the h text p version of the finite element method for domains with curved boundaries this paper analyzes the convergence of the h text p version of the finite element method for elliptic problems on curved domains it proves that when the boundary of the domain is piecewise analytic boundary conditions are piecewise analytic and the sides of the elements are analytic the h text p version has an exponential rate of convergence numerical computations are included the paper generalizes the results previously obtained by the authors the h text p version of finite element method part 1 the basic approximation results comp mech 1 1986 pp 21 41 the h text p version of finite element method part 2 general results and applications comp mech 1 1986 pp 203 220

adaptive cfd analysis for rotorcraft aerodynamics abstract an adaptive parallel computational fluid dynamics cfd technique is developed to compute rotor blade aerodynamics for this purpose an error indicator is formulated and coded into an adaptive finite element framework it is shown that the error indicator is effective in resolving the global features of the flow field furthermore for efficiency and problem size considerations once the interpolation errors are reduced to acceptable levels the adaptive refinement is done only in regions affected by the vortical flows to accomplish this a novel vortex core detection technique is used to capture vortex tubes the combination of interpolation error estimate and vortex core detection technique proved to be very effective in computing vortical flow field of rotor blades example adaptive parallel calculations of hovering rotor blades requiring 1 3 million tetrahedral elements are presented

reliability of automatic 3d mesh generation abstract this paper considers issues critical to ensuring the reliability of automatic three dimensional mesh generators building on basic concepts from geometric modeling consideration is given to i the definition and assurance of a valid finite element mesh ii the use of topological adjacency information to improve the reliability and efficiency of a meshing process and iii how the geometric approximations used during the construction of a geometric model must be explicitly considered if the mesh generator s reliability is to be ensured

geometrically accurate efficient and flexible quadrature techniques for the tetrahedral finite cell method abstract we illustrate the importance of geometrically accurate volume quadrature for obtaining optimal accuracy with non boundary fitted finite element discretizations when the problem domain is defined by sharp boundaries we consider the tetrahedral finite cell method tetfcm and replace its recursive subdivision based integration approach with geometrically accurate quadrature rules that emanate from higher order geometric parametrizations of cut tetrahedral elements the element wise parametrization procedure relies on the identification of the intersection topology and a series of higher order mappings based on lagrange polynomials we demonstrate with several 3d examples that geometrically faithful local parametrization ensures optimal accuracy while significantly reducing the number of quadrature points with respect to recursive subdivision on the other hand we highlight the strength of subdivision quadrature in the context of a patient specific workflow for the simulation based performance analysis of coupled bone implant configurations in particular we show that accuracy flexibility and computational efficiency of the tetfcm critically depend on flexibly applying the two different quadrature variants for fuzzy imaging data and sharp boundary representations respectively

toward a universal adaptive finite element strategy part 3 design of meshes abstract in this third paper in our series the issue of designing h p meshes which are optimal in some sense is addressed criteria for h p meshes are derived which are based on the idea of minimizing the estimated error over a mesh with a fixed number of degrees of freedom an optimization algorithm is developed based on these criteria and is applied to several model one dimensional and two dimensional elliptic boundary value problems numerical results indicate that the approach can lead to exponential rates of convergence

on shape preserving quadratic spline interpolation in this paper we discuss the design of algorithms for interpolating discrete data using c 1 quadratic splines in such a way that the monotonicity and or convexity of the data is preserved the analysis culminates in an interactive algorithm which takes full advantage of the flexibility which quadratic splines permit

integration by table look up for p version finite elements on curved tetrahedra abstract we develop a method of evaluating element level matrices and vectors associated with p version finite element computations on tetrahedral meshes with curved boundaries the procedure uses optimal interpolation formula q chen i babuska approximate optimal points for polynomial interpolation of real functions in an interval and in a triangle comput methods appl mech engrg 128 1995 405 417 q chen i babuska approximate optimal polynomial interpolation points in the tetrahedron comput methods appl mech engrg 137 1997 89 94 for non polynomial portions of integrands followed by exact integration exact integrals of product combinations of polynomial interpolants and shape functions are stored so that different integrals may be efficiently evaluated by a table look up we present error analysis for our scheme applied to curvilinear tetrahedral meshes with exact geometric representation of the boundary of the domain as defined in a geometric modelling system numerical results are presented for problems involving the helmholtz equation

an operator splitting method for the wigner poisson problem the wigner poisson equation describes the quantum mechanical motion of electrons in a self consistent electrostatic field the equation consists of a transport term and a non linear pseudodifferential operator in this paper we analyze an operator splitting method for the linear wigner equation and the coupled wigner poisson problem for this semidiscretization in time consistency and nonlinear stability are established in an l2 framework we present a numerical example to illustrate the method

