isogeometric structural shape optimization an old dilemma in structural shape optimization is the needed tight link between design model or geometric description and analysis model the intention of this paper is to show that isogeometric analysis offers a potential and promising way out of this dilemma to this end we show a structural shape optimization framework based on the isogeometric analysis approach with the discretization based on non uniform rational b splines nurbs the analysis model represents the structural geometry exactly furthermore nurbs enable efficient geometry control together with smooth boundaries they are the de facto standard in cad systems but are also widely used in a shape optimal design context to define the geometry representation and the design variables with the presented isogeometric approach to shape optimization the analysis model is inherently merged with the design model omitting the typically involved interplay between both we derive analytical sensitivities for nurbs discretizations which allow application of efficient gradient based optimization algorithms the present contribution is restricted to two dimensional problems of linear elasticity but the extension to three dimensions and other problem classes is straightforward some representative examples demonstrate and validate the methodology further the potential of boundary continuity control within isogeometric structural shape optimization is explored to trigger smooth or less smooth angular designs

isogeometric analysis using t splines we explore t splines a generalization of nurbs enabling local refinement as a basis for isogeometric analysis we review t splines as a surface design methodology and then develop it for engineering analysis applications we test t splines on some elementary two dimensional and three dimensional fluid and structural analysis problems and attain good results in all cases we summarize the current status of t splines their limitations and future possibilities

extended immersed boundary method using fem and rkpm abstract the proposed extended immersed boundary method eibm has several distinct features in comparison with the immersed boundary ib method in the ib method the interaction between the immersed elastic boundary and the surrounding viscous fluid is replaced with an equivalent body force distribution within the fluid domain the key ingredient of the ib method is the enforcement of the energy input from the equivalent body force into the fluid domain to be the same at all time as that of the elastic forces within the ib in eibm instead of the volumeless immersed elastic boundary we consider the submerged elastic solid which occupies a finite volume within the fluid domain in particular we replace the kinematic and dynamic matching of the fluid solid interface and the effect of the submerged solid with a judiciously chosen collection of equivalent nodal forces calculated in the context of finite element formulations the employment of the finite element representation enables a realistic stress analysis for the submerged solid subject to large deformations finally in eibm we also replace the discretized delta function commonly used in the ib method with the kernel functions in meshless reproducing kernel particle method rkpm with this improvement using the same finite support domain we could improve the discretized delta function from c 1 to c n continuity where n is chosen according to the required smoothness and resolution of such functions and more importantly enables the use of non uniform meshing in the fluid domain these extensions may eventually open doors to the modelling of complex biological fluid involving molecular cellular and flexible vessel flow interactions

subdivision surfaces a new paradigm for thin shell finite element analysis we develop a new paradigm for thin shell finite element analysis based on the use of subdivision surfaces for i describing the geometry of the shell in its undeformed configuration and ii generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the kirchhoff love theory of thin shells the particular subdivision strategy adopted here is loop s scheme with extensions such as required to account for creases and displacement boundary conditions the displacement fields obtained by subdivision are h2 and consequently have a finite kirchhoff love energy the resulting finite elements contain three nodes and element integrals are computed by a one point quadrature the displacement field of the shell is interpolated from nodal displacements only in particular no nodal rotations are used in the interpolation the interpolation scheme induced by subdivision is non local i e the displacement field over one element depend on the nodal displacements of the element nodes and all nodes of immediately neighbouring elements however the use of subdivision surfaces ensures that all the local displacement fields thus constructed combine conformingly to define one single limit surface numerical tests including the belytschko et al 10 obstacle course of benchmark problems demonstrate the high accuracy and optimal convergence of the method

local refinement of analysis suitable t splines we develop a local refinement algorithm for analysis suitable t splines which does not produce excessive propagation of control points we then demonstrate its use as an adaptive framework for isogeometric analysis analysis suitable t splines are a class of t splines which are linearly independent and form a partition of unity these properties coupled with local refinement make this class of t splines appealing as a basis for isogeometric analysis

