two step estimation for inhomogeneous spatial point processes summary the paper is concerned with parameter estimation for inhomogeneous spatial point processes with a regression model for the intensity function and tractable second order properties k function regression parameters are estimated by using a poisson likelihood score estimating function and in the second step minimum contrast estimation is applied for the residual clustering parameters asymptotic normality of parameter estimates is established under certain mixing conditions and we exemplify how the results may be applied in ecological studies of rainforests

solution of fluid structure interaction problems using a coupled finite element and variational boundary element technique this work is concerned with the numerical modeling of elasto acoustic problems applied to thin shells and specifically curved plates a finite element formulation of the elastic problem is coupled to a variational boundary element solution of the acoustic problem this solution to the acoustic problem proposed by mariem and hamdi j b mariem and m a hamdi int j num methods eng 24 1251 1267 1987 is implemented using high order isoparametric elements and attention is given to techniques of accelerating the numerical implementation for solutions at multiple frequencies these techniques include a reduction in the problem size through the use of symmetry and more importantly the interpolation of the fluid impedance matrix within the frequency regime the advantages in using this variational formulation are first the manner in which a highly singular integral operator is made amenable to numerical approximation second its application to nonclosed thin shells and third its numerical im

primal dual strategy for constrained optimal control problems an algorithm for efficient solution of control constrained optimal control problems is proposed and analyzed it is based on an active set strategy involving primal as well as dual variables for discretized problems sufficient conditions for convergence in finitely many iterations are given numerical examples are given and the role of the strict complementarity condition is discussed

second order optimality conditions for semilinear elliptic control problems with finitely many state constraints this paper deals with necessary and sufficient optimality conditions for control problems governed by semilinear elliptic partial differential equations with finitely many equality and inequality state constraints some recent results on this topic for optimal control problems based upon results for abstract optimization problems are compared with some new results using methods adapted to the control problems meanwhile the lagrangian formulation is followed to provide the optimality conditions in the first case the lagrangian and hamiltonian functions are used in the second statement finally we prove the equivalence of both formulations

going off grid computationally efficient inference for log gaussian cox processes this paper introduces a new method for performing computational inference on log gaussian cox processes the likelihood is approximated directly by making novel use of a continuously specified gaussian random field we show that for sufficiently smooth gaussian random field prior distributions the approximation can converge with arbitrarily high order while an approximation based on a counting process on a partition of the domain only achieves first order convergence the given results improve on the general theory of convergence of the stochastic partial differential equation models introduced by lindgren et al 2011 the new method is demonstrated on a standard point pattern data set and two interesting extensions to the classical log gaussian cox process framework are discussed the first extension considers variable sampling effort throughout the observation window and implements the method of chakraborty et al 2011 the second extension constructs a log gaussian cox process on the world s oceans the analysis is performed using integrated nested laplace approximation for fast approximate inference

an estimating function approach to inference for inhomogeneous neyman scott processes this article is concerned with inference for a certain class of inhomogeneous neyman scott point processes depending on spatial covariates regression parameter estimates obtained from a simple estimating function are shown to be asymptotically normal when the mother intensity for the neyman scott process tends to infinity clustering parameter estimates are obtained using minimum contrast estimation based on the k function the approach is motivated and illustrated by applications to point pattern data from a tropical rain forest plot

approximation of a nondifferentiable nonlinear problem related to mhd equilibria we present a simple method based on a variant of the implicit function theorem which leads to the existence of a part of a nontrivial solution branch of the nonlinear eigenvalue problem u u in u 1 on where is a two dimensional domain with boundary the advantage of this method is that we can apply it for analysing the approximation of the above problem by a finite element method the error analysis of the discrete problem appears immediately we give also an iteration scheme which allows to solve the approximate problem

