a hybrid method using wavelets for the numerical solution of boundary value problems on the interval abstract in this work various aspects of wavelet based methods for second order boundary value problems under galerkin framework are investigated based on the b spline multiresolution analysis mra on the line we propose a hybrid method on the interval which combines different treatments for interior and boundary splines by using this procedure the mra structure was conserved and hierarchical representations of the solution at different scales were obtained without much computational effort numerical examples are given to verify the effectiveness of the proposed method and the comparison with other techniques is presented

discontinuous galerkin methods for incompressible and nearly incompressible elasticity by nitsche s method we propose and analyze a discontinuous finite element method for nearly incompressible linear elasticity on triangular meshes we show optimal error estimates that are uniform with respect to poisson s ratio the method is thus locking free we also introduce an equivalent mixed formulation allowing for completely incompressible elasticity problems numerical results are presented

on the use of biorthogonal interpolating wavelets for large eddy simulation of turbulence recent work in the field of turbulence modelling has demonstrated the benefits of the wavelet based multiresolution analysis technique as a tool for the formulation of the large eddy simulation les equations in this formalism the les equations are obtained by projecting the navier stokes equations onto a hierarchy of wavelet spaces this paper investigates the use of biorthogonal interpolating wavelets as a basis for this projection placing special emphasis on the wavelet based differential operators that define this mapping a detailed analysis of their convergence properties is presented and compared to those of their orthogonal counterpart the daubechies wavelets based on this study we highlight the weaknesses of the unlifted interpolating wavelet representation for les sub grid modelling finally we establish a link between the unlifted framework and the sampling based les approach recently proposed in the literature

domain decomposition for linear elasticity with dg jumps and mortars in this article we present a domain decomposition method for solving a linear elasticity system data are transmitted by jumps as in a discontinuous galerkin method and mortars are introduced at the interfaces to dissociate the computation between neighboring subdomains a decoupling algorithm condenses the unknowns on the interface the matrix of the system is constructed by parallel computation numerical experiments confirming the theory are presented

locking free reissner mindlin elements without reduced integration abstract in a recent paper of arnold et al d n arnold f brezzi l d marini a family of discontinuous galerkin finite elements for the reissner mindlin plate j sci comput 22 2005 25 45 the ideas of discontinuous galerkin methods were used to obtain and analyze two new families of locking free finite element methods for the approximation of the reissner mindlin plate problem by following their basic approach but making different choices of finite element spaces we develop and analyze other families of locking free finite elements that eliminate the need for the introduction of a reduction operator which has been a central feature of many locking free methods for k 2 all the methods use piecewise polynomials of degree k to approximate the transverse displacement and possibly subsets of piecewise polynomials of degree k 1 to approximate both the rotation and shear stress vectors the approximation spaces for the rotation and the shear stress are always identical the methods vary in the amount of interelement continuity required in terms of smallest number of degrees of freedom the simplest method approximates the transverse displacement with continuous piecewise quadratics and both the rotation and shear stress with rotated linear brezzi douglas marini elements

a unified framework of continuous and discontinuous galerkin methods for solving the incompressible navier stokes equation abstract in this paper we propose a unified numerical framework for the time dependent incompressible navier stokes equation which yields the h 1 h div conforming and discontinuous galerkin methods with the use of different viscous stress tensors and penalty terms for pressure robustness under minimum assumption on galerkin spaces the semi and fully discrete stability is proved when a family of implicit runge kutta methods are used for time discretization furthermore we present a unified discussion on the penalty term numerical experiments are presented to compare our schemes with classical schemes in the literature in both unsteady and steady situations it turns out that our scheme is competitive when applied to well known benchmark problems such as taylor green vortex kovasznay flow potential flow lid driven cavity flow and the flow around a cylinder

a posteriori error estimates of discontinuous galerkin methods for the signorini problem a reliable and efficient a posteriori error estimator is derived for a class of discontinuous galerkin dg methods for the signorini problem a common property shared by many dg methods leads to a unified error analysis with the help of a constraint preserving enriching map the error estimator of dg methods is comparable with the error estimator of the conforming methods numerical experiments illustrate the performance of the error estimator

on the informativeness and accuracy of pooled testing in estimating prevalence of a rare disease application to hiv screening summary when screening for a rare disease the large number of expected false positives makes it difficult to obtain a positive estimate of prevalence using current screening methodology pooled testing not only reduces the probability of this occurring but also improves the accuracy of the estimator these findings are illustrated by screening for the human immunodeficiency virus

a hybrid high order discretisation of the brinkman problem robust in the darcy and stokes limits abstract in this work we develop and analyse a novel hybrid high order discretisation of the brinkman problem the method hinges on hybrid discrete velocity unknowns at faces and elements and on discontinuous pressures based on the discrete unknowns we reconstruct inside each element a stokes velocity one degree higher than face unknowns and a darcy velocity in the raviart thomas nedelec space these reconstructed velocities are respectively used to formulate the discrete versions of the stokes and darcy terms in the momentum equation along with suitably designed penalty contributions the proposed construction is tailored to yield optimal error estimates that are robust throughout the entire spectrum of local stokes or darcy dominated regimes as identified by a dimensionless number which can be interpreted as a friction coefficient the singular limit corresponding to the darcy equation is also fully supported by the method numerical examples corroborate the theoretical results this paper also contains two contributions whose interest goes beyond the specific method and application treated in this work an investigation of the dependence of the constant in the second korn inequality on star shaped domains and its application to the study of the approximation properties of the strain projector in general sobolev seminorms

