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

bi invariant metrics on the group of symplectomorphisms this paper studies the extension of the hofer metric and general finsler metrics on the hamiltonian symplectomorphism group ham m to the identity component symp 0 m of the symplectomorphism group in particular we prove that the hofer metric on ham m does not extend to a bi invariant metric on symp 0 m for many symplectic manifolds we also show that for the torus t 2n with the standard symplectic form no finsler metric on ham t 2n that satisfies a strong form of the invariance condition can extend to a bi invariant metric on symp 0 t 2 n another interesting result is that there exists no c 1 continuous bi invariant metric on symp 0 t 2n

an a posteriori error estimator for the p and hp versions of the finite element method an a posteriori error estimator is proposed in this paper for the p and hp versions of the finite element method in two dimensional linear elastostatic problems the local error estimator consists in an enhancement of an error indicator proposed by bertoti and szabo int j numer meth engng 1998 42 561 587 which is based on the minimum complementary energy principle in order to obtain the local error estimate this error indicator is corrected by a factor which depends only on the polynomial degree of the element the proposed error estimator shows a good effectivity index in meshes with uniform and non uniform polynomial distributions especially when the global error is estimated furthermore the local error estimator is reliable enough to guide p and hp adaptive refinement strategies

performance of the h p version of the finite element method with various elements the paper addresses the performance of square elements of type q p and q p q p and q p are elements of degree p analogous to the well known 9 and 8 noded elements for p 2 the performance is analysed theoretically for the class of analytic functions numerical experiments confirm the conclusions drawn from the theory the computational complexity of a solution algorithm is studied using timings of the computation on an alliant fx 8 computer the data show that high order elements are very effective for the considered class of solutions

theh p version of the finite element method for elliptic equations of order2m the problems of elliptic partial differential equations stemming from engineering problems are usually characterized by piecewise analytic data it has been shown in 3 4 5 that the solutions of the second order and fourth order equations belong to the spacesb 1 where the weighted sobolev norms of thek th derivatives are bounded bycd k l k l k l l 2 wherec andd are constants independent ofk in this case theh p version of the finite element method leads to an exponential rate of convergence measured in the energy norm 6 12 13 theh p version was implemented in the code probe1 18 and has been very successfully used in the industry we will discuss in this paper the generalization of these results for problems of order2m we will show also that the exponential rate can be achieved if the exact solution belongs to the spacesb 1 where the weighted sobolev norm of thek th derivatives is bounded bycd k l k l k l m 1 c andd are independent ofk in addition if the data is piecewise analytic then in fact the exact solution belongs to the spacesb m 1 problems of this type are related obviously to many engineering problems such as problems of plates and shells and are also important in connection with well known locking problems

parallel space time hp adaptive discretization scheme for parabolic problems abstract we introduce an integration scheme for parabolic problems our parallelizable method uses adaptive h p finite elements in space and finite differences in time the strategy can also be combined with a classical finite element method parallelization technique based on domain decomposition we verified the performance of our method against two different benchmarks in both two dimensional model problem on an l shaped domain and three dimensional pennes bioheat equation settings results show a significant speedup in computational time when compared with the sequential version of the algorithm moreover we develop a mathematical framework to analyze similar schemes which include h p spatial adaptivity our framework describes error propagation rigorously and as such allows to analyze convergence properties of these mixed methods

weighted analytic regularity in polyhedra we explain a simple strategy to establish analytic regularity for solutions of second order linear elliptic boundary value problems the abstract framework presented here helps to understand the proof of analytic regularity in polyhedral domains given in the authors paper in m costabel m dauge s nicaise analytic regularity for linear elliptic systems in polygons and polyhedra math models methods appl sci 22 8 2012 we illustrate this strategy by considering problems set in smooth domains in corner domains and in polyhedra

representing action indeterminacy and ramifications abstract we define and study a high level language for describing actions more expressive than the action language a introduced by gelfond and lifschitz the new language ar allows us to describe actions with indirect effects ramifications nondeterministic actions and actions that may be impossible to execute it has symbols for nonpropositional fluents and for the fluents that are exempt from the commonsense law of inertia temporal projection problems specified using the language ar can be represented as nested abnormality theories based on the situation calculus

