shape design sensitivity analysis for geometrically and materially nonlinear problems by the boundary element method abstract this paper is concerned with the determination of design sensitivity coefficients dscs for fully nonlinear problems i e problems with both material and geometric nonlincarities in solid mechanics the clastic strains arc assumed to be small but the nonclastic plastic or viscoplustic strains as well as rotations can be arbitrarily large dscs here refer to rates of change of response variables such as displacements or stresses in a deforming solid body with respect to parameters called design variables that define the initial undeformed shape of the body these dscs are history dependent the direct differentiation approach dda of the relevant derivative boundary element method dbem formulation is employed to obtain the dscs a general computer program is developed for the analysis of two dimensional plane strain and plane stress problems numerical results are obtained for illustrative problems and arc compared against direct solutions the results from the two methods agree almost perfectly for these problems this research has potential applications in the optimization of manufacturing processes such as extrusion rolling or forging

boundary integral equations for recovery of design sensitivities in shape optimization a new formulation for obtaining design sensitivities in shape optimization has been developed the formulation is based on a direct application of the material derivative concept to the appropriate boundary integral equations for displacements and stresses in an elastic solid as a check on accuracy the approach was applied to a uniformly loaded infinite plate containing an elliptical hole in this case the availability of an analytical solution made it possible to calculate errors exactly furthermore a wide range of stress states could be considered simply by varying the aspect ratio of the elliptical hole for convenience the design sensitivities were calculated with respect to changes in the major axis numerical convergence was established by comparing results based on four successive boundary meshes in general the predictions for both displacement and stress sensitivities were remarkably accurate

an algorithm for the optimization of directionally stretched triangulations a procedure for the optimization of stretched triangular grids is described the method is based on the construction and minimization of a function that represents a generalized version for stretched grids of a non linear spring system the function is minimized using a gradient method based on the steepest descent examples are provided to show the applicability of the method to computational fluid dynamics problems

the locally stabilized finite volume method for incompressible flow a locally stabilized finite volume method for the two dimensional incompressible flow governed by stationary stokes and navier stokes equations is investigated in this work a macroelement condition is introduced for constructing the local stabilized formulation for the problem the optimal l 2 error estimate of u h p h determined by stokes equations is also deduced some numerical examples are provided to check the efficiency of this method

the accuracy of cell vertex finite volume methods on quadrilateral meshes for linear first order hyperbolic equations in two dimensions we restate the cell vertex finite volume scheme as a finite element method on structured meshes consisting of distorted quadrilaterals the global error is shown to be of second order in various mesh dependent norms provided that the quadrilaterals are close to parallelograms in the sense that the distance between the midpoints of the diagonals is of the same order as the measure of the guadrilateral on tensor product nonuniform meshes the cell vertex scheme coincides with the familiar box scheme in this case second order accuracy is shown without any additional assumption on the regularity of the mesh which explains the insensitivity of the cell vertex scheme to mesh stretching in the coordinate directions observed in practice 17 refs

iterative solution techniques in boundary element analysis iterative techniques for the solution of the algebraic equations associated with the direct boundary element analysis bea method are discussed continuum structural response analysis problems are considered employing single and multi zone boundary element models with and without zone condensation the impact on convergence rate and computer resource requirements associated with the sparse and blocked matrices resulting in multi zone bea is studied both conjugate gradient and generalized minimum residual preconditioned iterative solvers are applied for these problems and the performance of these algorithms is reported included is a quantification of the impact of the preconditioning utilized to render the boundary element matrices solvable by the respective iterative methods in a time competitive with direct methods to characterize the potential of these iterative techniques we discuss accuracy storage and timing statistics in comparison with analogous information from direct sparse blocked matrix factorization procedures matrix populations that experience block fill in during the direct decomposition process are included with different degrees of preconditioning iterative equation solving is shown to be competitive with direct methods for the problems considered

on domain decomposition algorithms for covolume methods for elliptic problems in this paper some new two level additive schwarz domain decomposition methods are constructed and used as preconditioners for gmres for the nonsymmetric systems arising from the covolume methods for elliptic problems without any restriction on the coarse mesh size the convergence of the preconditioned gmres is obtained for both circumcentric and barycentric covolume methods with inexact solvers for subproblems the rates of convergence are shown to be independent of the number of subregions and these methods are optimal for generous overlap

