the geometry of r adaptive meshes generated using optimal transport methods the principles of mesh equidistribution and alignment play a fundamental role in the design of adaptive methods and a metric tensor and mesh metric are useful theoretical tools for understanding a method s level of mesh alignment or anisotropy we consider a mesh redistribution method based on the monge ampere equation which combines equidistribution of a given scalar density function with optimal transport it does not involve explicit use of a metric tensor although such a tensor must exist for the method and an interesting question to ask is whether or not the alignment produced by the metric gives an anisotropic mesh for model problems with a linear feature and with a radially symmetric feature we derive the exact form of the metric which involves expressions for its eigenvalues and eigenvectors the eigenvectors are shown to be orthogonal and tangential to the feature and the ratio of the eigenvalues corresponding to the level of anisotropy is shown to depend both locally and globally on the value of the density function and the amount of curvature we thereby demonstrate how the optimal transport method produces an anisotropic mesh along a given feature while equidistributing a suitably chosen scalar density function numerical results are given to verify these results and to demonstrate how the analysis is useful for problems involving more complex features including for a non trivial time dependant nonlinear pde which evolves narrow and curved reaction fronts

interval process model and non random vibration analysis abstract this paper develops an interval process model for time varying or dynamic uncertainty analysis when information of the uncertain parameter is inadequate by using the interval process model to describe a time varying uncertain parameter only its upper and lower bounds are required at each time point rather than its precise probability distribution which is quite different from the traditional stochastic process model a correlation function is defined for quantification of correlation between the uncertain but bounded variables at different times and a matrix decomposition based method is presented to transform the original dependent interval process into an independent one for convenience of subsequent uncertainty analysis more importantly based on the interval process model a non random vibration analysis method is proposed for response computation of structures subjected to time varying uncertain external excitations or loads the structural dynamic responses thus can be derived in the form of upper and lower bounds providing an important guidance for practical safety analysis and reliability design of structures finally two numerical examples and one engineering application are investigated to demonstrate the feasibility of the interval process model and corresponding non random vibration analysis method

on the minimum eccentric distance sum of bipartite graphs with some given parameters the eccentric distance sum is a novel graph invariant with vast potential in structure activity property relationships this graph invariant displays high discriminating power with respect to both biological activity and physical properties if g vg eg is a simple connected graph then the eccentric distance sum eds of g is defined as d g v vgeg v dg v where eg v is the eccentricity of the vertex v and dg v u vgdg u v is the sum of all distances from the vertex v much extremal work has been done on trees with some given parameters by yu et al 2011 25 li et al 2012 19 and geng et al 2013 6 it is natural to consider this extremal problem on bipartite graphs with some given parameters in this paper sharp lower bound on the eds in the class of all connected bipartite graphs with a given matching number q is determined the minimum eds is realized only by the graph kq n q the extremal graph with the minimum eds in the class of all the n vertex connected bipartite graphs of odd diameter is characterized all the extremal graphs having the minimum eds in the class of all connected n vertex bipartite graphs with a given vertex connectivity are identified as well

error estimation and anisotropic mesh refinement for 3d laminar aerodynamic flow simulations this article considers a posteriori error estimation and anisotropic mesh refinement for three dimensional laminar aerodynamic flow simulations the optimal order symmetric interior penalty discontinuous galerkin discretization which has previously been developed for the compressible navier stokes equations in two dimensions is extended to three dimensions symmetry boundary conditions are given which allow to discretize and compute symmetric flows on the half model resulting in exactly the same flow solutions as if computed on the full model using duality arguments an error estimation is derived for estimating the discretization error with respect to the aerodynamic force coefficients furthermore residual based indicators as well as adjoint based indicators for goal oriented refinement are derived these refinement indicators are combined with anisotropy indicators which are particularly suited to the discontinuous galerkin dg discretization two different approaches based on either a heuristic criterion or an anisotropic extension of the adjoint based error estimation are presented the performance of the proposed discretization error estimation and adaptive mesh refinement algorithms is demonstrated for 3d aerodynamic flows

