spectral lagrangian methods for collisional models of non equilibrium statistical states we propose a new spectral lagrangian based deterministic solver for the non linear boltzmann transport equation bte in d dimensions for variable hard sphere vhs collision kernels with conservative or non conservative binary interactions the method is based on symmetries of the fourier transform of the collision integral where the complexity in its computation is reduced to a separate integral over the unit sphere s d 1 the conservation of moments is enforced by lagrangian constraints the resulting scheme implemented in free space is very versatile and adjusts in a very simple manner to several cases that involve energy dissipation due to local micro reversibility inelastic interactions or elastic models of slowing down process our simulations are benchmarked with available exact self similar solutions exact moment equations and analytical estimates for the homogeneous boltzmann equation both for elastic and inelastic vhs interactions benchmarking of the simulations involves the selection of a time self similar rescaling of the numerical distribution function which is performed using the continuous spectrum of the equation for maxwell molecules as studied first in bobylev et al a v bobylev c cercignani g toscani proof of an asymptotic property of self similar solutions of the boltzmann equation for granular materials journal of statistical physics 111 2003 403 417 and generalized to a wide range of related models in bobylev et al a v bobylev c cercignani i m gamba on the self similar asymptotics for generalized non linear kinetic maxwell models communication in mathematical physics in press url the method also produces accurate results in the case of inelastic diffusive boltzmann equations for hard spheres inelastic collisions under thermal bath where overpopulated non gaussian exponential tails have been conjectured in computations by stochastic methods t v noije m ernst velocity distributions in homogeneously cooling and heated granular fluids granular matter 1 57 1998 m h ernst r brito scaling solutions of inelastic boltzmann equations with over populated high energy tails journal of statistical physics 109 2002 407 432 s j moon m d shattuck j swift velocity distributions and correlations in homogeneously heated granular media physical review e 64 2001 031303 i m gamba s rjasanow w wagner direct simulation of the uniformly heated granular boltzmann equation mathematical and computer modelling 42 2005 683 700 and rigorously proven in gamba et al i m gamba v panferov c villani on the boltzmann equation for diffusively excited granular media communications in mathematical physics 246 2004 503 541 39 and a v bobylev i m gamba v panferov moment inequalities and high energy tails for boltzmann equations with inelastic interactions journal of statistical physics 116 2004 1651 1682

a multiscale fast semi lagrangian method for rarefied gas dynamics in this paper we consider the extension of the method developed in dimarco and loubere 2013 22 23 with the aim of facing the numerical resolution of multi scale problems arising in rarefied gas dynamics the scope of this work is to consider situations in which the whole domain does not demand the use of a kinetic model everywhere this is the case of many realistic applications some regions of the computational domain require a microscopic description given by a kinetic model while the rest of the domain can be described by a coarser model of fluid type our aim is to show how the kinetic scheme developed in the pre cited articles is perfectly suited for building domain decomposition strategies which make the method more attractive with respect to classical numerical techniques for kinetic equations and multi scale realistic problems several numerical evidences are provided in this work in the two dimensional and three dimensional settings to assess the efficiency of the domain decomposition scheme

towards an ultra efficient kinetic scheme part i basics on the bgk equation in this paper we present a new ultra efficient numerical method for solving kinetic equations in this preliminary work we present the scheme in the case of the bgk relaxation operator the scheme being based on a splitting technique between transport and collision can be easily extended to other collisional operators as the boltzmann collision integral or to other kinetic equations such as the vlasov equation the key idea on which the method relies is to solve the collision part on a grid and then to solve exactly the transport linear part by following the characteristics backward in time the main difference between the method proposed and semi lagrangian methods is that here we do not need to reconstruct the distribution function at each time step this allows to tremendously reduce the computational cost of the method and it permits for the first time to the author s knowledge to compute solutions of full six dimensional kinetic equations on a single processor laptop machine numerical examples up to the full three dimensional case are presented which validate the method and assess its efficiency in 1d 2d and 3d

