global solutions for a semilinear two dimensional klein gordon equation with exponential type nonlinearity we prove the existence and uniqueness of global solutions for a cauchy problem associated to a semilinear klein gordon equation in two space dimensions our result is based on an interpolation estimate with a sharp constant obtained by a standard variational method 2006 wiley periodicals inc

sharp rellich sobolev inequalities and weighted adams inequalities involving hardy terms for bi laplacian abstract motivated by a recent work of dong lam and lu concerning the sharp weighted trudinger moser and caffarelli kohn nirenberg inequalities we derive a sharp rellich sobolev inequality on r n with n 5 and weighted adams inequalities involving hardy terms on r 4 the procedure is based on a quasi conformal mapping type transform and decomposition into spherical harmonics since the symmetrization arguments do not work in dealing with these inequalities

testing hypotheses in order in certain circumstances one wishes to test one hypothesis only if certain other hypotheses have been rejected this ordering of hypotheses simplifies the task of controlling the probability of rejecting any true hypothesis in an example from an observational study a treated group is shown to be further from both of two control groups than the two control groups are from each other

new geometric aspects of moser trudinger inequalities on riemannian manifolds the non compact case abstract in the first part of the paper we investigate some geometric features of moser trudinger inequalities on complete non compact riemannian manifolds by exploring rearrangement arguments isoperimetric estimates and gluing local uniform estimates via gromov s covering lemma we provide a coulhon saloff coste and varopoulos type characterization concerning the validity of moser trudinger inequalities on complete non compact n dimensional riemannian manifolds n 2 with ricci curvature bounded from below some sharp consequences are also presented both for non negatively and non positively curved riemannian manifolds respectively in the second part by combining variational arguments and a lions type symmetrization compactness principle we guarantee the existence of a non zero isometry invariant solution for an elliptic problem involving the n laplace beltrami operator and a critical nonlinearity on n dimensional homogeneous hadamard manifolds our results complement in several directions those of y yang j funct anal 2012

on the lack of compactness in the 2d critical sobolev embedding abstract this paper is devoted to the description of the lack of compactness of h rad 1 r 2 in the orlicz space our result is expressed in terms of the concentration type examples derived by p l lions 1985 in 24 the approach that we adopt to establish this characterization is completely different from the methods used in the study of the lack of compactness of sobolev embedding in lebesgue spaces and takes into account the variational aspect of orlicz spaces we also investigate the feature of the solutions of nonlinear wave equation with exponential growth where the orlicz norm plays a decisive role

variationally consistent extended fe model for 3d planar and curved imperfect interfaces abstract we propose an extended finite element method convergent to the asymptotic solution of a thin interface problem for both planar and curved imperfect interfaces in three dimensions the main advantage over standard cohesive zone models is the bulk mesh size independence with respect to standard extended finite element method in the proposed procedure blending and quadrature sub domains are not required the focus is on the evaluation of the accuracy of the proposed approach in solving three dimensional benchmark tests the numerical results are compared with those available from analytical solutions and spring like interface models

computational modeling of localized failure in solids xfem vs pf czm abstract this work addressesnumerical comparison between the extended finite element method xfem and the phase field regularized cohesive zone model pf czm wu 2017 2018a for the modeling of cohesive fracture induced localized failure in solids a novel implementation of the pf czm is proposed similarly to the xfem in which the added degrees of freedom characterizing the crack behavior are associated only with those nodes within a small sub domain representative benchmark examples show that both methods are independent of the mesh discretization for problems with the crack path known a priori both methods give almost coincident numerical results though the xfem is advantageous due to its high coarse mesh resolution for complex problems with arbitrary crack propagation even though some discrepancies are observed the numerical results given by both methods are also quantitatively similar if the predicted crack trajectories are close to each other despite the higher computational cost in this case the pf czm is much more favored due to its intrinsic capability of modeling complex crack configurations e g nucleation propagation merging and branching etc with no need of any extra strategy the above facts validate our previous theoretical analysis that the pf czm approaches asymptotically to a discontinuous czm for a vanishing length scale as it avoids most challenging issues exhibited by other approaches the pf czm is not only theoretically elegant but also numerically appealing for the modeling of localized failure in solids

second order sobolev type inequalities in the hyperbolic spaces abstract in this paper we establish several poincare sobolev type inequalities concerning to the laplace beltrami operator g in the hyperbolic space h n with n 5 these inequalities could be seen as the improved second order poincare inequality with remainder terms involving with the sharp rellich inequality or the sharp sobolev inequality in h n the novelty of these inequalities is that it combines both the sharp poincare inequality and the sharp rellich inequality or the sharp sobolev inequality for g in h n as a consequence we obtain the poincare sobolev inequality for the second order gjms operator p 2 in h n in dimension 4 we obtain an improvement of the sharp adams inequality and an adams inequality with exact growth for radial functions

an alternating digital tree adt algorithm for 3d geometric searching and intersection problems a searching algorithm is presented for determining which members of a set of n points in an n dimensional space lie inside a prescribed space subregion the algorithm is then extended to handle finite size objects as well as points in this form it is capable of solving problems such as that of finding the objects from a given set which intersect with a prescribed object the suitability of the algorithm is demonstrated for the problem of three dimensional unstructured mesh generation using the advancing front method

multiple test procedures for identifying the maximum safe dose we consider dose response studies for safety assessment of crop protection compounds and drugs and we offer a hypothesis testing approach for identifying the maximum dose level that is guaranteed to be safe with preassigned confidence the focus is on step down sd multiple test procedures for identifying the maximum safe dose we propose two classes of contrasts among the dose means as test statistics for these procedures pairwise contrasts pc and helmert contrasts hc the first procedure sd2pc consists of a sequence of ordinary t tests and is thus easy to apply but it can have very low power for certain step response functions the second procedure sd1hc does not suffer from this drawback but it requires a weak monotonicity assumption for its mathematical validity the powers of sd2pc and sd1hc are studied via monte carlo simulation we recommend sd2pc for linear response functions and sd1hc for step response functions the procedures are illustrated by applying them to data from an aquatic

