on the decay of solutions for porous elastic systems with history in this paper we study the asymptotic behavior to an one dimensional porous elasticity problem with history we show the lack of exponential stability when the porous dissipation or the elastic dissipation is absent and we show the lack of analyticity and exponential stability when the porous viscosity and the elastic dissipation are present

efficient nonlinear solvers for laplace beltrami smoothing of three dimensional unstructured grids the laplace beltrami system of nonlinear elliptic partial differential equations has utility in the generation of computational grids on complex and highly curved geometry discretization of this system using the finite element method accommodates unstructured grids but generates a large sparse ill conditioned system of nonlinear discrete equations the use of the laplace beltrami approach particularly in large scale applications has been limited by the scalability and efficiency of solvers this paper addresses this limitation by developing two nonlinear solvers based on the jacobian free newton krylov jfnk methodology a key feature of these methods is that the jacobian is not formed explicitly for use by the underlying linear solver iterative linear solvers such as the generalized minimal residual gmres method do not technically require the stand alone jacobian instead its action on a vector is approximated through two nonlinear function evaluations the preconditioning required by gmres is also discussed two different preconditioners are developed both of which employ existing algebraic multigrid amg methods further the most efficient preconditioner overall for the problems considered is based on a picard linearization numerical examples demonstrate that these solvers are significantly faster than a standard newton krylov approach a speedup factor of approximately 26 was obtained for the picard preconditioner on the largest grids studied here in addition these jfnk solvers exhibit good algorithmic scaling with increasing grid size

a fully discrete evolving surface finite element method in this paper we consider a time discrete evolving surface finite element method for the advection and diffusion of a conserved scalar quantity on a moving surface in earlier papers using a suitable variational formulation in time dependent sobolev space we proposed and analyzed a finite element method using surface finite elements on evolving triangulated surfaces ima j numer anal 25 2007 pp 385 407 math comp to appear optimal order l 2 gamma t and h 1 gamma t error bounds were proved for linear finite elements in this work we prove optimal order error bounds for a backward euler time discretization

finite volume transport on various cubed sphere grids the performance of a multidimensional finite volume transport scheme is evaluated on the cubed sphere geometry advection tests with prescribed winds are used to evaluate a variety of cubed sphere projections and grid modifications including the gnomonic and conformal mappings as well as two numerically generated grids by an elliptic solver and spring dynamics we explore the impact of grid non orthogonality on advection tests over the corner singularities of the cubed sphere grids using some variations of the transport scheme including the piecewise parabolic method with alternative monotonicity constraints the advection tests revealed comparable or better accuracy to those of the original latitudinal longitudinal grid implementation it is found that slight deviations from orthogonality on the modified cubed sphere quasi orthogonal grids do not negatively impact the accuracy in fact the more uniform version of the quasi orthogonal cubed sphere grids provided better overall accuracy than the most orthogonal and therefore much less uniform conformal grid it is also shown that a simple non orthogonal extension to the transport equation enables the use of the highly non orthogonal and computationally more efficient gnomonic grid with acceptable accuracy

numerical grid generation in arbitrary surfaces through a second order differential geometric model abstract in this paper a set of second order partial differential equations for the generation of coordinates in a given surface has been developed and then solved numerically to demonstrate its potential for surface coordinate generation the proposed equations are not some arbitrarily chosen equations but are a consequence of the formulae of gauss and thus carry with them an explicit dependence on the geometric properties of the given surface furthermore these equations are easy to solve and require only the specification of the bounding curves to provide the dirichlet boundary conditions for their solution results of coordinate generation both in simply and doubly connected regions on some known surfaces with the option of coordinate redistribution have been presented extension of this technique to arbitrary surfaces seems to be straightforward

recognizing the tractability in big data computing due to the limitation on computational power of existing computers the polynomial time does not works for identifying the tractable problems in big data computing this paper adopts the sublinear time as the new tractable standard to recognize the tractability in big data computing and the random access turing machine is used as the computational model to characterize the problems that are tractable on big data first two pure tractable classes are first proposed one is the class mathrm pl consisting of the problems that can be solved in polylogarithmic time by a ratm the another one is the class mathrm st including all the problems that can be solved in sublinear time by a ratm the structure of the two pure tractable classes is deeply investigated and they are proved mathrm pl i subsetneq mathrm pl i 1 and mathrm pl subsetneq mathrm st then two pseudo tractable classes mathrm ptr and mathrm pte are proposed mathrm ptr consists of all the problems that can solved by a ratm in sublinear time after a ptime preprocessing by reducing the size of input dataset mathrm pte includes all the problems that can solved by a ratm in sublinear time after a ptime preprocessing by extending the size of input dataset the relations among the two pseudo tractable classes and other complexity classes are investigated and they are proved that mathrm pt subseteq mathrm p sqcap mathrm t 0 q subsetneq mathrm ptr 0 q and mathrm pt p mathrm p

