local optimization based simplicial mesh untangling and improvement we present an optimization based approach for mesh untangling that maximizes the minimum area or volume of simplicial elements in a local submesh these functions are linear with respect to the free vertex position thus the problem can be formulated as a linear program that is solved by using the computationally inexpensive simplex method we prove that the function level sets are convex regardless of the position of the free vertex and hence the local subproblem is guaranteed to converge maximizing the minimum area or volume of mesh elements although well suited for mesh untangling is not ideal for mesh improvement and its use often results in poor quality meshes we therefore combine the mesh untangling technique with optimization based mesh improvement techniques and expand previous results to show that a commonly used two dimensional mesh quality criterion can be guaranteed to converge when starting with a valid mesh typical results showing the effectiveness of the combined untangling and smoothing techniques are given for both two and three dimensional simplicial meshes

application of log sobolov inequality to the stochastic dynamics of unbounded spin systems on the lattice abstract we consider a ferromagnetic lattice spin system with unbounded spins and investigate the relaxation property for the associated stochastic dynamics the glauber dynamics in the finite volume case we prove that the following two conditions are equivalent 1 the log sobolev inequality for the finite volume gibbs states holds uniformly in both the volume and the boundary condition 2 the finite volume glauber dynamics relaxes to equilibrium exponentially fast uniformly in the volume whenever it starts from a tempered configuration this can be considered as a complementary result to the ones previously obtained for infinite volume glauber dynamics by b zegarlinski 1996 comm math phys 175 401 432 our result can also be viewed as an extension of the equivalence theorem known for compact spin space settings

hydrodynamic scaling limits with deterministic initial configurations we discuss the hydrodynamic scaling limits starting with deterministic configurations for different models certain estimates on the entropy of the system are derived

simultaneous untangling and smoothing of tetrahedral meshes abstract the quality improvement in mesh optimisation techniques that preserve its connectivity are obtained by an iterative process in which each node of the mesh is moved to a new position that minimises a certain objective function the objective function is derived from some quality measure of the local submesh that is the set of tetrahedra connected to the adjustable or free node although these objective functions are suitable to improve the quality of a mesh in which there are non inverted elements they are not when the mesh is tangled this is due to the fact that usual objective functions are not defined on all r 3 and they present several discontinuities and local minima that prevent the use of conventional optimisation procedures otherwise when the mesh is tangled there are local submeshes for which the free node is out of the feasible region or this does not exist in this paper we propose the substitution of objective functions having barriers by modified versions that are defined and regular on all r 3 with these modifications the optimisation process is also directly applicable to meshes with inverted elements making a previous untangling procedure unnecessary this simultaneous procedure allows to reduce the number of iterations for reaching a prescribed quality to illustrate the effectiveness of our approach we present several applications where it can be seen that our results clearly improve those obtained by other authors

anisotropic mesh adaptation for 3d flows on structured and unstructured grids abstract this paper presents a mesh optimization methodology in three dimensions mom3d an initial mesh is continually adapted during the solution process without the need for global remeshing the adaptation procedure uses an interpolation error estimate whose magnitude and direction are controlled by the hessian the matrix of second derivatives of the solution this metric error is projected over mesh edges and drives the nodal movement scheme as well as the edge refinement and coarsening strategies these operations yield highly anisotropic grids in which the mesh movement significantly contributes to the stretching and realignment of the edges along unidirectional features of flow problems the results presented have been chosen to illustrate some important points first the method is gauged on problems with exact solutions demonstrating good agreement between the error estimate and the true error as well as an equidistribution of the error the cost effectiveness of grid adaptation is then addressed by determining the size of an anisotropic grid that would be equivalent to that of a given non adapted finer grid for the same error level the capture of sharp discontinuities through highly anisotropic grids is illustrated on a transonic flow flow in a gas turbine combustor demonstrates how automatically generated meshes can sometimes cause convergence difficulties and how mesh adaptation can cure these ills finally the flow over a wing nacelle pylon configuration is studied to further validate the solver mesh adaptation capabilities by comparing the numerical results against experiments

relative entropy and mixing properties of infinite dimensional diffusions let be a diffusion process taking values on the infinite dimensional space t z where t is the circle and with components satisfying the equations d i i dw i b i dt for some coefficients i and b i i z suppose we have an initial distribution and a sequence of times t n such that lim n s tn exists where s t is the semi group of the process we prove that if i and b i are bounded of finite range have uniformly bounded second order partial derivatives and inf i i 0 then is invariant