improved moser trudinger type inequalities in the hyperbolic space hn we establish an improved version of the moser trudinger inequality in the hyperbolic space hnhn n 2n 2 namely we prove the following result for any 0 n 1nn then we have supu c0 hn hn gu gndvolg hn u ndvolg 1 hn n n u nn 1 dvolg where n n n 11n 1 n 1 n 1 denotes the surface area of the unit sphere in rnrn and n t et j 0n 2tjj this improves the moser trudinger inequality in hyperbolic spaces obtained recently by mancini and sandeep 2010 by mancini et al 2013 and by adimurthi and tintarev 2010 for 0 0 in the limiting case n 1n n we prove a moser trudinger inequality with exact growth in hnhn supu c0 hn hn gu gndvolg n 1n n hn u ndvolg 11 hn u ndvolg hn n n u nn 1 1 u nn 1dvolg this improves the moser trudinger inequality with exact growth in hnhn established by lu and tang 2016 these inequalities are achieved from the comparison of the symmetric non increasing rearrangement of a function both in the hyperbolic and the euclidean spaces and the same inequalities in the euclidean space this approach seems to be new comparing with the previous ones

fluid structure interaction and multi body contact application to aortic valves in this article we present a partitioned procedure for fluid structure interaction problems in which contacts among different deformable bodies can occur a typical situation is the movement of a thin valve e g the aortic valve immersed in an incompressible viscous fluid e g the blood in the proposed strategy the fluid and structure solvers are considered as independent black boxes that exchange forces and displacements the structure solvers are moreover not supposed to manage contact by themselves the hypothesis of non penetration among solid objects defines a non convex optimization problem to solve the latter we use an internal approximation algorithm that is able to directly handle the cases of thin structures and self contacts a numerical simulation on an idealized aortic valve is finally realized with the aim of illustrating the proposed scheme

integration of singular enrichment functions in the generalized extended finite element method for three dimensional problems a mapping method is developed to integrate weak singularities which result from enrichment functions in the generalized extended finite element method the integration scheme is applicable to 2d and 3d problems including arbitrarily shaped triangles and tetrahedra implementation of the proposed scheme in existing codes is straightforward numerical examples for 2d and 3d problems demonstrate the accuracy and convergence properties of the technique copyright 2008 john wiley sons ltd

numerical integration for nonlinear problems of the finite cell method using an adaptive scheme based on moment fitting abstract fictitious domain methods such as the finite cell method simplify the discretization process significantly as the mesh is decoupled from the geometrical description however this simplification in the mesh generation results in broken cells which is why special integration methods are required usually adaptive integration schemes are applied resulting in a large number of integration points and thus an expensive numerical integration especially for nonlinear applications to perform the numerical integration more efficiently we propose an adaptive integration method using moment fitting thereby we present a moment fitting approach based on lagrange polynomials through gauss legendre points to circumvent having to solve the moment fitting equation system the performance of this integration method is shown by studying several numerical examples of the finite cell method for small and large strain problems in elastoplasticity

an unfitted nitsche method for incompressible fluid structure interaction using overlapping meshes we consider the extension of the nitsche method to the case of fluid structure interaction problems on unfitted meshes we give a stability analysis for the space semi discretized problem and show how this estimate may be used to derive optimal error estimates for smooth solutions irrespectively of the mesh interface intersection we also discuss different strategies for the time discretization using either fully implicit or explicit coupling loosely coupled schemes some numerical examples illustrate the theoretical discussion

modified sequentially rejective multiple test procedures abstract suppose that n hypotheses h 1 h 2 h n with associated test statistics t 1 t 2 t n are to be tested by a procedure with experimentwise significance level the probability of rejecting one or more true hypotheses smaller than or equal to some specified value a commonly used procedure satisfying this condition is the bonferroni b procedure which consists of rejecting h i for any i iff the associated test statistic t i is significant at the level n holm 1979 introduced a modified bonferroni procedure with greater power than the b procedure under holm s sequentially rejective bonferroni srb procedure if any hypothesis is rejected at the level n the denominator of for the next test is n 1 and the criterion continues to be modified in a stagewise manner with the denominator of reduced by 1 each time a hypothesis is rejected so that tests can be conducted at successively higher significance levels holm proved that the experimentwise significance level

an unfitted finite element method based on nitsche s method for elliptic interface problems in this paper we propose a method for the finite element solution of elliptic interface problem using an approach due to nitsche the method allows for discontinuities internal to the elements in the approximation across the interface we show that optimal order of convergence holds without restrictions on the location of the interface relative to the mesh further we derive a posteriori error estimates for the purpose of controlling functionals of the error and present some numerical examples

highly accurate surface and volume integration on implicit domains by means of moment fitting summary we introduce a new method for the numerical integration over curved surfaces and volumes defined by a level set function the method is based on the solution of a small linear system based on a simplified variant of the moment fitting equations numerical experiments suggest that the accuracy of the resulting quadrature rules exceeds the accuracy of traditional methods by orders of magnitude using moments up to an order of p the measured experimental orders of convergence exceed hp consequently their construction is very efficient because only coarse computational grids are required the conceptual simplicity allows for the application on very general grid types which is demonstrated by numerical experiments on quadrilateral triangular and hexahedral grids copyright 2013 john wiley sons ltd