contact with friction in multi material arbitrary lagrangian eulerian formulations using x fem a contact method with friction for the multi dimensional lagrangian step in multi material arbitrary lagrangian eulerian ale formulations is presented in our previous research the extended finite element method x fem was used to create independent fields i e velocity strain rate force mass etc for each material in the problem to model contact without friction the research presented here includes the extension to friction and improvements to the accuracy and robustness of our previous study the accelerations of the multi material nodes are obtained by coupling the material force and mass fields as a function of the prescribed contact similarly the velocities of the multi material nodes are recalculated using the conservation of momentum when the prescribed contact requires it the coupling procedures impose the same nodal velocity on the coupled materials in the direction normal to their interface during the time step update as a result the overlap of materials is prevented and unwanted separation does not occur three different types of contacts are treated perfectly bonded frictionless slip and slip with friction example impact problems are solved and the numerical solutions are presented copyright 2008 john wiley sons ltd

an extended finite element formulation for contact in multi material arbitrary lagrangian eulerian calculations a contact method for the multi dimensional lagrangian step in multi material arbitrary lagrangian eulerian ale formulations is presented the extended finite element method x fem is used to create independent fields i e velocity strain rate force mass etc for each material in the problem the accelerations of the multi material nodes are obtained by coupling the material force and mass fields as a function of the prescribed contact similarly the velocities of the multi material nodes are recalculated using the conservation of momentum when the prescribed contact requires it the coupling procedures impose the same nodal velocity on the coupled materials in the direction normal to their interface during the time step update as a result the overlap of materials is prevented and unwanted separation does not occur three different contacts are treated perfectly bonded frictionless slip and slip with friction example impact problems are solved and the numerical solutions are presented

stable time step estimation for multi material eulerian hydrocodes the time step estimates used in explicit multi material eulerian hydrocodes are based on a series of upper bound approximations that can lead to unnecessarily small time steps since the cost of the calculation is proportional to the number of time steps the underestimation of the time step size has a direct adverse effect on the cost an accurate method for calculating the stable time step size is presented with example calculations

a nine point scheme for the approximation of diffusion operators on distorted quadrilateral meshes a nine point scheme is presented for discretizing diffusion operators on distorted quadrilateral meshes the advantage of this method is that highly distorted meshes can be used without the numerical results being altered remarkably and it treats material discontinuities rigorously and offers an explicit expression for the face centered flux moreover it has only the cell centered unknowns we prove that the method is stable and has first order convergence on distorted meshes numerical experiments show that the method has second order or nearly second order accuracy on distorted meshes

an improvement of the two point flux approximation scheme on polygonal meshes abstract a new diffusion scheme satisfying the maximum principle on two dimensional 2d polygonal meshes is proposed being different from the existing schemes which are based on the nonlinear combination of the two one side fluxes the scheme in this paper is constructed by a modification of the conventional linear two point flux approximation tpfa scheme in which the two side flux is constructed to improve its accuracy on 2d skewed meshes the tpfa scheme is rewritten by adding a tangential part i e the tangential component of the flux multiplied with a nonlinear factor a new method for the discretization of the tangential part is presented so that both the conservation condition and the maximum principle are satisfied while the tpfa part remains unchanged moreover by virtue of the harmonic averaging points for the calculation of the tangential part the scheme has a minimal stencil similar to the tpfa scheme finally some numerical examples are presented to verify that it is second order accurate on 2d polygonal meshes for anisotropic diffusion problems

the finite volume scheme preserving extremum principle for diffusion equations on polygonal meshes we construct a new nonlinear finite volume scheme for diffusion equation on polygonal meshes and prove that the scheme satisfies the discrete extremum principle our scheme is locally conservative and has only cell centered unknowns numerical results are presented to show how our scheme works for preserving discrete extremum principle and positivity on various distorted meshes

duality and unified analysis of discrete approximations in structural dynamics and wave propagation comparison of p method finite elements with k method nurbs we study the discretization behavior of classical finite element and nurbs approximations on problems of structural vibrations and wave propagation we find that on the basis of equal numbers of degrees of freedom and bandwidth nurbs have superior approximation properties in fact we observe that the high mode behavior of classical finite elements is divergent with the order of approximation a surprisingly negative result on the other hand nurbs offer almost spectral approximation properties and all modes converge with increasing order of approximation