the finite volume element method for diffusion equations on general triangulations this paper develops discretization error estimates for the finite volume element method on general triangulations of a polygonal domain in mathcal r 2 using a special type of control volume the theory applies to diffusion equations of the form begin gathered nabla a nabla u f quad text in omega hfill u 0 quad text on partial omega hfill end gathered under fairly general conditions the theory establishes o h estimates of the error in a discrete mathcal h 1 seminorm under an additional assumption concerning local uniformity of the triangulation the estimate is improved to o h 2

the method of variably scaled radial kernels for solving two dimensional magnetohydrodynamic mhd equations using two discretizations the crank nicolson scheme and the method of lines mol abstract mhd equations have many applications in physics and engineering the model is coupled equations in velocity and magnetic field and has a parameter namely hartmann the value of hartmann number plays an important role in the equations when this parameter increases using different meshless methods makes the oscillations in velocity near the boundary layers in the region of the problem in the present paper a numerical meshless method based on radial basis functions rbfs is provided to solve mhd equations for approximating the spatial variable a new approach which is introduced by bozzini et al 2015 is applied the method will be used here is based on the interpolation with variably scaled kernels the methodology of the new technique is defining the scale function c on the domain r d then the interpolation problem from the data locations x j r d transforms to the new interpolation problem in the data locations x j c x j r d 1 bozzini et al 2015 the radial kernels used in the current work are multiquadrics mq inverse quadric iq and wendland s function of course the latter one is based on compactly supported functions to discretize the time variable two techniques are applied one of them is the crank nicolson scheme and another one is based on mol the numerical simulations have been carried out on the square and elliptical ducts and the obtained numerical results show the ability of the new method for solving this problem also in appendix we provide a computational algorithm for implementing the new technique in matlab software

a stabilized multi level method for non singular finite volume solutions of the stationary 3d navier stokes equations this paper proposes and analyzes a stabilized multi level finite volume method fvm for solving the stationary 3d navier stokes equations by using the lowest equal order finite element pair without relying on any solution uniqueness condition this multi level stabilized fvm consists of solving the nonlinear problem on the coarsest mesh and then performing one newton correction step on each subsequent mesh thus only solving a large linear system an optimal convergence rate for the finite volume approximations of nonsingular solutions is first obtained with the same order as that for the usual finite element solution by using a relationship between the stabilized fvm and a stabilized finite element method then the multi level finite volume approximate solution is shown to have a convergence rate of the same order as that of the stabilized finite volume solution of the stationary navier stokes equations on a fine mesh with an appropriate choice of the mesh size h j h j 1 2 j 1 ldots j finally numerical results presented validate our theoretical findings

the finite volume method based on stabilized finite element for the stationary navier stokes problem a finite volume method based on stabilized finite element for the two dimensional stationary navier stokes equations is investigated in this work a macroelement condition is introduced for constructing the local stabilized formulation for the problem we obtain the well posedness of the fvm based on stabilized finite element for the stationary navier stokes equations moreover for quadrilateral and triangular partition the optimal h 1 error estimate of the finite volume solution u h and l 2 error estimate for p h are introduced finally we provide a numerical example to confirm the efficiency of the fvm

sensitivity analysis formulation for three dimensional conduction heat transfer with complex geometries using a boundary element method a special boundary integral formulation had been proposed to analyse many engineering problems of conduction heat transfer in complex three dimensional geometries closely spaced surface and circular hole in infinite domain or simple modification of it by rezayat and burton one example of such geometries is the mold sets in the injection molding process in this paper an efficient and accurate approach for the design sensitivity analysis dsa is presented for these kinds of problems in the similar complex geometries using the direct differentiation approach dda based on the above special boundary integral formulation the present approach utilizes the implicit differentiation of the boundary integral equations with respect to the design variables radii and locations of circular holes to yield the sensitivity equations a sample problem heat transfer of injection molding cooling system is solved to demonstrate the accuracy of the present sensitivity analysis formulation although the techniques introduced here are applied to a particular problem in heat transfer of injection molding cooling system their potential application is quite broad

