high order methods for low reynolds number flows around moving obstacles based on universal meshes summary we propose a family of methods for simulating two dimensional incompressible low reynolds number flow around a moving obstacle whose motion is prescribed the methods make use of a universal mesh a fixed background mesh that adapts to the geometry of the immersed obstacle at all times by adjusting a few elements in the neighborhood of the obstacle s boundary the resulting mesh provides a conforming triangulation of the fluid domain over which discretizations of any desired order of accuracy in space and time can be constructed using standard finite element spaces together with off the shelf time integrators we demonstrate the approach by using taylor hood elements to approximate the fluid velocity and pressure to integrate in time we consider implicit runge kutta schemes as well as a fractional step scheme we illustrate the methods and study their convergence numerically via examples that involve flow around obstacles that undergo prescribed deformations copyright 2015 john wiley sons ltd

variational r adaption in elastodynamics we develop a variational r adaptive finite element framework for solid dynamic applications and explore its conceptual links with the theory of dynamic configurational forces the central idea underlying the proposed approach is to allow hamilton s principle of stationary action to determine jointly the evolution of the displacement field and the discretization of the reference configuration of the body this is accomplished by rendering the action stationary with respect to the material and spatial nodal coordinates simultaneously however we find that a naive consistent galerkin discretization of the action leads to intrinsically unstable solutions remarkably we also find that this unstable behavior is eliminated when a mixed multifield version of hamilton s principle is adopted additional features of the proposed numerical implementation include the use of uncoupled space and time discretizations the use of independent space interpolations for velocities and deformations the application of these interpolations over a continuously varying adaptive mesh and the application of mixed variational integrators with independent time interpolations for velocities and nodal parameters the accuracy robustness and versatility of the approach are assessed and demonstrated by way of convergence tests and selected examples

design and analysis of phase i clinical trials the phase i clinical trial is a study intended to estimate the so called maximum tolerable dose mtd of a new drug although there exists more or less a standard type of design for such trials its development has been largely ad hoc as usually implemented the trial design has no intrinsic property that provides a generally satisfactory basis for estimation of the mtd in this paper the standard design and several simple alternatives are compared with regard to the conservativeness of the design and with regard to point and interval estimation of an mtd 33rd percentile with small sample sizes using a markov chain representation we found several designs to be nearly as conservative as the standard design in terms of the proportion of patients entered at higher dose levels in monte carlo simulations two two stage designs are found to provide reduced bias in maximum likelihood estimation of the mtd in less than ideal dose response settings of the three methods considered for determining confidence intervals the delta method a method based on fieller s theorem and a likelihood ratio method none was able to provide both usefully narrow intervals and coverage probabilities close to nominal

high order gradients with the shifted boundary method an embedded enriched mixed formulation for elliptic pdes abstract we propose an extension of the embedded boundary method known as shifted boundary method to elliptic diffusion equations in mixed form e g darcy flow heat diffusion problems with rough coefficients etc our aim is to obtain an improved formulation that for linear finite elements is at least second order accurate for both flux and primary variable when either dirichlet or neumann boundary conditions are applied following previous work of nishikawa and mazaheri in the context of residual distribution methods we consider the mixed form of the diffusion equation i e with darcy type operators and introduce an enrichment of the primary variable this enrichment is obtained exploiting the relation between the primary variable and the flux variable which is explicitly available at nodes in the mixed formulation the proposed enrichment mimics a formally quadratic pressure approximation although only nodal unknowns are stored similar to a linear finite element approximation we consider both continuous and discontinuous finite element approximations and present two approaches a non symmetric enrichment which as in the original references only improves the consistency of the overall method and a symmetric enrichment which enables a full error analysis in the classical finite element context combined with the shifted boundary method these two approaches are extended to high order embedded computations and enable the approximation of both primary and flux gradient variables with second order accuracy independently on the type of boundary conditions applied we also show that the the primary variable is third order accurate when pure dirichlet boundary conditions are embedded

moving mesh methods in multiple dimensions based on harmonic maps in practice there are three types of adaptive methods using the finite element approach namely the h method p method and r method in the h method the overall method contains two parts a solution algorithm and a mesh selection algorithm these two parts are independent of each other in the sense that the change of the pdes will affect the first part only however in some of the existing versions of the r method also known as the moving mesh method these two parts are strongly associated with each other and as a result any change of the pdes will result in the rewriting of the whole code in this work we will propose a moving mesh method which also contains two parts a solution algorithm and a mesh redistribution algorithm our efforts are to keep the advantages of the r method e g keep the number of nodes unchanged and of the h method e g the two parts in the code are independent a framework for adaptive meshes based on the hamilton schoen yau theory was proposed by dvinsky in this work we will extend dvinsky s method to provide an efficient solver for the mesh redistribution algorithm the key idea is to construct the harmonic map between the physical space and a parameter space by an iteration procedure each iteration step is to move the mesh closer to the harmonic map this procedure is simple and easy to program and also enables us to keep the map harmonic even after long times of numerical integration the numerical schemes are applied to a number of test problems in two dimensions it is observed that the mesh redistribution strategy based on the harmonic maps adapts the mesh extremely well to the solution without producing skew elements for multi dimensional computations

analysis of triangle quality measures several of the more commonly used triangle quality measures are analyzed and compared proofs are provided to verify that they do exhibit the expected extremal properties the asymptotic behavior of these measures is investigated and a number of useful results are derived it is shown that some of the quality measures are equivalent in the sense of displaying the same extremal and asymptotic behavior and that it is therefore possible to achieve a concise classification of triangle quality measures