extended isogeometric analysis for simulation of stationary and propagating cracks summary a novel approach based on a combination of isogeometric analysis iga and extended fem is presented for fracture analysis of structures the extended isogeometric analysis is capable of an efficient analysis of general crack problems using nonuniform rational b splines as basis functions for both the solution field approximation and the geometric description and it can reproduce crack tip singular fields and discontinuity across a crack iga has attracted a lot of interest for solving different types of engineering problems and is now further extended for the analysis of crack stability and propagation in two dimensional isotropic media concepts of the extended fem are used in iga to avoid the necessity of remeshing in crack propagation problems and to increase the solution accuracy around the crack tip crack discontinuity is represented by the heaviside function and isotropic analytical displacement fields near a crack tip are reproduced by means of the crack tip enrichment functions also the lagrange multiplier method is used to impose essential boundary conditions moreover the subtriangles technique is utilized for improving the accuracy of integration by the gauss quadrature rule several two dimensional static and quasi static crack propagation problems are solved to demonstrate the efficiency of the proposed method and the results of mixed mode stress intensity factors are compared with analytical and extended fem results copyright 2011 john wiley sons ltd

a generalized finite element formulation for arbitrary basis functions from isogeometric analysis to xfem many of the formulations of cm rent research interest including iosogeometric methods and the extended finite element method use nontraditional basis functions some such as subdivision surfaces may not have convenient analytical representations the concept of an element if appropriate at all no longer coincides with the traditional definition developing a new software for each new class of basis functions is a large research burden especially if the problems involve large deformations non linear materials and contact the objective of this paper is to present a method that separates as much as possible the generation and evaluation of the basis functions from the analysis resulting in a formulation that can be implemented within the traditional structure of a finite clement program but that permits the use of arbitrary sets of basis functions that are defined only through the input file elements ranging from a traditional linear four node tetrahedron through a higher order element combining xfem and isogeometric analysis may be specified entirely through an input file without any additional programming examples of this framework to applications with lagrange elements isogeometric elements and xfem basis functions for fracture are presented

robustness of isogeometric structural discretizations under severe mesh distortion abstract this paper investigates higher order and higher continuity functions in isogeometric structural analysis under distortion of the control and physical meshes first the concepts behind isogeometric analysis are briefly reviewed the effect of perturbing control points upon the geometrical mapping is observed in the one dimensional setting the concept is extended to multiple dimensions with a series of cases where the interior of a cube is distorted in different ways and patch tests are performed to assess accuracy a circular fillet patch is introduced through the appropriate degeneration of a control mesh in order to address the problem of modeling small features in finite element models the fillet patch is tested with two problems of linear elasticity and is shown to be accurate the investigation is further extended to the setting of large deformation nearly incompressible nonlinear elasticity with two examples which make use of the recently proposed f projection method

fast integration and weight function blending in the extended finite element method two issues in the extended finite element method xfem are addressed efficient numerical integration of the weak form when the enrichment function is self equilibrating and blending of the enrichment the integration is based on transforming the domain integrals in the weak form into equivalent contour integrals it is shown that the contour form is computationally more efficient than the domain form especially when the enrichment function is singular and or discontinuous a method for alleviating the errors in the blending elements is also studied in this method the enrichment function is pre multiplied by a smooth weight function with compact support to allow for a completely smooth transition between enriched and unenriched subdomains a method for blending step function enrichment with singular enrichments is described it is also shown that if the enrichment is not shifted properly the weighted enrichment is equivalent to the standard enrichment an edge dislocation and a crack problem are used to benchmark the technique the influence of the variables that parameterize the weight function is analyzed the resulting method shows both improved accuracy and optimum convergence rates and is easily implemented into existing xfem codes

enforcing positivity with conservation for nine point scheme of nonlinear diffusion equations abstract the nine point scheme nps is a finite volume scheme for solving nonlinear diffusion equations on quadrilateral grids it s well known that the solution of the scheme on distorted grids cannot preserve positivity when all given data are nonnegative here for the nps of nonlinear diffusion problems we propose a conservative enforcing positivity algorithm cepa which is posterior correction of the discrete solution and allows the new solution preserves positivity as well as local conservation at each step of nonlinear iteration numerical results are presented to demonstrate that the accuracy of our algorithm of enforcing positivity with conservation is higher than some common procedures of positivity correction

an improved monotone finite volume scheme for diffusion equation on polygonal meshes we construct a new nonlinear monotone finite volume scheme for diffusion equation on polygonal meshes the new scheme uses the cell edge unknowns instead of cell vertex unknowns as the auxiliary unknowns in order to improve the accuracy of monotone scheme our scheme is locally conservative and has only cell centered unknowns numerical results are presented to show how our scheme works for preserving positivity on various distorted meshes specially numerical results show that the new scheme is robust and more accurate than the existing monotone scheme on some kinds of meshes