regularity and numerical solution of eigenvalue problems with piecewise analytic data this paper discusses the regularity of the eigenfunctions of eigenvalue problems with piecewise analytic data and the approximation of the eigenvalues and eigenfunctions of such problems a detailed and systematic numerical study of these approximations is presented together with an analysis of the numerical results in light of the theoretical results the specific aim is to assess the reliability of the theoretical results which are of an asymptotic nature as a guide to practical computations which may take place in the pre asymptotic phase and to look for characteristic features of the numerical results that are not completely explained by known theoretical results

reasoning about action i a possible worlds approach abstract reasoning about change is an important aspect of commonsense reasoning and planning in this paper we describe an approach to reasoning about change for rich domains where it is not possible to anticipate all situations that might occur the approach provides a solution to the frame problem and to the related problem that it is not always reasonable to explicitly specify all of the consequences of actions the approach involves keeping a single model of the world that is updated when actions are performed the update procedure involves constructing the nearest world to the current one in which the consequences of the actions under consideration hold the way we find the nearest world is to construct proofs of the negation of the explicit consequences of the expected action and to remove a premise in each proof from the current world computationally this construction procedure appears to be tractable for worlds like our own where few things tend to change with each action or where change is regular

topological rigidity of hamiltonian loops and quantum homology this paper studies the question of when a loop t 0 t 1 in the group symp m of symplectomorphisms of a symplectic manifold m is isotopic to a loop that is generated by a time dependent hamiltonian function loops with this property are said to be hamiltonian our main result is that hamiltonian loops are rigid in the following sense if is hamiltonian with respect to and if is a small perturbation of that preserves another symplectic form then is hamiltonian with respect to this allows us to get some new information on the structure of the flux group i e the image of 1 symp m under the flux homomorphism we give a complete proof of our result for some manifolds and sketch the proof in general the argument uses methods developed by seidel for studying properties of hamiltonian loops via the quantum homology of m

modeling of electromagnetic absorption scattering problems using hp adaptive finite elements a model problem for the steady state form of maxwell s equations is considered the problem is formulated in a weak form using a lagrange multiplier laying down a foundation for a general class of novel hp adaptive fe approximations a convergence proof for affine elements is presented the proposed method is illustrated and verified with a series of 2d experiments including elements with curved boundaries and nonhomogeneous media

simulation of wireline sonic logging measurements acquired with borehole eccentered tools using a high order adaptive finite element method the paper introduces a high order adaptive finite element method for simulation of sonic measurements acquired with borehole eccentered logging instruments the resulting frequency domain based algorithm combines a fourier series expansion in one spatial dimension with a two dimensional high order adaptive finite element method fem and incorporates a perfectly matched layer pml for truncation of the computational domain the simulation method was verified for various model problems including a comparison to a semi analytical solution developed specifically for this purpose numerical results indicate that for a wireline sonic tool operating in a fast formation the main propagation modes are insensitive to the distance from the center of the tool to the center of the borehole eccentricity distance however new flexural modes arise with an increase in eccentricity distance in soft formations we identify a new dipole tool mode which arises as a result of tool eccentricity

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

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

a two dimensional self adaptive hp finite element method for the characterization of waveguide discontinuities part i energy norm based automatic hp adaptivity abstract the accurate analysis and characterization of waveguide discontinuities is an important issue in microwave engineering in some cases the discontinuities are an unavoidable result of mechanical or electric transitions which effects have to be minimized in other cases the discontinuities are deliberately introduced into the waveguide to perform a certain electric function this is the first of two papers analyzing different types of rectangular waveguide discontinuities by using a fully automatic hp adaptive finite element method in this paper a fully automatic energy norm based hp adaptive finite element fe strategy applied to a number of relevant waveguide structures is presented the methodology produces exponential convergence rates in terms of the energy norm error of the solution against the problem size number of degrees of freedom extensive numerical results demonstrate the suitability of the hp method for solving different rectangular waveguide discontinuities these results illustrate the flexibility reliability and high accuracy of the method the self adaptive hp fem provides similar sometimes more accurate results than those obtained with semi analytical techniques such as the mode matching method for problems where semi analytical methods can be applied at the same time the hp fem provides the flexibility of modeling more complex waveguide structures and including the effects of dielectrics metallic screws round corners etc which cannot be easily considered when using semi analytical techniques in the second part the work is extended by presenting a fully automatic goal oriented hp adaptive fe in terms of the scattering or s parameters which are widely used in microwave engineering for the characterization of microwave devices