an improved stable xfem is xfem with a novel enrichment function for the computational modeling of cohesive cracks abstract owing to the solution space enriched with a priori known knowledge through the partition of unity the extended or generalized finite element method xfem gfem has been widely applied to the modeling of localized failure in solids as far as cohesive cracks are concerned in this work on the one hand the xfem enriched with heaviside function or the shifted one with respect to nodal values is of optimal accuracy but is prone to the issue of ill conditioned or even singular system matrix for arbitrary crack propagation on the other hand the stable xfem s xfem circumvents the ill conditioning issues by introducing the residual heaviside function with respect to its linear interpolant at the cost of losing accuracy e g spurious stress locking for discontinuities with non uniform displacement jumps aiming to reconcile the incompatibility between accuracy of the solution and conditioning of the system matrix this work addresses a simple yet effective improved stable xfem is xfem with a novel enrichment function both the xfem and s xfem are recovered as its particular cases with different approximation schemes for the bridging scale which incorporates information from both the continuous coarse scale and the discontinuous fine scale in the proposed is xfem as the enrichment basis functions are not contained in the standard polynomial space conditioning of the resulting system matrix is nearly insensitive to the mesh discontinuity configuration even if the crack path gets close to element nodes furthermore the is xfem with a small stabilization parameter is almost of the same accuracy as the xfem particularly pathological numerical results polluted by spurious stress locking exhibited in the s xfem are not observed across a fully softened discontinuity with non uniform displacement jumps as only the enrichment function is modified the proposed is xfem together with appropriate crack propagation criterion and tracking algorithm can be implemented easily in the existing xfem codes several representative numerical simulations of element and structure benchmark tests are presented to validate the proposed is xfem regarding both accuracy of the solution and conditioning of the system matrix

fourier analysis and optimal hardy adams inequalities on hyperbolic spaces of any even dimension abstract recently the second and third authors established the sharp hardy adams inequalities of second order derivatives with the best constants on the hyperbolic space b 4 of dimension four 40 adv math 2017 a key method used in dimension four in 40 is that the following hardy operator when n 4 and k 2 b n k u 2 d x i 1 k 2 i 1 2 b n u 2 1 x 2 2 k d x can be decomposed exactly as the product of fractional laplacians however such a decomposition in dimension four is no longer possible in the case n 4 and 2 k n 2 and the situation here is thus considerably more difficult and complicated therefore it remains open as whether a sharp hardy adams inequality still holds on higher dimensional hyperbolic space b n for n 4 the main purpose of this paper is to use a substantially new method of estimating the hardy operator to establish the sharp hardy adams inequalities on hyperbolic spaces b n for all even dimension n and n 4 as applications of such inequalities we will improve substantially the known adams inequalities on hyperbolic space b n in the literature and also strengthen the classical adams inequality and the hardy inequality on euclidean balls in any even dimension the later inequality can be viewed as the borderline case of the sharp hardy sobolev maz ya inequalities for higher order derivatives in high dimensions obtained recently by the second and third authors 41

concentration compactness principle for the sharp adams inequalities in bounded domains and whole space rn abstract we prove an improvement of the sharp adams inequality in w 0 m n m where is a bounded domain in r n inspired by lions concentration compactness principle for the sharp moser trudinger inequality our method gives an alternative approach to a concentration compactness principle in w 0 m n m recently established by do o and macedo furthermore we obtain a sharp threshold for m odd improving the one of do o and macedo our approach is also successfully applied to whole space r n to establish the improvements of the sharp adams inequalities in w m n m r n this type of improvement is still unknown in general except the case m 1 due to do o de souza de medeiros and severo our method is a further development of the one of cerny cianchi and hencl combining with some estimates for the decreasing rearrangement of a function in terms of the one of its higher order derivatives

the extended generalized finite element method an overview of the method and its applications an overview of the extended generalized finite element method gefm xfem with emphasis on methodological issues is presented this method enables the accurate approximation of solutions that involve jumps kinks singularities and other locally non smooth features within elements this is achieved by enriching the polynomial approximation space of the classical finite element method the gefm xfem has shown its potential in a variety of applications that involve non smooth solutions near interfaces among them are the simulation of cracks shear bands dislocations solidification and multi field problems copyright 2010 john wiley sons ltd

stepwise confidence intervals for monotone dose response studies in dose response studies one of the most important issues is the identification of the minimum effective dose med where the med is defined as the lowest dose such that the mean response is better than the mean response of a zero dose control by a clinically significant difference dose response curves are sometimes monotonic in nature to find the med various authors have proposed step down test procedures based on contrasts among the sample means in this article we improve upon the method of marcus and peritz 1976 journal of the royal statistical society series b 38 157 165 and implement the dose response method of hsu and berger 1999 journal of the american statistical association 94 468 482 to construct the lower confidence bound for the difference between the mean response of any nonzero dose level and that of the control under the monotonicity assumption to identify the med the proposed method is illustrated by numerical examples and simulation studies on power comparisons are presented

a note on multiple testing procedures in dose finding it is shown that in some recently proposed multiple test procedures for dose finding tamhane hochberg and dunnett 1996 biometrics 52 21 37 strong control of the familywise error is only guaranteed if order relations are assumed to hold among the means procedures that can be applied safely without assuming any restrictions on the means can be based on the classical many one comparisons of doses with the zero dose

adams inequality with the exact growth condition in ℝ4 adams inequality is an extension of the trudinger moser inequality to the case when the sobolev space considered has more than one derivative the goal of this paper is to give the optimal growth rate of the exponential type function in adams inequality when the problem is considered in the whole space 4 2014 wiley periodicals inc