monotone finite volume schemes for diffusion equations on polygonal meshes we construct a nonlinear finite volume fv scheme for diffusion equation on star shaped polygonal meshes and prove that the scheme is monotone i e it preserves positivity of analytical solutions for strongly anisotropic and heterogeneous full tensor coefficients our scheme has only cell centered unknowns and it treats material discontinuities rigorously and offers an explicit expression for the normal flux numerical results are presented to show how our scheme works for preserving positivity on various distorted meshes for both smooth and non smooth highly anisotropic solutions and numerical results show that our scheme appears to be approximate second order accuracy for the solution and first order accuracy for the flux

a finite volume method for approximating 3d diffusion operators on general meshes a finite volume method is presented for discretizing 3d diffusion operators with variable full tensor coefficients this method handles anisotropic non symmetric or discontinuous variable tensor coefficients while distorted non matching or non convex n faced polyhedron meshes can be used for meshes of polyhedra whose faces have not more than four edges the associated matrix is positive definite and symmetric if the diffusion tensor is symmetric a second order resp first order accuracy is numerically observed for the solution resp gradient of the solution

modeling holes and inclusions by level sets in the extended finite element method a methodology to model arbitrary holes and material interfaces inclusions without meshing the internal boundaries is proposed the numerical method couples the level set method s osher j a sethian j comput phys 79 1 1988 12 to the extended finite element method x fem n moes j dolbow t belytschko int j numer methods engrg 46 1 1999 131 in the x fem the finite element approximation is enriched by additional functions through the notion of partition of unity the level set method is used for representing the location of holes and material interfaces and in addition the level set function is used to develop the local enrichment for material interfaces numerical examples in two dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique

stable generalized iso geometric analysis sgiga for problems with discontinuities and singularities abstract numerical analysis of physical mathematical problems based on generalized extended isogeometric analysis suffers from the major drawbacks of sub optimal convergence rates and ill conditioning of system matrices blending elements and linear dependency of basis functions are some of the causes attributed to these drawbacks the presence of blending elements reduces the overall convergence rates and the ill conditioning of system matrices results in either increasing computational time when iterative solvers are used or erroneous results when direct solvers are employed in order to alleviate these drawbacks three different stable generalized isogeometric analysis sgiga methods are proposed in this paper in sgiga the enrichment functions are modified by shifting the enrichment function using linear or least square interpolant of the enrichment function problems with weak and strong discontinuities singularities and combination of both discontinuities and singularities are considered as case studies to illustrate the performance of the proposed sgiga methods from the results it is observed that sgiga yields optimal convergence rates as well as better conditioning of system matrices the results obtained from the proposed sgiga methods are also compared with the results from the established methods stable generalized finite element method sgfem and extended isogeometric analysis xiga to study the relative performances with respect to accuracy and conditioning

isogeometric schwarz preconditioners for linear elasticity systems isogeometric schwarz preconditioners are constructed and analyzed for both compressible elasticity in primal formulation and almost incompressible elasticity in mixed formulation these preconditioners require the solution of local elasticity problems on overlapping subdomains forming a decomposition of the problem domain and the solution of a coarse elasticity problem associated with the subdomain coarse mesh an h analysis of the preconditioner for the primal formulation of compressible elasticity yields an optimal convergence rate bound that is scalable in the number of subdomains and is linear in the ratio between subdomain and overlap sizes extensive numerical experiments in 2d and 3d confirm this theoretical bound and show that an analogous bound holds for the mixed formulation of almost incompressible elasticity the numerical tests also show the good preconditioner performance with respect to the polynomial degree p and regularity k of the isogeometric basis functions as well as with respect to the presence of discontinuous elastic coefficients in composite materials and to domain deformation