reasoning about actions steady versus stabilizing state constraints abstract in formal approaches to commonsense reasoning about actions the ramification problem denotes the problem of handling indirect effects which implicitly derive from so called state constraints we pursue a new distinction between two kinds of state constraints which will be proved crucially important for solving the general ramification problem steady constraints never not even for an instant cease being in force as such they give rise to truly instantaneous indirect effects of actions stabilizing state constraints on the other hand may be suspended for a short period of time after an action has occurred indirect effects deriving from these constraints materialize with a short lag this hitherto neglected distinction is shown to have essential impact on the ramification problem if stabilizing state constraints interact then approaches not based on so called causal propagation prove defective but causal propagation too is shown to risk producing anomalous models in case steady and stabilizing indirect effects are propagated indiscriminately motivated by these two observations we improve the theory of causal relationships and its fluent calculus axiomatization which both are methods of causal propagation so as to properly handle the distinction between steady and stabilizing constraints

isogeometric finite element data structures based on bezier extraction of t splines we develop finite element data structures for t splines based on bezier extraction generalizing our previous work for nurbs as in traditional finite element analysis the extracted bezier elements are defined in terms of a fixed set of polynomial basis functions the so called bernstein basis the bezier elements may be processed in the same way as in a standard finite element computer program utilizing exactly the same data processing arrays in fact only the shape function subroutine needs to be modified while all other aspects of a finite element program remain the same a byproduct of the extraction process is the element extraction operator this operator localizes the topological and global smoothness information to the element level and represents a canonical treatment of t junctions referred to as hanging nodes in finite element analysis and a fundamental feature of t splines a detailed example is presented to illustrate the ideas copyright 2011 john wiley sons ltd

on some hp adaptive finite element method for natural vibrations model eigenproblem results obtained by some hp adaptive fem are presented the fem is based on the texas 3 step strategy and the equilibrated residual method the focus is on numerical experiments the practical issues related to the above mentioned techniques are raised the potentials of the method for engineering applications are demonstrated

ramification and causality abstract in formal systems for reasoning about actions the ramification problem denotes the problem of handling indirect effects these effects are not explicitly represented in action specifications but follow from general laws describing dependencies among components of the world state an adequate treatment of indirect effects requires a suitably weakened version of the general law of persistence it also requires a method to avoid unintuitive changes suggested by the aforementioned dependency laws we propose a solution to the ramification problem that uses directed relations between two single effects stating the circumstances under which the occurrence of the first causes the second we argue for the necessity of an approach based on causality by elaborating the limitations of common paradigms employed to handle ramifications the principle of categorization and the policy of minimal change our abstract solution is realized on the basis of a particular action calculus namely the fluent calculus

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

optimal h p finite element methods abstract a theory of optimal petrov galerkin h p version finite element approximations is presented the optimal scheme is denned relative to a fine mesh solution space and relative to an arbitrary symmetric bilinear form the optimal method leads to a symmetric positive definite stiffness matrix which is independent of the coefficients of the given problem exhibits extra superconvergence properties and has a relative error that can be calculated exactly at each point in the problem domain various generalizations are also discussed including the connection of these methods with certain preconditioning schemes

finite element method for solving problems with singular solutions abstract numerical treatment of the elliptic boundary value problem with nonsmooth solution by the finite element method is discussed the nonsmoothness could have its origin in the unsmooth boundary or the differential equation this paper which is a survey of the recent results elaborates among others on the method of auxiliary mapping the partition of unity finite element method and the hp version of fem in three dimensions numerical examples illustrate mathematical results an