on the variational approximation of combined second and fourth order geometric evolution equations we present a variational formulation of combined motion by minus the laplacian of curvature and mean curvature flow as well as related flows the proposed scheme covers both the closed curve case and the case of curves that are connected via triple or quadruple junction points or intersect the external boundary on introducing a parametric finite element approximation we prove stability bounds and compare our scheme with existing approaches the presented scheme has very good properties with respect to the equidistribution of mesh points and if applicable area conservation

a computational model for organism growth based on surface mesh generation the generation of curvilinear coordinate meshes has been a powerful tool in computational fluid dynamics calculation in the computational modelling of the fluid flows around complex bodies such as an airfoil or a complete aircraft this same technique may be applied to many other computational models in this work the approach is used as part of a computational model to generate simple geometries associated with biological forms or organisms the model adopted was first proposed by cummings and simulates morphogenesis in terms of the geometrical changes occurring during the growth and development of simple organisms this model depends on the generation of a curvilinear coordinate mesh on the surface of an organism previous work has concentrated on the model and its use in generating axisymmetric shapes that are simple models of elementary organisms in this work we describe how the model may be extended to geometrical symmetry breaking this paper describes the methodology of this extension and demonstrates it in the simulation of tentacle growth the resulting computational technique makes it possible to link models of cell bio chemistry and surface deformation

on the exponential decay in thermoelasticity without energy dissipation and of type iii in presence of an absorbing boundary we study the asymptotic behavior of the solution of a 3d hyperbolic system arising in the green naghdi models of thermoelasticity of type ii and iii with a dissipative boundary condition for the displacement and prove that the energy exponentially decays in time

curve shortening flow coupled to lateral diffusion we present and analyze a semi discrete finite element scheme for a system consisting of a geometric evolution equation for a curve and a parabolic equation on the evolving curve more precisely curve shortening flow with a forcing term that depends on a field defined on the curve is coupled with a diffusion equation for that field the scheme is based on ideas of dziuk siam j numer anal 36 6 1808 1830 1999 for the curve shortening flow and dziuk and elliott ima j numer anal 27 2 262 292 2007 for the parabolic equation on the moving curve additional estimates are required in order to show convergence most notably with respect to the length element while in dziuk siam j numer anal 36 6 1808 1830 1999 an estimate of its error was sufficient we here also need to estimate the time derivative of the error which arises from the diffusion equation numerical simulation results support the theoretical findings

coordinate generation with precise controls over mesh properties abstract coordinate generation techniques with precise controls over mesh properties are mathematically developed the controls are precise because mesh properties can be explicitly specified within a local region independent of the mesh elsewhere the local regions can adjoin boundaries where a particular mesh form can greatly simplify a problem or can be used for a smooth juncture between distinct coordinate systems where in effect a branch cut with a prescribed geometry and mesh distribution can be obtained away from boundaries a local region can be given a particular mesh form to model internal objects or to simplify a problem

on the phase lag heat equation with spatial dependent lags abstract in this paper we investigate several qualitative properties of the solutions of the dual phase lag heat equation and the three phase lag heat equation in the first case we assume that the parameter t depends on the spatial position we prove that when 2 t q is strictly positive the solutions are exponentially stable when this property is satisfied in a proper sub domain but 2 t q 0 for all the points in the case of the one dimensional problem we also prove the exponential stability of solutions a critical case corresponds to the situation when 2 t q 0 in the whole domain it is known that the solutions are not exponentially stable we here obtain the polynomial stability for this case last section of the paper is devoted to the three phase lag case when t and depend on the spatial variable we here consider the case when q and t is a positive constant and obtain the analyticity of the semigroup of solutions exponential stability and impossibility of localization are consequences of the analyticity of the semigroup

boundary fitted coordinate systems for numerical solution of partial differential equations a review a comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given some general mathematical framework and error analysis common to such coordinate systems is also included the general categories of generating systems are those based on conformal mapping orthogonal systems nearly orthogonal systems systems produced as the solution of elliptic and hyperbolic partial differential equations and systems generated algebraically by interpolation among the boundaries also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation dynamically adaptive coordinate systems coupled with the physical solution and time dependent systems that follow moving boundaries are treated references reporting experience using such coordinate systems are reviewed as well as those covering the system development

stabilisation of a thermo elastic system under nonuniformly bounded disturbances in the boundary input abstractwe consider the exponential stabilisation for a thermo elastic system of type ii with nonuniformly bounded external disturbances in the boundary control we begin with finding feedback controls for the system without disturbances by lyapunov function approach then based on the resulting feedback control we give new dynamic feedback control laws that make the system exponentially stable by tracking disturbances exponentially through a time varying high gain observer we apply the linear operator semi group theory to prove the well posedness of the resulting closed system finally we prove that the solution of the closed loop system can approach zero polynomially or exponentially by the lyapunov function approach