the second generation shifted boundary method and its numerical analysis abstract recently the shifted boundary method sbm was proposed within the class of unfitted or immersed or embedded finite element methods by reformulating the original boundary value problem over a surrogate approximate computational domain the sbm avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning accuracy is maintained by modifying the original boundary conditions using taylor expansions hence the name of the method that shifts the location and values of the boundary conditions in this article we present enhanced variational sbm formulations for the poisson and stokes problems with improved flexibility and robustness these simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations first we show that these new sbm implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive second we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at dirichlet boundaries therefore avoiding the calibration of an additional stabilization parameter finally we prove enhanced l 2 estimates without the cumbersome assumption of earlier proofs that the surrogate domain is convex instead we rely on a conventional assumption that the boundary of the true domain is smooth which can also be replaced by requiring convexity of the true domain the aforementioned improvements open the way to a more general and efficient implementation of the shifted boundary method particularly in complex three dimensional geometries we complement these theoretical developments with numerical experiments in two and three dimensions

domain deformation mapping application to variational mesh generation the purposes of this article are first to expose the mathematical similarities between variational mesh generation and hyperelasticity theory and second to show how elements and tools of hyperelasticity theory can be employed for analysis and practical construction of domain deformation mappings utilized in variational mesh generation

a penalization method to take into account obstacles in incompressible viscous flows from the navier stokes brinkman model a penalization method has been derived by several authors to compute incompressible navier stokes equations around obstacles in this paper convergence theorems and error estimates are derived for two kinds of penalization the first one corresponds to l 2 penalization inducing a darcy equation in the solid body the second one corresponds to a h 1 penalization and induces a brinkman equation in the body numerical tests are performed to confirm the efficiency and accuracy of the method

inverse geometry heat transfer problem based on a radial basis functions geometry representation summary we present a methodology for solving a nonlinear inverse geometry heat transfer problem where the observations are temperature measurements at points inside the object and the unknown is the geometry of the volume where the problem is de ned the representation of the geometry is based on radial basis functions rbfs and the nonlinear inverse problem is solved using the iteratively regularized gauss newton method in our work we consider not only the problem with no geometry restrictions but also the bound constrained problem the methodology is used for the industrial application of estimating the location of the 1150 c isotherm in a blast furnace hearth based on measurements of the thermocouples located inside it we validate the solution of the algorithm against simulated measurements with different levels of noise and study its behavior on different regularization matrices finally we study the error behavior of the solution copyright c 2004 john wiley sons ltd

interpreting canonical correlation analysis through biplots of structure correlations and weights this paper extends the biplot technique to canonical correlation analysis and redundancy analysis the plot of structure correlations is shown to the optimal for displaying the pairwise correlations between the variables of the one set and those of the second the link between multivariate regression and canonical correlation analysis redundancy analysis is exploited for producing an optimal biplot that displays a matrix of regression coefficients this plot can be made from the canonical weights of the predictors and the structure correlations of the criterion variables an example is used to show how the proposed biplots may be interpreted

redundancy analysis for qualitative variables redundancy analysis also called principal components analysis of instrumental variables is a technique for two sets of variables one set being dependent of the other its aim is maximization of the explained variance of the dependent variables by a linear combination of the explanatory variables the technique is generalized to qualitative variables it then gives implicitly a simultaneous optimal scaling of the dependent qualitative variables examples are taken from the dutch life situation survey 1977 using satisfaction with life and happiness as dependent variables the analysis leads to one well being scale defined by the explanatory variables marital status schooling income and activity

a discontinuous galerkin based immersed boundary method with non homogeneous boundary conditions and its application to elasticity we propose a discontinuous galerkin based immersed boundary method for elasticity problems the resulting numerical scheme does not require boundary fitting meshes and avoids boundary locking by switching the elements intersected by the boundary to a discontinuous galerkin approximation special emphasis is placed on the construction of a method that retains an optimal convergence rate in the presence of non homogeneous essential and natural boundary conditions the role of each one of the approximations introduced is illustrated by analyzing an analog problem in one spatial dimension finally extensive two and three dimensional numerical experiments on linear and nonlinear elasticity problems verify that the proposed method leads to optimal convergence rates under combinations of essential and natural boundary conditions

using historical controls to adjust for covariates in trend tests for binary data abstract historical data often play an important role in helping interpret the results of a current study this article is motivated primarily by one specific application the analysis of data from rodent carcinogenicity studies by proposing a suitable informative prior distribution on the relationship between control outcome data and covariates we derive modified trend test statistics that incorporate historical control information to adjust for covariate effects frequentist and fully bayesian methods are presented and novel computational techniques are developed to compute the test statistics several attractive theoretical and computational properties of the proposed priors are derived in addition a semiautomatic elicitation scheme for the priors is developed our approach is used to modify a widely used prevalence test for carcinogenicity studies the proposed methodology is applied to data from a national toxicology program carcinogenicity experiment and is shown to provide helpful insight on t

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

insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures this is the peer reviewed version of the following article ruiz girones e oliver a socorro g cascon j escobar j m montenegro r sarrate j insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures international journal for numerical methods in engineering 2018 which has been published in final form at http onlinelibrary wiley com doi 10 1002 nme 5706 pdf this article may be used for non commercial purposes in accordance with wiley terms and conditions for self archiving

a predictive approach to the analysis of designed experiments abstract viewing the analysis of designed experiments as a model selection problem we introduce the use of a predictive bayesian criterion in this context based on the predictive density of a replicate experiment pdre a calibration of the criterion is provided to assist in the model choice the relationships of the proposed criterion to other prevalent criteria such as aic bic and mallows s c p are given an information theoretic criterion based on the pdre s of two competing models is also introduced and compared with the usual f statistic for two nested models examples are given to illustrate the proposed methodology