a distortion measure to validate and generate curved high order meshes on cad surfaces with independence of parameterization the first author was sponsored by cur from diue of the generalitat de catalunya and the european social fund grants fi dgr 11 and be dgr 12 and by the ferran sunyer i balaguer foundation grant fsb 13 the work of the corresponding author was partially supported by the boeing co us air force office of scientific research european commission through the boeing mit alliance the computational math program marie sklodowska curie actions hipermegaflows individual fellowship grant

mesh smoothing using a posteriori error estimates we develop a simple mesh smoothing algorithm for adaptively improving finite element triangulations the algorithm makes use of a posteriori error estimates which are now widely used in finite element calculations in this paper we derive the method present some numerical illustrations and give a brief analysis of the issue of uniqueness

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

tetrahedral mesh improvement via optimization of the element condition number the authors present a new shape measure for tetrahedral elements that is optimal in that it gives the distance of a tetrahedron from the set of inverted elements this measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetrahedron with positive volume using this shape measure they formulate two optimization objective functions that are differentiated by their goal the first seeks to improve the average quality of the tetrahedral mesh the second aims to improve the worst quality element in the mesh they review the optimization techniques used with each objective function and presents experimental results that demonstrate the effectiveness of the mesh improvement methods they show that a combined optimization approach that uses both objective functions obtains the best quality meshes for several complex geometries

new advantages to obtain accurate matrix inversion this paper presents a refinement algorithm for improving the inverse of a given nonsingular matrix here we also improve the previously presented results by setting an efficient refinement algorithm we finally presents the performances of the algorithm supporting by the introduced refitment

on the spectrum of the generator of an infinite system of interacting diffusions we study the spectrum of the operator generating an infinite dimensional diffusion process t in space here is a natural t invariant measure on which is a gibbs distribution corresponding to a formal hamiltonian h of an anharmonic crystal with a value of the inverse temperature 0 for small enough we establish the existence of an l invariant subspace such that has a distinctive character related to a quasi particle picture in particular has a lebesgue spectrum separated from the rest of the spectrum of l and concentrated near a point 1 0 giving the smallest non zero eigenvalue of a limiting problem associated with 0

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

area control in generating smooth and convex grids over general plane regions a new method adaptive smoothness functional to produce convex and smooth grids over general plane regions has been introduced in a recent work by the authors 10 this method belongs to the variational grid generation approach theoretical results showing that a convex grid over a region is obtained when this method is applied were presented the basic assumption was that at least one convex grid exists a procedure to control large cells bilateral smoothness functional in addition to smoothness and convexity was also presented experimental results showing the effectiveness of these methods were reported however no theoretical results were reported assuring that the area control can be always exerted this article continues the same line of research introducing a new version of the bilateral smoothness functional that improves the control of large areas unlike the former method theoretical results show the effectiveness of the new bilateral smoothness functional to exert such control optimal grids obtained with the new functional are compared with those reached using the older version demostrating the improvement

a new proof of moser s parabolic harnack inequality using the old ideas of nash in 1958 nash published his fundamental work on the local holder continuity of solutions of second order parabolic equations with coefficients which need not be smooth 8 the primary purpose of that work was to study the properties of the fundamental solution corresponding to the parabolic operator and from these properties to derive regularity for a general solution though the work is often cited in the literature about weak solutions of elliptic and parabolic equations one feels that nash s ideas were never fully understood and maybe still are not and that because of this the more understandable and seemingly more fruitful ideas of de giorgi 4 and moser 6 7 were subsequently adopted

achieving finite element mesh quality via optimization of the jacobian matrix norm and associated quantities part ii a framework for volume mesh optimization and the condition number of the jacobian matrix three dimensional unstructured tetrahedral and hexahedral finite element mesh optimization is studied from a theoretical perspective and by computer experiments to determine what objective functions are most effective in attaining valid high quality meshes the approach uses matrices and matrix norms to extend the work in part i to build suitable 3d objective functions because certain matrix norm identities which hold for 2 x 2 matrices do not hold for 3 x 3 matrices significant differences arise between surface and volume mesh optimization objective functions it is shown for example that the equivalence in two dimensions of the smoothness and condition number of the jacobian matrix objective functions does not extend to three dimensions and further that the equivalence of the oddy and condition number of the metric tensor objective functions in two dimensions also fails to extend to three dimensions matrix norm identities are used to systematically construct dimensionally homogeneous groups of objective functions the concept of an ideal minimizing matrix is introduced for both hexahedral and tetrahedral elements non dimensional objective functions having barriers are emphasized as the most logical choice for mesh optimization the performance of a number of objective functions in improving mesh quality was assessed on a suite of realistic test problems focusing particularly on all hexahedral whisker weaved meshes performance is investigated on both structured and unstructured meshes and on both hexahedral and tetrahedral meshes although several objective functions are competitive the condition number objective function is particularly attractive the objective functions are closely related to mesh quality measures to illustrate it is shown that the condition number metric can be viewed as a new tetrahedral element quality measure