a reconstruction algorithm with flexible stencils for anisotropic diffusion equations on 2d skewed meshes a new reconstruction algorithm is developed to obtain diffusion schemes with cell centered unknowns only the main characteristic of the new algorithm is the flexibility of stencils when the auxiliary unknowns are reconstructed with cell centered unknowns the stencils are selected depending on the mesh geometry and discontinuities of diffusion coefficients moreover an explicit expression is derived for interpolating the auxiliary unknowns in terms of cell centered unknowns and the auxiliary unknowns can be defined at any point on the edge the algorithm is applied to construct several new diffusion schemes whose effectiveness is illustrated by numerical experiments for anisotropic problems with or without discontinuities nearly second order accuracy is achieved on skewed meshes

shape optimization directly from cad an isogeometric boundary element approach using t splines abstract we develop a t spline isogeometric boundary element method igabem simpson et al 2012 scott et al 2013 simpson et al 2014 to shape sensitivity analysis and gradient based shape optimization in three dimensional linear elasticity contrary to finite element based isogeometric analysis iga approaches no parametrization of the volume is required hence the iterative optimization algorithm can be implemented directly from cad without any mesh generation or postprocessing step for returning the resulting structure to cad designers t splines also guarantee a water tight geometry without the manual geometrical repair work as with non uniform rational b splines nurbs we demonstrate the worth of the method by analysing problems with and without analytical solutions including engineering examples involving complex shapes additionally we provide all the derivations of the required sensitivities and the details pertaining to the geometries examined in the benchmarking to provide helpful reference problems for 3d shape optimization

a monotone finite volume scheme for diffusion equations on general non conforming meshes a nonlinear monotone finite volume scheme on general non conforming meshes for diffusion equations is introduced which deals with discontinuous tensor coefficients rigorously since the expression of normal flux depends on auxiliary unknowns defined at cell vertex including hanging nodes we propose a new method to eliminate vertex unknown by using primary unknowns at the centers of the cells sharing the vertex especially the unknowns defined on hanging nodes are eliminated by flux continuous conditions the resulting scheme is monotone and preserves positivity of analytical solutions for strongly anisotropic and heterogeneous full tensor coefficient problems numerical results show that the convergent order of the monotone scheme by different methods of eliminating vertex unknowns will vary remarkably and our new method can assure that it has almost second order accuracy and more accurate than some existing methods

discretization on unstructured grids for inhomogeneous anisotropic media part i derivation of the methods discretization methods are proposed for control volume formulations on polygonal and triangular grid cells in two space dimensions the methods are applicable for any system of conservation laws where the flow density is defined by a gradient law like darcy s law for porous media flow a strong feature of the methods is the ability to handle media inhomogeneities in combination with full tensor anisotropy this paper gives a derivation of the methods and the relation to previously published methods is also discussed a further discussion of the methods including numerical examples is given in the companion paper part ii siam j sci comput pp 1717 1736

extended finite element method for three dimensional crack modelling an extended finite element method x fem for three dimensional crack modelling is described a discontinuous function and the two dimensional asymptotic crack tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity this enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed stress intensity factors sifs for planar three dimensional cracks are presented which are found to be in good agreement with benchmark solutions copyright 2000 john wiley sons ltd

overlapping schwarz methods for isogeometric analysis we construct and analyze an overlapping schwarz preconditioner for elliptic problems discretized with isogeometric analysis the preconditioner is based on partitioning the domain of the problem into overlapping subdomains solving local isogeometric problems on these subdomains and solving an additional coarse isogeometric problem associated with the subdomain mesh we develop an h analysis of the preconditioner showing in particular that the resulting algorithm is scalable and its convergence rate depends linearly on the ratio between subdomain and overlap sizes for fixed polynomial degree p and regularity k of the basis functions numerical results in two and three dimensional tests show the good convergence properties of the preconditioner with respect to the isogeometric discretization parameters h p k number of subdomains n overlap size and also jumps in the coefficients of the elliptic operator

discretization on unstructured grids for inhomogeneous anisotropic media part ii discussion and numerical results a companion paper part i siam j sci comput 19 1998 pp 1700 1716 presents discretization methods for control volume formulations in two space dimensions properties of the developed methods are further discussed including rotational invariance and stability under the influence of anisotropy strong anisotropy may have to be handled by use of stretched grid cells numerical examples that demonstrate strengths and weaknesses of the methods are presented the examples focus on inhomogeneity anisotropy and rotational invariance