isogeometric boundary element method for calculating effective property of steady state thermal conduction in 2d heterogeneities with a homogeneous interphase abstract based on the generalized self consistent scheme gscs the isogeometric boundary element method igabem is used to calculate the effective thermal conductivity of two dimensional 2d steady state heat conduction heterogeneities with a homogeneous interphase the heat energy formulation and the boundary integral equations adopted in this paper only contain the temperatures from the inclusion interphase and interphase matrix interfaces respectively so that the effective thermal conductivity from the generalized self consistent model with a homogeneous interphase can be conveniently calculated in numerical implementation the non uniform rational b splines nurbs are employed not only to construct the exact interface shapes but also to approximate the interface temperatures the results show that the conductivity and the thickness of the homogeneous interphase have great influence on the effective thermal conductivity higher interphase thermal conductivity enhances the effective thermal conductivity whereas thinner thickness of the interphase results in the reduction of the effective thermal conductivity numerical examples show that the proposed method works well compared with the conventional quadratic isoparametric boundary element method

variational multiscale a posteriori error estimation for multi dimensional transport problems this paper presents an explicit a posteriori error estimator for the multi dimensional transport equation based on an approximation to the variational multiscale theory the technique is adequate for methods with a local error distribution such as stabilized methods yielding efficiencies close to one for both the hyperbolic and diffusive limit regarding the hyperbolic limit previous work is extended to multi dimensions adequate norms are proposed for the computation of the error and proper error intrinsic time scales are calculated for the bilinear quadrilateral and the linear triangle furthermore the model considers the element interface error along the element edges enabling the error prediction in the diffusive limit the success of the method can be explained by the fact that in stabilized methods the element local problem captures most of the error and the proposed error intrinsic time scales are an approximation to the solution of the dual problem the proposed technology which can be implemented straightforwardly in existing codes is extremely economical because it is a simple explicit postprocessing

some errors estimates for the box method we define and analyze several variants of the box method for discretizing elliptic boundary value problems in the plane our estimates show the error to be comparable to a standard galerkin finite element method using piecewise linear polynomials

optimal biquadratic finite volume element methods on quadrilateral meshes in this paper an optimal biquadratic finite volume element scheme is established and analyzed for elliptic equations on quadrilateral meshes it is proved that the new scheme has optimal o h 2 convergence rate in h 1 norm and o h 3 convergence rate in l 2 norm with the assumption that each element is an h 2 parallelogram

the mortar finite volume method with the crouzeix raviart element for elliptic problems abstract we construct and analyse a mortar finite volume method for the discretization for selfadjoint elliptic boundary value problems in r 2 this method is based on the mortar crouzeix raviart non conforming finite element spaces we prove the optimal order h 1 norm and l 2 norm error estimates between the exact solution and the mortar finite volume approximation of the elliptic problems

sensitivity analysis and optimal design in charge transport problems the focus of this paper is the accurate and efficient determination of sensitivities of electrostatic potential and charge density in charge transport problems and the use of these sensitivities to carry out optimal design direct differentiations of the boundary integral formulation of poisson s equation for charge conservation and of the non linear partial differential equation for current continuity are carried out to obtain equations satisfied by the sensitivities methods for solving the sensitivity equations are discussed a numerical implementation of the methods is validated through several examples it is demonstrated that the design sensitivity coefficients dscs of the quantities of interest in charge transport are obtained accurately and that optimal design problems can be solved efficiently using these dscs

conforming boundary elements in plane elasticity for shape design sensitivity the structural design sensitivity analysis of a two dimensional continuum using conforming continuous boundary elements is investigated implicit differentiation of the discretized boundary integral equations is performed to obtain design sensitivities in an efficient manner by avoiding the factorization of the perturbed matrices a singular formulation of the boundary element method is used implicit differentiation of the boundary integral equations produces terms that contain derivatives of the fundamental solutions employed in the analysis the behaviour of the singularity of these derivatives of the boundary element kernel functions with respect to the design variables is investigated a rigid body motion technique is presented to obtain the singular terms in the resulting sensitivity matrices thus avoiding the problems associated with their numerical integration a formulation for obtaining the design sensitivities of the continua under body forces of the gravitational and centrifugal types is also presented the design sensitivity results are seen to be of the same order of accuracy as the boundary element analysis results numerical data comparing the performance of conforming and non conforming formulations in the calculation of design sensitivities are also presented the accuracy of the present results is demonstrated through comparisons with existing analytical results