universal meshes a method for triangulating planar curved domains immersed in nonconforming meshes summary we introduce a new method to triangulate planar curved domains that transforms a specific collection of triangles in a background mesh to conform to the boundary in the process no new vertices are introduced and connectivities of triangles are left unaltered the method relies on a novel way of parameterizing an immersed boundary over a collection of nearby edges with its closest point projection to guarantee its robustness we require that the domain be c2 regular the background mesh be sufficiently refined near the boundary and that specific angles in triangles near the boundary be strictly acute the method can render both straight edged and curvilinear triangulations for the immersed domain the latter includes curved triangles that conform exactly to the immersed boundary and ones constructed with isoparametric mappings to interpolate the boundary at select points high order finite elements constructed over these curved triangles achieve optimal accuracy which has customarily proven difficult in numerical schemes that adopt nonconforming meshes aside from serving as a quick and simple tool for meshing planar curved domains with complex shapes the method provides significant advantages for simulating problems with moving boundaries and in numerical schemes that require iterating over the geometry of domains with no conformity requirements the same background mesh can be adopted to triangulate a large family of domains immersed in it including ones realized over several updates during the coarse of simulating problems with moving boundaries we term such a background mesh as a universal mesh for the family of domains it can be used to triangulate universal meshes hence facilitate a framework for finite element calculations over evolving domains while using only fixed background meshes furthermore because the evolving geometry can be approximated with any desired order numerical solutions can be computed with high order accuracy we present demonstrative examples using universal meshes to simulate the interaction of rigid bodies with stokesian fluids copyright 2014 john wiley sons ltd

approximate imposition of boundary conditions in immersed boundary methods we analyze several possibilities to prescribe boundary conditions in the context of immersed boundary methods as basic approximation technique we consider the finite element method with a mesh that does not match the boundary of the computational domain and therefore dirichlet boundary conditions need to be prescribed in an approximate way as starting variational approach we consider nitsche s methods and we then move to two options that yield non symmetric problems but that turned out to be robust and efficient the essential idea is to use the degrees of freedom of certain nodes of the finite element mesh to minimize the difference between the exact and the approximated boundary condition

torsional springs for two dimensional dynamic unstructured fluid meshes abstract dynamic fluid grids are commonly used for the solution of flow problems with moving boundaries they are often represented by a network of fictitious lineal springs that can become unreliable when the fluid mesh undergoes large displacements and or deformations in this paper we propose to control the arbitrary motion of two dimensional dynamic unstructured fluid grids with additional torsional springs we show that such springs can be designed to prohibit the interpenetration of neighboring triangles and therefore to provide the method of spring analogy with the robustness needed for enlarging its range of applications we illustrate our new dynamic mesh motion algorithm with several examples that highlight its advantages in terms of robustness quality and performance

multivariate methods for quantitative and qualitative data abstract in this paper several multivariate analysis methods are analyzed by means of the errors in variables model two specifications viz the principal relations and the principal factors model for the set of unobserved latent variables are introduced and shown to be complementary for particular choices of the error covariance matrix the general model reduces to several well known multivariate techniques including ordinary least squares principal components orthogonal regression and canonical correlations the same apparatus is used to arrive at a set of multivariate techniques in case the data is qualitative instead of quantitative the relationship with optimal scaling techniques for qualitative data is shown an empirical example is given of a regression involving a dependent latent variable having two ordered categorical indicator variables

solving variational problems and partial differential equations mapping into general target manifolds a framework for solving variational problems and partial differential equations that define maps onto a given generic manifold is introduced in this paper we discuss the framework for arbitrary target manifolds while the domain manifold problem was addressed in j comput phys 174 2 2001 759 the key idea is to implicitly represent the target manifold as the level set of a higher dimensional function and then implement the equations in the cartesian coordinate system where this embedding function is defined in the case of variational problems we restrict the search of the minimizing map to the class of maps whose target is the level set of interest in the case of partial differential equations we re write all the equation s geometric characteristics with respect to the embedding function we then obtain a set of equations that while defined on the whole euclidean space are intrinsic to the implicitly defined target manifold and map into it this permits the use of classical numerical techniques in cartesian grids regardless of the geometry of the target manifold the extension to open surfaces and submanifolds is addressed in this paper as well in the latter case the submanifold is defined as the intersection of two higher dimensional hypersurfaces and all the computations are restricted to this intersection examples of the applications of the framework here described include harmonic maps in liquid crystals where the target manifold is a hypersphere probability maps where the target manifold is a hyperplane chroma enhancement texture mapping and general geometric mapping between high dimensional manifolds

a design for phase i trials in completely or partially ordered groups we propose a design for dose finding for cytotoxic agents in completely or partially ordered groups of patients by completely ordered groups we mean that prior to the study there is clinical information that would indicate that for a given dose the groups can be ordered with respect to the probability of toxicity at that dose with partially ordered groups at a given dose only some of the groups can be ordered with respect to the probability of toxicity at that dose the method we propose includes elements of the parametric model used in the continual reassessment method combined with the hwang peddada order restricted estimation procedure we evaluate the operating characteristics of these designs in a family of dose toxicity curves representing complete and partial orders copyright 2017 john wiley sons ltd

a variational r adaption and shape optimization method for finite deformation elasticity this paper is concerned with the formulation of a variational r adaption method for finite deformation elastostatic problems the distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution the optimal mesh and in problems of shape optimization the equilibrium shapes of the system this is accomplished by minimizing the energy functional with respect to the nodal field values as well as with respect to the triangulation of the domain of analysis energy minimization with respect to the referential nodal positions has the effect of equilibrating the energetic or configurational forces acting on the nodes we derive general expressions for the configuration forces for isoparametric elements and nonlinear possibly anisotropic materials under general loading we illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications including the problem of a semi infinite crack in linear and nonlinear elastic bodies and the optimization of the shape of elastic inclusions

principal component analysis with external information on both subjects and variables a method for structural analysis of multivariate data is proposed that combines features of regression analysis and principal component analysis in this method the original data are first decomposed into several components according to external information the components are then subjected to principal component analysis to explore structures within the components it is shown that this requires the generalized singular value decomposition of a matrix with certain metric matrices the numerical method based on the qr decomposition is described which simplifies the computation considerably the proposed method includes a number of interesting special cases whose relations to existing methods are discussed examples are given to demonstrate practical uses of the method

on strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method we consider a problem stemming from recent models of phase transitions in stimulus responsive hydrogels wherein a sharp interface separates swelled and collapsed phases extended finite element methods that approximate the local solution with an enriched basis such that the mesh need not explicitly fit the interface geometry are emphasized attention is focused on the weak enforcement of the normal configurational force balance and various options for evaluating the jump in the normal component of the solute flux at the interface we show that as the reciprocal interfacial mobility vanishes it plays the role of a penalty parameter enforcing a pure dirichlet constraint eventually triggering oscillations in the interfacial velocity we also examine alternative formulations employing a lagrange multiplier to enforce this constraint it is shown that the most convenient choice of basis for the lagrange multiplier results in oscillations in the multiplier field and a decrease in accuracy and rate of convergence in local error norms suggesting a lack of stability in the discrete formulation under such conditions neither the direct evaluation of the gradient of the approximation at the phase interface nor the interpretation of the lagrange multiplier field provide a robust means to obtain the jump in the normal component of solute flux fortunately the adaptation and use of local domain integral methodologies considerably improves the flux evaluations several example problems are presented to compare and contrast the various techniques and methods

the extended finite element method for rigid particles in stokes flow a new method for the simulation of particulate flows based on the extended finite element method x fem is described in this method the particle surfaces need not conform to the finite element boundaries so that moving particles can be simulated without remeshing the near field form of the fluid flow about each particle is built into the finite element basis using a partition of unity enrichment allowing the simple enforcement of boundary conditions and improved accuracy over other methods on a coarse mesh we present a weak form of the equations of motion useful for the simulation of freely moving particles and solve example problems for particles with prescribed and unknown velocities copyright 2001 john wiley sons ltd

algebraically constrained extended edge element method exfem ac for resolution of multi material cells abstract surface effects are critical to the predictive simulation of electromagnetics as current tends to concentrate near material interfaces there are two principal difficulties in the accurate representation of these effects in discrete models first many applications of interest operate at large deformations where body fitted meshes are impractical second physics compatible discretizations of the governing equations require curl conforming edge elements for which no practical alternatives to body fitted meshes exist the main purpose of this paper is to develop such an alternative that avoids remeshing the problem our approach uses the existing edge element basis to dynamically construct an interface conforming basis we show that in the case of triangular grids in two dimensions our approach generates a basis that spans the same space as edge elements on an interface fitted mesh we also demonstrate the efficacy of the approach computationally

on the optimality of the simultaneous redundancy transformations the objective of this paper is to introduce and motivate additional properties and interpretations for the redundancy variables it is shown that these variables can be derived by application of certain invariance arguments and without reference to the index of redundancy in addition an optimality property for the variables is presented which is important whenever one restricts attention in a study to a subset of the redundancy variables this optimality property pertains to the subset rather than to the individual variables

immersed finite element method abstract in this paper the immersed finite element method ifem is proposed for the solution of complex fluid and deformable structure interaction problems encountered in many physical models in ifem a lagrangian solid mesh moves on top of a background eulerian fluid mesh which spans over the entire computational domain hence the mesh generation is greatly simplified moreover both fluid and solid domains are modeled with the finite element methods and the continuity between the fluid and solid sub domains are enforced via the interpolation of the velocities and the distribution of the forces with the reproducing kernel particle method rkpm delta function in comparison with the immersed boundary ib method the higher ordered rkpm delta function enables the fluid domain to have nonuniform spatial meshes with arbitrary geometries and boundary conditions the use of such kernel functions may eventually open doors to multi scale and multi resolution modelings of complex fluid structure interaction problems rigid and deformable spheres dropping in channels are simulated to demonstrate the unique capabilities of the proposed method the results compare well with the experimental data to the authors knowledge these are the first solutions that deal with particulate flows with very flexible solids

simulating curvilinear crack propagation in two dimensions with universal meshes summary we formulate a class of delicately controlled problems to model the kink free evolution of quasistatic cracks in brittle isotropic linearly elastic materials in two dimensions the evolving crack satisfies familiar principles griffith s criterion local symmetry and irreversibility a novel feature of the formulation is that in addition to the crack path the loading is also treated as an unknown specifically a scaling factor for prescribed dirichlet and neumann boundary conditions is computed as part of the solution to yield an always propagating and ostensibly kink free crack and a continuous loading history beyond the initial step a dimensionless statement of the problem depends only on the poisson s ratio of a homogeneous material and is in particular independent of its young s modulus and fracture toughness numerical resolution of the formulated problem relies on two new ideas the first is an algorithm to compute triangulations conforming to cracked domains by locally deforming a given background mesh in the vicinity of evolving cracks the algorithm is robust under mild assumptions on the sizes and angles of triangles near the crack and its smoothness hence a subset if not the entire family of cracked domains realized during the course of a simulation can be discretized with the same background mesh we term the latter a universal mesh for such a family of domains universal meshes facilitate adopting a discrete representation for the crack as splines in our examples preclude the need for local splitting retriangulation operations liberate the crack from following directions prescribed by the mesh and enable the adoption of standard fems to compute the elastic fields in the cracked solid second we employ a method specifically designed to approximate the stress intensity factors for curvilinear cracks we examine the performance of the resulting numerical method with detailed examples including comparisons with an exact solution of a crack propagating along a circular arc which we construct and comparisons with experimental fracture paths in all cases we observe convergence of computed paths their derivatives and loading histories with refinement of the universal mesh copyright 2014 john wiley sons ltd

imposing essential boundary conditions in mesh free methods imposing essential boundary conditions is a key issue in mesh free methods the mesh free interpolation does not verify the kronecker delta property and therefore the imposition of prescribed values is not as straightforward as for the finite element method the aim of this paper is to present a general overview on the existing techniques to enforce essential boundary conditions in galerkin based mesh free methods special attention is paid to the mesh free coupling with finite elements for the imposition of prescribed values and to methods based on a modification of the galerkin weak form particular examples are used to analyze and compare their performance in different situations