the weighted particle method for convection diffusion equations ii the anisotropic case on etend la methode particulaire utilisee dans la partie i pour les equations de convection diffusion aux operateurs de diffusion anisotrope des conditions plus complexes que dans le cas isotrope sont exigees pour les fonctions de cutoff une analyse d erreur detaillee est effectuee

a feti dp formulation of three dimensional elasticity problems with mortar discretization in this paper a feti dp formulation for three dimensional elasticity on nonmatching grids over geometrically nonconforming subdomain partitions is considered to resolve the nonconformity of the finite elements a mortar matching condition is imposed on the subdomain interfaces faces a feti dp algorithm is then built by enforcing the mortar matching condition in dual and primal ways in order to make the feti dp algorithm scalable a set of primal constraints which include average and momentum constraints over interfaces are selected from the mortar matching condition a condition number bound c 1 log h h 2 is then proved for the feti dp formulation for the elasticity problems with discontinuous material parameters only some faces need to be chosen as primal faces on which the average and momentum constraints are imposed numerical results are included

a method of finite element tearing and interconnecting and its parallel solution algorithm a novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented the spatial domain is partitioned into a set of totally disconnected subdomains each assigned to an individual processor lagrange multipliers are introduced to enforce compatibility at the interface nodes in the static case each floating subdomain induces a local singularity that is resolved in two phases first the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution next the contributions of these modes are related to the lagrange multipliers through an orthogonality condition a parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and lagrange multipliers which completes the solution of the problem when implemented on local memory multiprocessors this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring it is also suitable for parallel vector computers with shared memory moreover unlike parallel direct solvers it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations

the mixed mortar finite element method for the incompressible stokes problem convergence analysis our purpose is to prove that the mortar element method using local compatible mixed finite elements provides optimal convergence results when applied to the incompressible stokes equations

conservative numerical schemes for the vlasov equation abstract a new scheme for solving the vlasov equation using a phase space grid is proposed the algorithm is based on the conservation of the flux of particles and the distribution function is reconstructed using various techniques that allow control of spurious oscillations or preservation of the positivity several numerical results are presented in two and four dimensional phase space and the scheme is compared with the semilagrangian method this method is almost as accurate as the semilagrangian one and the local reconstruction technique is well suited for parallel computation

on the precision of the conditionally autoregressive prior in spatial models summary bayesian analyses of spatial data often use a conditionally autoregressive car prior which can be written as the kernel of an improper density that depends on a precision parameter that is typically unknown to include in the bayesian analysis the kernel must be multiplied by k for some k this article rigorously derives k n i 2 for the l2 norm car prior also called a gaussian markov random field model and k n i for the l1 norm car prior where n is the number of regions and i the number of islands disconnected groups of regions in the spatial map since i 1 for a spatial structure defining a connected graph this supports knorr held s 2002 in highly structured stochastic systems 260 264 suggestion that k n 1 2 in the l2 norm case instead of the more common k n 2 we illustrate the practical significance of our results using a periodontal example

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

multiplier spaces for the mortar finite element method in three dimensions we consider the construction of multiplier spaces for use with the mortar finite element method in three spatial dimensions on globally or locally quasi uniform meshes a set of abstract conditions is given for the multiplier spaces which are sufficient to guarantee a stable and convergent mortar approximation three examples of multipliers satisfying these conditions are presented the first one is a dual basis example while the remaining two are based on finite volumes finally the results of computational examples illustrating the theory are reported

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

bayesian spatial modeling of disease risk in relation to multivariate environmental risk fields the relationship between exposure to environmental chemicals during pregnancy and early childhood development is an important issue which has a spatial risk component in this context we have examined mental retardation and developmental delay mrdd outcome measures for children in a medicaid population in south carolina and sampled measures of soil chemistry e g as hg etc on a network of sites which are misaligned to the outcome residential addresses during pregnancy the true chemical concentration at the residential addresses is not observed directly and must be interpolated from soil samples in this study we have developed a bayesian joint model which interpolates soil chemical fields and estimates the associated mrdd risk simultaneously having multiple spatial fields to interpolate we have considered a low rank kriging method for the interpolation which requires less computation than bayesian kriging we performed a sensitivity analysis for a bivariate smoothing changing the number of knots and the smoothing parameter these analyses show that a low rank kriging method can be used as an alternative to a full rank kriging reducing computational burden however the number of knots for the low rank kriging model need to be selected with caution as a bivariate surface estimation can be sensitive to the choice of the number of knots

