tetrahedral mesh which automatically captures a triangulation of the surface points a simple algorithm for introducing a set of interior points permits a simple partition of the volume mesh into two disjoint sets of tetrahedra such that one set determines the interior of the solid while the second determines the exterior

a crank nicolson leapfrog stabilization we propose and analyze a linear stabilization of the crank nicolson leapfrog cnlf method that removes all time step cfl conditions for stability and controls the unstable mode it also increases the spd part of the linear system to be solved at each time step while increasing solution accuracy we give a proof of unconditional stability of the method as well as a proof of unconditional asymptotic stability of both the stable and unstable modes we illustrate two applications of the method uncoupling groundwater surface water flows and stokes flow plus a coriolis term

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

robust linear regression with broad distributions of errors abstract we consider the problem of linear fitting of noisy data in the case of broad say stable distributions of random impacts noise which can lack even the first moment this situation common in statistical physics of small systems in earth sciences in network science or in econophysics does not allow for application of conventional gaussian maximum likelihood estimators resulting in usual least squares fits such fits lead to large deviations of fitted parameters from their true values due to the presence of outliers the approaches discussed here aim onto the minimization of the width of the distribution of residua the corresponding width of the distribution can either be defined via the interquantile distance of the corresponding distributions or via the scale parameter in its characteristic function the methods provide the robust regression even in the case of short samples with large outliers and are equivalent to the normal least squares fit for the gaussian noises our discussion is illustrated by numerical examples

a new triangular and tetrahedral basis for high order hp finite element methods in this paper we describe the foundations of a new hierarchical modal basis suitable for high order hp finite element discretizations on unstructured meshes it is based on a generalized tensor product of mixed weight jacobi polynomials the generalized tensor product property leads to a low operation count with the use of sum factorization techniques variable p order expansions in each element are readily implemented which is a crucial property for efficient adaptive discretizations numerical examples demonstrate the exponential convergence for smooth solutions and the ability of this formulation to handle easily very complex two and three dmensional computational domains employing standard meshes

reaction diffusion on random spatial networks with scale free jumping rates via effective medium theory we study epidemic processes using a metapopulation approach on the line featuring random transport rates between arbitrarily distant sites an average transport network is found using a recently developed variant of the effective medium approximation ema that is capable of dealing with these long range connections using a feynman kac argument in the effective medium we derive an estimate on the size of the infected domain and reproduce the known result of its exponential growth in time we hereby demonstrate the applicability of long range ema to dynamical processes on networks more intricate than simple diffusion

the stabilized extrapolated trapezoidal finite element method for the navier stokes equations abstract we consider a fully discrete stabilized finite element method for the navier stokes equations which is unconditionally stable and has second order temporal accuracy of o k 2 hk spatial error the method involves a simple artificial viscosity stabilization of the linear system for the approximation of the new time level connected to anti diffusion of its effects at the old time level lowering the cell reynolds number of the oseen problem to o 1 the method requires only the solution of one linear system arising from an oseen problem per time step the effectiveness of the method is illustrated in several numerical experiments

implicit explicit methods for time dependent partial differential equations implicit explicit imex schemes have been widely used especially in conjunction with spectral methods for the time integration of spatially discretized partial differential equations pdes of diffusion convection type typically an implicit scheme is used for the diffusion term and an explicit scheme is used for the convection term reaction diffusion problems can also be approximated in this manner in this work we systematically analyze the performance of such schemes propose improved new schemes and pay particular attention to their relative performance in the context of fast multigrid algorithms and of aliasing reduction for spectral methods for the prototype linear advection diffusion equation a stability analysis for first second third and fourth order multistep imex schemes is performed stable schemes permitting large time steps for a wide variety of problems and yielding appropriate decay of high frequency error modes are identified numerical experiments demonstrate that weak decay

error estimates of the partitioned time stepping method for the evolutionary stokes darcy flows abstract this paper analyzes some new error estimates for a backward euler partitioned time stepping algorithm which was proposed in mu and zhu 2010 for the non stationary stokes darcy problem with beavers joseph saffman interface condition the well known mini elements and the linear lagrangian elements are used in the fluid flow region and the porous media flow region respectively we prove that the error estimates for the fluid velocity and the piezometric head in l 2 norm are optimal moreover under a modest time step restriction t c we prove that the error estimates for the fluid velocity and the piezometric head in h 1 norm are t 7 8 h and for the pressures in l 2 norm are t 3 4 h respectively