an adaptive remeshing strategy for flows with moving boundaries and fluid structure interaction the primary objective of this work is to extend the capability of the arbitrary lagrangian eulerian ale based strategy for solving fluid structure interaction problems this is driven by the fact that the ale mesh movement techniques will not be able to treat problems in which fluid structure interface experiences large motion in addition for certain problems the need arises to capture accurately flow features such as a region with high gradients of the solution variables this can be achieved by incorporating an adaptive remeshing procedure into the solution strategy as in our previous works comput methods appl mech eng 2006 195 1633 1666 comput methods appl mech eng 2006 195 5754 5779 here the fluid flow is governed by the incompressible navier stokes equations and modelled by using stabilized low order velocity pressure finite elements the motion of the fluid domain is accounted for by an arbitrary lagrangian eulerian ale strategy the flexible structure is represented by means of appropriate standard finite element formulations while the motion of the rigid body is described by rigid body dynamics for temporal discretization of both fluid and solid bodies the discrete implicit generalized method is employed the resulting strongly coupled set of non linear equations is then solved by means of a novel partitioned solution procedure which is based on the newton raphson methodology and incorporates full linearization of the overall incremental problem within the adaptive solution strategy the quality of fluid mesh and the solution quality indicator are evaluated regularly and compared against the appropriate remeshing criteria to decide whether a remeshing step is required the adaptive remeshing procedure follows closely the standard computational procedure in which the adaptive remeshing process produces a mesh that can capture salient features of the flow field for the problems under consideration in this work the motion of the fluid boundary very often results in boundaries with very high curvatures and a fluid domain that contain areas with small cross sections to be able to generate meshes that give result with acceptable accuracy these local geometrical features need to be included in determining the element density distribution the numerical examples demonstrate the robustness and efficiency of the methodology copyright 2007 john wiley sons ltd

fictitious domain finite element methods using cut elements i a stabilized lagrange multiplier method we propose a fictitious domain method where the mesh is cut by the boundary the primal solution is computed only up to the boundary the solution itself is defined also by nodes outside the domain

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

mesh smoothing using a posteriori error estimates we develop a simple mesh smoothing algorithm for adaptively improving finite element triangulations the algorithm makes use of a posteriori error estimates which are now widely used in finite element calculations in this paper we derive the method present some numerical illustrations and give a brief analysis of the issue of uniqueness

an unfitted finite element method using discontinuous galerkin in this paper we present a new approach to simulations on complex shaped domains the method is based on a discontinuous galerkin dg method using trial and test functions defined on a structured grid essential boundary conditions are imposed weakly via the dg formulation this method offers a discretization where the number of unknowns is independent of the complexity of the domain we will show numerical computations for an elliptic scalar model problem in 2 and 3 convergence rates for different polynomial degrees are studied

finite element analysis on implicitly defined domains an accurate representation based on arbitrary parametric surfaces in this paper we present some novel results and ideas for robust and accurate implicit representation of geometric surfaces in finite element analysis the novel contributions of this paper are threefold 1 describe and validate a method to represent arbitrary parametric surfaces implicitly 2 represent arbitrary solids implicitly including sharp features using level sets and boolean operations 3 impose arbitrary dirichlet and neumann boundary conditions on the resulting implicitly defined boundaries the methods proposed do not require local refinement of the finite element mesh in regions of high curvature ensure the independence of the domain s volume on the mesh do not rely on boundary regularization and are well suited to methods based on fixed grids such as the extended finite element method xfem numerical examples are presented to demonstrate the robustness and effectiveness of the proposed approach and show that it is possible to achieve optimal convergence rates using a fully implicit representation of object boundaries this approach is one step in the desired direction of tying numerical simulations to computer aided design cad similarly to the isogeometric analysis paradigm

a fictitious domain method for dirichlet problem and applications abstract in this article we discuss the solution of the dirichlet problem for a class of elliptic operators by a lagrange multiplier fictitious domain method this approach allows the use of regular grids and therefore of fast specialized solvers for problems on complicated geometries the resulting saddle point system can be solved by an uzawa conjugate gradient algorithm in the case of two dimensional problems a quasi optimal preconditioner has been found by fourier analysis and numerical experiments confirm its nice scaling properties the resulting methodology is applied to a nonlinear time dependent problem namely the flow of a viscous plastic medium in a cylindrical pipe showing the potential of this methodology for some classes of nonlinear problems

quantitative analysis of qualitative data this paper presents an overview of an approach to the quantitative analysis of qualitative data with theoretical and methodological explanations of the two cornerstones of the approach alternating least squares and optimal scaling using these two principles my colleagues and i have extended a variety of analysis procedures originally proposed for quantitative interval or ratio data to qualitative nominal or ordinal data including additivity analysis and analysis of variance multiple and canonical regression principal components common factor and three mode factor analysis and multidimensional scaling the approach has two advantages a if a least squares procedure is known for analyzing quantitative data it can be extended to qualitative data and b the resulting algorithm will be convergent three completely worked through examples of the additivity analysis procedure and the steps involved in the regression procedures are presented

high order finite element methods for moving boundary problems with prescribed boundary evolution abstract we introduce a framework for the design of finite element methods for two dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy both in space and in time at the core of our approach is the use of a universal mesh a stationary background mesh containing the domain of interest for all times that adapts to the geometry of the immersed domain by adjusting a small number of mesh elements in the neighborhood of the moving boundary the resulting method maintains an exact representation of the prescribed moving boundary at the discrete level or an approximation of the appropriate order yet is immune to large distortions of the mesh under large deformations of the domain the framework is general making it possible to achieve any desired order of accuracy in space and time by selecting a preferred and suitable finite element space on the universal mesh for the problem at hand and a preferred and suitable time integrator for ordinary differential equations we illustrate our approach by constructing a particular class of methods and apply them to a prescribed boundary variant of the stefan problem we present numerical evidence for the order of accuracy of our schemes in one and two dimensions