a new face oriented stabilized xfem approach for 2d and 3d incompressible navier stokes equations abstract we develop a new stabilized xfem based fixed grid approach for the transient incompressible navier stokes equations using cut elements our framework is based on a new flexible strategy to handle several degrees of freedom dofs at nodes required for complex shaped embedded meshes as they occur for fixed grid fluid structure interaction problems boundary conditions on embedded boundaries are imposed weakly using a nitsche type approach ghost penalty terms for velocity and pressure are added for stability reasons and to improve the conditioning of the system matrix the idea of ghost penalties previously developed for stokes problems is extended to the incompressible navier stokes equations by using face oriented fluid stabilizations for both viscous and convective dominated flows furthermore the need for additional terms to enforce boundary conditions for non viscous flows is addressed a detailed numerical study of our stabilized fluid formulation including studies of nitsche s parameter and the ghost penalty parameter shows optimal error convergence and a good system conditioning in the viscous and the convective dominated cases compared to other fixed grid fluid formulations our method is much more accurate and less sensitive to the location of the interface regarding the accuracy and the sensitivity with respect to the interface position a clear improvement could be observed for the viscous and pressure fluxes as well as for the imposition of the boundary condition results of a transient two dimensional high reynolds number flow over a cylinder and the flow over a thick plate in 3d confirm the applicability of the proposed method

higher order extended fem for weak discontinuities level set representation quadrature and application to magneto mechanical problems in this article we present the application of bilinear and biquadratic extended fem xfem formulations to model weak discontinuities in magnetic and coupled magneto mechanical boundary value problems for properly resolving the location of curved interfaces and the discontinuous physical behaviour the major part of the contribution is devoted to review and develop methods for level set representation of curved interfaces and numerical integration of the weak form in higher order xfem formulations in order to reduce the complexity of the representation of curved interfaces an element local approach that allows for an automated computation of the level set values and also improves the compatibility between the level set representation and the integration subdomains is proposed integration rules for polygons and strain smoothing are applied in conjunction with biquadratic elements and compared with curved integration subdomains eventually a coupled magneto mechanical demonstration problem is modelled and solved by xfem for demonstration purposes a magneto mechanical coupling due to magnetic stresses is considered errors and convergence rates are analysed for the different level set representations and numerical integration procedures as well as their dependence on the ratio of material parameters at an interface copyright c 2012 john wiley sons ltd

stepwise confidence intervals without multiplicity adjustment for dose response and toxicity studies abstract not all simultaneous inferences need multiplicity adjustment if the sequence of individual inferences is predefined and failure to achieve the desired inference at any step renders subsequent inferences unnecessary then multiplicity adjustment is not needed this can be justified using the closed testing principle to test appropriate hypotheses that are nested in sequence starting with the most restrictive one but what hypotheses are appropriate may not be obvious in some problems we give a fundamentally different confidence set based justification by partitioning the parameter space naturally and using the principle that exactly one member of the partition contains the true parameter in dose response studies designed to show superiority of treatments over a placebo negative control or a drug known to be efficacious active control the confidence set approach generates methods with meaningful guarantee against incorrect decision whereas previous applications of the closed testing app

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

equivalent polynomials for quadrature in heaviside function enriched elements summary one of the advantages of partition of unity fems like the extended fem is the ability of modeling discontinuities independent of the mesh structure the enrichment of the element functional space with discontinuous or non differentiable functions requires when the element stiffness is computed partitioning into subdomains for quadrature however the arbitrary intersection between the base mesh and the discontinuity plane generates quadrature subdomains of complex shape this is particularly true in three dimensional problems where quite sophisticate methodologies have been presented in the literature for the element stiffness evaluation the present work addresses the problem of heaviside function enrichments and is based on the replacement of the discontinuous enrichment function with the limit of an equivalent polynomial defined on the entire element domain this allows for the use of standard gaussian quadrature in the elements crossed by the discontinuity the work redefines conceptually the first version of the equivalent polynomial methodology introduced in 2006 allowing a much broader applicability as a consequence equivalent polynomials can be computed for all continuum element families in one two and three dimensions copyright 2014 john wiley sons ltd

sharp exponential integrability for critical riesz potentials and fractional laplacians on rn abstract we derive sharp adams inequalities for the riesz and more general riesz like potentials on the whole of r n as a consequence we obtain sharp moser trudinger inequalities for the critical sobolev spaces w n r n 0 n these inequalities involve fractional laplacians higher order gradients general homogeneous elliptic operators with constant coefficients and general trace type borel measures

equivalent moser type inequalities in r2 and the zero mass case abstract we first investigate concentration and vanishing phenomena concerning moser type inequalities in the whole plane which involve complete and reduced sobolev norms in particular we show that the critical ruf inequality is equivalent to an improved version of the subcritical adachi tanaka inequality which we prove to be attained then we consider smooth compactly supported functions with respect to the dirichlet norm 2 and we prove an optimal lorentz zygmund type inequality with explicit extremals and from which can be derived classical inequalities in h 1 r 2 such as the adachi tanaka inequality and a version of ruf s inequality

adams inequalities on measure spaces abstract in 1988 adams obtained sharp moser trudinger inequalities on bounded domains of r n the main step was a sharp exponential integral inequality for convolutions with the riesz potential in this paper we extend and improve adams results to functions defined on arbitrary measure spaces with finite measure the riesz fractional integral is replaced by general integral operators whose kernels satisfy suitable and explicit growth conditions given in terms of their distribution functions natural conditions for sharpness are also given most of the known results about moser trudinger inequalities can be easily adapted to our unified scheme we give some new applications of our theorems including sharp higher order moser trudinger trace inequalities sharp adams moser trudinger inequalities for general elliptic differential operators scalar and vector valued for sums of weighted potentials and for operators in the cr setting

multiple testing in clinical trials the basic ideas of multiple testing are outlined and the problem of how to control the probability of erroneous decisions is discussed the main emphasis is on the concept of the multiple level of significance controlling the experiment or family error in the strong sense which can be achieved by applying the principle of closed tests various practical situations encountered in multiple testing in clinical trials are considered more than one end point more than two treatments such as comparisons with a single control comparisons using ordered alternatives all pairwise comparisons and contrast methods and more than one trial tests based on global statistics the union intersection principle and other criteria are discussed the application of the multiple test concept in sequential sampling is investigated finally some comments are made on multiple power multiple confidence intervals and directed decisions