smoothing methods and semismooth methods for nondifferentiable operator equations we consider superlinearly convergent analogues of newton methods for nondifferentiable operator equations in function spaces the superlinear convergence analysis of semismooth methods for nondifferentiable equations described by a locally lipschitzian operator in rn is based on rademacher s theorem which does not hold in function spaces we introduce a concept of slant differentiability and use it to study superlinear convergence of smoothing methods and semismooth methods in a unified framework we show that a function is slantly differentiable at a point if and only if it is lipschitz continuous at that point an application to the dirichlet problems for a simple class of nonsmooth elliptic partial differential equations is discussed

a partition of unity method for a class of fourth order elliptic variational inequalities abstract we consider a partition of unity method pum for a class of fourth order elliptic variational inequalities on convex polygonal domains that include obstacle problems of simply supported kirchhoff plates and elliptic distributed optimal control problems with pointwise state constraints as special cases by including singular functions in the local approximation spaces we are able to show that the partition of unity method converges optimally numerical results that corroborate the theoretical estimates are also presented

comment getting into space with a weight problem this article will focus its discussion on accounting for the complex design when analyzing survey data and on spatial modeling with respect to the former this article considers two approaches direct use of the weights and a model based approach using a spatial model to acknowledge clustering with respect to spatial modeling this article describes the stochastic partial differential equations spdes lindgren et al 2011 approach to modeling

an explicit link between gaussian fields and gaussian markov random fields the stochastic partial differential equation approach continuously indexed gaussian fields gfs are the most important ingredient in spatial statistical modelling and geostatistics the specification through the covariance function gives an intuitive interpretation of the field properties on the computational side gfs are hampered with the big n problem since the cost of factorizing dense matrices is cubic in the dimension although computational power today is at an all time high this fact seems still to be a computational bottleneck in many applications along with gfs there is the class of gaussian markov random fields gmrfs which are discretely indexed the markov property makes the precision matrix involved sparse which enables the use of numerical algorithms for sparse matrices that for fields in r 2 only use the square root of the time required by general algorithms the specification of a gmrf is through its full conditional distributions but its marginal properties are not transparent in such a parameterization we show that using an approximate stochastic weak solution to linear stochastic partial differential equations we can for some gfs in the matern class provide an explicit link for any triangulation of r d between gfs and gmrfs formulated as a basis function representation the consequence is that we can take the best from the two worlds and do the modelling by using gfs but do the computations by using gmrfs perhaps more importantly our approach generalizes to other covariance functions generated by spdes including oscillating and non stationary gfs as well as gfs on manifolds we illustrate our approach by analysing global temperature data with a non stationary model defined on a sphere less

exact bayesian inference in spatiotemporal cox processes driven by multivariate gaussian processes summary we present a novel inference methodology to perform bayesian inference for spatiotemporal cox processes where the intensity function depends on a multivariate gaussian process dynamic gaussian processes are introduced to enable evolution of the intensity function over discrete time the novelty of the method lies on the fact that no discretization error is involved despite the non tractability of the likelihood function and infinite dimensionality of the problem the method is based on a markov chain monte carlo algorithm that samples from the joint posterior distribution of the parameters and latent variables of the model a particular choice of the dominating measure to obtain the likelihood function is shown to be crucial to devise a valid markov chain monte carlo algorithm the models are defined in a general and flexible way but they are amenable to direct sampling from the relevant distributions because of careful characterization of its components the models also enable the inclusion of regression covariates and or temporal components to explain the variability of the intensity function these components may be subject to relevant interaction with space and or time real and simulated examples illustrate the methodology followed by concluding remarks

numerical methods for reaction diffusion problems with non differentiable kinetics we consider a class of steady state semilinear reaction diffusion problems with non differentiable kinetics the analytical properties of these problems have received considerable attention in the literature we take a first step in analyzing their numerical approximation we present a finite element method and establish error bounds which are optimal for some of the problems in addition we also discuss a finite difference approach numerical experiments for one and two dimensional problems are reported