a local solution approach for adaptive hierarchical refinement in isogeometric analysis abstract adaptively refining the state variables and fast solving the equations are two key issues in isogeometric analysis currently existing research more focuses on the first issue while the efficiency issue is not elaborated when the overall equations are solved at each refinement step this article develops an approach to promote the efficiency by locally solving the equations that govern the refined variables at each refinement step here hierarchical refinement of the state variables in nurbs is adopted and transformational matrix that transforms the basis functions from the current level to the refined level is utilized to handle the relations between the equations at different levels by dividing the coefficient matrix into blocks and estimating the error of state variables for different blocks we represent the global solution method in a hierarchical structure and separately construct and solve equations to obtain the solution for each level in the structure we validate the proposed method by some steady heat transfer and structural analysis problems in domains with different dimensionality we have compared the numerical result accuracy as well as the time cost of the proposed method with those of current available refinement approaches and it turns out to be very promising

explicit algorithms for the nonlinear dynamics of shells abstract a finite element formulation and algorithm for the nonlinear analysis of the large deflection materially nonlinear response of impulsively loaded shells is presented a unique feature of this algorithm is the use of a bilinear four node quadrilateral element with single point quadrature and a simple hourglass control which is orthogonal to rigid body modes on an element level and does not compromise the consistency of the equations the geometric nonlinearities are treated by using a corotational description wherein a coordinate system that rotates with the material is embedded at the integration point thus the algorithm is directly applicable to anisotropic materials without any corrections for frame invariance of material property tensors this algorithm can treat about 200 element time steps per cpu second on a cyber 170 730 computer in the explicit time integration mode numerous results are presented for both elastic and elastic plastic problems with large strains that show that the method in most cases is comparable in accuracy with an earlier version of this algorithm employing a cubic triangular plate shell element but substantially faster

adaptive isogeometric analysis by local h refinement with t splines isogeometric analysis based on non uniform rational b splines nurbs as basis functions preserves the exact geometry but suffers from the drawback of a rectangular grid of control points in the parameter space which renders a purely local refinement impossible this paper demonstrates how this difficulty can be overcome by using t splines instead t splines allow the introduction of so called t junctions which are related to hanging nodes in the standard fem obeying a few straightforward rules rectangular patches in the parameter space of the t splines can be subdivided and thus a local refinement becomes feasible while still preserving the exact geometry furthermore it is shown how state of the art a posteriori error estimation techniques can be combined with refinement by t splines numerical examples underline the potential of isogeometric analysis with t splines and give hints for further developments

a cell functional minimization scheme for parabolic problem we are interested in a robust and accurate finite volume scheme for 2 d parabolic problems derived from the cell functional minimization approach the scheme has a local stencil is locally conservative treats discontinuity rigorously and leads to a symmetric positive definite linear system since the scheme has both cell centered unknowns and cell edge unknowns the computational cost is an issue and a parallel algorithm is then suggested based on nonoverlapping domain decomposition approach the interface condition is of the dirichlet robin type and has a parameter l by choosing this parameter properly the convergence of the iteration process could be sped up numerical results for linear and nonlinear problems demonstrate the good performance of the cell functional minimization scheme and its parallel version on distorted meshes

efficient quadrature for nurbs based isogeometric analysis abstract we initiate the study of efficient quadrature rules for nurbs based isogeometric analysis a rule of thumb emerges the half point rule indicating that optimal rules involve a number of points roughly equal to half the number of degrees of freedom or equivalently half the number of basis functions of the space under consideration the half point rule is independent of the polynomial order of the basis efficient rules require taking into account the precise smoothness of basis functions across element boundaries several rules of practical interest are obtained and a numerical procedure for determining efficient rules is presented we compare the cost of quadrature for typical situations arising in structural mechanics and fluid dynamics the new rules represent improvements over those used previously in isogeometric analysis

variational multiscale residual based turbulence modeling for large eddy simulation of incompressible flows we present an les type variational multiscale theory of turbulence our approach derives completely from the incompressible navier stokes equations and does not employ any ad hoc devices such as eddy viscosities we tested the formulation on forced homogeneous isotropic turbulence and turbulent channel flows in the calculations we employed linear quadratic and cubic nurbs a dispersion analysis of simple model problems revealed nurbs elements to be superior to classical finite elements in approximating advective and diffusive processes which play a significant role in turbulence computations the numerical results are very good and confirm the viability of the theoretical framework