two laplacians for the distance matrix of a graph abstract we introduce a laplacian and a signless laplacian for the distance matrix of a connected graph called the distance laplacian and distance signless laplacian respectively we show the equivalence between the distance signless laplacian distance laplacian and the distance spectra for the class of transmission regular graphs there is also an equivalence between the laplacian spectrum and the distance laplacian spectrum of any connected graph of diameter 2 similarities between n as a distance laplacian eigenvalue and the algebraic connectivity are established

distance spectra of graphs a survey abstract in 1971 graham and pollack established a relationship between the number of negative eigenvalues of the distance matrix and the addressing problem in data communication systems they also proved that the determinant of the distance matrix of a tree is a function of the number of vertices only since then several mathematicians were interested in studying the spectral properties of the distance matrix of a connected graph computing the distance characteristic polynomial and its coefficients was the first research subject of interest thereafter the eigenvalues attracted much more attention in the present paper we report on the results related to the distance matrix of a graph and its spectral properties

correlation analysis of non probabilistic convex model and corresponding structural reliability technique compared with the probability approach the non probabilistic convex model only requires a small amount of samples to obtain the variation bounds of the imprecise parameters and whereby makes the reliability analysis very convenient and economical in this paper we attempt to propose and create a correlation analysis technique mathematically for the non probabilistic convex model and based on it develop an effective method to construct the multidimensional ellipsoids on the uncertainty a marginal convex model is defined to describe the variation range of each uncertain parameter and a covariance is defined to represent the correlation degree of two uncertain parameters for a multidimensional problem the covariance matrix and correlation matrix can be created through all marginal convex models and covariances based on which the required ellipsoid on the uncertainty can be conveniently achieved by combining the correlation analysis technique and the reliability index approach a non probabilistic reliability analysis method is also developed for uncertain structures six numerical examples are presented to demonstrate the effectiveness of the present method

distance spectra and distance energy of integral circulant graphs the distance energy of a graph g is a recently developed energy type invariant defined as the sum of absolute values of the eigenvalues of the distance matrix of g there was a vast research for the pairs and families of non cospectral graphs having equal distance energy and most of these constructions were based on the join of graphs a graph is called circulant if it is cayley graph on the circulant group i e its adjacency matrix is circulant a graph is called integral if all eigenvalues of its adjacency matrix are integers integral circulant graphs play an important role in modeling quantum spin networks supporting the perfect state transfer in this paper we characterize the distance spectra of integral circulant graphs and prove that these graphs have integral eigenvalues of distance matrix d furthermore we calculate the distance spectra and distance energy of unitary cayley graphs in conclusion we present two families of pairs g1 g2 of integral circulant graphs with equal distance energy in the first family g1 is subgraph of g2 while in the second family the diameter of both graphs is three

on cartesian product of euclidean distance matrices abstract if a r m m and b r n n we define the product a b as a b a j n j m b where denotes the kronecker product and j n is the n n matrix of all ones we refer to this product as the cartesian product of a and b since if d 1 and d 2 are the distance matrices of graphs g 1 and g 2 respectively then d 1 d 2 is the distance matrix of the cartesian product g 1 g 2 we study cartesian products of euclidean distance matrices edms we prove that if a and b are edms then so is the product a b we show that if a is an edm and u is symmetric then a u is an edm if and only if u c j n for some c it is shown that for edms a and b a b is spherical if and only if both a and b are spherical if a and b are edms then we derive expressions for the rank and the moore penrose inverse of a b in the final section we consider the product a b for arbitrary matrices for a r m m b r n n we show that all nonzero minors of a b of order m n 1 are equal an explicit formula for a nonzero minor of order m n 1 is proved the result is shown to generalize the familiar fact that the determinant of the distance matrix of a tree on n vertices does not depend on the tree and is a function only of n