higher order accurate difference solutions of vortex generation from a circular cylinder in an oscillatory flow abstract a higher order difference solution method is presented for viscous flow around an oscillating body the navier stokes equation in a rotational form which conserves both momentum and kinetic energy is approximated into a difference form by a fourth order compact differencing in a general boundary fitted curvilinear coordinate system a time marching procedure is derived and the high resolution property is demonstrated with the computations of some simple problems the simulation of a viscous flow around a circular cylinder sinusoidally oscillating at low keulegan carpenter number elucidates fairly well the sequential viscous flow mechanism of boundary layer development flow separation and vortex shedding with pairing

a unified procedure for construction of theories of deformable media i classical continuum physics a new unified procedure for constructing continuum theories of deformable media is presented and used in this and a companion paper the procedure starts with a balance of energy and derives from it all the relevant balance laws that may also include those that are associated with thermal electrical and magnetic effects the basic energetic ingredients that are included in the balance of energy depend of course on the nature of the particular theory of material behaviour desired the advantage of the new procedure becomes especially apparent when one considers formulation of a new theory of material behaviour for which additional balance laws involving new kinetic quantities are required to accompany any additional basic kinematic and thermal variables additional to those in the classical formulation indeed in the formulation of such new theories usually little or no previous information is available concerning properties of the new kinetic quantities in the additional balance laws and in this connection the unified procedure of this paper provides a simple attractive setting for deriving the basic equations that are automatically consistent with the energy balance in this paper first the basic features of the new procedure are illustrated in the context of classical thermomechanics generalizations of this thermomechanical theory are then discussed in two cases 1 in the presence of an additional kinematic variable and 2 in the presence of full electromagnetic effects both of these generalizations bring out some interesting novel features when new theories are being constructed

variational integrators for the dynamics of thermo elastic solids with finite speed thermal waves this paper formulates variational integrators for finite element discretizations of deformable bodies with heat conduction in the form of finite speed thermal waves the cornerstone of the construction consists in taking advantage of the fact that the green naghdi theory of type ii for thermo elastic solids has a hamiltonian structure thus standard techniques to construct variational integrators can be applied to finite element discretizations of the problem the resulting discrete in time trajectories are then consistent with the laws of thermodynamics for these systems for an isolated system they exactly conserve the total entropy and nearly exactly conserve the total energy over exponentially long periods of time moreover linear and angular momenta are also exactly conserved whenever the exact system does for definiteness we construct an explicit second order accurate algorithm for affine tetrahedral elements in two and three dimensions and demonstrate its performance with numerical examples

adaptive zoning for singular problems in two dimensions abstract winslow s method for the automatic generation of computation meshes is extended to adaptively vary the zone sizes and orthogonality of grid lines in the resulting mesh through simple analysis and numerical examples the adaptive mesh is shown to give significant increases in accuracy in the computation of singular problems

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

a robust elliptic grid generator a variational principle is proposed that results in a robust elliptic grid generator having many of the strengths of original winslow or homogeneous thompson thames mastin method httm the new grid generator places grid lines more uniformly over the domain than does httm without loss of orthogonality numerically generated examples are given to demonstrate these effects grid quality measures are introduced to quantify differences between discrete grids both the httm and the new grid generator can generate folded grids on certain pathological regions but overall they are very robust grid weighting for solution adaptive calculations is briefly considered generalization of the new method to surface and volume grid generation is straightforward

practical aspects of formulation and solution of moving mesh partial differential equations moving mesh partial differential equations mmpdes are used in the mmpde moving mesh method to generate adaptive moving meshes for the numerical solution of time dependent problems how mmpdes are formulated and solved is crucial to the efficiency and robustness of the method in this paper several practical aspects of formulating and solving mmpdes are studied they include spatial balance scaling invariance effective control of mesh concentration bounds on time steps multiple sub steps and two level mesh movement numerical results are also given c 2001 academic press

generation of orthogonal grids with control of spacing abstract a methodology for generating orthogonal curvilinear grids is applied to two dimensional domains an important feature of the methodology is its ability to control effectively the grid spacing especially near the boundaries this paper summarizes the governing equations used for grid generation then the numerical procedure is described with special emphasis on the scheme used to enhance stability and accuracy of the solution the significance of the distortion function and the way it is used to control grid spacing are illustrated in geometries commonly found in engine combustion chambers the influence of various parameters including number of grid points relaxation factor and range of values of the distorion function on the performance of the method are also investigated it is concluded that the methodology can successfully produce smooth orthogonal grids with control of spacing in symmetric and nonsymmetric domains