empirical bayes estimates of age standardized relative risks for use in disease mapping there have been many attempts in recent years to map incidence and mortality from diseases such as cancer such maps usually display either relative rates in each district as measured by a standardized mortality ratio smr or some similar index or the statistical significance level for a test of the difference between the rates in that district and elsewhere neither of these approaches is fully satisfactory and we propose a new approach using empirical bayes estimation the resulting estimators represent a weighted compromise between the smr the overall mean relative rate and a local mean of the relative rate in nearby areas the compromise solution depends on the reliability of each individual smr and on estimates of the overall amount of dispersion of relative rates over different districts

schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions domain decomposition methods provide powerful preconditioners for the iterative solution of the large systems of algebraic equations that arise in finite element or finite difference approximations

spatial regression and spillover effects in cluster randomized trials with count outcomes this paper describes methodology for analyzing data from cluster randomized trials with count outcomes taking indirect effects as well spatial effects into account indirect effects are modeled using a novel application of a measure of depth within the intervention arm both direct and indirect effects can be estimated accurately even when the proposed model is misspecified we use spatial regression models with gaussian random effects where the individual outcomes have distributions overdispersed with respect to the poisson and the corresponding direct and indirect effects have a marginal interpretation to avoid spatial confounding we use orthogonal regression in which random effects represent spatial dependence using a homoscedastic and dimensionally reduced modification of the intrinsic conditional autoregression model we illustrate the methodology using spatial data from a pair matched cluster randomized trial against the dengue mosquito vector aedes aegypti done in trujillo venezuela

comparison of the shakhov kinetic equation and dsmc method as applied to space vehicle aerothermodynamics abstract the paper is devoted to the comparative study of shakhov model kinetic equation and direct simulation monte carlo dsmc solutions as applied to high speed flow of a monatomic gas over generic three dimensional space vehicle under angle of attack the corresponding calculations are carried out using nesvetay and smile software packages developed by the authors satisfactory agreement is shown for surface distribution of pressure friction and heat transfer coefficients despite very different modeling approaches and computational meshes employed it is thus shown that the use of the model kinetic equations with approximate collision integrals provides accurate results for high speed external monatomic gas flows over complex three dimensional geometries at acceptable computational cost

a consistency result for a discrete velocity model of the boltzmann equation in this paper we study the link between a certain class of discrete velocity models dvms and the boltzmann equation those models possess an infinite number of velocities laying on a regular grid of step h in r3 our aim is to prove that it is possible to construct models consistent with the boltzmann equation i e such that the discrete collision term can be seen as an approximation of the collision integral of the boltzmann equation

a preconditioner for the feti dp formulation with mortar methods in two dimensions in this paper we consider a dual primal feti feti dp method for elliptic problems on nonmatching grids the feti dp method is a domain decomposition method that uses lagrange multipliers to match solutions continuously across subdomain boundaries in the sense of dual primal variables we use the mortar matching condition as the continuity constraints for the feti dp formulation we construct a preconditioner for the feti dp operator and show that the condition number of the preconditioned feti dp operator is bounded by c max i 1 ldots n left 1 log left h i h i right right 2 where h i and h i are sizes of domain and mesh for each subdomain respectively and c is a constant independent of h i s and h i s we allow jumps of coefficients of elliptic problems across subdomain boundaries numerical results are included

partitioning degrees of freedom in hierarchical and other richly parameterized models hodges and sargent 2001 have developed a measure of a hierarchical model s complexity degrees of freedom df that is consistent with definitions for scatterplot smoothers is interpretable in terms of simple models and enables control of a fit s complexity by means of a prior distribution on complexity but although df describes the complexity of the whole fitted model in general it remains unclear how to allocate df to individual effects here we present a new definition of df for arbitrary normal error linear hierarchical models consistent with that of hodges and sargent that naturally partitions the n observations into df for individual effects and for error the new conception of an effect s df is the ratio of the effect s modeled variance matrix to the total variance matrix this provides a way to describe the sizes of different parts of a model e g spatial clustering vs heterogeneity to place df based priors on smoothing parameters and to describe how a smoothed effect competes with