boundary element solution of heat convection diffusion problems abstract a boundary element method is described in detail for the solution of two dimensional steady state convective heat diffusion problems in homogeneous and isotropic media with both linear and nonlinear boundary conditions through an exponential variable transformation the introduction of fundamental solutions and the use of green s theorem the problem is reduced to one involving values of temperature and or heat flux in the form of an integral only along the boundary the integral is solved numerically for three examples two of them have linear boundary conditions and their numerical results are compared with the corresponding analytical solutions the other has a nonlinear boundary condition due to heat radiation and an iterative procedure is applied to obtain the numerical solution the fictitious source formulation leading to the boundary element solution of the same problems is discussed as an alternative the extension of the method to formulate transient and or three dimensional convective heat diffusion problems is also described and the relevant fundamental solutions are given finally the exponential variable transformation is applied to construct a functional of variational principle which leads to developing a finite element formulation of the problems with a banded symmetric stiffness matrix

sparse approximate inference for spatio temporal point process models abstractspatio temporal log gaussian cox process models play a central role in the analysis of spatially distributed systems in several disciplines yet scalable inference remains computationally challenging both due to the high resolution modeling generally required and the analytically intractable likelihood function here we exploit the sparsity structure typical of spatially discretized log gaussian cox process models by using approximate message passing algorithms the proposed algorithms scale well with the state dimension and the length of the temporal horizon with moderate loss in distributional accuracy they hence provide a flexible and faster alternative to both nonlinear filtering smoothing type algorithms and to approaches that implement the laplace method or expectation propagation on block sparse latent gaussian models we infer the parameters of the latent gaussian model using a structured variational bayes approach we demonstrate the proposed framework on simulation studies with bo

a feasible active set method for strictly convex quadratic problems with simple bounds a primal dual active set method for quadratic problems with bound constraints is presented which extends the infeasible active set approach of kunisch and rendl siam j optim 14 2003 pp 35 52 based on a guess of the active set a primal dual pair x alpha is computed that satisfies stationarity and the complementary condition if x is not feasible the variables connected to the infeasibilities are added to the active set and a new primal dual pair x alpha is computed this process is iterated until a primal feasible solution is generated then a new active set is determined based on the feasibility information of the dual variable alpha strict convexity of the quadratic problem is sufficient for the algorithm to stop after a finite number of steps with an optimal solution computational experience indicates that this approach also performs well in practice

out of core solver for large multi zone boundary element matrices in this paper an out of core solver is developed for a three dimensional elastostatic boundary element program this program includes multi regions which enables a large model to be divided into a number of homogeneous sub models each with their own material properties the system matrix produced by multi regions is sparse blocked and unsymmetric in character and so reduces disc space and solution time the solver presented in this paper utilizes efficiently the structure of this matrix by holding only non zero parts of this matrix in a sequential unformatted direct access file reading in as much of the file as possible into the working space performing gauss elimination then writing part of the matrix back to file the maximum utilization of working space is particularly important on vector machines as vector activity is maximized whilst record read write is minimized the effect of multi regions on cpu is demonstrated on both the convex and cray machines

symmetric galerkin boundary formulations employing curved elements accounts of the symmetric galerkin approach to boundary element analysis bea have recently been published this paper attempts to add to the understanding of this method by addressing a series of fundamental issues associated with its potential computational efficiency a new symmetric galerkin theoretical formulation for both the harmonic heat conduction and the biharmonic elasticity problem that employs regularized singular and hypersingular boundary integral equations bies is presented the novel use of regularized bies in the galerkin context is shown to allow straightforward incorporation of curved isoparametric elements a symmetric reusable intrinsic sample point risp numerical integration algorithm is shown to produce a galerkin i e double integration strategy that is competitive with its counterpart i e singular integration procedure in the collocation bea approach when the time saved in the symmetric equation solution phase is also taken into account this new formulation is shown to be capable of employing hypersingular bies while obviating the requirement of c 1 continuity a fact that allows the employment of the popular continuous element technology the behavior of the symmetric galerkin bea method with regard to both direct and iterative equation solution operations is also addressed a series of example problems are presented to quantify the performance of this symmetric approach relative to the more conventional unsymmetric bea in terms of both accuracy and efficiency it is concluded that appropriate implementations of the symmetric galerkin approach to bea indeed have the potential to be competitive with if not superior to collocation based bea for large scale problems