conservation form of the navier stokes equations in general nonsteady coordinates introduction r interest in the generation of general bodyoriented curvilinear coordinate systems for the purpose of solving the complete navier stokes system of equations for subsonic and supersonic flows has given rise to many forms of presentations of the equations both in conservative and nonconservative formulations based on the available solutions of the gasdynamic equations e g ref 5 the conservation law form of the equations seems definitely preferable particularly when shocks are present although the above statement cannot be repeated in a definitive sense for the case of viscous subsonic and supersonic flow prediction through the navier stokes equations nevertheless it is expected that the conservation law form may eventually be more acceptable for numerical purposes the purpose of this paper is to derive the conservation law form of the navier stokes equations in general nonsteady coordinate systems in a simple and direct fashion previous work on this subject has been done by mcvittie viviand and vinokur it will be shown in this note that the equations in the conservation law form can be obtained simply by a little manipulation of some standard vector and tensor formulas

a re examination of the basic postulates of thermomechanics this paper is mainly concerned with a re examination of the basic postulates and the consequent procedure for the construction of the constitutive equations of material behaviour in thermomechanics however the implication of the basic postulates and the significance of the related procedure for the development of the constitutive equations is also illustrated in some detail in the context of flow of heat in a rigid solid with particular reference to the propagation of thermal waves at finite speed more specifically after briefly examining the nature of the basic equations of motion for a system of particles within the scope of the classical newtonian mechanics the basic postulates of the purely mechanical theory for a continuum including its specialization for a rigid body is re examined this includes some differences from the usual procedure on the subject next thermal variables are introduced and after observing a useful analogy between the thermal and mechanical variables a discussion of a theory of heat or a purely thermal theory is provided which differs from the usual development in the classical thermodynamics a detailed application of the latter development is then made to the problem of heat flow in a stationary rigid solid using several different and well motivated constitutive equations special cases of these include linearized theories of the classical heat flow by conduction and of heat flow transmitted as thermal waves the remainder of the paper is concerned with thermal mechanical theory of deformable media along with discussions of a number of related issues on the subject

modeling cell movement and chemotaxis using pseudopod based feedback a computational framework is presented for the simulation of eukaryotic cell migration and chemotaxis an empirical pattern formation model based on a system of nonlinear reaction diffusion equations is approximated on an evolving cell boundary using an arbitrary lagrangian eulerian surface finite element method ale sfem the solution state is used to drive a mechanical model of the protrusive and retractive forces exerted on the cell boundary movement of the cell is achieved using a level set method results are presented for cell migration with and without chemotaxis the simulated behavior is compared with experimental results of migrating dictyostelium discoideum cells

strongly damped wave equations with critical nonlinearities abstract this note deals with the strongly damped nonlinear wave equation u t t u t u f u t g u h with dirichlet boundary conditions where both the nonlinearities f and g exhibit a critical growth while h is a time independent forcing term the existence of an exponential attractor of optimal regularity is proven as a corollary a regular global attractor of finite fractal dimension is obtained

bounds for some non standard problems in porous flow and viscous green naghdi fluids a e green f r s and p m naghdi developed a new theory of continuum mechanics based on an entropy identity rather than an entropy inequality in particular within the framework of this theory they developed a new set of equations to describe viscous flow the new theory additionally involves vorticity and spin of vorticity we here derive energy bounds for a class of problem in which the initial data are given as a combination of data at time t 0 and at a later time t t such problems are in vogue in the mathematical literature and may be used for example to give estimates of solution behaviour in an improperly posed problem where one wishes to continue a solution backward in time in addition we derive similar energy bounds for a solution to the brinkman forchheimer equations of viscous flow in porous media

energy decay of type iii linear thermoelastic plates with memory abstract we analyze the decay properties of the solution semigroups generated by an abstract version of the linear systems u t t 2 u t 0 t t t u t 0 and u t t 2 u t 0 t t 0 s t t s d s u t 0 ruling the evolution of linear thermoelastic plates within the theory of heat conduction of type iii

a computational method for the coupled solution of reaction diffusion equations on evolving domains and manifolds in this paper we devise a moving mesh finite element method for the approximate solution of coupled bulk surface reaction diffusion equations on an evolving two dimensional domain fundamental to the success of the method is the robust generation of bulk and surface meshes for this purpose we use a novel moving mesh partial differential equation mmpde approach the developed method is applied to model problems with known analytical solutions these experiments indicate second order spatial and temporal accuracy coupled bulk surface problems occur frequently in many areas in particular in the modelling of eukaryotic cell migration and chemotaxis we apply the method to a model of the two way interaction of a migrating cell in a chemotactic field where the bulk region corresponds to the extracellular region and the surface to the cell membrane