adjoint recovery of superconvergent functionals from pde approximations motivated by applications in computational fluid dynamics a method is presented for obtaining estimates of integral functionals such as lift or drag that have twice the order of accuracy of the computed flow solution on which they are based this is achieved through error analysis that uses an adjoint pde to relate the local errors in approximating the flow solution to the corresponding global errors in the functional of interest numerical evaluation of the local residual error together with an approximate solution to the adjoint equations may thus be combined to produce a correction for the computed functional value that yields the desired improvement in accuracy numerical results are presented for the poisson equation in one and two dimensions and for the nonlinear quasi one dimensional euler equations the theory is equally applicable to nonlinear equations in complex multi dimensional domains and holds great promise for use in a range of engineering disciplines in which a few integral quantities are a key output of numerical approximations

proof for four conjectures about the distance laplacian and distance signless laplacian eigenvalues of a graph abstract the distance laplacian matrix l g of a graph g is defined to be l g diag tr d g where d g denotes the distance matrix of g and diag tr denotes the diagonal matrix of the vertex transmissions in g similarly the distance signless laplacian matrix of g is defined as q g diag tr d g the eigenvalues of l g and q g are called the distance laplacian and distance signless laplacian eigenvalues respectively in this paper four conjectures proposed by m aouchche and p hansen about the largest and the second largest distance laplacian eigenvalues and the second largest distance signless laplacian eigenvalue of a graph are proved

distance spectral radius of graphs with r pendent vertices abstract let g n r be the class of all connected graphs of order n with r pendent vertices in this paper we determine the unique graph with minimal distance spectral radius in g n r in addition we determine the unique graph with maximal distance spectral radius in g n r for each r 2 3 n 3 n 2 n 1

extremal cacti of given matching number with respect to the distance spectral radius a cactus is a connected graph in which any two cycles have at most one common vertex the distance spectral radius g of a graph g is the largest eigenvalue of the distance matrix d g recently many researchers proposed the use of g as a molecular structure descriptor of alkanes in this paper we characterize n vertex cyclic cactus with given matching number m which minimizes the distance spectral radius the resulting cactus also minimizes the hosoya index the wiener index and the randic index in the same class of graphs

the effect of graft transformations on distance signless laplacian spectral radius abstract for a connected graph g the distance signless laplacian spectral radius of g is the spectral radius of its distance signless laplacian matrix q g defined as q g t r g d g where t r g is the diagonal matrix of vertex transmissions of g and d g is the distance matrix of g in this paper we study the effect of three types of graft transformations to decrease and or increase the distance signless laplacian spectral radius as applications on one hand we determine the unique graphs with minimum distance signless laplacian spectral radius among non starlike trees among non caterpillar trees and among non starlike non caterpillar trees respectively and determine the unique trees with third and forth minimum distance signless laplacian spectral radius respectively and on the other hand we determine the unique graphs with maximum distance signless laplacian spectral radius among trees with given maximum degree among trees of a perfect matching with maximum degree among non starlike trees among non caterpillar trees among non starlike non caterpillar trees and among unicyclic odd cycle graphs respectively and determine the unique trees with second and third maximum distance signless laplacian spectral radius respectively and the unique connected graph with second maximum distance signless laplacian spectral radius

on the first two largest distance laplacian eigenvalues of unicyclic graphs abstract the distance laplacian eigenvalues of a connected graph g are the eigenvalues of its distance laplacian matrix l g defined as l g t r g d g where t r g is the diagonal matrix of vertex transmissions of g and d g is the distance matrix of g in this paper we determine the unique unicyclic graphs with maximum largest distance laplacian eigenvalue and minimum second largest distance laplacian eigenvalue respectively

sharp bounds on the distance spectral radius and the distance energy of graphs the d eigenvalues 1 2 p of a graph g are the eigenvalues of its distance matrix d and form the d spectrum of g denoted by specd g the greatest d eigenvalue is called the d spectral radius of g denoted by 1 the d energy ed g of the graph g is the sum of the absolute values of its d eigenvalues in this paper we obtain some lower bounds for 1 and characterize those graphs for which these bounds are best possible we also obtain an upperbound for ed g and determine those maximal d energy graphs