effects of residual smoothing on the posterior of the fixed effects in disease mapping models disease mapping models for areal data often have fixed effects to measure the effect of spatially varying covariates and random effects with a conditionally autoregressive car prior to account for spatial clustering in such spatial regressions the objective may be to estimate the fixed effects while accounting for the spatial correlation but adding the car random effects can cause large changes in the posterior mean and variance of fixed effects compared to the nonspatial regression model this article explores the impact of adding spatial random effects on fixed effect estimates and posterior variance diagnostics are proposed to measure posterior variance inflation from collinearity between the fixed effect covariates and the car random effects and to measure each region s influence on the change in the fixed effect s estimates by adding the car random effects a new model that alleviates the collinearity between the fixed effect covariates and the car random effects is developed and extensions of these methods to point referenced data models are discussed

dual primal feti methods for linear elasticity dual primal feti methods are nonoverlapping domain decomposition methods where some of the continuity constraints across subdomain boundaries are required to hold throughout the iterations as in primal iterative substructuring methods while most of the constraints are enforced by lagrange multipliers as in one level feti methods these methods are used to solve the large algebraic systems of equations that arise in elliptic finite element problems the purpose of this article is to develop strategies for selecting these constraints which are enforced throughout the iterations such that good convergence bounds are obtained that are independent of even large changes in the stiffness of the subdomains across the interface between them the algorithms are described in terms of a change of basis that has proven to be quite robust in practice a theoretical analysis is provided for the case of linear elasticity and condition number bounds are established that are uniform with respect to arbitrarily large jumps in the young s modulus of the material and otherwise depend only polylogarithmically on the number of unknowns of a single subdomain the strategies have already proven quite successful in large scale implementations of these iterative methods 2006 wiley periodicals inc

spatial analyses of periodontal data using conditionally autoregressive priors having two classes of neighbor relations attachment loss the extent of a tooth s root in millimeters that is no longer attached to surrounding bone by periodontal ligament is often used to measure the current state of a patient s periodontal disease and monitor disease progression attachment loss data can be analyzed using a conditionally autoregressive car prior distribution that smooths fitted values toward neighboring values however it may be desirable to have more than one class of neighbor relation in the spatial structure so the different classes of neighbor relations can induce different degrees of smoothing for example we may wish to allow smoothing of neighbor pairs bridging the gap between teeth to differ from smoothing of pairs that do not bridge such gaps adequately modeling the spatial structure may improve the monitoring of periodontal disease progression this article develops a two neighbor relation car model to handle this situation and presents associated theory to help explain the sometimes unusual posterior distr

fluid solver independent hybrid methods for multiscale kinetic equations in some recent works g dimarco and l pareschi comm math sci 1 2006 pp 155 177 multiscale model simul 6 2008 pp 1169 1197 we developed a general framework for the construction of hybrid algorithms which are able to face efficiently the multiscale nature of some hyperbolic and kinetic problems here in contrast to previous methods we construct a method form fitting to any type of finite volume or finite difference scheme for the reduced equilibrium system thanks to the coupling of monte carlo techniques for the solution of the kinetic equations with macroscopic methods for the limiting fluid equations we show how it is possible to solve multiscale fluid dynamic phenomena faster than using traditional deterministic stochastic methods for the full kinetic equations in addition due to the hybrid nature of the schemes the numerical solution is affected by fewer fluctuations than are standard monte carlo schemes applications to the boltzmann bgk equation are presented to show the performance of the new methods in comparison with classical approaches used in the simulation of kinetic equations