orthogonal grids around convex bodies using foliations a new technique for the construction of orthogonal grids around convex bodies is presented the method which is analytical or numerical depending on how the body boundary is expressed is based on the development of geometric foliations that follow a prescribed direction for instance the prevailing direction of flow around convex bodies of arbitrary shape the construction of these foliations is straightforward and does not require the solution of any system of algebraic or differential equations nor the use of iterative procedures the method is applicable both to two and three dimensional domains since it is based solely on the concept of local curtvature the lines or surfaces given by the foliations of first and second order together with the complementary orthogonal lines respectively define the orthogonal two or three dimensional grids

application of variational methods in the fixed and adaptive grid generation abstract the present paper is devoted to the development of a system of partial differential equations for the purpose of generating fixed and adaptive numerical grids the resulting equations are applicable to both two and three dimensional grid generation problems equations have also been presented for both the fixed and adaptive grids in curved surfaces

elliptic grid generation conclusions some modi cations for the restriction and prolongation process of multigrid methods have been presented that are necessary for the simulation of complex supersonic ow elds damping of the restricted residual error and blending between a second order central and a rst order upwind prolongation enable convergence in supersonic ows and resulted in strong reductions in cpu time the advantageof this kind of blending is the reduction to rst order prolongationat shock waves only

updates of relational views the problem of translating updates of database views is studied view updates are disambi guated by requiring that a specified view complement i e a second view that contains all the information omitted from the given view remain constant during the translation some of the computational problems related to the apphcafion of this general methodology in the context of relational databases are studied projective views of databases that consist of a single relation and satisfy funcuonal dependencies are emphasized after characterizing complementary views the authors show that finding a minimum complement of a given view is np complete the problem of translating the insertion of a tuple into a view is then studied in detail and the results are extended to the cases of deletion and replacement of a tuple finally the explicit functional dependencies a new kind of dependency that intuitively states that some part of the database information can be computed from the rest are defined and studied

space time discontinuous galerkin method for nonlinear water waves a space time discontinuous galerkin dg finite element method for nonlinear water waves in an inviscid and incompressible fluid is presented the space time dg method results in a conservative numerical discretization on time dependent deforming meshes which follow the free surface evolution the algorithm is higher order accurate both in space and time and closely related to an arbitrary lagrangian eulerian ale approach a detailed derivation of the numerical algorithm is given including an efficient procedure to solve the nonlinear algebraic equations resulting from the space time discretization numerical examples are shown on a series of model problems to demonstrate the accuracy and capabilities of the method

on the complexity of sampling query feedback restricted database repair of functional dependency violations an inconsistent database is a database instance violating integrity constraints a repair of an inconsistent database is a maximal consistent subset sampling from the repair space is an alternative approach meeting the needs of many applications in this paper we introduce a new class of repair query feedback restricted repair based on the feedback on user s witness query we first map out a picture of both data and combined complexities of repair existence problems under different cases to identify the intractable cases especially we show that if the query is a projection or a union query then the decision problem is np complete even worse if the query is a conjunctive query the decision problem becomes 2 p complete however we prove that the combined complexity of the repair existence problem is in logspace when the witness query is a selection join query and this conclusion also implies that the combined complexity of side effect free deletion propagation problem under group deletion is in logspace which is not considered in previous works additionally we provide a polynomial random repair sampling algorithm under combined complexity at last we revisit the key preserving condition 1 and show that it will simplify the problem i e some cases become tractable for certain key preserving views as opposed to their counterparts that are not key preserving

convergence and structural stability in thermoelasticity we analyze the equations of thermoelasticity in a linear approximation first we prove that the solution depends continuously on changes in two thermal constants next we investigate how the solution of thermoelasticity of type iii converges to the solution of the usual thermoelasticity and to the solution of thermoelasticity without energy dissipation consequently we can also obtain an estimate of the approximation when we compare the classical thermoelasticity with thermoelasticity without energy dissipation last section investigates the structural stability in the class of thermoelasticity without energy dissipation

volume conserving smoothing for piecewise linear curves surfaces and triple lines abstract we present smoothing algorithms for piecewise linear curves surfaces and triple lines of intersection of surfaces that are based on the the idea of sequentially relaxing either individual nodes or edges in the mesh each relaxation is designed both to smooth the mesh and to conserve down to round off error the area or volume enclosed by the curve or surface for the case of smoothing surfaces and lines of intersection of surfaces each relaxation consists of a pure smoothing component and a volume conserving correction which is chosen to be of minimum norm since surfaces and triple intersection lines can be conservatively smoothed the algorithms are suitable for improving multimaterial grids used by physics simulations where exactly conserving the volume of each individual material may be a requirement or at least highly desirable the algorithms are also suitable for smoothing piecewise linear functions of one or two variables while simultaneously preserving their integrals we show examples of the application of the more powerful edge based algorithms to curve surface and multimaterial volume grids and to a thin film simulation