on distance matrices and laplacians we consider distance matrices of certain graphs and of points chosen in a rectangular grid formulae for the inverse and the determinant of the distance matrix of a weighted tree are obtained results concerning the inertia and the determinant of the distance matrix of an unweighted unicyclic graph are proved if d is the distance matrix of a tree then we obtain certain results for a perturbation of d 1 as an example it is shown that if l is the laplacian matrix of an arbitrary connected graph then d 1 l 1 is an entrywise positive matrix we consider the distance matrix of a subset of a rectangular grid of points in the plane if we choose m k 1 points not containing a closed path in an m k grid then a formula for the determinant of the distance matrix of such points is obtained

distance matrix and laplacian of a tree with attached graphs a tree with attached graphs is a tree together with graphs defined on its partite sets we introduce the notion of incidence matrix laplacian and distance matrix for a tree with attached graphs formulas are obtained for the minors of the incidence matrix and the laplacian and for the inverse and the determinant of the distance matrix the case when the attached graphs themselves are trees is studied more closely several known results including the matrix tree theorem are special cases when the tree is a star the case when the attached graphs are paths is also of interest since it is related to the transportation problem

optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval an optimization method for uncertain structures is suggested based on convex model and a satisfaction degree of interval in the investigated problem the uncertainty only exists in constraints convex model is used to describe the uncertainty in which the intervals of the uncertain parameters are only needed not necessarily to know the precise probability distributions a satisfaction degree of interval which represents the possibility that one interval is smaller than another is employed to deal with the uncertain constraints based on a predetermined satisfaction degree level the uncertain constraints are transformed to deterministic ones and the transformed optimization problem can be solved by traditional optimization methods for complex structural problems that the optimization model cannot be expressed in an explicit form the interval analysis method is adopted to calculate the intervals of the constraints efficiently and whereby eliminate the optimization nesting two numerical examples have been presented to demonstrate the efficiency of the suggested method

an anisotropic error indicator based on zienkiewicz zhu error estimator application to elliptic and parabolic problems the anisotropic error indicator presented in m picasso comm numer methods engrg 19 2003 pp 13 23 in the frame of the laplace equation is extended to elliptic and parabolic problems our error indicator is derived using the anisotropic interpolation estimates of l formaggia and s perotto numer math 89 2001 pp 641 667 l formaggia and s perotto numer math 2002 doi 10 1007 s002110200415 together with a zienkiewicz zhu error estimator to approach the error gradient a numerical study of the effectivity index is proposed for elliptic diffusion convection and parabolic problems an adaptive algorithm is implemented aimed at controlling the relative estimated error

on the distance and distance signless laplacian spectral radii of bicyclic graphs abstract the unique graphs with minimum and second minimum distance distance signless laplacian respectively spectral radii are determined among bicyclic graphs with fixed number of vertices

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

time accurate anisotropic goal oriented mesh adaptation for unsteady flows we present a new algorithm for combining an anisotropic goal oriented error estimate with the mesh adaptation fixed point method for unsteady problems the minimization of the error on a functional provides both the density and the anisotropy stretching of the optimal mesh they are expressed in terms of state and adjoint this method is used for specifying the mesh for a time sub interval a global fixed point iterates the re evaluation of meshes and states over the whole time interval until convergence of the space time mesh applications to unsteady blast wave and acoustic wave euler flows are presented

the generalized distance matrix of digraphs abstract let d g and d q g d i a g t r d g be the distance matrix and distance signless laplacian matrix of a simple strongly connected digraph g respectively where d i a g t r diag d 1 d 2 d n be the diagonal matrix with vertex transmissions of the digraph g to track the gradual change of d g into d q g in this paper we propose to study the convex combinations of d g and d i a g t r defined by d g d i a g t r 1 d g 0 1 this study reduces to merging the distance spectral and distance signless laplacian spectral theories the eigenvalue with the largest modulus of d g is called the d spectral radius of g denoted by g we determine the digraph which attains the maximum or minimum d spectral radius among all strongly connected digraphs moreover we also determine the digraphs which attain the minimum d spectral radius among all strongly connected digraphs with given parameters such as dichromatic number vertex connectivity or arc connectivity