discontinuous galerkin and mimetic finite difference methods for coupled stokes darcy flows on polygonal and polyhedral grids we study locally mass conservative approximations of coupled darcy and stokes flows on polygonal and polyhedral meshes the discontinuous galerkin dg finite element method is used in the stokes region and the mimetic finite difference method is used in the darcy region dg finite element spaces are defined on polygonal and polyhedral grids by introducing lifting operators mapping mimetic degrees of freedom to functional spaces optimal convergence estimates for the numerical scheme are derived results from computational experiments supporting the theory are presented

locally conservative coupling of stokes and darcy flows a locally conservative numerical method for solving the coupled stokes and darcy flows problem is formulated and analyzed the approach employs the mixed finite element method for the darcy region and the discontinuous galerkin method for the stokes region a discrete inf sup condition and optimal error estimates are derived

estimating the mean of an increasing stochastic process at a censored stopping time abstract data often come in the form of a longitudinal series say n whose observation has been stopped either by a terminal event u e g death or censoring event c e g lost to follow up when n is not deterministic it is generally not possible to use standard survival analysis tools e g the kaplan meier estimator to consistently estimate functionals of the distribution of n u because of induced informative censoring various seemingly unrelated estimators recently have been proposed to handle this difficulty within the context of specific problems ranging from the analysis of quality adjusted survival data to recurrent event data to lifetime medical cost data in this article i consider a general framework containing each of these specific examples as a special case propose a class of estimators for the mean of the stopped longitudinal process and establish the asymptotic properties of this class of estimators connections between the aforementioned estimators are established

simultaneous space time adaptive wavelet solution of nonlinear parabolic differential equations dynamically adaptive numerical methods have been developed to efficiently solve differential equations whose solutions are intermittent in both space and time these methods combine an adjustable time step with a spatial grid that adapts to spatial intermittency at a fixed time the same time step is used for all spatial locations and all scales this approach clearly does not fully exploit space time intermittency we propose an adaptive wavelet collocation method for solving highly intermittent problems e g turbulence on a simultaneous space time computational domain which naturally adapts both the space and time resolution to match the solution besides generating a near optimal grid for the full space time solution this approach also allows the global time integration error to be controlled the efficiency and accuracy of the method is demonstrated by applying it to several highly intermittent 1d t dimensional and 2d t dimensional test problems in particular we found that the space time method uses roughly 18 times fewer space time grid points and is roughly 4 times faster than a dynamically adaptive explicit time marching method while achieving similar global accuracy

a non conforming piecewise quadratic finite element on triangles it is shown in this paper that non conforming finite elements on the triangle using second degree polynomials can be easily built and used indeed they appear as an enriched version of the standard piecewise quadratic six node element this work is divided into two parts in the first we present the basic properties of the element namely how it can be built and basic error estimates we also show that this element exhibits a very peculiar regularity property in the second part we apply our element to the approximation of viscous incompressible flows and more generally to the approximation of incompressible materials

korn s inequalities for piecewise h 1 vector fields korn s inequalities for piecewise h 1 vector fields are established they can be applied to classical nonconforming finite element methods mortar methods and discontinuous galerkin methods

a three dimensional quadratic nonconforming element we define a second degree nonconforming element on tetrahedra we build a basis for the opproximation space derived from this element we prove a discrete regularity property similar to the one that holds for the corresponding two dimensional element

uniformly convergent interior penalty methods using multilinear approximations for problems in elasticity interior penalty methods for linear elasticity when used with bilinear elements are effective in the context of compressible materials however they may produce poor approximations with these elements in the nearly incompressible regime we propose a new general interior penalty formulation and prove that it is uniformly convergent with respect to the compressibility parameter for multilinear elements the new formulation is a modification of well known methods nonsymmetric incomplete and symmetric interior penalty galerkin through underintegration of selected edge terms

a discontinuous stabilized mortar method for general 3d elastic problems first the present paper is concerned with the extension to linearized elastodynamics of the optimal results known in statics for the mortar method it also analyzes and tests a new couple of displacements lagrange multipliers for the method as proposed independently by ben belgacem f ben belgacem a stabilized domain decomposition method with non matching grids for the stokes problem in three dimensions siam j numer anal 42 2 2004 667 685 and the authors p hauret methodes numeriques pour la dynamique des structures non lineaires incompressibles a deux echelles numerical methods for the dynamic analysis of two scale incompressible nonlinear structures ph d thesis ecole polytechnique 2004 finally questions of practical implementation in the presence of curved interfaces are addressed and validated from the numerical point of view

a hybrid high order locking free method for linear elasticity on general meshes abstract we devise an arbitrary order locking free method for linear elasticity the method relies on a pure displacement primal formulation and leads to a symmetric positive definite system matrix with compact stencil the degrees of freedom are vector valued polynomials of arbitrary order k 1 on the mesh faces so that in three space dimensions the lowest order scheme only requires 9 degrees of freedom per mesh face the method can be deployed on general polyhedral meshes the key idea is to reconstruct the symmetric gradient and divergence inside each mesh cell in terms of the degrees of freedom by solving inexpensive local problems the discrete problem is assembled cell wise using these operators and a high order stabilization bilinear form locking free error estimates are derived for the energy norm and for the l 2 norm of the displacement with optimal convergence rates of order k 1 and k 2 respectively for smooth solutions on general meshes the theoretical results are confirmed numerically and the cpu cost is evaluated on both standard and polygonal meshes

a low order nonconforming finite element for reissner mindlin plates we propose a locking free element for plate bending problems based on the use of nonconforming piecewise linear functions for both rotations and deflections we prove optimal error estimates with respect to both the meshsize and the analytical solution regularity