continuous interior penalty finite element method for oseen s equations in this paper we present an extension of the continuous interior penalty method of douglas and dupont interior penalty procedures for elliptic and parabolic galerkin methods in computing methods in applied sciences lecture notes in phys 58 springer verlag berlin 1976 pp 207 216 to oseen s equations the method consists of a stabilized galerkin formulation using equal order interpolation for pressure and velocity to counter instabilities due to the pressure velocity coupling or due to a high local reynolds number we add a stabilization term giving l2 control of the jump of the gradient over element faces edges in two dimensions to the standard galerkin formulation boundary conditions are imposed in a weak sense using a consistent penalty formulation due to nitsche we prove energy type a priori error estimates independent of the local reynolds number and give some numerical examples recovering the theoretical results

generalized gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method new gaussian integration schemes are presented for the efficient and accurate evaluation of weak form integrals in the extended finite element method for discontinuous functions we construct gauss like quadrature rules over arbitrarily shaped elements in two dimensions without the need for partitioning the finite element a point elimination algorithm is used in the construction of the quadratures which ensures that the final quadratures have minimal number of gauss points for weakly singular integrands we apply a polar transformation that eliminates the singularity so that the integration can be performed efficiently and accurately numerical examples in elastic fracture using the extended finite element method are presented to illustrate the performance of the new integration techniques

improving the accuracy of xfem crack tip fields using higher order quadrature and statically admissible stress recovery this study is concerned with improving the accuracy of crack tip fields obtained using the extended generalized finite element method xfem first the numerical integration of the element stiffness matrices which guarantees convergence with quadrature of not only the regular nodal displacements but also additional degrees of freedom corresponding to the enrichment functions is studied as the accuracy of the stresses obtained by direct differentiation of the converged with quadrature regular nodal displacements and of the coefficients corresponding to enrichment functions is still not satisfactory a statically admissible stress recovery sar scheme is introduced sar uses basis functions which meet the equilibrium equations within the domain and the local traction conditions on the boundary and moving least squares mls to fit the stresses at sampling points e g quadrature points obtained by the xfem important parameters controlling the accuracy of crack tip fields using the xfem and sar namely the order of quadrature the number of retained terms in the crack tip asymptotic field the number of enriched layers and use of arbitrary branch functions a proper choice of the sampling points in the enriched element and the size of the domain of influence doi of mls are investigated copyright 2005 john wiley sons ltd

unfitted extended finite elements for composite grids abstract we consider an extended finite elements method to handle the case of composite independent unstructured grids that lead to unfitted meshes in particular we address the case of two overlapped meshes a background and a foreground one where the thickness of the latter is smaller than the elements of the background mesh this situation may lead to elements split into several portions thus generating polyhedral elements we detail the corresponding discrete formulation for the poisson problem with discontinuous coefficients we also provide some technical details for the 3d implementation finally we provide some numerical examples with the aim of showing the effectiveness of the proposed formulation

a sharp inequality of j moser for higher order derivatives in fact go nwl 1 where wnis the area of the surface of the unit n ball also he notes that if 3 exceeds go then 1 can no longer hold with some co independent of the u satisfying 2 the fact that this result holds for some 3 0 independent of u has been observed now by several authors with a variety of proofs see 24 20 23 22 10 4 1 2 13 14 for example the earliest of these arguments expands the exponential function in a power series then observing that the norm in the imbedding

the design and analysis of the generalized finite element method abstract in this paper we introduce the generalized finite element method gfem as a combination of the classical finite element method fem and the partition of unity method pum the standard finite element spaces are augmented by adding special functions which reflect the known information about the boundary value problem and the input data e g the singular functions obtained from the local asymptotic expansion of the exact solution in the neighborhood of a corner point etc the special functions are multiplied with the partition of unity corresponding to the standard linear vertex shape functions and pasted together with the existing finite element basis to construct an augmented conforming finite element space in this way the local approximability afforded by the special functions is included in the approximation while maintaining the existing infrastructure of finite element codes the major features of the gfem are 1 the essential boundary conditions can be imposed exactly as in the standard fem unlike other partition of unity based methods where this is a major issue 2 the accuracy of the numerical integration of the entries of the stiffness matrix and load vector is controlled adaptively so that the errors in integration of the special functions do not affect the accuracy of the constructed approximation this issue also has not been sufficiently addressed in other implementations of partition of unity or meshless methods and 3 linear dependencies in the system of equations are resolved by employing an easy modification of the direct linear solver the power of the gfem for solving problems in domains with complex geometry with less error and less computer resources than the standard fem is illustrated by numerical examples

on the elimination of quadrature subcells for discontinuous functions in the extended finite element method the introduction of discontinuous non differentiable functions in the extended finite element method allows to model discontinuities independent of the mesh structure however to compute the stiffness matrix of the elements intersected by the discontinuity a subdivision of the elements into quadrature subcells aligned with the discontinuity line is commonly adopted in the paper it is shown how standard gauss quadrature can be used in the elements containing the discontinuity without splitting the elements into subcells or introducing any additional approximation the technique is illustrated and developed in one two and three dimensions for crack and material discontinuity problems

quadrature schemes for arbitrary convex concave volumes and integration of weak form in enriched partition of unity methods abstract quadrature schemes are constructed based on moment fitting equations to integrate polynomials over arbitrary convex concave volumes that arise among others in enriched partition of unity finite element methods epum the building block of the scheme involves the divergence theorem of multivariable calculus which is used to integrate the base functions an efficient and robust point distribution method is proposed and the quadrature weights at the corresponding points are obtained by solving a least squares problem the method is applied initially to integrate given polynomial functions over complex volumes and further to simulate simple three dimensional fluid dynamic problems which involve very complex volumes when solved with epum accuracy of the present quadrature construction scheme is demonstrated by comparing the results with the available exact numerical solutions and efficiency of the method is proved by comparing the computational time with that of the widely used tessellation method