on distance spectral radius of graphs abstract we determine the unique tree of given domination number with minimum distance spectral radius and the unique connected graph tree of given domination number with maximum distance spectral radius we also determine the unique tree of given bipartition size with minimum distance spectral radius and the unique connected bipartite graph tree of given bipartition size with maximum distance spectral radius finally we determine the unique trees with the second and the third minimum maximum respectively distance spectral radii among the trees on n 6 vertices

connectivity diameter independence number and the distance spectral radius of graphs abstract the distance spectral radius of a graph is the largest eigenvalue of its distance matrix x l zhang 2012 31 determined the n vertex graphs of given diameter with the minimum distance spectral radius in this paper we generalize this result by characterizing the graphs of order n with given connectivity and diameter having minimum distance spectral radius in addition we determine the minimum distance spectral radius of graphs among the n vertex graphs with given connectivity and independence number and characterize the corresponding extremal graph thus determining the minimum distance spectral radius of graphs among n vertex graphs with given connectivity resp independence number

anisotropic norm oriented mesh adaptation for a poisson problem we present a novel formulation for the mesh adaptation of the approximation of a partial differential equation pde the discussion is restricted to a poisson problem the proposed norm oriented formulation extends the goal oriented formulation since it is equation based and uses an adjoint at the same time the norm oriented formulation somewhat supersedes the goal oriented one since it is basically a solution convergent method indeed goal oriented methods rely on the reduction of the error in evaluating a chosen scalar output with the consequence that as mesh size is increased more degrees of freedom only this output is proven to tend to its continuous analog while the solution field itself may not converge a remarkable quality of goal oriented metric based adaptation is the mathematical formulation of the mesh adaptation problem under the form of the optimization in the well identified set of metrics of a well defined functional in the new proposed formulation we amplify this advantage we search in the same well identified set of metrics the minimum of a norm of the approximation error the norm is prescribed by the user and the method allows addressing the case of multi objective adaptation like for example in aerodynamics adaptating the mesh for drag lift and moment in one shot in this work we consider the basic linear finite element approximation and restrict our study to l 2 norm in order to enjoy second order convergence numerical examples for the poisson problem are computed

an l lp mesh adaptive method for computing unsteady bi fluid flows this paper discusses the contribution of mesh adaptation to high order convergence of unsteady multi fluid flow simulations on complex geometries the mesh adaptation relies on a metric based method controlling the lp norm of the interpolation error and on a mesh generation algorithm based on an anisotropic delaunay kernel the mesh adaptive time advancing is achieved thanks to a transient fixed point algorithm to predict the solution evolution coupled with a metric intersection in the time procedure in the time direction we enforce the equidistribution of the error i e the error minimization in l norm this adaptive approach is applied to an incompressible navier stokes model combined with a level set formulation discretized on triangular and tetrahedral meshes applications to interface flows under gravity are performed to evaluate the performance of this method for this class of discontinuous flows copyright 2010 john wiley sons ltd

interval field model and interval finite element analysis uncertain parameters with inherent spatial variability are commonly encountered in engineering modeling of this kind of spatial uncertainty plays a fundamental role in structural uncertainty analysis which provides a necessary basis for subsequent uncertainty propagation through the system an interval field model for quantification of spatial uncertain parameters is proposed by which only the upper and lower bounds of the spatial uncertain parameters rather than their precise probability distributions are required the dependency can be fully considered by the proposed interval field model with the information of dependency an interval k l expansion is presented as a combination of deterministic functions with uncorrelated standard interval variables through which the continuous spatial interval field with dependency can be expressed only by very limited intervals necessary mathematical illustrations are provided for the proposed interval field model and the interval k l expansion the sampling method for the interval field model is given providing a robust numerical analysis basis for subsequent structural uncertainty analysis when the interval field model is applied in finite element analysis of structures with spatial uncertain parameters the non deterministic equilibrium equations with interval factors is then formulated the mcs method and the perturbation method are developed for solution of the derived interval equilibrium equations the feasibility and validity of the proposed interval field model and corresponding interval finite element methods are verified by numerical examples where the upper and lower bounds of the responses such as the displacements and the stresses of structures with spatial uncertain parameters are computed and compared