finite subgroups of ham and symp let x omega be a compact symplectic manifold of dimension 2n and let text ham x omega be its group of hamiltonian diffeomorphisms we prove the existence of a constant c depending on x but not on omega such that any finite subgroup g subset text ham x omega has an abelian subgroup a subseteq g satisfying g a le c and a can be generated by n elements or fewer if b 1 x 0 we prove an analogous statement for the entire group of symplectomorphisms of x omega if b 1 x ne 0 we prove the existence of a constant c depending only on x such that any finite subgroup g subset text symp x omega has a subgroup n subseteq g which is either abelian or 2 step nilpotent and which satisfies g n le c these results are deduced from the classification of the finite simple groups the topological rigidity of hamiltonian loops and the following theorem which we prove in this paper let e be a complex vector bundle over a compact connected smooth and oriented manifold m suppose that the real rank of e is equal to the dimension of m and that langle e e m rangle ne 0 where e e is the euler class of e then there exists a constant c such that for any prime p and any finite p group g acting on e by vector bundle automorphisms preserving an almost complex structure on m there is a subgroup g 0 subseteq g satisfying m g 0 ne emptyset and g g 0 le c

the multi level hp method for three dimensional problems dynamically changing high order mesh refinement with arbitrary hanging nodes abstract one main challenge of the h p version of the finite element method is the high implementational complexity of the method resulting from the added need of handling hanging nodes appropriately the multi level h p formulation recently introduced for two dimensional applications aims at alleviating these difficulties without compromising the approximation quality this is achieved by changing from the conventional refine by replacement approach to a refine by superposition idea the current work shows that the multi level h p approach can be extended naturally to three dimensional refinement without increasing the complexity of the rule set ensuring linear independence and compatibility of the shape functions in this way a three dimensional h p refinement scheme is formulated in which hanging nodes are avoided by definition this ease of complexity allows for a highly flexible discretization kernel featuring arbitrary irregular meshes and a continuous refinement and coarsening throughout the simulation runtime different numerical examples demonstrate that even in the presence of singularities this novel refinement scheme yields exponential convergence with respect to both the number of unknowns and the computational time it is further shown that the refinement scheme is able to capture complex solution features that demand for three dimensional refinement patterns the dynamic discretization properties of the approach are demonstrated by continuously refining and coarsening the mesh during the simulation runtime to keep the refinement zone local to a moving singularity finally it is shown that the high approximation power of the multi level h p scheme also carries over to curved geometries common in engineering practice without a significant detrimental effect on the conditioning of the stiffness matrix

virtual moduli cycles and gromov witten invariants of noncompact symplectic manifolds this paper constructs and studies the gromov witten invariants and their properties for noncompact geometrically bounded symplectic manifolds two localization formulas for gw invariants are also proposed and proved as applications we get solutions of the generalized string equation and dilation equation and their variants the more solutions of wdvv equation and quantum products on cohomology groups are also obtained for the symplectic manifolds with finitely dimensional cohomology groups to realize these purposes we further develop the language introduced by liu tian to describe the virtual moduli cycle defined by liu tian fukaya ono li tian ruan and siebert

fourier series expansion in a non orthogonal system of coordinates for the simulation of 3d dc borehole resistivity measurements abstract we describe a new method to simulate 3d borehole resistivity measurements at zero frequency dc the method combines the use of a fourier series expansion in a non orthogonal system of coordinates with an existing 2d goal oriented higher order self adaptive hp finite element algorithm the new method is suitable for simulating measurements acquired with borehole logging instruments in deviated wells it delivers high accuracy simulations and it enables a considerable reduction of the computational complexity with respect to available 3d simulators since the number of fourier modes basis functions needed to solve practical applications is limited typically below 10 furthermore numerical results indicate that the optimal 2d grid based on the 0th fourier mode also called central fourier mode can be employed to efficiently solve the final 3d problem thereby avoiding the expensive construction of optimal 3d grids specifically for a challenging through casing resistivity application we reduce the computational time from several days using a 3d simulator to just 2 h with the new method while gaining accuracy the new simulation method can be easily extended to different physical phenomena with similar geometries as those arising in the simulation of 3d borehole electrodynamics and sonic acoustics coupled with elasticity measurements in addition the method is especially suited for inversion since we demonstrate that the number of fourier modes needed for the exact representation of the materials is limited to only one the central mode for the case of borehole measurements acquired in deviated wells