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

delaunay triangulation in computational fluid dynamics abstract a method which utilises the delaunay criterion is described by which computational grids consisting of assemblies of triangles or tetrahedra can be constructed an algorithm is briefly outlined to construct the triangulation and its dual the voronoi diagram issues related to how to construct boundary conforming grids from such a triangulation are addressed and details are presented of how grid points within the domain can be generated automatically the point generation algorithm utilises either the given boundary point distribution or for grid adaption a background mesh computational aspects of constructing the triangulation in both 2 and 3 dimensions are covered examples of meshes and flow computations for a range of aerospace geometries are presented

recent developments in imex methods with time filters for systems of evolution equations this report presents a summary of the numerical analysis of time filters used to control the unstable mode in the crank nicolson leapfrog discretization of evolution equations

fast and accurate simulations of air cooled structures there are fields of engineering for which the cad based navier stokes solvers are too expensive architecture and medicine for blood flows are two such examples mesh generation and adaptation is also a bottleneck because the users are not expected to have the know how we report here on a navier stokes solver for incompressible temperature and time dependent flows dedicated to architectural applications the building blocks are not new a finite element method with time implicit pressure projection steps and mesh adaptativity but putting them together in an easy to use and efficient 3d code is the challenge which motivates this paper for non engineering applications the user interface is a big problem in an earlier attempt we designed freefem3d based on a fictitious domain discretization thus avoiding boundary fitted mesh however it turned out that the display of the solutions requires a boundary fitted mesh it is possible to generate a feasible surface mesh for graphics but it is much more difficult to generate a feasible surface mesh for fem in this project the user interface is taken from freefem3d then with a marching cube algorithm we produce a graphic only feasible mesh finally a surface mesh adapted to a fem computation is constructed with an adaptation module and the result is used as input to a delaunay volumic mesh generator the solver is optimized and parallelized all modules are the authors work three applications are presented for which the data preparation takes less than a day and results are obtained overnight on a pc cluster one of the application is presented in details it is an air cooling system for a canister containing radio nucleides

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

algebraic mesh quality metrics quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics the theory based on the jacobian and related matrices provides a means of constructing classifying and evaluating mesh quality metrics the jacobian matrix is factored into geometrically meaningful parts a nodally invariant jacobian matrix can be defined for simplicial elements using a weight matrix derived from the jacobian matrix of an ideal reference element scale and orientation invariant algebraic mesh quality metrics are defined the singular value decomposition is used to study relationships between metrics equivalence of the element condition number and mean ratio metrics is proved the condition number is shown to measure the distance of an element to the set of degenerate elements algebraic measures for skew length ratio shape volume and orientation are defined abstractly with specific examples given two combined metrics shape volume and shape volume orientation are algebraically defined and examples of such metrics are given algebraic mesh quality metrics are extended to nonsimplicial elements a series of numerical tests verifies the theoretical properties of the metrics defined

analysis of long time stability and errors of two partitioned methods for uncoupling evolutionary groundwater surface water flows the most effective simulations of the multiphysics coupling of groundwater to surface water must involve employing the best groundwater codes and the best surface water codes partitioned methods which solve the coupled problem by successively solving the subphysics problems have recently been studied for the stokes darcy coupling with convergence established over bounded time intervals with constants growing exponentially in t this report analyzes and tests two such partitioned noniterative domain decomposition methods for the fully evolutionary stokes darcy problem under a modest time step restriction of the form delta t leq c where c c physical parameters we prove unconditional long time over 0 leq t infty stability of both partitioned methods from this we derive an optimal error estimate that is uniform in time over 0 leq t infty