axisymmetric thermoelastic shape sensitivity analysis and its application to turbine disc design a general method for shape design sensiti vityi analysis sdsa as applied to an axisymmetric thermoelasticity problem is presented using the material derivative concept and the adjoint variable method the sensitivity of a general functional composed of thermal and mechanical quantities is considered the method for deriving the sensitivity formula is based on standard direct thermal and elastic boundary integral equation formulation it is then applied to obtain explicit formulas for a representative displacement and stress constraint imposed on a sector of the boundary results of numerical implementation are presented for weight minimization of a turbine disc under thermomechanical loading the sensitivities of the displacement and stress constraint calculated by the formulas are compared with those by finite differences optimum shape obtained under the thermomechanical loading is discussed with that under the mechanical loading only clearly showing the practical importance of the sdsa of thermoelastic systems

on the finite volume element method the finite volume element method fve is a discretization technique for partial differential equations it uses a volume integral formulation of the problem with a finite partitioning set of volumes to discretize the equations then restricts the admissible functions to a finite element space to discretize the solution this paper develops discretization error estimates for general selfadjoint elliptic boundary value problems with fve based on triangulations with linear finite element spaces and a general type of control volume we establisho h estimates of the error in a discreteh 1 semi norm under an additional assumption of local uniformity of the triangulation the estimate is improved too h 2 results on the effects of numerical integration are also included

a finite volume method based on the crouzeix raviart element for elliptic pde s in two dimensions we introduce and analyse a finite volume method for the discretization of elliptic boundary value problems in mathbb r 2 the method is based on nonuniform triangulations with piecewise linear nonconforming spaces we prove optimal order error estimates in the l 2 norm and a mesh dependent h 1 norm

axisymmetric viscoplastic deformation by the boundary element method abstract this paper presents a boundary element formulation and numerical implementation of the problem of small axisymmetric deformation of viscoplastic bodies while the extension from planar to axisymmetric problems can be carried out fairly simply for the finite element method fem this is far from true for the boundary element method bem the primary reason for this fact is that the axisymmetric kernels in the integral equations of the bem contain elliptic functions which cannot be integrated analytically even over boundary elements and internal cells of simple shape thus special methods have to be developed for the efficient and accurate numerical integration of these singular and sensitive kernels over discrete elements the accurate determination of stress rates by differentiation of the displacement rates presents another formidable challenge a successful numerical implementation of the boundary element method with elementwise called the mixed approach or pointwise called the pure bem or bem approach determination of stress rates has been carried out a computer program has been developed for the solution of general axisymmetric viscoplasticity problems comparisons of numerical results from the bem and fem for several illustrative problems are presented and discussed in the paper it is possible to get direct solutions for the simpler class of problems for cylinders of uniform cross section and these solutions are also compared with the bem and fem results for such cases

boundary element shape sensitivity analysis for thermal problems with nonlinear boundary conditions implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solid objects subjected to nonlinear boundary conditions is shown to generate an accurate and economical approach for the computation of shape sensitivities for this class of problems this approach involves the employment of analytical derivatives of boundary element kernel functions with respect to shape design variables a formulation is presented that can consistently account for both temperature dependent convection and radiation boundary conditions several iterative strategies are presented for the solution of the resulting sets of nonlinear equations and the computational performances examined in detail multizone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized nonlinear boundary conditions or regions of geometric insensitivity to design variables a series of nonlinear example problems are presented that have closed form solutions 39 refs

a discontinuous finite volume method for a coupled fracture model abstract in this paper we present a discontinuous finite volume method for a hybrid dimensional coupled fracture model on triangular meshes in matrix and fracture the pressure is approximated by the discontinuous and continuous piecewise linear elements and in order to retain local conservation property the velocity is sought in the discontinuous lowest order raviart thomas element space and piecewise linear element space the proposed numerical scheme is only associated with the pressure so we avoid solving an indefinite saddle point problem in addition the discontinuous method eliminates the continuity of approximate functions across the interelement boundary so it has the advantage of high localizability and easy handling of complicated geometries optimal order error estimates for the pressure and velocity are proved and numerical experiments are carried out to confirm our theoretical analysis