triangular and quadrilateral surface mesh quality optimization using local parametrization a procedure is presented to improve the quality of surface meshes while maintaining the essential characteristics of the discrete surface the surface characteristics are preserved by repositioning mesh vertices in a series of element based local parametric spaces such that the vertices remain on the original discrete surface the movement of the mesh vertices is driven by a non linear numerical optimization process two optimization approaches are described one which improves the quality of elements as much as possible and the other which improves element quality but also keeps the new mesh as close as possible to the original mesh

the direct variational grid generation method extended to curves the direct variational grid generation method is extended to weighted grids on smooth curves in r 3 by introducing a new weighted chord functional the new functional is positive definite at a global minimum but not everywhere convex lack of convexity appears to a significant obstacle in extending the direct variational approach to surface grid generation

mathematical aspects of variational grid generation ii abstract variational grid generation techniques are now used to produce grids suitable for solving numerical partial differential equations in irregular geometries in this paper the existence and uniqueness of solutions of the volume and smoothness problems that are used in variational grid generation are studied an analysis of the euler lagrange el equations near the identity shows that the volume problem is difficult these variational problems use a reference grid to specify the properties of the desired grid replication of reference grid properties is analyzed examples are given that show the effectiveness of the reference grid concept

energy bounds for some non standard problems in thermoelasticity a e green f r s and p m naghdi developed two theories of thermoelasticity called type ii and type iii which are likely to be more natural candidates for the identification of a thermoelastic body than the usual theory we here derive energy bounds for a class of problem in which the initial data are given as a combination of data at time t 0 and at a later time t t such problems are in vogue in the mathematical literature and may be used for example to give estimates of solution behaviour in an improperly posed problem where one wishes to continue a solution backward in time

a generalization of the caginalp phase field system with neumann boundary conditions abstract we study a generalized caginalp phase field system based on the theory of type iii heat conduction proposed by green and naghdi and supplemented with neumann boundary conditions in contrast to the dirichlet case the system exhibits a lack of dissipation on the thermal displacement variable however minus its spatial average is dissipative and we are able to prove the existence of the global attractor with optimal regularity for the associated semigroup

generalized vortex lattice method for planar supersonic flow the generalized vortex lattice method for oscillating lifting surfaces in subsonic flow is extended to the supersonic planar regime

unstructured surface mesh adaptation using the laplace beltrami target metric approach this paper develops a set of adaptive surface mesh equations by using a harmonic morphism which is a special case of a harmonic map these equations are applicable both to structured and unstructured surface meshes provided that the underlying surface is given in a parametric form by representing the target metric of the mesh as a sum of a coarse grained component and a component quadratic in surface gradients an improved surface mesh may be obtained the weak form of the grid equations is solved using the finite element approximation which reduces the grid equations to a nonlinear algebraic set examples of structured and unstructured meshes are used to illustrate the applicability of the proposed approach

parameter estimation in variational grid generation two approaches to numerical variational grid generation use a linear combination of three variational problems to control the properties of the grid previously the parameters in the linear combination were determined by experimentation good estimates for these parameters can be obtained from simple model problems

achieving finite element mesh quality via optimization of the jacobian matrix norm and associated quantities part i a framework for surface mesh optimization structured mesh quality optimization methods are extended to optimization of unstructured triangular quadrilateral and mixed finite element meshes n ew interpretations of well known nodally bssed objective functions are made possible using matrices and matrix norms the matrix perspective also suggests several new objective functions particularly significant is the interpretation of the oddy metric and the smoothness objective functions in terms of the condition number of the metric tensor and jacobian matrix respectively objective functions are grouped according to dimensionality to form weighted combinations a simple unconstrained local optimum is computed using a modiiied n ewton iteration the optimization approach was implemented in the cubit mesh generation code and tested on several problems results were compared against several standard element based quaiity measures to demonstrate that good mesh quality can be achieved with nodally based objective functions

spatial behavior for some non standard problems in linear thermoelasticity without energy dissipation in the present paper we consider a prismatic cylinder occupied by an anisotropic and homogeneous compressible linear thermoelastic material within the framework of the linear theory of thermoelasticity without energy dissipation the cylinder is subject to zero body force and heat supply and zero lateral specific boundary conditions and the motion is induced by a time dependent displacement and thermal displacement specified pointwise over the base further the motion is constrained such that the displacement thermal displacement velocity and temperature variation at points in the cylinder and at a prescribed time are in given proportions to but not identical with their respective initial values it is shown that certain integrals of the solution spatially evolve with respect to the axial variable conditions are derived that show the integrals exhibit alternative behavior and in particular for the semi infinite cylinder that there is either at least exponential growth or at most exponential decay provided the elasticity tensor is positive definite or strongly elliptic