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

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

an imprint and merge algorithm incorporating geometric tolerances for conformal meshing of misaligned assemblies a size tolerant algorithm for imprinting and merging adjacent part geometries is presented in this paper this approach cleans up misaligned and dirty assembly geometry that is intended for conformal mesh generation the algorithm first discretizes the boundary edges of adjacent faces into linear segments the segments are then intersected and a partial intersection graph is calculated from the intersection results the intersections are calculated by accounting for size tolerances to minimize the effect of misaligned parts on the meshing process the partial intersection graph is next used to imprint the adjacent faces as appropriate the imprints are generated using virtual geometry so that the tolerant topology created therein can be employed several examples are given to demonstrate the resulting improvement in the mesh quality of conformal meshes the approach is shown to work robustly with misaligned and poorly defined parts

transport properties of random walks on scale free regular lattice hybrid networks we study numerically the mean access times for random walks on hybrid disor dered structures formed by embedding scale free networks into regular lattices considering different transition rates for steps across lattice bonds f and across network shortcuts f for fast shortcuts f f 1 and low shortcut densities traversal time data collapse onto a universal curve while a crossover behavior that can be related to the percolation threshold of the scale free network component is identified at higher shortcut densities in analogy to similar observations reported recently in newman watts small world networks further more we observe that random walk traversal times are larger for networks with a higher degree of inhomogeneity in their shortcut distribution and we discuss access time distri butions as functions of the initial and final node degrees these findings are relevant in particular when considering the optimization of existing information networks by the addi tion of a small number of fast shortcut connections

decoupled schemes for a non stationary mixed stokes darcy model we study numerical methods for solving a non stationary mixed stokes darcy problem that models coupled fluid flow and porous media flow a decoupling approach based on interface approximation via temporal extrapolation is proposed for devising decoupled marching algorithms for the mixed model error estimates are derived and numerical experiments are conducted to demonstrate the computational effectiveness of the decoupling approach

tetrahedral mesh generation and optimization based on centroidal voronoi tessellations the centroidal voronoi tessellation based delaunay triangulation cvdt provides an optimal distribution of generating points with respect to a given density function and accordingly generates a high quality mesh in this paper we discuss algorithms for the construction of the constrained cvdt from an initial delaunay tetrahedral mesh of a three dimensional domain by establishing an appropriate relationship between the density function and the specified sizing field and applying the lloyd s iteration the constrained cvdt mesh is obtained as a natural global optimization of the initial mesh simple local operations such as edges faces flippings are also used to further improve the cvdt mesh several complex meshing examples and their element quality statistics are presented to demonstrate the effectiveness and efficiency of the proposed mesh generation and optimization method copyright 2003 john wiley sons ltd

a first order hyperbolic framework for large strain computational solid dynamics part i total lagrangian isothermal elasticity abstract this paper introduces a new computational framework for the analysis of large strain fast solid dynamics the paper builds upon previous work published by the authors gil et al 2014 48 where a first order system of hyperbolic equations is introduced for the simulation of isothermal elastic materials in terms of the linear momentum the deformation gradient and its jacobian as unknown variables in this work the formulation is further enhanced with four key novelties first the use of a new geometric conservation law for the co factor of the deformation leads to an enhanced mixed formulation advantageous in those scenarios where the co factor plays a dominant role second the use of polyconvex strain energy functionals enables the definition of generalised convex entropy functions and associated entropy fluxes for solid dynamics problems moreover the introduction of suitable conjugate entropy variables enables the derivation of a symmetric system of hyperbolic equations dual of that expressed in terms of conservation variables third the new use of a tensor cross product 61 greatly facilitates the algebraic manipulations of expressions involving the co factor of the deformation fourth the development of a stabilised petrov galerkin framework is presented for both systems of hyperbolic equations that is when expressed in terms of either conservation or entropy variables as an example a polyconvex mooney rivlin material is used and for completeness the eigen structure of the resulting system of equations is studied to guarantee the existence of real wave speeds finally a series of numerical examples is presented in order to assess the robustness and accuracy of the new mixed methodology benchmarking it against an ample spectrum of alternative numerical strategies including implicit multi field fraeijs de veubeke hu washizu variational type approaches and explicit cell and vertex centred finite volume schemes