fixed rank kriging for very large spatial data sets summary spatial statistics for very large spatial data sets is challenging the size of the data set n causes problems in computing optimal spatial predictors such as kriging since its computa tional cost is of order a73 in addition a large data set is often defined on a large spatial domain so the spatial process of interest typically exhibits non stationary behaviour over that domain a flexible family of non stationary covariance functions is defined by using a set of basis functions that is fixed in number which leads to a spatial prediction method that we call fixed rank kriging specifically fixed rank kriging is kriging within this class of non stationary covariance functions it relies on computational simplifications when n is very large for obtaining the spatial best linear unbiased predictor and its mean squared prediction error for a hidden spatial process a method based on minimizing a weighted frobenius norm yields best estimators of the covari ance function parameters which are then substituted into the fixed rank kriging equations the new methodology is applied to a very large data set of total column ozone data observed over the entire globe where n is of the order of hundreds of thousands

gaussian predictive process models for large spatial data sets with scientific data available at geocoded locations investigators are increasingly turning to spatial process models for carrying out statistical inference over the last decade hierarchical models implemented through markov chain monte carlo methods have become especially popular for spatial modelling given their flexibility and power to fit models that would be infeasible with classical methods as well as their avoidance of possibly inappropriate asymptotics however fitting hierarchical spatial models often involves expensive matrix decompositions whose computational complexity increases in cubic order with the number of spatial locations rendering such models infeasible for large spatial data sets this computational burden is exacerbated in multivariate settings with several spatially dependent response variables it is also aggravated when data are collected at frequent time points and spatiotemporal process models are used with regard to this challenge our contribution is to work with what we call predictive process models for spatial and spatiotemporal data every spatial or spatiotemporal process induces a predictive process model in fact arbitrarily many of them the latter models project process realizations of the former to a lower dimensional subspace thereby reducing the computational burden hence we achieve the flexibility to accommodate non stationary non gaussian possibly multivariate possibly spatiotemporal processes in the context of large data sets we discuss attractive theoretical properties of these predictive processes we also provide a computational template encompassing these diverse settings finally we illustrate the approach with simulated and real data sets

uncertainty quantification and weak approximation of an elliptic inverse problem we consider the inverse problem of determining the permeability from the pressure in a darcy model of flow in a porous medium mathematically the problem is to find the diffusion coefficient for a linear uniformly elliptic partial differential equation in divergence form in a bounded domain in dimension d le 3 from measurements of the solution in the interior we adopt a bayesian approach to the problem we place a prior random field measure on the log permeability specified through the karhunen loeve expansion of its draws we consider gaussian measures constructed this way and study the regularity of functions drawn from them we also study the lipschitz properties of the observation operator mapping the log permeability to the observations combining these regularity and continuity estimates we show that the posterior measure is well defined on a suitable banach space furthermore the posterior measure is shown to be lipschitz with respect to the data in the hellinger metric giving rise to a form of well posedness of the inverse problem determining the posterior measure given the data solves the problem of uncertainty quantification for this inverse problem in practice the posterior measure must be approximated in a finite dimensional space we quantify the errors incurred by employing a truncated karhunen loeve expansion to represent this meausure in particular we study weak convergence of a general class of locally lipschitz functions of the log permeability and apply this general theory to estimate errors in the posterior mean of the pressure and the pressure covariance under refinement of the finite dimensional karhunen loeve truncation

a galerkin symmetric boundary element method in elasticity formulation and implementation a symmetric boundary element method based on a weighted residual galerkin approach for elastoplastic analysis is revisited and its computer implementation for two dimensional homogeneous problems is described