distance spectral radius of trees with given number of segments abstract a segment of a tree is a path subtree whose terminal vertices are branching or pendant vertices we determine the structure of trees that maximize the distance spectral radius among trees with given order and number of segments and among trees with given order and number of vertices of degree 2 respectively

on the distance spectral radius of cacti abstract a cactus is a connected graph in which any two cycles have at most one common vertex in this article we determine the unique graph with minimal distance spectral radius in the class of all cacti with n vertices and k cycles also we determine the unique graph with minimal distance spectral radius in the class of all cacti with n vertices and r pendent vertices moreover we determine the class of cacti in which the maximal distance spectral radius among all cacti with n vertices and k cycles is attained

3d transient fixed point mesh adaptation for time dependent problems application to cfd simulations this paper deals with the adaptation of unstructured meshes in three dimensions for transient problems with an emphasis on cfd simulations the classical mesh adaptation scheme appears inappropriate when dealing with such problems hence another approach based on a new mesh adaptation algorithm and a metric intersection in time procedure suitable for capturing and track such phenomena is proposed more precisely the classical approach is generalized by inserting a new specific loop in the main adaptation loop in order to solve a transient fixed point problem for the mesh solution couple to perform the anisotropic metric intersection operation we apply the simultaneous reduction of the corresponding quadratic form regarding the adaptation scheme an anisotropic geometric error estimate based on a bound of the interpolation error is proposed the resulting computational metric is then defined using the hessian of the solution the mesh adaptation stage surface and volume is based on the generation by global remeshing of a unit mesh with respect to the prescribed metric a 2d model problem is used to illustrate the difficulties encountered then 2d and 3d complexes and representative examples are presented to demonstrate the efficiency of this method

fully anisotropic goal oriented mesh adaptation for 3d steady euler equations this paper studies the coupling between anisotropic mesh adaptation and goal oriented error estimate the former is very well suited to the control of the interpolation error it is generally interpreted as a local geometric error estimate on the contrary the latter is preferred when studying approximation errors for pdes it generally involves non local error contributions consequently a full and strong coupling between both is hard to achieve due to this apparent incompatibility this paper shows how to achieve this coupling in three steps first a new a priori error estimate is proved in a formal framework adapted to goal oriented mesh adaptation for output functionals this estimate is based on a careful analysis of the contributions of the implicit error and of the interpolation error second the error estimate is applied to the set of steady compressible euler equations which are solved by a stabilized galerkin finite element discretization a goal oriented error estimation is derived it involves the interpolation error of the euler fluxes weighted by the gradient of the adjoint state associated with the observed functional third rewritten in the continuous mesh framework the previous estimate is minimized on the set of continuous meshes thanks to a calculus of variations the optimal continuous mesh is then derived analytically thus it can be used as a metric tensor field to drive the mesh adaptation from a numerical point of view this method is completely automatic intrinsically anisotropic and does not depend on any a priori choice of variables to perform the adaptation 3d examples of steady flows around supersonic and transsonic jets are presented to validate the current approach and to demonstrate its efficiency

the generalized distance matrix abstract let d g and d i a g t r denote the distance matrix and diagonal matrix of the vertex transmissions of a simple connected graph g respectively the distance signless laplacian matrix of g is defined as d q g d i a g t r d g heretofore the spectral properties of d g and d q g have attracted much more attention in the present paper we propose to study the convex combinations d g of d i a g t r and d g defined as d g d i a g t r 1 d g 0 1 this study sheds new light on d g and d q g some spectral properties of d g are given and a few open problems are discussed furthermore we take effort to obtain some upper and lower bounds of spectral radius of d g finally the generalized distance spectra of some graphs obtained by operations are also studied