a parallel fast algorithm for computing the helmholtz integral operator in 3 d layered media in this paper we propose a parallel fast algorithm for computing the product of the discretized helmholtz integral operator in layered media and a vector in o n qn z 2n xn ylogn xn y operations here n xn yn z is the number of sources and n q is the number of quadrature points used in the evaluation of the sommerfeld integral in the definition of layered media green s function for problems in thin layer media n z o 1 such a product forms the key step of many iterative solvers such as the krylov subspace based gmres and bicgstab for linear systems arising from the integral equation methods for the helmholtz equations the fast solver is based on two important techniques which reduce the cost of quadrature summations in the sommerfeld contour integral for green s functions in 3 d layered media the first technique is the removal of surface pole effects along the real axis integration contour by identifying the pole locations with a discrete wavelet transform in the second technique we apply a window based high frequency filter to shorten the contour length as a result the integral operator for the 3 d layered media can be efficiently written as a sum of 2 d hankel cylindrical integral operators and the latter can be calculated by either a tree code or a 2 d wideband fast multipole method in a fast manner numerical results show the efficiency and parallelism of the proposed fast algorithm

two lower order nonconforming rectangular elements for the reissner mindlin plate in this paper we propose two lower order nonconforming rectangular elements for the reissner mindlin plate the first one uses the conforming bilinear element to approximate both components of the rotation and the modified nonconforming rotated q 1 element to approximate the displacement whereas the second one uses the modified nonconforming rotated q 1 element to approximate both the rotation and the displacement both elements employ a projection operator to overcome the shear force locking we prove that both methods converge at optimal rates uniformly in the plate thickness t in both the h 1 and l 2 norms and consequently they are locking free

discrete multiresolution analysis using hermite interpolation biorthogonal multiwavelets we generalize harten s interpolatory multiresolution representation to include hermite interpolation compact hermite interpolation with optimal order accuracy is used in both the decomposition and reconstruction algorithm the resulting multiple basis functions biorthogonal multiwavelets are symmetric or skew symmetric compact and analytic harten s approach has several advantages the multiresolution scheme is inherently discrete nonperiodic boundary conditions are easy to implement and the representation can be extended to nonuniform grids in bounded domains we demonstrate the compression features of the new multiple basis functions by application to several examples

weakly over penalized discontinuous galerkin schemes for reissner mindlin plates without the shear variable this paper introduces a new locking free formulation that combines the discontinuous galerkin methods with weakly over penalized techniques for reissner mindlin plates we derive optimal a priori error estimates in both the energy norm and l 2 l2 norm for polynomials of degree k 2 k 2 and we extend the results concerning the energy norm to higher order polynomial degrees numerical tests confirm our theoretical predictions

a finite element method with discontinuous rotations for the mindlin reissner plate model we present a continuous discontinuous finite element method for the mindlin reissner plate model based on continuous polynomials of degree k 2 for the transverse displacements and discontinuous polynomials of degree k 1 for the rotations we prove a priori convergence estimates uniformly in the thickness of the plate and thus show that locking is avoided we also derive a posteriori error estimates based on duality together with corresponding adaptive procedures for controlling linear functionals of the error finally we present some numerical results

an adaptive wavelet method for nonlinear differential algebraic equations abstract a multi resolution collocation method with specially designed spline wavelet is presented to numerically solve a system of nonlinear differential algebraic equations of index one in circuit simulation as the wavelet collocation method is applied to such system we will have to solve large nonlinear algebraic equations for the algebraic equations we give a modified newton type iterative method which bases on two wavelet adaptive techniques we prove the convergence the stability and the complexity on the adaptive method reported here the new approach could effectively reduce computational costs and storage requirements to large extent numerical experiments are given to further illustrate the method s principle

optimality of group testing in the presence of misclassification several optimality properties of dorfman s 1943 group testing procedure are derived for estimation of the prevalence of a rare disease whose status is classified with error exact ranges of disease prevalence are obtained for which group testing provides more efficient estimation when group size increases

a review of geometric transformations for nonrigid body registration this paper provides a comprehensive and quantitative review of spatial transformations models for nonrigid image registration it explains the theoretical foundation of the models and classifies them according to this basis this results in two categories physically based models described by partial differential equations of continuum mechanics e g linear elasticity and fluid flow and basis function expansions derived from interpolation and approximation theory e g radial basis functions b splines and wavelets recent work on constraining the transformation so that it preserves the topology or is diffeomorphic is also described the final section reviews some recent evaluation studies the paper concludes by explaining under what conditions a particular transformation model is appropriate

discrete signal matching using coarse to fine wavelet basis functions in this paper we propose a matching algorithm to estimate accurate and dense displacements between two signals the displacements are characterized by a coarse to fine wavelet representation which is a linear combination of hierarchical basis functions developed by cai and wang siam numer anal 33 3 1996 937 the coarser scale basis function has larger support while the finer scale basis function has smaller support during the iterative minimization process the basis functions are utilized as large to small windows in selecting global to local regions for signal matching the estimated wavelet coefficients are then used to reconstruct the signal in a coarse to fine manner two sets of synthetic examples one with small displacement and the other with large displacements have been employed to illustrate the advantages of the wavelet based method this method has been applied to estimate the dense disparity between stereo images in several real examples and the results demonstrate its effectiveness

kernel bundle diffeomorphic image registration using stationary velocity fields and wendland basis functions in this paper we propose a multi scale multi kernel shape compactly supported kernel bundle framework for stationary velocity field based image registration wendland kernel bundle stationary velocity field wkb svf we exploit the possibility of directly choosing kernels to construct a reproducing kernel hilbert space rkhs instead of imposing it from a differential operator the proposed framework allows us to minimize computational cost without sacrificing the theoretical foundations of svf based diffeomorphic registration in order to recover deformations occurring at different scales we use compactly supported wendland kernels at multiple scales and orders to parameterize the velocity fields and the framework allows simultaneous optimization over all scales the performance of wkb svf is extensively compared to the 14 non rigid registration algorithms presented in a recent comparison paper on both mgh10 and cumc12 datasets the accuracy of wkb svf is improved when compared to other registration algorithms in a disease specific application for intra subject registration atrophy scores estimated using the proposed registration scheme separates the diagnostic groups of alzheimer s and normal controls better than the state of the art segmentation technique experimental results show that wkb svf is a robust flexible registration framework that allows theoretically well founded and computationally efficient multi scale representation of deformations and is equally well suited for both inter and intra subject image registration