trudinger moser type inequalities with logarithmic weights in dimension n abstract we consider borderline embeddings of trudinger moser type for weighted sobolev spaces in bounded domains in r n the embeddings go into orlicz spaces with exponential growth functions it turns out that the most interesting weights are powers of the logarithm for which an explicit dependence of the maximal growth functions can be established corresponding moser type results are also proved with explicit sharp exponents in the particular case of a logarithmic weight with the limiting exponent n 1 a maximal growth of double exponential type is obtained while for any larger exponent the embedding goes into l

a two stage stepwise estimation procedure this article proposes a two stage simultaneous confidence procedure for the comparisons of k pairs of population means without using multiplicity adjustment of more than two populations the proposed procedure can be broadly applied to parametric or nonparametric models it is robust and versatile because its derivation only utilizes a partitioning approach in conjunction with a bivariate adjustment without any assumption on the underlying distribution to elucidate the application the proposed procedure is intertwined with the estimation of the therapeutic window of a drug it provides confidence limits for the efficacy and the toxicity of the effective doses highest ineffective dose safe doses and lowest unsafe dose simultaneously such estimation information facilitates follow up studies in clinical trials as an illustrative example the new procedure is applied to analyze a data set on molecular cancer therapeutics regarding the apoptotic killing effects of different chemical compounds on two leukemia cell lines

multiple test procedures for dose finding the problem of identifying the lowest dose level for which the mean response differs from that at the zero dose level is considered a general framework for stepwise testing procedures that use contrasts among the dose level means is proposed using this framework several new procedures are derived these and some existing procedures including that of williams 1971 biometrics 27 103 117 1972 biometrics 28 519 531 are compared analytically and by an extensive simulation study for the normal theory balanced one way layout case it is pointed out that the procedures based on the so called step and basin contrasts proposed by ruberg 1989 journal of american statistical association 84 816 822 have excessively high type i familywise error rates fwes and hence they should not be used some findings of the simulation study are as follows for monotone dose mean configurations williams procedure and two step down test procedures based on helmert and linear contrasts offer the best performance for nonmonotone dose mean configurations the performance of williams procedure does degrade somewhat but the other two procedures are still the best for more complex designs a simple step down test procedure that uses any alpha level tests not necessarily t tests to compare each dose level with the zero dose level controls the fwe and is the only alternative available but its power is rather low especially under nonmonotone configurations step up procedures are generally dominated by step down procedures when the same contrasts are used although the differences are not great

a regularized xfem model for the transition from continuous to discontinuous displacements this work focuses on the modelling through the extended finite element method of structural problems characterized by discontinuous displacement as a model problem an elastic isotropic domain characterized by a displacement discontinuity across a surface is studied a regularization of the displacement field is introduced depending on a scalar parameter the regularized solution is defined in a layer the emerging strain and stress fields are independently modelled using specific constitutive assumptions in particular it is shown that the mechanical work spent within the regularization layer can be interpreted as an interface work provided that a spring like constitutive law is adopted the accuracy of the integration procedures adopted for the stiffness matrix is assessed as highly non linear terms appear standard gauss quadrature is compared with adaptive quadrature and with a new technique based on an equivalent polynomial approach one and two dimensional results are reported for varying discretization size regularization parameter and constitutive parameters copyright 2007 john wiley sons ltd

nitsche xfem for the coupling of an incompressible fluid with immersed thin walled structures abstract in this paper we introduce a nitsche xfem method for fluid structure interaction problems involving a thin walled elastic structure lagrangian formalism immersed in an incompressible viscous fluid eulerian formalism the fluid domain is discretized with an unstructured mesh not fitted to the solid mid surface mesh weak and strong discontinuities across the interface are allowed for the velocity and pressure respectively the fluid solid coupling is enforced consistently using a variant of nitsche s method with cut elements robustness with respect to arbitrary interface intersections is guaranteed through suitable stabilization several coupling schemes with different degrees of fluid solid time splitting implicit semi implicit and explicit are investigated a series of numerical test in 2d involving static and moving interfaces illustrates the performance of the different methods proposed

locating the peaks of solutions via the maximum principle ii a local version of the method of moving planes let be a bounded smooth domain in r 2n n 2 the well known moser trudinger inequality ensures the nonlinear functional jp u is bounded from below if and only if 2n 2 2n n n 1 w 2n where j u 1 2 f n 2 u 2 log f e u dx in x h n u j u h j 1 n 1 2 and 2n is the area of the unit sphere s 2n 1 in r 2n in this paper we prove the inf u x jp u is always attained for p 2n the existence of minimizers of jp at the critical value p 2n is a delicate problem the proof depends on the blowup analysis for a sequence of bubbling solutions here we develop a local version of the method of moving planes to exclude the boundary bubbling the existence of minimizers for jp at the critical value p 2n is in contrast to the case of two dimensions

sharp threshold nonlinearity for maximizing the trudinger moser inequalities abstract we study existence of maximizer for the trudinger moser inequality with general nonlinearity of the critical growth on r 2 as well as on the disk we derive a very sharp threshold nonlinearity between the existence and the non existence in each case in asymptotic expansions with respect to growth and decay of the function the expansions are explicit using apery s constant we also obtain an asymptotic expansion for the exponential radial sobolev inequality on r 2