a q1 finite volume element scheme for anisotropic diffusion problems on general convex quadrilateral mesh abstract in this paper we study a q 1 finite volume element scheme for anisotropic diffusion problems on general convex quadrilateral mesh it is known that the coercivity is the basement for some other theoretical results stability h 1 and l 2 error estimates etc and the existing results were mainly obtained on h 1 parallelogram meshes with scalar diffusion coefficients for the cases of full diffusion tensors and arbitrary convex quadrilateral meshes we obtain a necessary and sufficient condition for the positive definiteness of the cell matrix related to the cell bilinear form based on this result a sufficient condition is suggested to guarantee the coercivity of the scheme more interesting is that this sufficient condition covers the traditional h 1 parallelogram mesh assumption and has an explicit expression by which one can easily judge on any diffusion tensor and any mesh with arbitrary mesh size h 0 moreover an h 1 error estimate is obtained without the h 1 parallelogram assumption and some numerical results are also provided to validate the theoretical results

design sensitivity coefficients for elasto viscoplastic problems by boundary element methods this paper is concerned with accurate and efficient determination of design sensitivity coefficients dscs for solid mechanics problems with small strains and rotations but with material non linearities present elasto plastic or elasto viscoplastic problems this approach is based on direct differentiation dda of the relevant derivative boundary element method dbem formulation of the problem analytical differentiation of the dbem equations leads to singular integral equations for the dscs with weakly logarithmically for 2 d singular kernels which are easy to deal with also stress components and their sensitivities are obtained on the boundary of a body with great accuracy these quantities are typically difficult to obtain accurately from finite element methods fem a computer program for general two dimensional plane strain and plane stress problems has been developed based on the above formulation numerical results are presented for some sample problems and these are compared against direct solutions the agreement between the dbem and direct solutions is excellent for these examples

convergence of finite volume schemes for poisson s equation on nonuniform meshes an error analysis of a family of cell center finite volume schemes for poisson s equation on cartesian product nonuniform meshes in two dimensions is presented optimal order error estimates are derived in the discrete h 1 norm under minimum smoothness requirements on the exact solution and without any additional assumption on the regularity of the mesh on quasi uniform meshes analogous estimates are obtained in the maximum norm

flaw identification using the boundary element method in this paper a new boundary element formulation is presented for the identification of the location and size of internal flaws in two dimensional structures an introduction to inverse analysis is given with special reference to methods of flaw identification along with a brief review of the optimization methods employed both the standard boundary element and the dual boundary element method are presented with the dual boundary element method proposed as the basis for the new formulation the flaw identification method is presented along with the computation of the boundary displacement and traction derivatives and the specialized analytical integration used for cracked boundaries examples are given to demonstrate the accuracy of the sensitivity values and the performance of flaw location

a boundary contour formulation for design sensitivity analysis in two dimensional linear elasticity abstract a formulation for computing first order shape design sensitivities in two dimensional 2 d linear elastostatics by the boundary contour method bcm along with a numerical implementation using quadratic boundary elements is presented in this paper here the direct differentiation approach is analytically applied to the appropriate boundary contour equations in order to derive the sensitivities of all the physical quantities displacements tractions and stresses on the boundary as well as those for displacements and stresses inside the body under consideration the nonsingular formulation of the bcm is used for computing the boundary displacements and boundary stresses at off contour regular points a regular boundary point is a point on the boundary where it is locally smooth an off contour point lies inside a boundary element their corresponding sensitivities are obtained in a straightforward manner from the resulting regular sensitivity formulation also the stress sensitivities at the boundary nodes can be recovered easily from the global displacement shape functions described in a cartesian coordinate system finally through three numerical examples for which analytical solutions exist it is shown that the bcm can provide remarkably accurate numerical results for shape sensitivities

finite volume methods for convection diffusion problems derivation stability and error analysis in both discrete h 1 and l 2 norms for cell centered finite volume approximations of convection diffusion problems are presented various upwind strategies are investigated the theoretical results are illustrated by numerical examples

variational multiscale a posteriori error estimation for systems the euler and navier stokes equations this paper extends explicit a posteriori error estimators based on the variational multiscale theory to systems of equations in particular the emphasis is placed on flow problems the euler and navier stokes equations three error estimators are proposed the standard the naive and the upper bound numerical results show that with a very economical algorithm the attained global and local efficiencies for the naive approach are reasonably close to unity whereas the standard and upper bound approaches give respectively approximate lower and higher error estimates