convergence of ipdg for coupled time dependent navierstokes and darcy equations a numerical method is proposed and analyzed for the coupled time dependent navierstokes equations and darcy equations existence and uniqueness of the solution are obtained under a small data condition a priori error estimates are derived numerical examples confirm the theoretical convergence rates

a locking free weak galerkin finite element method for elasticity problems in the primal formulation this paper presents an arbitrary order locking free numerical scheme for linear elasticity on general polygonal polyhedral partitions by using weak galerkin wg finite element methods like other wg methods the key idea for the linear elasticity is to introduce discrete weak strain and stress tensors which are defined and computed by solving inexpensive local problems on each element such local problems are derived from weak formulations of the corresponding differential operators through integration by parts locking free error estimates of optimal order are derived in a discrete h 1 norm and the usual l 2 norm for the approximate displacement when the exact solution is smooth numerical results are presented to demonstrate the efficiency accuracy and the locking free property of the weak galerkin finite element method

bv estimates for mortar methods in linear elasticity this paper is concerned with the convergence of mortar methods applied to linear elasticity we prove that the conventional mesh dependent norms used in the analysis of mortar methods are bounded below by the bv norm when combined with standard results this bound establishes a decomposition independent and mesh independent proof of the convergence of mortar methods in linear elasticity

wavelet optimized finite difference method with non static re gridding the main aim of wavelet based numerical methods for solving partial differential equations is to develop adaptive schemes in order to achieve accuracy and computational efficiency the wavelet optimized finite difference method wofd uses wavelets to generate appropriate grids to apply finite difference method its standard implementation carries out static re griddings after a fixed number of time steps we present an effective implementation of wofd method that reduces the number of static re griddings hence leading to reduction of flops without significant loss of accuracy numerical experiments are performed on different cases of heat and schrodinger equations

adaptive stabilization of discontinuous galerkin methods for nonlinear elasticity analytical estimates this is the second of two papers in which we motivate introduce and analyze a new type of strategy for the stabilization of discontinuous galerkin dg methods in nonlinear elasticity problems the foremost goal behind it is to enhance the robustness of the method without deteriorating the accuracy of the resulting solutions its distinctive property is that for nonlinear elastic problems the stabilization term is solution dependent and hence it is termed an adaptive stabilization mechanism the key contribution of this paper is the construction of a stabilization strategy for which the method is perfectly stable since the stabilization parameters can be explicitly computed as part of the numerical solution this is accomplished through the main result of this paper which consists of a theorem that provides lower bounds for the size of the stabilization parameters numerical examples confirm the guaranteed stability of the resulting method however they also show that the computed lower bounds overestimate the minimum amount of stabilization needed negatively affecting the approximation properties of the method these results underscore the fact that a better understanding of the stabilization mechanisms is needed in order to construct a method that is both robust and efficient

two robust nonconforming hbox h 2 elements for linear strain gradient elasticity we propose two finite elements to approximate a boundary value problem arising from strain gradient elasticity which is a high order perturbation of the linearized elastic system our elements are hbox h 2 nonconforming while hbox h 1 conforming we show both elements converge in the energy norm uniformly with respect to the perturbation parameter

a least squares method for linear elasticity using a patch reconstructed space abstract we propose a discontinuous least squares finite element method for solving the linear elasticity the approximation space is obtained by patch reconstruction with only one unknown per element we apply the l 2 norm least squares principle with the weak imposition of the continuity across the interior faces to the stress displacement formulation the optimal convergence order under the energy norm is attained numerical results of the linear elasticity are presented to verify the error estimates our method enjoys the advantages of discontinuous galerkin methods and in addition we illustrate the great simplicity in implementation the robustness and the improved efficiency of our method

the nonconforming virtual element method for elasticity problems abstract we present the nonconforming virtual element method for linear elasticity problems in the pure displacement formulation this method is uniformly convergent for the nearly incompressible case the optimal convergence in the h 1 norm is proved under some regularity assumptions we mention that for the lowest order case on triangular meshes the nonconforming virtual element method coincides with the nonconforming finite element method presented by brenner and sung 1992 19 up to an approximation of the right hand side besides we also present the nonconforming virtual element method for the pure traction problem which is proved to be uniformly convergent with respect to the lame constant finally we demonstrate the optimal convergence and stability of the nonconforming virtual element method by some numerical results

using group testing to estimate a proportion and to test the binomial model group testing has been extensively studied as an efficient way to classify units as defective or satisfactory when the proportion p of defectives is small it can also be used to estimate p often substantially reducing the mean squared error mse of p and cost per unit information group testing is useful for larger p in the estimation problem than in the classification problem but for larger p more care must be taken in choosing the group size k k being too large not only increases mse p but adversely affects the robustness of p to both errors in testing misclassification and errors in the assumed binomial model procedures that retest units from defective groups if even feasible are shown to reduce cost per unit information very little in the estimation problem but can provide useful information for testing the model methods are given for using data from tests of unequal sized groups to estimate p and for testing the validity of the binomial model

an observation on korn s inequality for nonconforming finite element methods by utilizing a simple observation on traces of rigid motions we are able to strengthen a result of brenner 2004 on korn s inequality for nonconforming finite element methods the approach here is tightly connected to the theory developed in brenner s work our motivation for the analysis was the desire to show that a robust darcy stokes element satisfies korn s inequality and to achieve this the stronger result seems necessary