an unfitted formulation for the interaction of an incompressible fluid with a thick structure via an xfem dg approach a numerical procedure that combines an extended finite element formulation and a discontinuous galerkin technique is presented with the final aim of providing an effective tool for the simulation of three dimensional 3d fluid structure interaction problems in this work we consider a thick structure immersed in a fluid we describe the numerical models and discuss the specific implementation issues arising in three dimensions finally 3d numerical results are provided to show the effectiveness of the approach

efficient implementation of finite element methods on nonmatching and overlapping meshes in three dimensions in recent years a number of finite element methods have been formulated for the solution of partial differential equations on complex geometries based on nonmatching or overlapping meshes examples of such methods are the fictitious domain method the extended finite element method and nitsche s method in all these methods integrals must be computed over cut cells or subsimplices which is challenging to implement especially in three space dimensions in this note we address the main challenges of such an implementation and demonstrate good performance of a fully general code for automatic detection of mesh intersections and integration over cut cells and subsimplices as a canonical example of an overlapping mesh method we consider nitsche s method which we apply to poisson s equation and a linear elastic problem

sensitivity analysis for equivalence and difference in an observational study of neonatal intensive care units in randomized experiments it is sometimes important to demonstrate that two treatments do not differ greatly in their effects or to demonstrate that the treatments have very different effects on one outcome but similar effects on another outcome these demonstrations may take the form of rejecting a null hypothesis of inequivalence in an equivalence test or rejecting a null hypothesis of equal and inequivalent effects on two outcomes the procedures often express a complex hypothesis in terms of component hypotheses and combine the component significance levels to test the complex hypothesis if used in a randomized trial randomization provides valid significance levels for each component test and hence also for the combined procedure in an observational study that is in a study of treatments that were not randomly assigned there is typically concern that significance levels for testing hypotheses about treatment effects may be distorted by failure to control for some unobserved pretreatment cov

high order extended finite element method for cracked domains the aim of the paper is to study the capabilities of the extended finite element method xfem to achieve accurate computations in non smooth situations such as crack problems although the xfem method ensures a weaker error than classical nite element methods the rate of convergence is not improved when the mesh parameter h is going to zero because of the presence of a singularity the di culty can be overcome by modifying the enrichment of the nite element basis with the asymptotic crack tip displacement solutions as well as with the heaviside function numerical simulations show that the modi ed xfem method achieves an optimal rate of convergence i e like in a standard nite element method for a smooth problem

on the hyper elastic formulation of the immersed boundary method abstract the immersed boundary ib method is both a mathematical formulation and a numerical method for fluid structure interaction problems in which immersed incompressible visco elastic bodies or boundaries interact with an incompressible fluid previous formulations of the ib method were not able to treat appropriately immersed materials of finite nonzero thickness modeled by general hyper elastic constitutive laws because of the lack of appropriate transmission conditions between the immersed body and the surrounding fluid in the case of a nonzero jump in normal stress at the solid fluid interface such a jump does not arise when the solid is comprised of fibers that run parallel to the interface but typically does arise in other cases e g when the solid contains elastic fibers that terminate at the solid fluid interface we present a derivation of the ib method that takes into account in an appropriate way the missing term the derivation presented in this paper starts from a separation of the stress that appears in the principle of virtual work the stress is divided into its fluid like and solid like components and each of these two terms is treated in its natural framework i e the eulerian framework for the fluid like stress and the lagrangian framework for the solid like stress we describe how the ib method can be used in conjunction with standard formulations of continuum mechanics models for immersed incompressible elastic materials and present some illustrative numerical experiments

existence and non existence of radial solutions for elliptic equations with critical exponent in ℝ2 where 2 2 n n 2 is the critical sobolev exponent for the embedding h 52 c l2 0 criticality and subcriticality play important rbles concerning the solvability of equation 1 1 using by now classical variational methods one sees that equation 1 1 is solvable i f f has subcritical growth and satisfies some additional hypotheses while for f u iuip u the well known pohoiaev identity shows that the solvability of equation 1 1 is lost if p reaches 2 and r is starshaped in their important paper 6 brezis nirenberg showed that for n e 4 solvability is regained if one adds a lower order linear term to the critical term more precisely they showed that for f r ar lr12 2r one has a denotes the 1st eigenvalue of a on ha r

dislocations by partition of unity a new finite element method for accurately modelling the displacement and stress fields produced by a dislocation is proposed the methodology is based on a local enrichment of the finite element space by closed form solutions for dislocations in infinite media via local partitions of unity this allows the treatment of both arbitrary boundary conditions and interfaces between materials the method can readily be extended to arrays of dislocations 3d problems large strains and non linear constitutive models results are given for an edge dislocation in a hollow cylinder and in an infinite medium for the cases of a glide plane intersecting a rigid obstacle and an interface between two materials copyright 2005 john wiley sons ltd

integrating strong and weak discontinuities without integration subcells and example applications in an xfem gfem framework partition of unity methods such as the extended finite element method allows discontinuities to be simulated independently of the mesh int j numer meth engng 1999 45 601 620 this eliminates the need for the mesh to be aligned with the discontinuity or cumbersome re meshing as the discontinuity evolves however to compute the stiffness matrix of the elements intersected by the discontinuity a subdivision of the elements into quadrature subcells aligned with the discontinuity is commonly adopted in this paper we use a simple integration technique proposed for polygonal domains int j nuttier meth engng 2009 80 1 103 134 doi 10 1002 nme 2589 to suppress the need for element subdivision numerical results presented for a few benchmark problems in the context of linear elastic fracture mechanics and a multi material problem show that the proposed method yields accurate results owing to its simplicity the proposed integration technique can be easily integrated in any existing code copyright c 2010 john wiley sons ltd