first order conditions for nonsmooth discretized constrained optimal control problems this paper studies first order conditions karush kuhn tucker conditions for discretized optimal control problems with nonsmooth constraints we present a simple condition which can be used to verify that a local optimal point satisfies the first order conditions and that a point satisfying the first order conditions is a global or local optimal solution of the optimal control problem

numerical sensitivity analysis for the quantity of interest in pde constrained optimization in this paper we consider the efficient computation of derivatives of a functional the quantity of interest which depends on the solution of a pde constrained optimization problem with inequality constraints and which may be different from the cost functional the optimization problem is subject to perturbations in the data we derive conditions under with the quantity of interest possesses first and second order derivatives with respect to the perturbation parameters an algorithm for the efficient evaluation of these derivatives is developed with considerable savings over a direct approach especially in the case of high dimensional parameter spaces the computational cost is shown to be small compared to that of the overall optimization algorithm numerical experiments involving a parameter identification problem for navier stokes flow and an optimal control problem for a reaction diffusion system are presented which demonstrate the efficiency of the method

approximation of bayesian inverse problems for pdes inverse problems are often ill posed with solutions that depend sensitively on data in any numerical approach to the solution of such problems regularization of some form is needed to counteract the resulting instability this paper is based on an approach to regularization employing a bayesian formulation of the problem which leads to a notion of well posedness for inverse problems at the level of probability measures the stability which results from this well posedness may be used as the basis for quantifying the approximation in finite dimensional spaces of inverse problems for functions this paper contains a theory which utilizes this stability property to estimate the distance between the true and approximate posterior distributions in the hellinger metric in terms of error estimates for approximation of the underlying forward problem this is potentially useful as it allows for the transfer of estimates from the numerical analysis of forward problems into estimates for the solution of the related inverse problem it is noteworthy that when the prior is a gaussian random field model controlling differences in the hellinger metric leads to control on the differences between expected values of polynomially bounded functions and operators including the mean and covariance operator the ideas are applied to some non gaussian inverse problems where the goal is determination of the initial condition for the stokes or navier stokes equation from lagrangian and eulerian observations respectively

approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations summary structured additive regression models are perhaps the most commonly used class of models in statistical applications it includes among others generalized linear models generalized additive models smoothing spline models state space models semiparametric regression spatial and spatiotemporal models log gaussian cox processes and geostatistical and geoadditive models we consider approximate bayesian inference in a popular subset of structured additive regression models latent gaussian models where the latent field is gaussian controlled by a few hyperparameters and with non gaussian response variables the posterior marginals are not available in closed form owing to the non gaussian response variables for such models markov chain monte carlo methods can be implemented but they are not without problems in terms of both convergence and computational time in some practical applications the extent of these problems is such that markov chain monte carlo sampling is simply not an appropriate tool for routine analysis we show that by using an integrated nested laplace approximation and its simplified version we can directly compute very accurate approximations to the posterior marginals the main benefit of these approximations is computational where markov chain monte carlo algorithms need hours or days to run our approximations provide more precise estimates in seconds or minutes another advantage with our approach is its generality which makes it possible to perform bayesian analysis in an automatic streamlined way and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged

hypersingular integrals in boundary element fracture analysis a new general purpose boundary element method for domains with cracks has been recently developed this technique avoids the use of a multi domain decomposition by including an additional integral equation expressing the boundary condition on the crack the principal requirement of this technique is the analytic determination of certain hypersingular integrals of the green s function which arise from this equation in order to establish the applicability of this method for fracture these integrals are evaluated herein for the kelvin solution of the three dimensional navier equations of linear elasticity numerical results for fracture problems using the single domain boundary element analysis are also presented