diffusive corrections to asymptotics of a strong field quantum transport equation abstract the asymptotic analysis of a linear high field wigner bgk equation is developed by a modified chapman enskog procedure by an expansion of the unknown wigner function in powers of the knudsen number evolution equations are derived for the terms of zeroth and first order in in particular a quantum drift diffusion equation for the position density of electrons with an order correction on the field terms is obtained well posedness and regularity of the approximate problems are established and a rigorous proof that the difference between exact and asymptotic solutions is of order 2 uniformly in time and for arbitrary initial data is given

a straightforward structure to construct shape functions for variable p order meshes this paper describes a method for specifying variable p order meshes based on the topological hierarchy of mesh entities defining the finite elements a decomposition of p version mesh entity shape functions into a product of a function defined over the mesh entity and a blending function defined over the elements that the mesh entity bounds is presented the decomposed shape functions allow the effective construction of the shape functions and derivatives needed to construct element matrices for variable p enrichment

optimal finite element interpolation on curved domains this paper is devoted to a general theory of approximation of functions in finite element spaces in particular the case is considered where the functions to be interpolated are on the one hand not very smooth and on the other are defined on curved domains thus a number of well known optimal interpolation results are generalized

the h p and h p versions of the finite element methods in 1 dimension part iii the adaptive h p version abstract the paper is the third and final part in the series of three devoted to the detailed analysis of the three basic versions of the finite element method in one dimension the first part analyzed the p version and the second part concentrated on the h and h p version this paper analyzes a theoretical frame of the adaptive h p version and based on it the authors provide concrete algorithm for the one dimensional problem it is proven that in the case that the solution has x sub alpha type singularity the adaptive algorithm give an exponential rate of convergence very close to the optimal one analyzed in the second part of the paper additional keyword error analysis

approximate optimal points for polynomial interpolation of real functions in an interval and in a triangle the main results of this paper are the analysis of the quality of approximation of polynomial interpolation and the computation of the approximate optimal interpolation points in the triangle we introduce various norms for the interpolation operator computational results indicate that for a given polynomial degree the set that minimizes the mean l2 norm of the interpolation operator is close to the smallest lebesgue constant interpolation set in particular for the triangle this set gives the smallest lebesgue constant currently known

the generation of triangular meshes for nurbs enhanced fem summary this paper presents the first method that enables the fully automatic generation of triangular meshes suitable for the so called non uniform rational b spline nurbs enhanced finite element method nefem the meshes generated with the proposed approach account for the computer aided design boundary representation of the domain given by nurbs curves the characteristic element size is completely independent of the geometric complexity and of the presence of very small geometric features the proposed strategy allows to circumvent the time consuming process of de featuring complex geometric models before a finite element mesh suitable for the analysis can be produced a generalisation of the original definition of a nefem element is also proposed enabling to treat more complicated elements with an edge defined by several nurbs curves or more than one edge defined by different nurbs three examples of increasing difficulty demonstrate the applicability of the proposed approach and illustrate the advantages compared with those of traditional finite element mesh generators finally a simulation of an electromagnetic scattering problem is considered to show the applicability of the generated meshes for finite element analysis 2016 the authors international journal for numerical methods in engineering published by john wiley sons ltd

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

toward a universal h p adaptive finite element strategy part 1 constrained approximation and data structure abstract this is the first of a series of papers devoted to the development of an adaptive finite element method to solve various boundary value problems arising in solid and fluid mechanics the paper deals with the general concepts of h p finite element methods constrained approximation and data structure and related issues several numerical examples illustrate the main ideas of the method

approximation properties of the h p version of the finite element method abstract the paper surveys the approximation and convergence properties of the h p version of the finite element method the basic theoretical results together with the main ideas of the proofs numerical examples are given

an analysis of the wigner poisson problem with inflow boundary conditions abstract we present a study of the wigner poisson problem in a bounded spatial domain with non homogeneous and time dependent inflow boundary conditions this system of nonlinearly coupled equations is a mathematical model for quantum transport of charges in a semiconductor with external contacts we prove well posedness of the linearized n dimensional problem as well as existence and uniqueness of a global in time regular solution of the one dimensional nonlinear problem