identifying effective and or safe doses by stepwise confidence intervals for ratios typical randomized clinical dose finding studies consist of the comparison of several doses of a drug versus a placebo interest lies in estimating relevant doses among those under investigation for efficacy and safety variables such as the minimum effective dose or the maximum safe dose or estimating both doses simultaneously step down procedures have been proposed for comparing the standardized differences of the dose groups against placebo in this paper we consider the ratio of population means and propose stepwise confidence intervals for these ratios these confidence intervals do not require multiplicity adjustments and yield the same decisions as the associated test procedures in addition several power concepts are investigated within the present framework the results allow sample size determination in the design phase of a study for the probability of estimating correctly the dose of interest auxiliary results of a numerical study show the range of application of these methods

quadrature rules for triangular and tetrahedral elements with generalized functions quadrature rules are developed for exactly integrating products of polynomials and generalized functions over triangular and tetrahedral domains these quadrature rules greatly simplify the implementation of finite element methods that involve integrals over volumes and interfaces that are not coincident with the element boundaries specifically the integrands considered here consist of a quadratic polynomial multiplied by a heaviside or dirac delta function operating on a linear polynomial this form allows for exact integration of expressions obtained from linear finite elements over domains and interfaces defined by a linear level set function exact quadrature rules are derived that involve fixed quadrature point locations with weights that depend continuously on the nodal level set values compared with methods involving explicit integration over subdomains the quadrature rules developed here accommodate degenerate interface geometries without any need for special consideration and provide analytical jacobian information describing the dependence of the integrals on the nodal level set values the accuracy of the method is demonstrated for a simple conduction problem with the neumann and robin type boundary conditions copyright 2007 john wiley sons ltd

adams inequalities for bi laplacian and extremal functions in dimension four let be a smooth oriented bounded domain be the sobolev space and be the first eigenvalue of the bi laplacian operator 2 then for any a 0a o we have and the above supremum is infinity when a o this strengthens adams inequality in dimension 4 d adams a sharp inequality of j moser for high order derivatives ann of math 128 1988 365 398 where he proved the above inequality holds for a 0 moreover we prove that for sufficiently small a an extremal function for the above inequality exists as a special case of our results we thus show that there exists with such that this establishes the existence of an extremal function of the original adams inequality in dimension 4

numerical integration over arbitrary polygonal domains based on schwarz christoffel conformal mapping this paper presents a new numerical integration technique oil arbitrary polygonal domains the polygonal domain is mapped conformally to the unit disk using schwarz christoffel mapping and a midpoint quadrature rule defined oil this unit disk is used this method eliminates the need for a two level isoparametric mapping usually required moreover the positivity of the jacobian is guaranteed numerical results presented for a few benchmark problems in the context of polygonal finite elements show that the proposed method yields accurate results

sharp adams type inequalities in ℝⁿ adams inequality for bounded domains r4 states that the supremum of e 32 u dx over all functions u w 2 2 0 with u 2 1 is bounded by a constant depending on only this bound becomes infinite for unbounded domains and in particular for r4 we prove that if u 2 is replaced by a suitable norm namely u u u 2 then the supremum of e 32 u 1 dx over all functions u w 2 2 0 with u 1 is bounded by a constant independent of the domain furthermore we generalize this result to any w m n m 0 with rn and m an even integer less than n

existence and nonexistence of extremals for critical adams inequalities in r4 and trudinger moser inequalities in r2 abstract though much progress has been made with respect to the existence of extremals of the critical first order trudinger moser inequalities in w 1 n r n and higher order adams inequalities on finite domain r n whether there exists an extremal function for the critical higher order adams inequalities on the entire space r n still remains open the current paper represents the first attempt in this direction by considering the critical second order adams inequality in the entire space r 4 the classical blow up procedure cannot apply to solving the existence of critical adams type inequality because of the absence of the polya szego type inequality in this paper we develop some new ideas and approaches based on a sharp fourier rearrangement principle see 31 sharp constants of the higher order gagliardo nirenberg inequalities and optimal poly harmonic truncations to study the existence and nonexistence of the maximizers for the adams inequalities in r 4 of the form s sup u h 2 1 r 4 exp 32 2 u 2 1 u 2 d x where 32 2 we establish the existence of the threshold where 32 2 2 b 2 2 and b 2 1 24 2 such that s is attained if 32 2 and is not attained if 32 2 this phenomenon has not been observed before even in the case of first order trudinger moser inequality therefore we also establish the existence and non existence of an extremal function for the trudinger moser inequality on r 2 furthermore the symmetry of the extremal functions can also be deduced through the fourier rearrangement principle

a high order discontinuous galerkin method for compressible flows with immersed boundaries summary we present a higher order discretization scheme for the compressible euler and navier stokes equations with immersed boundaries our approach makes use of a discontinuous galerkin dg discretization in a domain that is implicitly defined by means of a level set function the zero iso contour of this level set function is considered as an additional domain boundary where we weakly enforce boundary conditions in the same manner as in boundary fitted cells in order to retain the full order of convergence of the scheme it is crucial to perform volume and surface integrals in boundary cells with high accuracy this is achieved using a linear moment fitting strategy moreover we apply a non intrusive cell agglomeration technique that averts problems with very small and ill shaped cuts the robustness accuracy and convergence properties of the scheme are assessed in several two dimensional test cases for the steady compressible euler and navier stokes equations approximation orders range from zero to four even though the approach directly generalizes to even higher orders in all test cases with a sufficiently smooth solution the experimental order of convergence matches the expected rate for dg schemes this article is protected by copyright all rights reserved

a hybrid method to estimate the minimum effective dose for monotone and non monotone dose response relationships this article proposes a new multiple testing approach for estimation of the minimum effective dose allowing for non monotonous dose response shapes the presented approach combines the advantages of two commonly used methods it is shown that the new approach controls the error rate of underestimating the true minimum effective dose monte carlo simulations indicate that the proposed method outperforms alternative methods in many cases and is only marginally worse in the remaining situations