a family of second order methods for convex ell _1 l1 regularized optimization this paper is concerned with the minimization of an objective that is the sum of a convex function f and an ell 1 l1 regularization term our interest is in active set methods that incorporate second order information about the function f to accelerate convergence we describe a semismooth newton framework that can be used to generate a variety of second order methods including block active set methods orthant based methods and a second order iterative soft thresholding method the paper proposes a new active set method that performs multiple changes in the active manifold estimate at every iteration and employs a mechanism for correcting these estimates when needed this corrective mechanism is also evaluated in an orthant based method numerical tests comparing the performance of three active set methods are presented

riemann manifold langevin and hamiltonian monte carlo methods the paper proposes metropolis adjusted langevin and hamiltonian monte carlo sampling methods defined on the riemann manifold to resolve the shortcomings of existing monte carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations the methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for metropolis hastings or indeed hamiltonian monte carlo and metropolis adjusted langevin algorithms this allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the markov chain the methodology proposed exploits the riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold providing highly efficient convergence and exploration of the target density the performance of these riemann manifold monte carlo methods is rigorously assessed by performing inference on logistic regression models log gaussian cox point processes stochastic volatility models and bayesian estimation of dynamic systems described by non linear differential equations substantial improvements in the time normalized effective sample size are reported when compared with alternative sampling approaches matlab code that is available from http www ucl ac uk statistics research rmhmc allows replication of all the results reported

efficient analytical integration of symmetric galerkin boundary integrals over curved elements elasticity formulation abstract substantial improvements are reported in the computational efficiency of galerkin boundary element analysis bea 1employing curved continuous boundary elements for elasticity problems a direct analytical treatment of the singular and hypersingular double integrations employing a limit to the boundary definition is adapted to gain computational economy symbolic manipulation has been employed to derive the analytical expressions for the singular contributions to these double integrals the analytical regularization procedure separates the potentially singular galerkin integrands into an essentially singular but simple part plus a regular remainder that can be integrated numerically the exact finite contributions from the simplified singular terms are then computed analytically it is shown that the key to containing the explosive growth in the length of the formulae associated with such a hybrid analytical numerical integration scheme is the strategic timing of when to take the limit to the boundary this regularization also isolates the contribution from the curvature of the boundary element thus facilitating enhanced computational efficiency in problems with many straight elements although the evaluation of the integrals of the kelvin fundamental solution essentially follows the procedures described earlier for the scalar laplace equation the analytical treatment is now more involved in terms of the complexity and number of terms present in each of these second rank tensor kernel functions the complete analytical formulation is explicitly provided in a series of tables example problems indicate that with these techniques galerkin symmetric bea can be more efficient than collocation for moderate or large scale problems

soap film smoothing summary conventional smoothing methods sometimes perform badly when used to smooth data over complex domains by smoothing inappropriately across boundary features such as peninsulas solutions to this smoothing problem tend to be computationally complex and not to provide model smooth functions which are appropriate for incorporating as components of other models such as generalized additive models or mixed additive models we propose a class of smoothers that are appropriate for smoothing over difficult regions of 2 which can be represented in terms of a low rank basis and one or two quadratic penalties the key features of these smoothers are that they do not smooth across boundary features that their representation in terms of a basis and penalties allows straightforward incorporation as components of generalized additive models mixed models and other non standard models that smoothness selection for these model components is straightforward to accomplish in a computationally efficient manner via generalized cross validation akaike s information criterion or restricted maximum likelihood for example and that their low rank means that their use is computationally efficient

a level set approach for the solution of a state constrained optimal control problem state constrained optimal control problems for linear elliptic partial differential equations are considered the corresponding first order optimality conditions in primal dual form are analyzed and linked to a free boundary problem resulting in a novel algorithmic approach with the boundary interface between the active and inactive sets as optimization variable the new algorithm is based on the level set methodology the speed function involved in the level set equation for propagating the interface is computed by utilizing techniques from shape optimization encouraging numerical results attained by the new algorithm are reported on