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

conservative semi lagrangian schemes for vlasov equations conservative methods for the numerical solution of the vlasov equation are developed in the context of the one dimensional splitting in the case of constant advection these methods and the traditional semi lagrangian ones are proven to be equivalent but the conservative methods offer the possibility to add adequate filters in order to ensure the positivity in the non constant advection case they present an alternative to the traditional semi lagrangian schemes which can suffer from bad mass conservation in this time splitting setting

a simple derivation of deletion diagnostic results for the general linear model with correlated errors a general simple and intuitive derivation is provided for diagnostics associated with the deletion of arbitrary subsets for the linear model with general covariance structure these are seen to be most simply expressed even for the well studied case of independent and identically distributed data in terms of a residual known variously as the conditional residual the deletion prediction residual and the cross validation residual particularly simple specializations arise when the subsets are of size 1 and of size 2 but the method is easy to apply for all subsets and to conditional deletions

a low variance deviational simulation monte carlo for the boltzmann equation we present an efficient particle method for solving the boltzmann equation the key ingredients of this work are the variance reduction ideas presented in baker and hadjiconstantinou l l baker n g hadjiconstantinou variance reduction for monte carlo solutions of the boltzmann equation physics of fluids 17 2005 art no 051703 and a new collision integral formulation which allows the method to retain the algorithmic structure of direct simulation monte carlo dsmc and thus enjoy the numerous advantages associated with particle methods such as a physically intuitive formulation computational efficiency due to importance sampling low memory usage no discretization in velocity space and the ability to naturally and accurately capture discontinuities in the distribution function the variance reduction achieved by simulating only the deviation from equilibrium results in a significant computational efficiency advantage for low signal flows e g low flow speed compared to traditional particle methods such as dsmc in particular the resulting method can capture arbitrarily small deviations from equilibrium at a computational cost that is independent of the magnitude of this deviation the method is validated by comparing its predictions with dsmc solutions for spatially homogeneous and inhomogeneous problems

derivation of the lattice boltzmann method by means of the discrete ordinate method for the boltzmann equation in this note we show that the lattice boltzmann bgk method in common use can be derived from the boltzmann equation itself according to the present derivation it is apparent that the equation thus derived can be reduced to the navier stokes equation at a limit of small knudsen number since the equation thus derived is the boltzmann equation itself hence the present derivation method gives us a simple and flexible recipe to construct the lattice boltzmann method and makes it easy to construct an extended lattice boltzmann method in various ways 15 refs 1 fig

convergence of a weighted particle method for solving the boltzmann b g k equation we consider in this paper the numerical solution of the b g k model for the boltzmann equation the numerical method used here was introduced by mas gallic transport theory statist phys 16 1987 pp 885 887 using the results of perthame and pulvirenti arch rational mech anal 125 1993 pp 289 295 we first derive a uniqueness result for the b g k model and also regularity properties of the solution which are necessary for our analysis we then prove following mas gallic and poupaud transport theory statist phys 17 1988 pp 311 345 the convergence of the numerical approximation for the b g k model finally some numerical experiments are presented

the two level feti method for static and dynamic plate problems part i an optimal iterative solver for biharmonic systems abstract we present a lagrange multiplier based substructuring method for solving iteratively large scale systems of equations arising from the finite element discretization of static and dynamic plate bending problems the proposed method is essentially an extension of the feti domain decomposition algorithm to fourth order problems the main idea is to enforce exactly the continuity of the transverse displacement field at the substructure corners throughout the preconditioned conjugate projected gradient iterations this results in a two level feti substructuring method where the condition number of the preconditioned interface problem does not grow with the number of substructures and grows at most polylogarithmically with the number of elements per substructure these theoretically proven optimal convergence properties of the new feti method are numerically demonstrated for several finite element plate bending static and transient problems the two level iterative solver presented in this paper is applicable to a large family of biharmonic time independent as well as time dependent systems it is also extendible to shell problems

bayesian modeling of multivariate spatial binary data with applications to dental caries dental research gives rise to data with potentially complex correlation structure assessments of dental caries yield a binary outcome indicating the presence or absence of caries experience for each surface of each tooth in a subject s mouth in addition to this nesting caries outcome exhibit spatial structure among neighboring teeth we develop a bayesian multivariate model for spatial binary data using random effects autologistic regression that controls for the correlation within tooth surfaces and spatial correlation among neighboring teeth using a sample from a clinical study conducted at the medical university of south carolina we compare this autologistic model with covariates to alternative models to demonstrate the improvement in predictions and also to assess the effects of covariates on caries experience