the implicit closest point method for the numerical solution of partial differential equations on surfaces many applications in the natural and applied sciences require the solutions of partial differential equations pdes on surfaces or more general manifolds the closest point method is a simple and accurate embedding method for numerically approximating pdes on rather general smooth surfaces however the original formulation is designed to use explicit time stepping this may lead to a strict time step restriction for some important pdes such as those involving the laplace beltrami operator or higher order derivative operators to achieve improved stability and efficiency we introduce a new implicit closest point method for surface pdes the method allows for large stable time steps while retaining the principal benefits of the original method in particular it maintains the order of accuracy of the discretization of the underlying embedding pde it works on sharply defined bands without degrading the accuracy of the method and it applies to general smooth surfaces it also is very simple and may be applied to a rather general class of surface pdes convergence studies for the in surface heat equation and a fourth order biharmonic problem are given to illustrate the accuracy of the method we demonstrate the flexibility and generality of the method by treating flows involving diffusion reaction diffusion and fourth order spatial derivatives on a variety of interesting surfaces including surfaces of mixed codimension

testing the significance of the successive components in redundancy analysis in this paper we study the interrelationships between two sets of data measured on the same subjects via redundancy analysis we consider redundancy analysis from an inferential point of view under the hypothesis of multinormality tests of significance are obtained for each successive redundancy component so that only the significant factors are retained for prediction purposes an example illustrates the method

unimodal models to relate species to environment to assess the impact of environmental change on biological communities knowledge about species environment relationships is indispensable ecologists attempt to uncover the relationships between species and environment from data obtained from field surveys in the survey species are scored on their presence or their abundance at each of several sampling sites and environmental variables that ecologists believe to be important are measured the research that led to this thesis aimed to unravel the assumptions required for the application of statistical methods that are popular among ecologists to analyse such data from a statistical point of view species data are difficult to analyse there are many species involved 10 500 many species occur at a few sites only so the data contain numerous zeroes relations between species and environmental variables are not linear but unimodal a plant for example preferably grows under for that species optimal moisture conditions and is encountered less frequently at drier or wetter sites a mathematical model for a unimodal relationship is the gaussian response model standard statistical methods such as linear regression principal components analysis and canonical correlation analysis are often inappropriate for analysing species data because they are based on linear relationships one of the methods that ecologists use instead is correspondence analysis this thesis contributes to the understanding of the underlying response model with correspondence analysis species and sites are arranged to discover the structure in the data ordination and the arrangement is subsequently related to environmental variables it is an indirect method to detect relations between species and environment hence r h whittaker s term indirect gradient analysis correspondence analysis has been invented around 1935 but did not receive interest from ecologists before 1973 when m o hill derived the technique once more as the repeated application of weighted averaging a method that was familiar to ecologists ever since 1930 weighted averaging has the advantage of being simple to apply the method can be used for two different aims 1 to estimate the optimum of a species for an environmental variable and 2 to estimate the value of an environmental variable at a site from known optima of the species present calibration in chapter 2 estimating optima by weighted averaging is compared with the results of non linear regression on the basis of the gaussian response model under particular conditions both methods agree precisely in other cases weighted averaging gives a biased estimate of the optimum and non linear regression is the method to be preferred an additional advantage of non linear regression is that it can also be used to fit response models with more than one environmental variable in chapter 3 weighted averaging to estimate the value of an environmental variable is compared with calibration on the basis of the gaussian response model also in this context the techniques are sometimes equivalent chapter 4 deals with correspondence analysis it is shown that under particular conditions correspondence analysis approximates ordination on the basis of the gaussian response model which is computationally much more complicated to detect relations indirect methods have an important disadvantage the impact of some environmental variables on the species composition can be so large that the impact of other interesting environmental variables may fail to be detected this problem can be overcome by using non linear regression but with many species and environmental variables this is laborious in chapter 5 a simpler direct method is proposed canonical correspondence analysis in chapter 6 canonical correspondence analysis turns out to be a multivariate extension of weighted averaging the results can be displayed graphically in chapter 7 an extension with covariables is discussed which leads to partial canonical correspondence analysis chapter 7 also shows that gaussian models and hence canonical correspondence analysis are relevant to the analysis of contingency tables chapter 8 describes a study to estimate ecological amplitudes of plant species with respect to ellenberg s moisture scale from species data alone the question that is addressed as well is how consequent ellenberg s moisture indicator values are finally chapter 9 cross tabulates various gradient analysis techniques by the type of problem regression calibration ordination etc and the response model linear or unimodal furthermore improvements are proposed for detrended correspondence analysis a computer program named mom is written which can perform most of the methods discussed

two phase flows on interface refined grids modeled with vof staggered finite volumes and spline interpolants abstract a two phase 2d model that combines the volume of fluid vof method with implicit staggered finite volumes discretization of the navier stokes equation is presented staggered finite volumes are developed on the basis of nonconforming crouzeix raviart finite elements where all components of the velocity lie in the middle of the element edges and the pressure degrees of freedom are found in the centers of mass of the elements staggered finite volumes extend marker and cell mac regular staggered grids to unstructured mesh a linear saddle point problem resulting from either the discretization or the newton method is solved for all unknown pressures and velocities interface is represented with spline interpolants which follow the vof distribution adaptive mesh refinement is used to obtain a high level of uniform refining at the domain of dependence of the interface the aligned grid is obtained by irregular refining of the cells which are intersected by a curve the boundaries of its elements coincide with the slope segments going through the intersections of the curve with the underlying regular elements boundary the deformable computational grids are used only to discretize the navier stokes equation the advection of volume fractions is done on the advection mesh which corresponds to highest regular refining on the computational grid approximation of the surface tension on spline interpolants offers a straightforward way to describe correctly the pressure jumps on interface fitted staggered grids this allows deletion of the anomalous currents around a statical bubble and their effective reduction in real simulations on the aligned grid the continuity of the viscous stress is modeled exactly due to the finite volume approach using the proposed numerical techniques single bubble rise is analyzed

mesh deformation using the biharmonic operator the use of the biharmonic operator for deforming a mesh in an arbitrary lagrangian eulerian simulation is investigated the biharmonic operator has the advantage that two conditions can be specified on each boundary of the mesh this allows both the position and the normal mesh spacing along a boundary to be controlled which is important for two fluid interfaces and periodic boundaries at these boundaries we can simultaneously fix the position of the boundary and ensure that the normal mesh spacing is continuous across the boundary in addition results for deforming surfaces show that greater surface deformation can be tolerated when using biharmonic equations compared to approaches using second order partial differential equations a final advantage is that with the biharmonic operator the integrity of a grid in a moving boundary layer can be preserved as the boundary moves the main disadvantage of the approach is its increased computational expense