shape preserving splines in constructing wowa operators comment on paper by v torra in fuzzy sets and systems 113 2000 389 396 v torra in 8 presents an algorithm for constructing weighted owa operators 7 using interpolation de nition 1 in 8 his method relies on the construction of a monotone increasing functionw x that interpolates the points i n j6i wj together with the origin where the weights wj denote relative importance or reliability of information sources in addition to being monotone the functionw x is required to be a straight line if the data permits as the interpolant v torra uses the monotonicity preserving quadratic spline of mcallister and roulier 5 which has also been used for representation of membership functions in 3 i would like to draw attention to another simpler algorithm for constructing monotone quadratic interpolating spline due to schumaker 6 schumaker s algorithm requires speci cation of slopes at data points however these slopes can be selected automatically using the method by butland 2 the modi ed algorithm is described in detail in 4 and the pseudocode is presented in 1 in 4 it was proven that with butland slopes both algorithms produce identical results however schumaker s algorithm is far less complicated more e cient and requires fewer additional

the effect of numerical quadrature in the p version of the finite element method we investigate the use of numerical quadrature in the p version of the finite element method we describe a set of minimal conditions that the quadrature rules should satisfy for various types of elements under sufficient assumptions of smoothness we establish optimality of the asymptotic rate of convergence some computational results are presented which illustrate under what conditions overintegration may be useful

conservative multimoment transport along characteristics for discontinuous galerkin methods a set of algorithms based on characteristic discontinuous galerkin methods is presented for tracer transport on the sphere the algorithms are designed to reduce message passing interface communica

the p version of the finite element method for three dimensional curved thin walled structures in this paper we present an implementation of a three dimensional p version for structural problems of solids with almost arbitrarily curved surfaces applying the blending function method complex structures can often be modelled by a few p elements being the basis for a higher order approximation numerical examples will demonstrate that the p version with anisotropic ansatz spaces allows to predict the structural behaviour of three dimensional plates and shells with approximately the same amount of degrees of freedom as in the two dimensional case yet significantly more accurate due to the three dimensional model furthermore it is advantageous to compute complex structures exclusively with three dimensional discretizations as no special elements are needed to model the transition from dimensionally reduced formulations like plates or shells to fully three dimensional solid elements using the p version with anisotropic ansatz spaces the whole structure can be efficiently discretized with solid elements even if the aspect ratio of the elements becomes very large copyright 2001 john wiley sons ltd

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

geometry representation issues associated with p version finite element computations this paper addresses issues related to accurate geometry representation for p version finite elements on curved three dimensional domains specific options to account for domain geometry information during element level computation are identified accuracy requirements on the geometry related approximations to preserve the optimal rate of finite element error convergence for second order elliptic boundary value problems are given an element geometric mapping scheme based on blending the exact shape of the domain boundary is described that can either be used directly during element integrations or used to construct element level geometric approximations of required accuracy smoothness issues of the rational blends on simplex topologies are discussed and a numerical example based on the solution of poisson s equation in three dimensions is presented to illustrate the impact of the rational blends on the optimal rate of finite element error convergence

shell finite cell method a high order fictitious domain approach for thin walled structures abstract this article presents a generalization of the recently proposed finite cell method to thin walled structures this approach uses a combination of well known fictitious domain methods with high order hierarchical ansatz spaces known from the p version of the finite element method whereas the original concept embeds a three dimensional structure in a simple domain being meshed into a grid of cube shaped cells the extension presented in this paper applies the fictitious domain approach to a two dimensional master domain defined in the parameter plane of the geometric model implementation details are discussed and numerical benchmark problems show the high accuracy and computational efficiency of the new approach it is also remarked that the present approach can easily be carried over to isogeometric analysis opening an attractive possibility to simulate trimmed nurbs surfaces

mesh generation in curvilinear domains using high order elements the ability to construct suitable computational meshes is currently a significant limiting factor in the development of compact high order algorithms in very complex geometries compact high order algorithms such as spectral element or p type finite element techniques offer the potential of high accuracy if the solution is smooth and a well behaved mapping exists between the local sub domains and a standard region in this paper we address the problem of coupling high order algorithms with unstructured mesh generation and cad representation techniques we present three complementary strategies to alleviate the problem of generation of elemental regions with singular elemental mappings the first strategy investigates the influence of an anisometric parametric surface representation on the quality of high order unstructured meshes we show that a straightforward splitting of a standard linear mesh for use in a high order method can lead to the generation of distorted possibly invalid meshes even for simple computational domains such as cubes the second strategy uses hybrid meshes applying prismatic elements near curvilinear boundaries in the third and final strategy we investigate the use of curvature driven surface discretization to incorporate higher order information about the surface into the mesh generation using the computational reconstruction of the arterial bypass graft as an example computational domain we demonstrate how the combination of all three strategies leads to a valid high order discretization of the computational domain copyright 2001 john wiley sons ltd