an extension of the crouzeix raviart space to general meshes with application to quasi incompressible linear elasticity and stokes flow in this work we introduce a discrete functional space on general polygonal or polyhedral meshes which mimics two important properties of the standard crouzeix raviart space namely the continuity of mean values at interfaces and the existence of an interpolator which preserves the mean value of the gradient inside each element the construction borrows ideas from both cell centered galerkin and hybrid finite volume methods the discrete function space is defined from cell and face unknowns by introducing a suitable piecewise affine reconstruction on a fictitious pyramidal subdivision of the original mesh two applications are considered in which the discrete space plays an important role namely i the design of a locking free primal as opposed to mixed method for quasi incompressible planar elasticity on general polygonal meshes ii the design of an inf sup stable method for the stokes equations on general polygonal or polyhedral meshes in this context we also propose a general modification applicable to any suitable discretization which guarantees that the velocity approximation is unaffected by the presence of large irrotational body forces provided a helmholtz decomposition of the right hand side is available the relation between the proposed methods and classical finite volume and finite element schemes on standard meshes is investigated finally similar ideas are exploited to mimic key properties of the lowest order raviart thomas space on general polygonal or polyhedral meshes

analysis of some quadrilateral nonconforming elements for incompressible elasticity in this work some nonconforming elements on arbitrary quadrilateral meshes in solving incompressible elastic equations are analyzed a uniform optimal convergence rate is established at the incompressible limit nu 0 5 for both displacement and stresses or pressure in the case of incompressible flow

a stabilized non conforming finite element method for incompressible flow in this paper we extend the recently introduced edge stabilization method to the case of non conforming finite element approximations of the linearized navier stokes equation to get stability also

using divergence free wavelets for the numerical solution of the 2 d stationary navier stokes equations a galerkin wavelet scheme is presented for solving the 2 d stationary navier stokes equations using the scaling generator of the divergence free wavelets moreover some boundary generators are constructed to improve the approximation accuracy finally the optimal error estimates and the numerical results are reported

a unified stabilized mixed finite element method for coupling stokes and darcy flows abstract a stabilized mixed finite element method for solving the coupled stokes and darcy flows problem is formulated and analyzed the approach utilizes the same nonconforming crouzeix raviart element discretization on the entire domain a discrete inf sup condition and an optimal a priori error estimate are derived finally some numerical examples verifying the theoretical predictions are presented

a wavelet optimized adaptive multi domain method the formulation and implementation of wavelet based methods for the solution of multi dimensional partial differential equations in complex geometries is discussed utilizing the close connection between daubechies wavelets and finite difference methods on arbitrary grids we formulate a wavelet based collocation method well suited for dealing with general boundary conditions and nonlinearities to circumvent problems associated with completely arbitrary grids and complex geometries we propose to use a multi domain formulation in which to solve the partial differential equation with the ability to adapt the grid as well as the order of the scheme within each subdomain besides supplying the required geometric flexibility the multi domain formulation also provides a very natural load balanced data decomposition suitable for parallel environments the performance of the overall scheme is illustrated by solving two dimensional hyperbolic problems

poincare friedrichs inequalities for piecewise h 1 functions poincare friedrichs inequalities for piecewise h1 functions are established they can be applied to classical nonconforming finite element methods mortar methods and discontinuous galerkin methods

two scale dirichlet neumann preconditioners for elastic problems with boundary refinements abstract the present work deals with the efficient resolution of elastostatics problems on domains with boundary refinements the proposed approach separates the boundary refinements from the interior of the domain by the mortar method and uses dirichlet neumann preconditioners to solve the corresponding algebraic system we prove that the simplest dirichlet neumann algorithm achieves independence of the condition number of the preconditioned system with respect to the number and the size of the small details nevertheless the situation no longer prevails when the refined boundary is clamped an enhanced preconditioner is then designed by the introduction of a coarse space to mitigate the aforementioned sensitivity some numerical tests are performed to confirm the analysis and the tools are extended by the proposition of a quasi newton method in the case of nonlinear elasticity this paper is an extended version of a work presented at the dd16 conference with proofs and complete numerical results

primal stabilized hybrid and dg finite element methods for the linear elasticity problem abstract primal stabilized hybrid finite element methods for the linear elasticity problem are proposed consisting of locally discontinuous galerkin problems in the primal variable coupled to a global problem in the multiplier which is identified with the trace of the displacement field numerical analysis covering both continuous or discontinuous interpolations of the multiplier shows that the proposed formulation preserves the main properties of the associate dg method such as consistency stability boundedness and optimal rates of convergence in the energy norm and in the l 2 norm for adjoint consistent formulations convergence studies confirm the optimal rates of convergence predicted by the numerical analysis presented here and a local post processing technique is proposed to recover stress approximations with improved rates of convergence in h div norm

robustness of group testing in the estimation of proportions in binomial group testing unlike one at a time testing the test unit consists of a group of individuals and each group is declared to be defective or nondefective a defective group is one that is presumed to include one or more defective e g infected positive individuals and a nondefective group to contain only nondefective individuals the usual binomial model considers the individuals being grouped as independent and identically distributed bernoulli random variables under the binomial model and presuming that groups are tested and classified without error it has been shown that when the proportion of defective individuals is low group testing is often preferable to individual testing for identifying infected individuals and for estimating proportions of defectives we discuss the robustness of group testing for estimating proportions when the underlying assumptions of i no testing errors and ii independent individuals are violated to evaluate the effect of these model violations two dilution effect models and a serial correlation model are considered group testing proved to be quite robust to serial correlation in the presence of a dilution effect smaller group sizes should be used but most of the benefits of group testing can still be realized