sef view deletion under bounded condition abstract deletion propagation problem has been an important role in data lineage is a classic problem in the database research on data provenance and quality as a more restricted version of classic view update problem in relational databases it is defined on a given database d a monotonic relational algebraic query q and its materialized view v of d deletion propagation aims to find a tuple set d whose deletion from d guarantees that the result of q is exactly the view v minus an intended deletion v i e d will not produce side effect on view such d is side effect free if no side effect produced by deleting it from d we study the complexity of finding side effect free deletion in this paper we also consider the functional dependency restricted version deletion propagation problem b dp which generalizes the computational issues involved in data lineage it is to find the d not only view side effect free but also without introducing inconsistency with respect to the predefined functional dependencies both data and combined complexity of b dp are studied under both single and group deletion plenty of analysis are provided on this problem with respect to queries in different classes on either complexity aspect

on uniqueness and continuous dependence in type iii thermoelasticity abstract this note is concerned with the linear and linearised type iii thermoelastic theory proposed by green and naghdi first the continuous dependence of the solutions upon the initial data and supply terms is established for noncentrosymmetric bodies then a uniqueness result for centrosymmetric materials is established

finite difference solutions of the euler equations in the vicinity of sharp edges attempts have been made to explain why finite difference solutions of the euler equations can describe flows with large vortical structures around sharp edged bodies the present paper is concerned with the influence of a singular sharp edge on the truncation error for a set of discretized euler equations an analysis is conducted of the distribution of the truncation error of one finite difference approximation of the euler equations near a sharp edge of a thin plate the analysis leads to a determination of the size of the region of the neighborhood of such a singularity attention is given to the consistency of a discretization of the euler equations and numerical experiments

vorticity jump in surface coordinates across a shock in nonsteady flow we obtain hayes formulas in the coordinates attached to an arbitrarily moving and deforming shock surface that occurs in nonsteady flows the formulas given here can be incorporated in a flow solver that uses a coordinate system attached to a moving and deforming shock surface

surface grid generation in the tangent plane abstract recent work has shown that parametrically formulated surface grid generation algorithms are severely limited by solution bifurcations of the discretized equations such bifurcations become apparent if the given surface has points of high curvature the present study demonstrates that discrete equations derived from an alternative physical variables formulation do not result in similar bifurcations however the natural formulation using physical variables is not entirely successful on surface of high curvature due to excessive truncation error in the solution grid it is shown that both bifurcations and truncation error are overcome by formulating the grid generation equations in terms of projections of the physical variables onto the surface tangent plane

a synopsis of elliptic pde models for grid generation this paper is devoted to an analytical comparison of the various elliptic partial differential equation pde models which are in current use for grid generation these comparisons particularly between the equations from the laplace poisson system and the equations from a gaussian approach have yielded useful expressions connecting the 3d laplacians and the surface beltramians this effort specifically been successful when the transverse coordinate leaving the surface is orthogonal to the surface equations which are derivable from cartesian type poisson and those obtained by using the variational priciple in surface coordinates have also been considered

coordinate system control adaptive meshes the discussion of the formulation and properties of the adaptive mesh algorithm is as complete as space permits as should be clear from the discussion adaptive gridding is most useful for singular perturbation problems where localized regions with large gradients develop spontaneously often choosing the correct weight function is not trivial and sometimes it is appropriate to cause the mesh to respond to structure in several dependent variables simultaneously

stability and geometric conservation laws for ale formulations the aim of this paper is to investigate a model ale scheme with respect to various possible choices of time discretizations for each time scheme we investigate the relationships between stability and the so called geometric conservation laws gcl we shall see that gcl condition proves neither necessary nor sufficient for stability in doing so we review some known theoretical results and we prove some new stability results for space time ale discretizations some new error estimates are also presented several numerical experiments confirm the theory

a note on discontinuity waves in type iii thermoelasticity two recent nonlinear theories of thermoelasticity developed by green and naghdi are examined it is shown that in type ii theory second sound is permissible and both mechanical and temperature waves may propagate in type iii theory we show that the situation is more analogous to that in classical nonlinear thermoelasticity one wave propagates and a homothermal temperature wave is allowed

computational conformal mapping for surface grid generation the paper describes the development and application of a new approach for formulating an elliptic generation system on parametrically defined surfaces the present derivation of the surface equations proceeds in two steps first conformal mapping of smooth surfaces onto rectangular regions is utilized to derive a first order system of partial differential equations analogous to beltrami s system for quasi conformal mapping of planar regions second a general elliptic generation system for three dimensional surfaces including forcing functions is formulated based on beltrami s system and quasi conformal mapping the resulting elliptic system is solved using an iterative method on arbitrary surfaces represented analytically by rational b splines the overall effect of this approach is a reliable and versatile elliptic method for generating and improving surface grids examples will be presented to demonstrate the application of the method in constructing practical grids

variational methods for generating meshes on surfaces in three dimensions variational methods for generating meshes are developed for arbitrary surfaces in three dimensions several variational principles are written down for surfaces the corresponding elliptic equations are listed and several simple examples are given in addition a short discussion of planar methods and relative scaling of integrals are included in this paper for completeness