stochastic analysis of tree like data structures the purpose of this article is to present two types of data structures binary search trees and usual combinatorial binary trees although they constitute the same set of rooted trees they are constructed via completely different rules and thus the underlying probabilistic models are different too both kinds of data structure can be analysed by probabilistic and stochastic tools binary search trees more or less with martingales and binary trees which can be considered as a special case of galton watson trees with stochastic processes it is also an aim of this article to demonstrate the strength of analytical methods in specific parts of probability theory related to combinatorial problems and we especially make use of the concept of generating functions one reason for the use of generating functions is that recursive combinatorial descriptions can be translated to relations for generating functions and another is that analytical properties of these generating functions can be used to derive asymptotic probabilistic relations

a new nonlinear finite volume scheme preserving positivity for diffusion equations in this paper we present a new nonlinear finite volume scheme preserving positivity for diffusion equations the main feature of the scheme is the assumption that the values of auxiliary unknowns are nonnegative is avoided two nonnegative parameters are introduced to define a new nonlinear two point flux in which one point is the cell center and the other is the midpoint of cell edge the final flux on the edge is obtained by the continuity of normal flux numerical results show that the accuracy of both solution and flux for our new scheme is superior to that of some existing monotone schemes

a multidimensional unified gas kinetic scheme for radiative transfer equations on unstructured mesh abstract in order to extend the unified gas kinetic scheme ugks to solve radiative transfer equations in a complex geometry a multidimensional asymptotic preserving implicit method on unstructured mesh is constructed in this paper with an implicit formulation the cfl condition for the determination of the time step in ugks can be much relaxed and a large time step is used in simulations differently from previous direction by direction ugks on orthogonal structured mesh on unstructured mesh the interface flux transport takes into account multi dimensional effect where gradients of radiation intensity and material temperature in both normal and tangential directions of a cell interface are included in the flux evaluation the multiple scale nature makes the ugks be able to capture the solutions in both optically thin and thick regions seamlessly in the optically thick region the condition of cell size being less than photon s mean free path is fully removed and the ugks recovers a solver for diffusion equation in such a limit on unstructured mesh for a distorted quadrilateral mesh the ugks goes to a nine point scheme for the diffusion equation and it naturally reduces to the standard five point scheme for a orthogonal quadrilateral mesh numerical computations covering a wide range of transport regimes on unstructured and distorted quadrilateral meshes will be presented to validate the current approach

arbitrary discontinuities in space time finite elements by level sets and x fem an enriched finite element method with arbitrary discontinuities in space time is presented the discontinuities are treated by the extended finite element method x fem which uses a local partition of unity enrichment to introduce discontinuities along a moving hyper surface which is described by level sets a space time weak form for conservation laws is developed where the rankine hugoniot jump conditions are natural conditions of the weak form the method is illustrated in the solution of first order hyperbolic equations and applied to linear first order wave and non linear burgers equations by capturing the discontinuity in time as well as space results are improved over capturing the discontinuity in space alone and the method is remarkably accurate implications to standard semi discretization x fem formulations are also discussed copyright 2004 john wiley sons ltd

b and f projection methods for nearly incompressible linear and non linear elasticity and plasticity using higher order nurbs elements abstract this paper presents projection methods to treat the incompressibility constraint in small and large deformation elasticity and plasticity within the framework of isogeometric analysis after reviewing some fundamentals of isogeometric analysis we investigate the use of higher order non uniform rational b splines nurbs within the b projection method the higher continuity property of such functions is explored in nearly incompressible applications and shown to produce accurate and robust results a new non linear f projection method based on a modified minimum potential energy principle and inspired by the b method is proposed for the large deformation case it leads to a symmetric formulation for which the consistent linearized operator for fully non linear elasticity is derived and used in a newton raphson iterative procedure the performance of the methods is assessed on several numerical examples and results obtained are shown to compare favorably with other published techniques

cell centered finite volume methods with flexible stencils for diffusion equations on general nonconforming meshes a cell centered finite volume method is presented for discretizing diffusion operator on general nonconforming meshes the node values are accurately approximated using a new weighted interpolation formula in which the calculation of the weight is adaptive to both geometric parameters and diffusion coefficients it follows that an explicit expression composed of cell centered unknowns only is obtained for the discretization of normal flux numerical results demonstrate that linear solutions are reproduced exactly on the nonconforming random grids and that the convergence rate is close to second order for non linear or discontinuous problems