prediction diagnostics for spatial linear models case deletion diagnostics are developed for detecting observations that are influential for prediction in linear models with a general covariance matrix a primary application of such results is in universal kriging and the related methodologies of ordinary kriging and intrinsic random function kriging in these applications the linear model and the covariance matrix of the data are determined by the locations at which observations are taken computational formulae are given that make the procedures feasible the diagnostics are illustrated using an example

time relaxed monte carlo methods for the boltzmann equation a new family of monte carlo schemes is introduced for the numerical solution of the boltzmann equation of rarefied gas dynamics the schemes are inspired by the wild sum expansion of the solution of the boltzmann equation for maxwellian molecules and consist of a novel time discretization of the equation in particular high order terms in the expansion are replaced by the equilibrium maxwellian distribution the two main features of the schemes are high order accuracy in time and asymptotic preservation the first property allows to recover accurate solutions with time steps larger than those required by direct simulation monte carlo dsmc while the latter guarantees that for the vanishing knudsen number the numerical solution relaxes to the local maxwellian conservation of mass momentum and energy are preserved by the scheme numerical results on several space homogeneous problems show the improvement of the new schemes over standard dsmc applications to a one dimensional shock wave problem are also presented

towards an ultra efficient kinetic scheme part ii in a recent paper we presented a new ultra efficient numerical method for solving kinetic equations of the boltzmann type dimarco and loubere 2013 17 the key idea on which the method relies is to solve the collision part on a grid and then to solve exactly the transport part by following the characteristics backward in time on the contrary to classical semi lagrangian methods one does not need to reconstruct the distribution function at each time step this allows to tremendously reduce the computational cost and to perform efficient numerical simulations of kinetic equations up to the six dimensional case without parallelization however the main drawback of the method developed was the loss of spatial accuracy close to the fluid limit in the present work we modify the scheme in such a way that it is able to preserve the high order spatial accuracy for extremely rarefied and fluid regimes in particular in the fluid limit the method automatically degenerates into a high order method for the compressible euler equations numerical examples are presented which validate the method show the higher accuracy with respect to the previous approach and measure its efficiency with respect to well known schemes direct simulation monte carlo finite volume muscl weno

feti dp a dual primal unified feti method part i a faster alternative to the two level feti method the feti method and its two level extension feti 2 are two numerically scalable domain decomposition methods with lagrange multipliers for the iterative solution of second order solid mechanics and fourth order beam plate and shell structural problems respectively the feti 2 method distinguishes itself from the basic or one level feti method by a second set of lagrange multipliers that are introduced at the subdomain cross points to enforce at each iteration the exact continuity of a subset of the displacement field at these specific locations in this paper we present a dual primal formulation of the feti 2 concept that eliminates the need for that second set of lagrange multipliers and unifies all previously developed one level and two level feti algorithms into a single dual primal feti dp method we show that this new feti dp method is numerically scalable for both second order and fourth order problems we also show that it is more robust and more computationally efficient than existing feti solvers particularly when the number of subdomains and or processors is very large copyright 2001 john wiley sons ltd

high order numerical methods for the space non homogeneous boltzmann equation in this paper we present accurate methods for the numerical solution of the boltzmann equation of rarefied gas the methods are based on a time splitting technique the transport is solved by a third order accurate in space positive and flux conservative pfc method the collision step is treated by a fourier approximation of the collision integral which guarantees spectral accuracy in velocity coupled with several high order integrators in time strang splitting is used to achieve second order accuracy in space and time several numerical tests illustrate the properties of the methods