a variational approach to boundary element elastodynamic analysis and extension to multidomain problems abstract time dependent discontinuities of both tractions and displacements are considered on the boundary of a homogeneous linear elastic solid conceived as embedded in the elastic space the analysis of the dynamic response of the solid to external actions is formulated in the time domain by means of suitable integral representations of boundary displacements and of boundary tractions using time dependent fundamental solutions the integral operator generated is proven to be symmetric in both space and time with respect to a time convolutive bilinear form as a consequence the history of boundary tractions and displacements along any assigned time interval 0 is shown to be characterized by a variational theorem the variational formulation developed is generalized to zonewise homogeneous systems and to elastically constrained bodies the linear algebraic equations generated by boundary element modelling in space and time turn out to exhibit symmetry of the coefficient matrix

sgbem with lagrange multipliers applied to elastic domain decomposition problems with curved interfaces using non matching meshes an original approach to the solution of linear elastic domain decomposition problems by the symmetric galerkin boundary element method is developed the approach is based on searching for the saddle point of a new potential energy functional with lagrange multipliers the interfaces can be either straight or curved open or closed the two coupling conditions equilibrium and compatibility along an interface are fulfilled in a weak sense by means of lagrange multipliers interface displacements and tractions which enables non matching meshes to be used at both sides of interfaces between subdomains the accuracy and robustness of the method is tested by several numerical examples where the numerical results are compared with the analytical solution of the solved problems and the convergence rates of two error norms are evaluated for h refinements of matching and non matching boundary element meshes copyright 2010 john wiley sons ltd

a coupling of multi zone curved galerkin bem with finite elements for independently modelled sub domains with non matching nodes in elasticity when the different parts of a structure are modelled independently by bem or fem methods it is sometimes necessary to put the parts together without remeshing of the nodes along the part interfaces frequently the nodes do not match along the interface in this work the symmetric galerkin multi zone curved boundary element is a fully symmetric formulation and is the method used for the boundary element part for bem fem coupling it is then necessary to interpolate the tractions in between the non matching nodes for the fem part finally the coupling is achieved by transforming the finite element domains to equivalent boundary element domains in a block symmetric formulation this system is then coupled with a boundary element domain with non matching nodes in between copyright 2004 john wiley sons ltd

smoothing methods for nonsmooth nonconvex minimization we consider a class of smoothing methods for minimization problems where the feasible set is convex but the objective function is not convex not differentiable and perhaps not even locally lipschitz at the solutions such optimization problems arise from wide applications including image restoration signal reconstruction variable selection optimal control stochastic equilibrium and spherical approximations in this paper we focus on smoothing methods for solving such optimization problems which use the structure of the minimization problems and composition of smoothing functions for the plus function x many existing optimization algorithms and codes can be used in the inner iteration of the smoothing methods we present properties of the smoothing functions and the gradient consistency of subdifferential associated with a smoothing function moreover we describe how to update the smoothing parameter in the outer iteration of the smoothing methods to guarantee convergence of the smoothing methods to a stationary point of the original minimization problem

excursion and contour uncertainty regions for latent gaussian models in several areas of application ranging from brain imaging to astrophysics and geostatistics an important statistical problem is to find regions where the process studied exceeds a certain level estimating such regions so that the probability for exceeding the level in the entire set is equal to some predefined value is a difficult problem connected to the problem of multiple significance testing in this work a method for solving this problem as well as the related problem of finding credible regions for contour curves for latent gaussian models is proposed the method is based on using a parametric family for the excursion sets in combination with a sequential importance sampling method for estimating joint probabilities the accuracy of the method is investigated by using simulated data and an environmental application is presented

semismooth newton and augmented lagrangian methods for a simplified friction problem in this paper a simplified friction problem and iterative second order algorithms for its solution are analyzed in infinite dimensional function spaces motivated from the dual formulation a primal dual active set strategy and a semismooth newton method for a regularized problem as well as an augmented lagrangian method for the original problem are presented and their close relation is analyzed local as well as global convergence results are given by means of numerical tests we discuss among others convergence properties the dependence on the mesh and the role of the regularization and illustrate the efficiency of the proposed methodologies