discontinuous galerkin finite element approximation of nonlinear second order elliptic and hyperbolic systems we develop the convergence analysis of discontinuous galerkin finite element approximations to symmetric second order quasi linear elliptic and hyperbolic systems of partial differential equations in divergence form in a bounded spatial domain in mathbb r d subject to mixed dirichlet neumann boundary conditions optimal order asymptotic bounds are derived on the discretization error in each case without requiring the global lipschitz continuity or uniform monotonicity of the stress tensor instead only local smoothness and a garding inequality are used in the analysis

an adaptive wavelet vaguelette algorithm for the solution of pdes the paper first describes a fast algorithm for the discrete orthonormal wavelet transform and its inverse without using the scaling function this approach permits to compute the decomposition of a function into a lacunary wavelet basis i e a basis constituted of a subset of all basis functions up to a certain scale without modification the construction is then extended to operator adapted biorthogonal wavelets this is relevant for the solution of certain nonlinear evolutionary pdes where a priori information about the significant coefficients is available we pursue the approach described in j frohlich and k schneider europ j mech b fluids13 439 1994 which is based on the explicit computation of the scalewise contributions of the approximated function to the values at points of hierarchical grids here we present an improved construction employing the cardinal function of the multiresolution the new method is applied to the helmholtz equation and illustrated by comparative numerical results it is then extended for the solution of a nonlinear parabolic pde with semi implicit discretization in time and self adaptive wavelet discretization in space results with full adaptivity of the spatial wavelet discretization are presented for a one dimensional flame front as well as for a two dimensional problem

isogeometric divergence conforming b splines for the unsteady navier stokes equations divergence conforming b splines are developed for application to the incompressible navier stokes equations on geometrically mapped domains these enable smooth pointwise divergence free solutions and thus satisfy mass conservation in the strongest possible sense semi discrete methods based on divergence conforming b splines are shown to conserve linear and angular momentum and satisfy balance laws for energy vorticity enstrophy and helicity these are geometric structure preserving quantities and numerical simulations that are sensitive to them are shown to be qualitatively correct and quantitatively accurate the methods developed are anticipated to open new doors to the practical calculation of complex flows and to studies of their physical behavior

the existence and uniqueness of solution to wavelet collocation the study of the numerical solutions of pdes with wavelet collocation has yielded a number of substantial results however the existence and uniqueness of solution has not been discussed yet in this paper the existence and uniqueness of solution to wavelet collocation for elliptic equations is established and discussed moreover wavelet collocation is applied to numerical example to examine its appropriateness according to numerical example and analysis it is seen that the existence and uniqueness of solution of this paper is feasible and the new theory is meaningful for developing wavelet collocation

on the poincare friedrichs inequality for piecewise h 1 functions in anisotropic discontinuous galerkin finite element methods the purpose of this paper is to propose a proof for the poincare friedrichs inequality for piecewise h 1 functions on anisotropic meshes by verifying suitable assumptions involved in the newly proposed proof we show that the poincare friedrichs inequality for piecewise h 1 functions holds independently of the aspect ratio which characterizes the shape regular condition in finite element analysis in addition under the maximum angle condition we establish the poincare friedrichs inequality for the crouzeix raviart non conforming linear finite element counterexamples show that the maximum angle condition is only sufficient

a conservative stable finite element method for stokes flow and nearly incompressible linear elasticity on rectangular grid abstract in this paper we discuss finite element methods for the incompressible stokes problem and the nearly incompressible linear elasticity problem specifically we present a finite element pair for the incompressible stokes problem which satisfies the discrete inf sup condition and the discrete korn s inequality and moreover which is element wise conservative the pair provides a locking free method for the nearly incompressible linear elasticity problem without reduced integration

estimating ordered binomial proportions with the use of group testing summary this paper considers group testing when the probability of response is increasing across the levels of an observed covariate we illustrate how previously known results in order restricted inference can be extended to situations wherein data are collected according to a group testing protocol and we derive maximum likelihood estimators for proportions under the increasing order restriction and group testing model finally we show how the use of group testing can dramatically reduce the bias and mean squared error of isotonic regression estimators obtained from one at atime testing these proposed methods are illustrated using data from an observational hiv study conducted in houston texas

guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity we obtain fully computable a posteriori error estimators for the energy norm of the error in second order conforming and nonconforming finite element approximations in planar elasticity these estimators are completely free of unknown constants and give a guaranteed numerical upper bound on the norm of the error the estimators are shown to also provide local lower bounds up to a constant and higher order data oscillation terms numerical examples are presented illustrating the theory and confirming the effectiveness of the estimator

a strongly conservative finite element method for the coupled stokes biot model abstract in this paper based on interior penalty discontinuous galerkin method and mixed finite element method we consider a strongly conservative discretization for the rearranged stokes biot model theoretical analysis and numerical modeling are carried out from the view of mathematics we firstly present the existence and uniqueness of solution of the numerical scheme then the analysis of stability and priori error estimates are derived from the point of numerical simulation we report the numerical examples under uniform meshes which well validate the analysis of convergence and the strong mass conservation

adaptive multiresolution collocation methods for initial boundary value problems of nonlinear pdes we have designed a cubic spline wavelet like decomposition for the sobolev space h 0 2 i where i is a bounded interval based on a special point value vanishing property of the wavelet basis functions a fast discrete wavelet transform dwt is constructed this dwt will map discrete samples of a function to its wavelet expansion coefficients in at most 7n log n operations using this transform we propose a collocation method for the initial boundary value problem of nonlinear partial differential equations pdes then we test the efficiency of the dwt and apply the collocation method to solve linear and nonlinear pdes