a new jameson schmidt turkel smooth particle hydrodynamics algorithm for large strain explicit fast dynamics this paper presents a new smooth particle hydrodynamics sph computational framework for large strain explicit solid dynamics a mixed based set of total lagrangian conservation laws bonet et al 2015 gil et al 2016 is presented in terms of the linear momentum and an extended set of geometric strain measures comprised of the deformation gradient its co factor and the jacobian taking advantage of this representation the main aim of this paper is the adaptation of the very efficient jameson schmidt turkel jst algorithm jameson et al 1981 extensively used in computational fluid dynamics to a sph based discretisation of the mixed based set of conservation laws with three key distinct novelties first a conservative jst based sph computational framework is presented with emphasis in nearly incompressible materials second the suppression of numerical instabilities associated with the non physical zero energy modes is addressed through a well established stabilisation procedure third the use of a discrete angular momentum projection algorithm is presented in conjunction with a monolithic total variation diminishing runge kutta time integrator in order to guarantee the global conservation of angular momentum for completeness exact enforcement of essential boundary conditions is incorporated through the use of a lagrange multiplier projection technique a series of challenging numerical examples e g in the near incompressibility regime are examined in order to assess the robustness and accuracy of the proposed algorithm the obtained results are benchmarked against a wide spectrum of alternative numerical strategies

three dimensional unstructured mesh generation part 3 volume meshes abstract volume meshes are generated through three dimensional triangulation and interior point creation based on the surface meshes to deal with non convex geometries boundary surface conformity is gained via edge swapping boundary edge and surface recovery and the robustness of the algorithm has been discussed in terms of the accuracy of geometric judgements the performane of the mesh generator has been investigated by means of numerical experiments and examples have been tested to validate the mesh generator the possibility of extension of this mesh generator to incorporate with analysis programs in terms of adaptive analysis has been explored this paper is also designed to briefly address mesh quality measures quality statistics and mesh smoothing techniques using mesh quality metrics visual quality assessment has been discussed furthermore several general ways of visual representation of volume meshes have been introduced

a novel energy based approach for merging finite elements a novel approach for merging two intersecting finite elements is presented and demonstrated the solution mimics concepts from biology and uses principles rooted in continuum mechanics the problem of attaching or merging two coincident finite elements is common when using the plastering technique as part of the advancing front method this problem is particularly challenging for 3 d meshes of non convex shapes some automatic meshing methods require portions of the partially formed mesh to coincide and merge this problem is generally solved with heuristic rules which lack generality and may have difficulties with unforeseen situations the problem of merging two overlapping polyhedra may also appear in other applications such as computer graphics and cad software a new approach to address the problem of merging is presented here this solution does not utilize heuristic rules but rather uses an approach based on minimization of strain energy a fully automatic merging routine has been created that can address in an optimum way any situation of two nearby or overlapping elements that are to be merged this approach with minor adjustments is suitable for most types of 3 d elements

delaunay s mesh of a convex polyhedron in dimension d application to arbitrary polyhedra this paper presents a method for creating a delaunay triangulation connected to a set of specified points the theoretical aspect is recalled for an arbitrary dimension and the method is discussed in order to derive a practical approach valid for dimensions 2 and 3 which is simple robust and well adapted to computation convex polyhedral and arbitrary polyhedral situations are introduced

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