h p spectral element methods for three dimensional elliptic problems on non smooth domains this paper is devoted to the study of non conforming h p spectral element methods for three dimensional elliptic problems on non smooth domains using parallel computers to overcome the singularities which arise in the neighbourhoods of vertices edges and vertex edges we use local systems of coordinates together with geometric meshes which become finer near corners and edges we provide estimates for the error and the computational complexity of our method and present results of numerical simulations that have been performed to validate the theoretical estimates obtained in 22

the p and h p versions of the finite element method basic principles and properties in the classical form of the finite element method called the hversion piecewise polynomials of fixed degree p are used and the mesh size h is decreased for accuracy in this paper we discuss the fundamental theoretical ideas behind the relatively recent p version and h p version in the p version a fixed mesh is used and p is allowed to increase the h p version combines both approaches the authors describe and explain the basic properties and characteristics of these newer versions especially in areas where their behavior is significantly different from that of the h version simplified proofs of key concepts are included and computational illustrations of several results are provided a benchmark comparison between the various versions in included

reasoning about action ii the qualification problem abstract we present a computationally effective approach to representing and reasoning about actions with many qualifications the approach involves treating actions as qualified not by specific facts that may or may not hold when the action is executed but instead as potentially qualified by general constraints describing the domain being investigated specifically we suggest that the result of the action be computed without considering these qualifying domain constraints and take the action to be qualified if and only if any of the constraints is violated after the computation is complete our approach is presented using the framework developed in 6 where we discussed a solution to the frame and ramification problems based on the notion of possible worlds and compared the computational requirements of that solution to the needs of more conventional ones in the present paper we show that the domain constraint approach to qualification coupled with the possible worlds approach described earlier has the remarkable property that essentially no computational resources are required to confirm that an action is unqualified as before we also make a quantitative comparison between the resources needed by our approach and those required by other formulations

a relative seidel morphism and the albers map in this note we introduce a relative or lagrangian version of the seidel homomorphism that assigns to each homotopy class of paths in ham m starting at the identity and ending on the subgroup that preserves a given lagrangian submanifold l an element in the floer homology of l we show that these elements are related to the absolute seidel elements by the albers map we also study for later use the effect of reversing the signs of the symplectic structure as well as the orientations of the generators and of the operations on the floer homologies

symplectic diffeomorphisms and the flux homomorphism let x be a connected smooth manifold without boundary we will write difff ox for the group of all compactly supported diffeomorphisms of x which preserve the symplectic form o2 topologized as usual as the direct limit of the subgroups diff x of all diffeomorphisms with support in the fixed compact set k let diff oox be its identity component the flux is locally a homomorphism from a neighbourhood of the identity in diffo ox to h x r see calabi 6 it gives rise to a global homomorphism s o from the universal cover of difffo0x to hi x f and hence to a homomorphism

implicit dynamics in the material point method abstract a time implicit discretization is derived and validated for the material point method mpm the resulting non linear discrete equations are solved using newton s method combined with either the conjugate gradient method or the generalized minimum residual method these newton krylov solvers are implemented in a matrix free fashion for numerical efficiency a description of the algorithms and evaluation of their performance is presented on all test problems if the time step is chosen appropriately the implicit solution technique is more efficient than an explicit method without loss of desired features in the solutions in a dramatic example time steps 10 000 times the explicit step size are possible for the large deformation compression of a cylindrical billet at 1 2 the computational cost

cohomologically symplectic spaces toral actions and the gottlieb group aspects of symplectic geometry are explored from a homotopical viewpoint in particular the question of whether or not a given toral action is hamiltonian is shown to be independent of geometry rather a new homotopical obstruction is described which detects when an action is hamiltonian this new entity the ae invariant allows many results of symplectic geometry to be generalized to manifolds which are only cohomologically symplectic in the sense that there is a degree 2 cohomology class which cups to a top class furthermore new results in symplectic geometry also arise from this homotopical approach