finite volume methods for elasticity with weak symmetry we introduce a new cell centered finite volume discretization for elasticity with weakly enforced symmetry of the stress tensor the method is motivated by the need for robust discretization methods for deformation and flow in porous media and falls in the category of multi point stress approximations mpsa by enforcing symmetry weakly the resulting method has additional flexibility beyond previous mpsa methods this allows for a construction of a method which is applicable to all grid types and in particular the method amends a crucial shortcoming in previous mpsa methods for simplex grids by formulating the method as a discrete variational problem we prove convergence of the new method for a wide range of problems with conditions that can be verified at the time of discretization we present the first set of comprehensive numerical tests for the mpsa methods in three dimensions covering cartesian and simplex grids with both heterogeneous and nearly incompressible media the tests show that the new method consistently is second order convergent in displacement despite being lowest order with a rate that mostly is between 1 and 2 for stresses the results further show that the new method is more robust and computationally cheaper than previous mpsa methods

an adaptive spline wavelet adi sw adi method for two dimensional reaction diffusion equations we study a spline wavelet alternative direction implicit sw adi algorithm for solving two dimensional reaction diffusion equations this algorithm is based on a collocation method for pdes with a specially designed spline wavelet for the sobolev spaceh2 i on a closed intervali by using the tensor product nature of adaptive wavelet meshes we propose a sw adi method for two dimensional problems the proposed sw adi method is an efficient time dependent adaptive method with second order accuracy for solutions with localized phenomena such as in flame propagations issues like new boundary wavelets for more accurate boundary conditions adaptive strategy for two dimensional meshes data structure and storage and implementation details and numerical results will be discussed

a locking free solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of lagrangian elements abstract this paper presents a new finite element solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of the classical bilinear or trilinear lagrangian elements it solves the primal variable displacement in the strain div formulation and can handle both displacement and traction boundary conditions it is a locking free solver based on conforming finite elements the solver has second order accuracy in displacement and first order accuracy in stress and dilation divergence of displacement as validated by theoretical analysis and illustrated by numerical experiments on benchmarks deal ii implementation is also discussed

second generation wavelet collocation method for the solution of partial differential equations an adaptive numerical method for solving partial differential equations is developed the method is based on the whole new class of second generation wavelets wavelet decomposition is used for grid adaptation and interpolation while a new o n hierarchical finite difference scheme which takes advantage of wavelet multilevel decomposition is used for derivative calculations the treatment of nonlinear terms and general boundary conditions is a straightforward task due to the collocation nature of the algorithm in this paper we demonstrate the algorithm for one particular choice of second generation wavelets namely lifted interpolating wavelets on an interval with uniform regular sampling the main advantage of using second generation wavelets is that wavelets can be custom designed for complex domains and irregular sampling thus the strength of the new method is that it can be easily extended to the whole class of second generation wavelets leaving the freedom and flexibility to choose the wavelet basis depending on the application

a space time discontinuous galerkin method for the elastic wave equation abstract in this work we present a new high order space time discretization method based on a discontinuous galerkin paradigm for the second order visco elastodynamics equation after introducing the method we show that the resulting space time discontinuous galerkin formulation is well posed stable and retains optimal rate of convergence with respect to the discretization parameters namely the mesh size and the polynomial approximation degree a set of two and three dimensional numerical experiments confirms the theoretical bounds

a posteriori error analysis of finite element methods for reissner mindlin plates this paper develops an a posteriori error control theory of finite element methods for reissner mindlin plates which states that one can derive a uniformly reliable and efficient a posteriori error estimate for a given scheme by only 1 checking three conditions 2 designing three functions and one parameter 3 bounding the last three terms of the abstract estimator we apply this theory to two classes of methods and achieve robust a posteriori error controls for them

a stabilized mixed finite element method for coupled stokes and darcy flows with transport abstract in this article we present a stabilized mixed finite element method for solving the coupled stokes and darcy flow equations with a solute transport the mathematical model includes the velocity and pressure equations and concentration equation where the viscosity depends on the concentration we propose a mixed weak formulation and use the nonconforming piecewise crouzeix raviart finite element piecewise constant and conforming piecewise linear finite element to approximate velocity pressure and concentration respectively the existence uniqueness of the approximate solution are obtained and optimal order a priori error estimates are derived no assumption on the boundness of the infinity norms of approximate velocity or concentration or the restriction about the time step and spatial meshsize is needed due to a new weak formulation introduced for the concentration equation numerical examples are presented to verify the theoretical results

a fast adaptive wavelet collocation algorithm for multidimensional pdes a fast multilevel wavelet collocation method for the solution of partial differential equations in multiple dimensions is developed the computational cost of the algorithm is independent of the dimensionality of the problem and is o n where n is the total number of collocation points the method can handle general boundary conditions the multilevel structure of the algorithm provides a simple way to adapt computational refinements to local demands of the solution high resolution computations are performed only in regions where singularities or sharp transitions occur numerical results demonstrate the ability of the method to resolve localized structures such as shocks which change their location and steepness in space and time the present results indicate that the method has clear advantages in comparison with well established numerical algorithms

nonconforming finite element methods for the equations of linear elasticity in the adaptation of nonconforming finite element methods to the equations of elasticity with traction boundary conditions the main difficulty in the analysis is to prove that an appropriate discrete version of korn s second inequality is valid such a result is shown to hold for nonconforming piecewise quadratic and cubic finite elements and to be false for nonconforming piecewise linears optimal order error estimates uniform for poisson ratio v e 0 1 2 are then derived for the corresponding p2 and p3 methods this contrasts with the use of c finite elements where there is a deterioration in the convergence rate as v 1 2 for piecewise polynomials of degree 3 modifications of the continuous methods and the nonconforming linear method which also give uniform optimal order error estimates are discussed