spline parameterization method for 2d and 3d geometries based on t mesh optimization abstract we present a method to obtain high quality spline parameterization of 2d and 3d geometries for their use in isogeometric analysis as input data the proposed method demands a boundary representation of the domain and it constructs automatically a spline transformation between the physical and parametric domains parameterization of the interior of the object is obtained by deforming isomorphically an adapted parametric t mesh onto the physical domain by applying a t mesh untangling and smoothing procedure which is the key of the method mesh optimization is based on the mean ratio shape quality measure the spline representation of the geometry is calculated by imposing interpolation conditions using the data provided by one to one correspondence between the meshes of the parametric and physical domains we give a detailed description of the proposed technique and show some examples also we present some examples of the application of isogeometric analysis in geometries parameterized with our method

simultaneous untangling and smoothing of moving grids in this work a technique for simultaneous untangling and smoothing of meshes is presented it is based on an extension of an earlier mesh smoothing strategy developed to solve the computational mesh dynamics stage in fluid structure interaction problems in moving grid problems mesh untangling is necessary when element inversion happens as a result of a moving domain boundary the smoothing strategy formerly published by the authors is defined in terms of the minimization of a functional associated with the mesh distortion by using a geometric indicator of the element quality this functional becomes discontinuous when an element has null volume making it impossible to obtain a valid mesh from an invalid one to circumvent this drawback the functional proposed is transformed in order to guarantee its continuity for the whole space of nodal coordinates thus achieving the untangling technique this regularization depends on one parameter making the recovery of the original functional possible as this parameter tends to 0 this feature is very important consequently it is necessary to regularize the functional in order to make the mesh valid then it is advisable to use the original functional to make the smoothing optimal finally the simultaneous untangling and smoothing technique is applied to several test cases including 2d and 3d meshes with simplicial elements as an additional example the application of this technique to a mesh generation case is presented copyright 2008 john wiley sons ltd

a grid generator based on 4 triangles conforming mesh refinement algorithms a procedure to generate 2d meshes of triangles in a quite general fashion allowing for local and selective mesh refinement is presented and discussed the grid generator is based on the iterative application of 4 triangles conforming mesh refinement algorithms for triangulations which are also introduced in this paper these algorithms are modified versions of those proposed in int j numer methods eng 20 745 756 1984 and they can be used for global refinement of a grid as well as for local refinement the grid generator works in the following way given any initial coarse triangulation which properly defines the geometry of the problem a set of user defined refinement subregions ri i 1 2 n and an associated set of tolerance parameters hi an irregular and conforming final triangulation is automatically constructed in such a way that the diameter of all the triangles contained in ri is smaller than hi i 1 2 n moreover all angles in the final triangulation are greater than or equal to half the smallest angle in the initial coarse one the refinement is propagated only to assure the conformity and smoothness of the grid and consequently the number of involved nodes will be minimized the refinement of the final mesh will be determined by the subregions ri and the parameters ni and will be essentially independent of the initial coarse grid the 4 triangles conforming mesh refinement algorithms are presented and their properties discussed the implementation of these techniques is discussed and examples of the application of the grid generator are given

invariance implies gibbsian some new results we investigate stationary distributions of stochastic gradient systems in riemannian manifolds and prove that under certain assumptions such distributions are symmetric these results are extended to countable products of finite dimensional manifolds and applied to gibbs distributions in the case where the single spin spaces are riemannian manifolds in particular we obtain a new result concerning the question whether all invariant measures are gibbsian actually we consider a more general object weak elliptic equations for measures which on the one hand yields the results obtained stronger than the above mentioned statements and on the other hand enables us to give simpler proofs of more general than previously known facts applications to concrete models of lattice systems over d with not necessarily compact spin space are presented also in the case d 3 under certain assumptions of decay of interaction