on the impossibility of localization in linear thermoelasticity in the middle of the 1990s green naghdi proposed three theories of thermoelasticity that they labelled as types i ii and ii the type ii theory which is also called thermoelasticity without energy dissipation is conservative and the solutions cannot decay with respect to time it is well known that in general in the linear theories of thermoelasticity of types i and iii the solutions decay with respect to time in many situations this decay is at least exponential in this paper we study whether this decay can be fast enough to guarantee the solutions to be zero in a finite time we investigate the impossibility of the localization in time of the solutions of linear thermoelasticity for the theories of green naghdi this means that the only solution that vanishes after a finite time is the null solution the main idea is to show the uniqueness of solutions for the backward in time problem to be precise for type iii thermoelasticity we will prove the impossibility of localization of solutions in the case of bounded domains and for the type i thermoelasticity in the case of exterior domains even when the solutions can be unbounded whether the spatial variable goes to infinity

theoretical foundation of the equations for the generation of surface coordinates references 1 alien h j and perkins e w characteristics of flow over inclined bodies of revolution naca rm a50l07 march 1951 fiechter m wirbelsysteme schlanker rotationskorper und die aerodynamischen kra fte dglr jahrbuch 1969 pp 77 85 hunt b l asymmetric vortex forces and wakes on slender bodies aiaa paper 82 1336 aug 1982 kompenhans j and hartmann k strftmungssichtbarmachung an einem hochangestellten ogivkreiszylinderrumpf mit hilfe der laser lichtschnittmethode dfvlr fb 86 45 1986 prandtl l and tietjens o applied hydroand aeromechanics mcgraw hill new york and london 1934 foeppl l wirbelbewegung hinter einem kreiszylinder sitz ber kdnigl bay akademie d wissenschaften math phys klasse jg 1913 munchen jan 1913 sun y c shen s f and zhu z a numerical simulation of the flow development behind a circular cylinder started from rest and a criterion for investigating unsteady separating flows ada mechanica vol 71 jan 1988 pp 1 20 dyer d e fiddes s p and smith j h b asymmetric vortex formation from cones at incidence a simple inviscid model aeronautical quarterly vol 33 nov 1982 pp 293 312 ng t on leading edge vortex and its control aiaa paper 89 3346 aug 1989 yi8 gao 0 gpo a sai3 a surface christoffel symbols of the second kind

on the configurational force balance in thermomechanics the aim of this paper is a new formulation of the configurational force balance in the general framework of thermomechanics to this end invariance requirements of the configurational working are used following an approach proposed by gurtin to define the notion of working in a more general framework the ideas of green and naghdi concerning the basic postulates of thermomechanics are invoked and used consistently the main results are that the configurational forces balance in the general setting of thermomechanics without the invocation of constitutive relations and the pseudo momentum equation for classical and dissipationless thermoelasticity finally we give an application to fracture theory we show that in classical thermoelasticity the derived pseudo momentum balance provides a crack driving force consistent with the well known expression of the energy release rate

determination of surfaces using beltramians at the separation of two fluid media this paper describes a model formed of a set of elliptic partial differential equations involving beltramians of coordinates for generating the curved surfaces at the separation of two different media the main point is that the differential equations are formed in such a way that the sum of the local principal curvatures appears explicitly which in turn depends on the physical and chemical properties of the two media this dependence is quite obvious as far as the problem of surface tension is concerned the developed partial differential equations have been solved numerically for the simple case of a fluid in contact with a vertical wall and for generation of the surface of revolution due to the capillary effect in a tube of small radius these examples demonstrate the application of the method when the surface tension is important the method may be of value in tackling other problems such as the generation of synclastic and anticlastic surfaces provided that the local principal curvatures can be related to the coordinates by using some physical principle

surface grid generation based on elliptic pde models abstract elliptic grid generation methods for the construction of surface grids are discussed an improved elliptic surface grid generation method for parametric surfaces will be presented two methods of imposing grid orthogonality have been implemented several control function options are available for maintaining a desired distribution of grid points on the surface the overall effect of these improvements is a reliable and versatile elliptic method for generating and improving surface grids examples will be presented to demonstrate the application of the method in generating practical grids

variational curve and surface grid generation abstract variational algorithms that control the lengths of grid lines cell areas and the orthogonality of grid lines can be used for generating boundary conforming grids on surfaces additional geometric control is provided by using a reference grid while solution adaptivity is achieved by using weights in a typical application the reference grid can be used to produce an exponential compression of the grid at a boundary while the solution adaptive weights are used to make the grid spacing inversely proportional to the gradient when the gradient is large of some solution being computed on the grid the grid is adapted on both the interior and boundary of the surface the algorithm performs these tasks with exceptional precision as demonstrated in the examples presented here