a parallel hp fem infrastructure for three dimensional structural acoustics this paper describes a parallel three dimensional numerical infrastructure for the solution of a wide range of time harmonic problems in structural acoustics and vibration high accuracy and rate of error convergence in the mid frequency regime is achieved by the use of hp finite and infinite element approximations the infrastructure supports parallel computation in both single and multi frequency settings multi frequency solves utilize concurrent factoring of the frequency dependent linear algebraic systems and are naturally scalable scalability of large scale single frequency problems is realized by using feti dp an iterative domain decomposition scheme numerical examples are presented to cover applications in vibratory response of fluid filled elastic structures as well as radiation and scattering from elastic structures submerged in an infinite acoustic medium we demonstrate both the numerical accuracy as well as parallel scalability of the infrastructure in terms of problem parameters that include wavenumber and number of frequencies polynomial degree of finite infinite element approximations as well as the number of processors scalability and accuracy is evaluated for both single and multiple frequency sweeps on four high performance parallel computing platforms sgi altix sgi origin ibm p690 sp and linux cluster results show good performance on shared as well as distributed memory architecture copyright 2006 john wiley sons ltd

the h p and h p versions of the finite element method in 1 dimension this paper is the first one in the series of three which are addressing in detail the properties of the three basic versions of the finite element method in the one dimensional setting the main emphasis is placed on the analysis when the exact solution has singularity of x type the first part analyzes thep version the second theh version and generalh p version and the final third part addresses the problems of the adaptiveh p version

on the three dimensional wigner poisson problem with inflow boundary conditions abstract we study the wigner poisson problem in a bounded spatial domain with non homogeneous and time dependent inflow boundary conditions this system is a quantum model of charge transport in a semiconductor device coupled with reservoirs in presence of a self consistent potential and of an external one we state a local in time well posedness result for the problem the main difficulty is proving in the three dimensional case that the non linear potential term is a lipschitz perturbation of the affine streaming operator in an appropriately weighted l 2 space

the h p and h p versions of the finite element method in 1 dimension part ii the error analysis of the h and h p versions the paper is the second in the series of three devoted to the detailed analysis of the three basic versions of the finite element method in one dimensional setting the first part 1 analyzed thep version the present one concentrates on theh andh p versions

the p version of the finite element method in the p version of the finite element method the triangulation is fixed and the degree p of the piecewise polynomial approximation is progressively increased until some desired level of precision is reached in this paper we first establish the basic approximation properties of some spaces of piecewise polynomials defined on a finite element triangulation these properties lead to an a priori estimate of the asymptotic rate of convergence of the p version the estimate shows that the p version gives results which are not worse than those obtained by the conventional finite element method called the h version in which h represents the maximum diameter of the elements when quasi uniform triangulations are employed and the basis for comparison is the number of degrees of freedom furthermore in the case of a singularity problem we show under conditions which are usually satisfied in practice that the rate of convergence of the p version is twice that of the h version with quasi uniform mesh inve

optimization of a regularized distortion measure to generate curved high order unstructured tetrahedral meshes we present a robust method for generating high order nodal tetrahedral curved meshes the approach consists of modifying an initial linear mesh by first introducing high order nodes second displacing the boundary nodes to ensure that they are on the cad surface and third smoothing and untangling the mesh obtained after the displacement of the boundary nodes to produce a valid curved high order mesh the smoothing algorithm is based on the optimization of a regularized measure of the mesh distortion relative to the original linear mesh this means that whenever possible the resulting mesh preserves the geometrical features of the initial linear mesh such as shape stretching and size we present several examples to illustrate the performance of the proposed algorithm furthermore the examples show that the implementation of the optimization problem is robust and capable of handling situations in which the mesh before optimization contains a large number of invalid elements we consider cases with polynomial approximations up to degree ten large deformations of the curved boundaries concave boundaries and highly stretched boundary layer elements the meshes obtained are suitable for high order finite element analyses

nurbs enhanced finite element method nefem the development of nurbs enhanced finite element method nefem is revisited this technique allows a seamless integration of the cad boundary representation of the domain and the finite element method fem the importance of the geometrical model in finite element simulations is addressed and the benefits and potential of nefem are discussed and compared with respect to other curved finite element techniques

the wignerpoisson x system in wiener algebra in this paper we concern over a class of the wignerpoisson x system introduced and developed by bao etal 2003 mauser 2001 and stimming 2005 respectively the model describes the quantum mechanical motion of particles under the influence of the nonlocal hartree potential and a local power term exchange potential the existence and uniqueness of local mild solution to the n dimensional n 1 3 cauchy problems are established on the space of some integrable functions whose inverse fourier transforms are also integrable

h p adaptive finite element methods in computational fluid dynamics the principal ideas of h p adaptive finite element methods for fluid dynamics problems are discussed applications include acoustics compressible euler and both compressible and incompressible navier stokes equations several numerical examples illustrate the presented concepts