design sensitivity coefficients for linear elastic bodies with zones and corners by the derivative boundary element method abstract the subject of this paper is the efficient and accurate determination of design sensitivity coefficients dscs in an elastic solid with zones and corners direct differentiation of the relevant derivative boundary element method dbem formulation of the problem is carried out here corners and zones in a body are treated carefully with conforming elements a numerical implementation of the method is carried out with isoparametric quadratic boundary elements the power of this approach is demonstrated through several numerical examples it is shown that the dscs of the various mechanical quantities of interest are obtained accurately and efficiently in one example even the dsc of the stress at a corner with respect to the corner angle is obtained very accurately by this method

boundary formulations for shape sensitivity of temperature dependent conductivity problems used in concert with the kirchhoff transformation implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solids with temperature dependent thermal conductivity is shown to generate an accurate and economical approach for computation of shape sensitivities for problems with specified temperature and heat flux boundary conditions a linear problem results for both the analysis and sensitivity analysis in problems with either convection or radiation boundary conditions a non linear problem is generated several iterative strategies are presented for the solution of the resulting sets of non linear equations and the computational performances examined in detail multi zone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized non iinear boundary conditions or regions of geometric insensitivity to design variables a series of non linear example problems is presented that have closed form solutions exact anaytical expressions tor the shape sensitivities associated with these problems are developed and these are compared with the sensitivities computed using the boundary element formulation

transient thermoelasticity and other body force effects in boundary element shape sensitivity analysis several new formulations for structural design sensitivity analysis dsa of elastic solids are presented that consistently account for steady and transient thermal loading along with centrifugal and gravity loading the approach employs implicit differentiation of the discretized boundary integral equations and facilitates the production of accurate and efficient computational procedures that obviate the need for matrix factorizations in the dsa step for centrifugal gravity and general thermal loading a new dsa concept employing a particular integral technique is developed for centrifugal gravity and steady thermal effects a surface integration approach is also presented and the two methods compared alternative strategies for modelling the behaviour of temperature distributions of evolving shapes undergoing shape optimization and the ramifications of these strategies in the dsa process are also discussed it is shown that for certain classes of thermoelastic problems shape optimization can be performed without the need to incorporate thermal analysis or dsa into the overall process a thermoelastic surface stress sensitivity analysis formulation is presented that does not require additional numerical integration a new thermoelastic sharp corner traction component consistent sensitivity analysis formulation is also presented this technique is shown to work for any initial stress distribution numerical sensitivity results are presented for many problems with analytical solutions

finite volume schemes for hamilton jacobi equations we introduce two classes of monotone finite volume schemes for hamilton jacobi equations the corresponding approximating functions are piecewise linear defined on a mesh consisting of triangles the schemes are shown to converge to the viscosity solution of the hamilton jacobi equation

reanalysis for structural modifications in boundary element responseand design sensitivity analysis a reanalysis technique is presented for obtaining changes in response variables due to changes in design parameters with the boundary element method the approach is considered for static response analysis and design sensitivity analysis two iterative schemes one based on total quantities and another based on incremental quantities are developed numerical results are obtained for analyses using 1 single zone discretization 2 multizone discretization and 3 multizone discretization with condensation

on the accuracy of the finite volume element method based on piecewise linear polynomials we present a general error estimation framework for a finite volume element fve method based on linear polynomials for solving second order elliptic boundary value problems this framework treats the fve method as a perturbation of the galerkin finite element method and reveals that regularities in both the exact solution and the source term can affect the accuracy of fve methods in particular the error estimates and counterexamples in this paper will confirm that the fve method cannot have the standard o h2 convergence rate in the l2 norm when the source term has the minimum regularity only being in l2 even if the exact solution is in h2

numerical simulation of the gas flow in a circuit breaker a computational methodology for the solution of unsteady two dimensional axisymmetric euler equations within geometries with moving boundaries is presented the flow simulation is carried out by applying a finite volume method which makes use of a lagrangian eulerian version of roe s approximate riemann solver the domain discretization is handled via unstructured triangular grids grid adaptation is applied on the basis of geometric and physical requirements the importance of the implicit treatment of the space conservation laws based on geometric analysis is evoked the procedure for reconstructing roe s method for moving meshes is described and validated finally the ability of the method for the prediction of the transient flow in a circuit breaker during its opening phase is illustrated

uniform convergence of finite volume element method with crouzeix raviart element for non self adjoint and indefinite elliptic problems in this paper we consider the finite volume element method based on the crouzeix raviart element and prove the existence uniqueness and uniform convergence of the finite volume element approximations for the non self adjoint and indefinite elliptic problems under minimal elliptic regularity assumption