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

the distance eigenvalues of the complements of unicyclic graphs abstract in this paper we determine the unique graph among complements of unicyclic graphs which maximizes the distance spectral radius we also characterize the unique graph among complements of unicyclic graphs of diameter three which maximizes the least distance eigenvalues

can adaptive grid refinement produce grid independent solutions for incompressible flows abstract this paper studies if adaptive grid refinement combined with finite volume simulation of the incompressible rans equations can be used to obtain grid independent solutions of realistic flow problems it is shown that grid adaptation based on metric tensors can generate series of meshes for grid convergence studies in a straightforward way for a two dimensional airfoil and the flow around a tanker ship the grid convergence of the observed forces is sufficiently smooth for numerical uncertainty estimation grid refinement captures the details of the local flow in the wake which is shown to be grid converged on reasonably sized meshes thus grid convergence studies using automatic refinement are suitable for high reynolds incompressible flows

convex and quasiconvex functions on trees and their applications abstract we introduce convex and quasiconvex functions on trees and prove that for a tree the eccentricity transmission and weight functions are strictly quasiconvex it is shown that the perron vector of the distance matrix is strictly convex whereas the perron vector of the distance signless laplacian is quasiconvex for a tree in the class of all trees with a given number of pendent vertices we prove that the distance laplacian and distance signless laplacian spectral radius are both maximized at a dumbbell among all trees with fixed maximum degree we prove that the broom is the unique tree that maximizes the distance laplacian and distance signless laplacian spectral radius we find the unique graph that maximizes the distance spectral radius in the class of all unicyclic graphs of girth g on n vertices also we find the unique graph that maximizes the distance signless laplacian and the distance laplacian spectral radius in the class of all unicyclic graphs on n vertices

grid adaptation for functional outputs application to two dimensional inviscid flows this paper presents an error estimation and grid adaptive strategy for estimating and reducing simulation errors in integral outputs functionals of partial differential equations adaptive criteria are derived using an adjoint based error correction technique that relates the local residual errors of both the primal and adjoint solutions to the global error in the prescribed functional this relationship allows local error contributions to be used as indicators in a grid adaptive strategy designed to produce specially tuned grids for accurately estimating the chosen functional in this paper attention is limited to two dimensional inviscid flows using a standard finite volume discretization although the procedure may be readily applied to other types of multidimensional problems and discretizations numerical examples demonstrate that the proposed adaptive procedure compares favorably in terms of accuracy efficiency and robustness relative to a commonly used gradient based adaptive method

multidimensional parallelepiped model a new type of non probabilistic convex model for structural uncertainty analysis summary non probabilistic convex models need to be provided only the changing boundary of parameters rather than their exact probability distributions thus such models can be applied to uncertainty analysis of complex structures when experimental information is lacking the interval and the ellipsoidal models are the two most commonly used modeling methods in the field of non probabilistic convex modeling however the former can only deal with independent variables while the latter can only deal with dependent variables this paper presents a more general non probabilistic convex model the multidimensional parallelepiped model this model can include the independent and dependent uncertain variables in a unified framework and can effectively deal with complex multi source uncertainty problems in which dependent variables and independent variables coexist for any two parameters the concepts of the correlation angle and the correlation coefficient are defined through the marginal intervals of all the parameters and also their correlation coefficients a multidimensional parallelepiped can easily be built as the uncertainty domain for parameters through the introduction of affine coordinates the parallelepiped model in the original parameter space is converted to an interval model in the affine space thus greatly facilitating subsequent structural uncertainty analysis the parallelepiped model is applied to structural uncertainty propagation analysis and the response interval of the structure is obtained in the case of uncertain initial parameters finally the method described in this paper was applied to several numerical examples copyright 2015 john wiley sons ltd

a goal oriented anisotropic hp mesh adaptation method for linear convection diffusion reaction problems abstract we deal with the numerical solution of linear convection diffusion reaction equations using the h p variant of the discontinuous galerkin method on triangular grids we develop a mesh adaptive algorithm which modifies the size and shape of mesh elements and the corresponding polynomial approximation degrees in order to decrease the error in a target functional under the given tolerance we recall some theoretical results and describe in detail several technical aspects of this approach numerical experiments demonstrating the accuracy efficiency and robustness of the algorithm are presented