preconditioners for the dual primal feti methods on nonmatching grids numerical study the feti dp method is a substructuring method that uses lagrange multipliers to match the continuity condition on the subdomain boundaries for the feti dp method on non matching grids two different formulations are known with respect to how to employ the mortar matching condition keeping step with the developments of the feti dp methods a variety of preconditioners for the feti dp operator have been developed however there has not been any numerical study for the feti dp method which compares those preconditioners on nonmatching grids while there have been a few papers for numerical study on the comparison of feti preconditioners therefore we present the numerical study of four different preconditioners for two dimensional elliptic problems the numerical results confirm the superiority of the preconditioner by kim and lee 1 for noncomparably nonmatching grids while the superiority of the preconditioner by dryja and widlund 2 is confirmed for matching grids and comparably nonmatching grids

case deletion diagnostics for mixed models mixed linear models arise in many areas of application standard estimation methods for mixed models are sensitive to bizarre observations such influential observations can completely distort an analysis and lead to inappropriate actions and conclusions we develop case deletion diagnostics for detecting influential observations in mixed linear models diagnostics for both fixed effects and variance components are proposed computational formulas are given that make the procedures feasible the methods are illustrated using examples

a neumann dirichlet preconditioner for a feti dp formulation of the two dimensional stokes problem with mortar methods a feti dp dual primal finite element tearing and interconnecting formulation for the two dimensional stokes problem with mortar methods is considered separate sets of unknowns are used for velocity on interfaces and the mortar constraints are enforced on the velocity unknowns by lagrange multipliers average constraints on edges are further introduced as primal constraints to solve the stokes problem correctly and to obtain a scalable feti dp algorithm a neumann dirichlet preconditioner is shown to give a condition number bound c maxi 1 n 1 log hi hi 2 where hi and hi are the subdomain size and the mesh size respectively and the constant c is independent of the mesh parameters hi and hi

iterative substructuring preconditioners for mortar element methods in two dimensions the mortar methods are based on domain decomposition and they allow for the coupling of different variational approximations in different subdomains the resulting methods are nonconforming but still yield optimal approximations in this paper we will discuss iterative substructuring algorithms for the algebraic systems arising from the discretization of symmetric second order elliptic equations in two dimensions both spectral and finite element methods for geometrically conforming as well as nonconforming domain decompositions are studied in each case we obtain a polylogarithmic bound on the condition number of the preconditioned matrix

restricted spatial regression methods implications for inference the issue of spatial confounding between the spatial random effect and the fixed effects in regression analyses has been identified as a concern in the statistical literature multiple authors have

dimension reduction and alleviation of confounding for spatial generalized linear mixed models summary non gaussian spatial data are very common in many disciplines for instance count data are common in disease mapping and binary data are common in ecology when fitting spatial regressions for such data one needs to account for dependence to ensure reliable inference for the regression coefficients the spatial generalized linear mixed model offers a very popular and flexible approach to modelling such data but this model suffers from two major shortcomings variance inflation due to spatial confounding and high dimensional spatial random effects that make fully bayesian inference for such models computationally challenging we propose a new parameterization of the spatial generalized linear mixed model that alleviates spatial confounding and speeds computation by greatly reducing the dimension of the spatial random effects we illustrate the application of our approach to simulated binary count and gaussian spatial data sets and to a large infant mortality data set

existence stability and convergence of solutions of discrete velocity models to the boltzmann equation we prove the convergence of finite difference approximations to solutions of the boltzmann equation an essential step is the proof of convergence of discrete approximations to the collision integral this proof relies on our previous results on the consistency of this approximation for the space homogeneous problem we prove strong convergence of our discrete approximation to the strong solution of the boltzmann equation in the space dependent case we prove weak convergence to diperna lions solutions

a fast solver for navier stokes equations in the lamina regime using mortar finite element and boundary element methods a multistep method is used to solve the navier stokes equations formulated with vorticity and stream function each time step is decomposed into three stages a convection step using the character

linear multistep methods for optimal control problems and applications to hyperbolic relaxation systems abstract we are interested in high order linear multistep schemes for time discretization of adjoint equations arising within optimal control problems first we consider optimal control problems for ordinary differential equations and show loss of accuracy for adams moulton and adams bashforth methods whereas bdf methods preserve high order accuracy subsequently we extend these results to semi lagrangian discretizations of hyperbolic relaxation systems computational results illustrate theoretical findings