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

additive average schwarz method for a crouzeix raviart finite volume element discretization of elliptic problems with heterogeneous coefficients in this paper we introduce an additive schwarz method for a crouzeix raviart finite volume element discretization of a second order elliptic problem with discontinuous coefficients where the discontinuities are both inside the subdomains and across and along the subdomain boundaries we show that depending on the distribution of the coefficient in the model problem the parameters describing the generalized minimal residual method gmres convergence rate of the proposed method depend linearly on the mesh parameters inlineequation not available see fulltext also under certain restrictions on the distribution of the coefficient the convergence of the gmres method is independent of jumps in the coefficient

mortar upwind finite volume element method for convection diffusion problems abstract in this paper we consider the mortar upwind finite volume element method with local linear conforming finite element space for the convection diffusion problems and show that the mortar upwind finite volume element approximations derived are convergent with optimal order in the h 1 norm

direct differentiation formulation for boundary element shape sensitivity analysis of axisymmetric elastic solids abstract an efficient direct differentiation method by continuum approach is presented for the shape design sensitivity analysis of axisymmetric elastic solids the method is purely based on the axisymmetric boundary integral equation formulation a new boundary integral equation for sensitivity analysis is derived by taking material derivative to the same integral identity that was used in the adjoint method as sensitivities in terms of the shape design variables are directly calculated by solving the new bie the singular boundary condition which may arise in the adjoint method is avoided in the present direct method to validate the theoretical formulation numerical implementation is done for three examples for a hollow disk and a thick walled cylinder problem with analytic solution the sensitivities by present method are compared with analytic sensitivities for an example of a spherical vessel being rather practical the sensitivities are compared with those by finite differences

a boundary integral formulation for complex three dimensional geometries a new boundary integral formulation is proposed to analyse the heat transfer in complex three dimensional geometries one example of such geometry is the die sets in the injection moulding process networks of cooling conduits within the mould and the closely spaced die surfaces require special attention both in formulation and numerical treatment of the integral equations the proposed formulation couples the boundary formula the gradient of the boundary formula and the exterior formula the derivation of the integral equations is presented here along with an efficient method for integration of some of the kernels in these equations and a semi analytical procedure for the integration of the highly singular integrands which result from differentiating the boundary formula although the techniques introduced here are applied to a particular problem in heat transfer their potential application is much broader

on the construction and analysis of high order locally conservative finite volume type methods for one dimensional elliptic problems locally conservative finite volume type methods based on continuous piecewise polynomial functions of degree r ge 2 are introduced and analyzed in the context of indefinite elliptic problems in one space dimension the new methods extend and generalize the classical finite volume method based on piecewise linear functions we derive a priori error estimates in the l2 h1 and l infty norm and discuss superconvergence effects for the error and its derivative explicit residual based a posteriori error bounds in the l2 and energy norm are also derived we compute the experimental order of convergence and show the results of an adaptive algorithm based on the a posteriori error estimates

boundary element implicit differentiation equations for design sensitivities of axisymmetric structures abstract design sensitivity analysis of axisymmetric elastic media is formulated using boundary elements the kernels for sensitivity matrices are obtained through implicit differentiation of the corresponding boundary element elasticity kernels the singular terms are obtained by applying the boundary displacements and tractions and their respective sensitivities for the rigid body motion mode and the inflation mode the equations for the recovery of sensitivities of axisymmetric boundary stresses are presented as a check on accuracy the approach is applied to a series of examples for which analytical elasticity solutions are available the predictions for both displacement and stress sensitivities are accurate additional examples are provided to demonstrate the versatility of the present approach

adaptive remeshing for compressible flow computations an adaptive mesh procedure for improving the quality of steady state solutions of the euler equations in two dimensions is described the procedure is implemented in conjunction with a finite element solution algorithm using linear triangular elements and an explicit time stepping scheme the mesh adaptation is accomplished by regeneration using information provided by the computed solution on the current mesh the meshes produced are characterised by the appearance of stretched elements in the vicinity of one dimensional flow features and can exhibit a large variation in element size this allows solutions of enhanced quality to be produced in a computationally efficient manner