linear relations among k sets of variables a family of solutions for linear relations amongk sets of variables is proposed it is shown how these solutions apply fork 2 and how they can be generalized from there tok 3

prior elicitation variable selection and bayesian computation for logistic regression models summary bayesian selection of variables is often difficult to carry out because of the challenge in specifying prior distributions for the regression parameters for all possible models specifying a prior distribution on the model space and computations we address these three issues for the logistic regression model for the first we propose an informative prior distribution for variable selection several theoretical and computational properties of the prior are derived and illustrated with several examples for the second we propose a method for specifying an informative prior on the model space and for the third we propose novel methods for computing the marginal distribution of the data the new computational algorithms only require gibbs samples from the full model to facilitate the computation of the prior and posterior model probabilities for all possible models several properties of the algorithms are also derived the prior specification for the first challenge focuses on the observables in that the elicitation is based on a prior prediction yo for the response vector and a quantity ao quantifying the uncertainty in yo then yo and ao are used to specify a prior for the regression coefficients semi automatically examples using real data are given to demonstrate the methodology

unified analysis of finite element methods for problems with moving boundaries we present a unified analysis of finite element methods for problems with prescribed moving boundaries in particular we study an abstract parabolic problem posed on a moving domain with prescribed evolution discretized in space with a finite element space that is associated with a moving mesh that conforms to the domain at all times the moving mesh is assumed to evolve smoothly in time except perhaps at a finite number of remeshing times where the solution is transferred between finite element spaces via a projection a key result of our analysis is an abstract estimate for the l 2 norm of the error between the exact and semidiscrete solutions at a fixed positive time expressed in terms of the total variation in time of a quantity that measures the difference between the exact solution at time t and its elliptic projection onto the finite element space at time t specializing the abstract estimate to particular choices of the mesh motion strategy finite element space and projector leads to e

the numerical approximation of a delta function with application to level set methods it is shown that a discrete delta function can be constructed using a technique developed by anita mayo the fast solution of poisson s and the biharmonic equations on irregular regions siam j sci comput 21 1984 285 299 for the numerical solution of elliptic equations with discontinuous source terms this delta function is concentrated on the zero level set of a continuous function in two space dimensions this corresponds to a line and a surface in three space dimensions delta functions that are first and second order accurate are formulated in both two and three dimensions in terms of a level set function the numerical implementation of these delta functions achieves the expected order of accuracy

conditions under which canonical correlation and redundancy maximization produce identical results summary redundancy analysis was proposed as an alternative to canonical correlation van den wollenberg 1977 the following paper examines the conditions under which canonical correlation and redundancy analysis produce identical solutions it is shown that identical results are possible when all nonzero eigenvalues of the correlation matrix of the criterion variables are equal as a special case when there is only one canonical root or when all criterion variables are uncorrelated canonical correlation and redundancy analysis produce identical results

on structural shape optimization using an embedding domain discretization technique summary this contribution presents a novel approach to structural shape optimization that relies on an embedding domain discretization technique the evolving shape design is embedded within a uniform finite element background mesh which is then used for the solution of the physical state problem throughout the course of the optimization we consider a boundary tracking procedure based on adaptive mesh refinement to separate between interior elements exterior elements and elements intersected by the physical domain boundary a selective domain integration procedure is employed to account for the geometric mismatch between the uniform embedding domain discretization and the evolving structural component thereby we avoid the need to provide a finite element mesh that conforms to the structural component for every design iteration as it is the case for a standard lagrangian approach to structural shape optimization still we adopt an explicit shape parametrization that allows for a direct manipulation of boundary vertices for the design evolution process in order to avoid irregular and impracticable design updates we consider a geometric regularization technique to render feasible descent directions for the course of the optimization this article is protected by copyright all rights reserved

a stable generalized extended p hierarchical fem for three dimensional linear elastic fracture mechanics abstract in this paper the quadratic stable generalized finite element method sgfem proposed in sanchez rivadeneira and duarte 2019 is extended to 3 d fracture problems with non planar crack surfaces and curved crack fronts this sgfem is based on p hierarchical fem enrichments and its approximation space is the same as in its gfem counterpart singular enrichments are modified using a discontinuous finite element interpolant for conditioning control this leads with the proper choice of enrichments to stiffness matrices with a scaled condition number of o h 2 the same order as in the standard fem the robustness of the method with respect to the position of a crack relative to the mesh is demonstrated a scalar implementation of singular enrichments that can exactly reproduce the first term of the mode i ii and iii of the asymptotic expansion of the elasticity solution is presented improved approximations of signed distance functions based on integration sub elements are also presented convergence studies of a fully 3 d fracture problem with a non planar crack surface and a curved crack front are presented they show that the convergence rate of the proposed method on a sequence of uniform meshes is three times higher than quadratic quarter point finite elements

analysis of a method to parameterize planar curves immersed in triangulations we prove that a planar c 2 regular boundary gamma can always be parameterized with its closest point projection pi over a certain collection of edges gamma h in an ambient triangulation by making simple assumptions on the background mesh for gamma h we select the edges that have both vertices on one side of gamma and belong to a triangle that has a vertex on the other side by imposing restrictions on the size of triangles near the curve and by requesting that certain angles in the mesh be strictly acute we prove that pi gamma h rightarrow gamma is a homeomorphism and that it is c 1 on each edge in gamma h and we provide bounds for the jacobian of the parameterization the assumptions on the background mesh are both easy to satisfy in practice and conveniently verified in computer implementations the parameterization analyzed here was previously proposed by the authors and applied to the construction of high order curved finite elements on a class of planar piecewise c 2 c