image registration using wavelet based motion model an image registration algorithm is developed to estimate dense motion vectors between two images using the coarse to fine wavelet based motion model this motion model is described by a linear combination of hierarchical basis functions proposed by cai and wang siam numer anal 33 3 937 970 1996 the coarser scale basis function has larger support while the finer scale basis function has smaller support with these variable supports in full resolution the basis functions serve as large to small windows so that the global and local information can be incorporated concurrently for image matching especially for recovering motion vectors containing large displacements to evaluate the accuracy of the wavelet based method two sets of test images were experimented using both the wavelet based method and a leading pyramid spline based method by szeliski et al international journal of computer vision 22 3 199 218 1996 one set of test images taken from barron et al international journal of computer vision 12 43 77 1994 contains small displacements the other set exhibits low texture or spatial aliasing after image blurring and contains large displacements the experimental results showed that our wavelet based method produced better motion estimates with error distributions having a smaller mean and smaller standard deviation

an adaptive multilevel wavelet collocation method for elliptic problems an adaptive multilevel wavelet collocation method for solving multi dimensional elliptic problems with localized structures is described the method is based on multi dimensional second generation wavelets and is an extension of the dynamically adaptive second generation wavelet collocation method for evolution problems int j comp fluid dyn 17 2003 151 wavelet decomposition is used for grid adaptation and interpolation while a hierarchical finite difference scheme which takes advantage of wavelet multilevel decomposition is used for derivative calculations the multilevel structure of the wavelet approximation provides a natural way to obtain the solution on a near optimal grid in order to accelerate the convergence of the solver an iterative procedure analogous to the multigrid algorithm is developed the overall computational complexity of the solver is o n where n is the number of adapted grid points the accuracy and computational efficiency of the method are demonstrated for the solution of two and three dimensional elliptic test problems

a locking free nonconforming triangular element for planar elasticity with pure traction boundary condition a new nonconforming triangular element for the equations of planar linear elasticity with pure traction boundary conditions is considered by virtue of construction of the element the discrete version of korn s second inequality is directly proved to be valid convergence rate of the finite element methods is uniformly optimal with respect to l error estimates in the energy norm and l 2 norm are o h 2 and o h 3 respectively

on a wavelet based method for the numerical simulation of wave propagation a wavelet based method for the numerical simulation of acoustic and elastic wave propagation is developed using a displacement velocity formulation and treating spatial derivatives with linear operators the wave equations are rewritten as a system of equations whose evolution in time is controlled by first order derivatives the linear operators for spatial derivatives are implemented in wavelet bases using an operator projection technique with nonstandard forms of wavelet transform using a semigroup approach the discretized solution in time can be represented in an explicit recursive form based on taylor expansion of exponential functions of operator matrices the boundary conditions are implemented by augmenting the system of equations with equivalent force terms at the boundaries the wavelet based method is applied to the acoustic wave equation with rigid boundary conditions at both ends in 1 d domain and to the elastic wave equation with a traction free boundary conditions at a free surface in 2 d spatial media the method can be applied directly to media with plane surfaces and surface topography can be included with the aid of distortion of the grid describing the properties of the medium the numerical results are compared with analytic solutions based on the cagniard technique and show high accuracy the wavelet based approach is also demonstrated for complex media including highly varying topography or stochastic heterogeneity with rapid variations in physical parameters these examples indicate the value of the approach as an accurate and stable tool for the simulation of wave propagation in general complex media

a two stage adaptive group testing procedure for estimating small proportions abstract a method for adaptively estimating a proportion p using group testing procedures is presented and analyzed with emphasis placed on a two stage procedure this estimator is compared to the usual group testing estimator via asymptotic and small sample relative efficiency the adaptive estimator is generally recommended with the restriction that adaptations i e adjustments of group size are based on at least 10 measurements responses but if one is confident that one has a very good a priori estimate of p then the usual estimator is recommended monte carlo simulations show that a normal approximation is adequate for generating confidence intervals with confidence coefficients as high as 95

a three level bddc algorithm for mortar discretizations in this paper a three level balancing domain decomposition by constraints bddc algorithm is developed for the solutions of large sparse algebraic linear systems arising from the mortar discretization of elliptic boundary value problems the mortar discretization is considered on geometrically nonconforming subdomain partitions in two level bddc algorithms the coarse problem needs to be solved exactly however its size will increase with the increase of the number of the subdomains to overcome this limitation the three level algorithm solves the coarse problem inexactly while a good rate of convergence is maintained this is an extension of previous work the three level bddc algorithms for standard finite element discretization estimates of the condition numbers are provided for the three level bddc method and numerical experiments are also discussed

group testing regression models with dilution submodels group testing where specimens are tested initially in pools is widely used to screen individuals for sexually transmitted diseases however a common problem encountered in practice is that group testing can increase the number of false negative test results this occurs primarily when positive individual specimens within a pool are diluted by negative ones resulting in positive pools testing negatively if the goal is to estimate a population level regression model relating individual disease status to observed covariates severe bias can result if an adjustment for dilution is not made recognizing this as a critical issue recent binary regression approaches in group testing have utilized continuous biomarker information to acknowledge the effect of dilution in this paper we have the same overall goal but take a different approach we augment existing group testing regression models that assume no dilution with a parametric dilution submodel for pool level sensitivity and estimate all parameters using maximum likelihood an advantage of our approach is that it does not rely on external biomarker test data which may not be available in surveillance studies furthermore unlike previous approaches our framework allows one to formally test whether dilution is present based on the observed group testing data we use simulation to illustrate the performance of our estimation and inference methods and we apply these methods to 2 infectious disease data sets

locking free adaptive discontinuous galerkin fem for linear elasticity problems an adaptive discontinuous galerkin finite element method for linear elasticity problems is presented we develop an a posteriori error estimate and prove its robustness with respect to nearly incompressible materials absence of volume locking furthermore we present some numerical experiments which illustrate the performance of the scheme on adaptively refined meshes