on the distance spectral radius of bipartite graphs abstract in this paper we determine the unique graph with minimum distance spectral radius among all connected bipartite graphs of order n with a given matching number moreover we characterize the graphs with minimal distance spectral radius in the class of all connected bipartite graphs with a given vertex connectivity

bounds analysis of a beam based on the convex model of uncertain foundation a methodology of bounds analysis based on the convex set of uncertainty is presented an infinitely long beam on an uncertain foundation is subjected to a moving force with constant speed the steady state vibration is analysed in the context of the finite element method uncertainty variables representing the uncertain fluctuation of foundation stiffness is confined within a convex hull given as a hyperellipse the fluctuation of dynamic responses of the beam that is the vertical deflection and the bending moment are approximated to a first order with respect to the uncertainty variables the upper and lower bounds of the response fluctuations are identified on the boundary of the convex model by means of the lagrange multiplier method numerical analysis demonstrates the validity of the proposed formulation for various constant speeds of the moving force the analysis is summarized in terms of the worst response which is the maximum absolute value of the response within the identified bounds

anisotropic delaunay mesh generation anisotropic meshes are triangulations of a given domain in the plane or in higher dimensions with elements elongated along prescribed directions anisotropic triangulations are known to be well suited for interpolation of functions or solving pdes assuming that the anisotropic shape requirements for mesh elements are given through a metric field varying over the domain we propose a new approach to anisotropic mesh generation relying on the notion of anisotropic delaunay meshes an anisotropic delaunay mesh is defined as a mesh in which the star of each vertex v consists of simplices that are delaunay for the metric associated to vertex v this definition works in any dimension and allows us to define a simple refinement algorithm the algorithm takes as input a domain and a metric field and provides after completion an anisotropic mesh whose elements are sized and shaped according to the metric field

an a priori anisotropic goal oriented error estimate for viscous compressible flow and application to mesh adaptation abstract we present a goal oriented error analysis for the calculation of low reynolds steady compressible flows with anisotropic mesh adaptation the error analysis is of a priori type its central principle is to express the right hand side of the error equation often referred as the local error as a function of the interpolation error of a collection of fields present in the nonlinear partial differential equations this goal oriented error analysis is the extension of 39 done for inviscid flows to laminar viscous flows by adding viscous terms the main benefits of this approach in comparison to other error estimates in the literature is that the optimal anisotropy of the mesh directly appears in the error analysis and is not obtained from an ad hoc variable nor a local analysis as a consequence an optimum is obtained and the convergence of the mesh adaptive process is very fast i e generally the convergence is obtained after 5 to 10 mesh adaptation cycle then using the continuous mesh framework an optimal metric is analytically obtained from the error estimation applications to mesh adaptive calculations of flows past airfoils are presented

new anisotropic a priori error estimates we prove a priori anisotropic estimates for the l 2 and h 1 interpolation error on linear finite elements the full information about the mapping from a reference element is employed to separate the contribution to the elemental error coming from different directions this new h 1 error estimate does not require the maximal angle condition the analysis has been carried out for the 2d case but may be extended to three dimensions numerical experiments have been carried out to test our theoretical results

on the distance spectral radius of some graphs abstract for a connected graph the distance spectral radius is the largest eigenvalue of its distance matrix in this paper we determine the unique graph with minimum distance spectral radius among all connected graphs of order n with a given diameter moreover we determine the unique graph with maximum distance spectral radius among the catacondensed hexagonal systems with h hexagons

on least distance eigenvalues of trees unicyclic graphs and bicyclic graphs abstract the connected graphs with least distance eigenvalues in 2 383 0 and the trees with least distance eigenvalues in 2 2 0 have been known we determine the trees with least distance eigenvalues in 3 5 2 2 and the unicyclic and bicyclic graphs with least distance eigenvalues in 2 2 2 383 we also determine the trees with the k th largest least distance eigenvalues for every positive integer k up to 28 and the unicyclic and bicyclic graphs with the k th largest least distance eigenvalues respectively for any positive integer k