heterogeneity in phase i clinical trials prior elicitation and computation using the continual reassessment method heterogeneity in a phase i clinical trial patient population may lead to distinctly different dose response relationships along covariate values for a given target probability of toxicity this implies different maximum tolerated doses mtds for each distinct subpopulation within the framework of o quigley pepe and fisher s 1990 continual reassessment method we propose the notion of average and patient specific mtds by augmenting the dose response model with other covariates to account for such differences a method to elicit prior distributions on the dose and other covariate parameters are proposed based on the predictive approach of ibrahim and laud 1994 laud and ibrahim 1995 and ibrahim ryan and chen 1998 this approach relies on prior predictions for the response vector y 0 and a quantity a 0 specifying uncertainty in y 0 then y 0 and a 0 are used to specify a prior for the regression coefficients in a semi automatic fashion the elicitation scheme for y 0 uses results from previous phase i cancer clinical trials the average and patient specific mtds and an elicitation method are demonstrated in logistic regression examples

solving dirichlet boundary value problems on curved domains by extensions from subdomains we present a technique for numerically solving dirichlet boundary value problems for second order elliptic equations on domains omega with curved boundaries this is achieved by using suitably defined extensions from polyhedral subdomains textsf d h the problem of dealing with curved boundaries is thus reduced to the evaluations of simple line integrals the technique is independent of the representation of the boundary of the space dimension and allows for the use of only polyhedral elements we apply this technique to the hybridizable discontinuous galerkin method and provide extensive numerical experiments showing that the convergence properties of the resulting method are the same as those for the case in which omega textsf d h whenever the distance of textsf d h to partial omega is of order h in particular we find that when using polynomial approximations of degree k on the polyhedral subdomains textsf d h both the scalar and vector unknowns converge with the optimal order of k 1 in the whole domain omega for k ge0 moreover we also find that for k ge1 both a postprocessing of the scalar unknown in the polyhedral subdomain textsf d h as well as its extension from it converge with order k 2 the extension also converges with order 2 for k 0

analysis of stiffness in the immersed boundary method and implications for time stepping schemes the immersed boundary method is known to exhibit a high degree of numerical stiffness associated with the interaction of immersed elastic fibres with the surrounding fluid we perform a linear analysis of the underlying equations of motion for immersed fibres and identify a discrete set of fibre modes which are associated solely with the presence of the fibre this work generalises our results in a previous paper 1995 siam j appl math 55 1577 by incorporating the effect of spreading the singular fibre force over a finite smoothing radius corresponding to the approximate delta function used in the immersed boundary method we investigate the stability of the fibre modes their stiffness and their dependence on the problem parameters focusing on the influence of smoothing we then extend the analytical results to include the effect of time discretisation and draw conclusions about the time step restrictions on various explicit schemes as well as the convergence rates for an iterative semi implicit method we draw comparisons with computations and show how the results can be applied to help in choosing alternate time stepping schemes that are specially tailored to handle the stiffness in immersed fibres in particular we present numerical results that show how fully explicit runge kutta schemes perform in comparison with the best of the semi implicit schemes currently in use

parameterization of planar curves immersed in triangulations with application to finite elements we construct a method for the parameterization of a class of planar piecewise c2 curves over a collection of edges in an ambient triangulation the map from the collection of edges to the curve is the closest point projection a distinguishing feature of the method is that edges in the ambient triangulation need not interpolate the curve we formulate conditions on the ambient triangulations so that the resulting parameterization over its selected edges is i bijective ii maps simple connected collection of edges to simple connected components of the curve and iii is c1 within each edge of the collection these properties of the parameterization make it particularly useful in the construction of high order finite element approximation spaces on planar curves immersed in triangulations we discuss this application and illustrate it with numerical examples the parameterization method applies to a large class of planar curves including most ones of interest in engineering and computer graphics applications and to a large family of triangulations including acute angled triangulations copyright 2011 john wiley sons ltd

the fixed mesh ale approach applied to solid mechanics and fluid structure interaction problems in this paper we propose a method to solve solid mechanics and fluid structure interaction problems using always a fixed background mesh for the spatial discretization the main feature of the method is that it properly accounts for the advection of information as the domain boundary evolves to achieve this we use an arbitrary lagrangian eulerian ale framework the distinctive characteristic being that at each time step results are projected onto a fixed background mesh for solid mechanics problems subject to large strains the fixed mesh fm ale method avoids the element stretching found in fully lagrangian approaches for fsi problems fm ale allows for the use of a single background mesh to solve both the fluid and the structure copyright 2009 john wiley sons ltd

a stable generalized extended fem with discontinuous interpolants for fracture mechanics abstract this paper presents numerical studies with three classes of quadratic generalized fem gfem approximations and shows that all of them lead to errors that are orders of magnitude smaller than the fem with quarter point elements provided that appropriate enrichments are selected however all of them lead to severely ill conditioned systems of equations with a condition number up to o h 10 in the case of the gfem based on a quadratic partition of unity enrichment modifications able to address the ill conditioning of quadratic gfem approximations while preserving their optimal convergence are proposed a robust enrichment modification strategy based on a discontinuous fe interpolant is proposed to control the conditioning of branch function enrichment the discontinuous fe interpolant is a generalization of the continuous one used with the stable gfem sgfem we show that sgfem spaces based on p hierarchical fem enrichments are the same as their gfem counterparts this guarantees that both gfem and sgfem spaces will lead to the same solution this is not the case for the other classes of second order spaces the robustness of the proposed approximation spaces with respect to the crack location in the mesh is also demonstrated

an extension of wollenberg s redundancy analysis an extension of wollenberg s redundancy analysis is proposed to derivey variates corresponding to the optimalx variates these variates are maximally correlated with the givenx variates and depending upon the standardization chosen they also have certain properties of orthogonality

a discontinuous galerkin based immersed boundary method a numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced the proposed method is conceptually simple and free of user defined parameters starting with a conforming finite element mesh the key ingredient is to switch those elements intersected by the dirichlet boundary to a discontinuous galerkin approximation and impose the dirichlet boundary conditions strongly by virtue of relaxing the continuity constraint at those elements boundary locking is avoided and optimal order convergence is achieved this is shown through numerical experiments in reaction diffusion problems copyright 2008 john wiley sons ltd