adaptive unstructured volume remeshing ii application to two and three dimensional level set simulations of multiphase flow in part i adaptive unstructured volume remeshing i the method j comput phys in press we presented an adaptive remeshing algorithm that automatically adjusts the size of the elements of meshes of unstructured triangles 2d and unstructured tetrahedra 3d with time and position in the computational domain in order to efficiently resolve the relevant physical scales here we illustrate the performance of an implementation of the algorithm in finite element level set simulations of deformable droplet and fluid fluid interface interactions breakup and coalescence in multiphase flows the wide range of length scales characterizing the dynamics are accurately resolved as demonstrated by comparison to experiments and to theoretical and sharp interface boundary integral numerical results the computational cost is found to be competitive even with respect to boundary integral methods for the first time using an interface capturing level set method we successfully simulate the inertia driven impact and rebound of a liquid droplet from a liquid interface and find agreement with recent experimental results

a three field stabilized finite element method for fluid structure interaction elastic solid and rigid body limit summary we propose a full eulerian framework for solving fluid structure interaction fsi problems based on a unified formulation in which the fsis are modelled by introducing an extra stress in the momentum equation the obtained three field velocity pressure and stress system is solved using a stabilized finite element method the key feature of this unified formulation is the ability to describe different kind of interactions between the fluid and the structure which can be either elastic or a perfect rigid body without the need of treating this last case via penalization the level set method combined with a dynamic anisotropic mesh adaptation is used to track the fluid solid interface copyright 2015 john wiley sons ltd

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

3d tetrahedral unstructured and anisotropic mesh generation with adaptation to natural and multidomain metric in this paper we present a 3d tetrahedral unstructured and anisotropic mesh generator that is not based on the delaunay frontal or octree method instead it proceeds by local optimizations and uses an anisotropic shape criterion to fit a metric field then we introduce a new 3d metric field that tightens the mesh around interfaces when the calculation domain is divided in several subdomains and a 3d metric field that places enough elements through each subdomain thickness without introducing too many nodes in the other directions finally we show some applications for material forming geometries

a fixed mesh method for incompressible flow structure systems with finite solid deformations a fixed mesh algorithm is proposed for simulating flow structure interactions such as those occurring in biological systems in which both the fluid and solid are incompressible and the solid deformations are large several of the well known difficulties in simulating such flow structure interactions are avoided by formulating a single set of equations of motion on a fixed eulerian mesh the solid s deformation is tracked to compute elastic stresses by an overlapping lagrangian mesh in this way the flow structure interaction is formulated as a distributed body force and singular surface force acting on an otherwise purely fluid system these forces which depend on the solid elastic stress distribution are computed on the lagrangian mesh by a standard finite element method and then transferred to the fixed eulerian mesh where the joint momentum and continuity equations are solved by a finite difference method the constitutive model for the solid can be quite general for the force transfer standard immersed boundary and immersed interface methods can be used and are demonstrated we have also developed and demonstrated a new projection method that unifies the transfer of the surface and body forces in a way that exactly conserves momentum the interface is still effectively sharp for this approach the spatial convergence of the method is observed to be between first and second order as in most immersed boundary methods for membrane flows the algorithm is demonstrated by the simulations of an advected elastic disk a flexible leaflet in an oscillating flow and a model of a swimming jellyfish

the fixed mesh ale approach for the numerical approximation of flows in moving domains in this paper we propose a method to approximate flow problems in moving domains using always a given grid for the spatial discretization and therefore the formulation to be presented falls within the category of fixed grid methods even though the imposition of boundary conditions is a key ingredient that is very often used to classify the fixed grid method our approach can be applied together with any technique to impose approximately boundary conditions although we also describe the one we actually favor our main concern is to properly account for the advection of information as the domain boundary evolves to achieve this we use an arbitrary lagrangian eulerian framework the distinctive feature being that at each time step results are projected onto a fixed background mesh that is where the problem is actually solved

notes on bell sejnowski pdf matching neuron this article investigates the behavior of a single input single unit neuron model of the bell sejnowski class which learn through the maximum entropy principle in order to understand its probability density function matching ability

a second order accurate symmetric discretization of the poisson equation on irregular domains in this paper we consider the variable coefficient poisson equation with dirichlet boundary conditions on an irregular domain and show that one can obtain second order accuracy with a rather simple discretization moreover since our discretization matrix is symmetric it can be inverted rather quickly as opposed to the more complicated nonsymmetric discretization matrices found in other second order accurate discretizations of this problem multidimensional computational results are presented to demonstrate the second order accuracy of this numerical method in addition we use our approach to formulate a second order accurate symmetric implicit time discretization of the heat equation on irregular domains then we briefly consider stefan problems

multidimensional density shaping by sigmoids an estimate of the probability density function of a random vector is obtained by maximizing the output entropy of a feedforward network of sigmoidal units with respect to the input weights classification problems can be solved by selecting the class associated with the maximal estimated density newton s optimization method applied to the estimated density yields a recursive estimator for a random variable or a random sequence a constrained connectivity structure yields a linear estimator which is particularly suitable for real time prediction a gaussian nonlinearity yields a closed form solution for the network s parameters which may also be used for initializing the optimization algorithm when other nonlinearities are employed a triangular connectivity between the neurons and the input which is naturally suggested by the statistical setting reduces the number of parameters applications to classification and forecasting problems are demonstrated

on a multiscale approach to the transient stokes problem dynamic subscales and anisotropic space time discretization abstract in this article we analyze some residual based stabilization techniques for the transient stokes problem when considering anisotropic time space discretizations we define an anisotropic time space discretization as a family of time space partitions that does not satisfy the condition h 2 c t with c uniform with respect to h and t standard residual based stabilization techniques are motivated by a multiscale approach approximating the effect of the subscales onto the large scales one of the approximations is to consider the subscales quasi static neglecting their time derivative it is well known that these techniques are unstable for anisotropic time space discretizations we show that the use of dynamic subscales where the subscales time derivatives are not neglected solves the problem and prove optimal convergence and stability results that are valid for anisotropic time space discretizations also the improvements related to the use of orthogonal subscales are addressed

mixed stabilized finite element methods in nonlinear solid mechanics part i formulation abstract this paper exploits the concept of stabilized finite element methods to formulate stable mixed stress displacement and strain displacement finite elements for the solution of nonlinear solid mechanics problems the different assumptions and approximations used to derive the methods are exposed the proposed procedure is very general applicable to 2d and 3d problems implementation and computational aspects are also discussed showing that a robust application of the proposed formulation is feasible numerical examples show that the results obtained compare favorably with those obtained with the corresponding irreducible formulation

using a signed distance function for the simulation of metal forming processes formulation of the contact condition and mesh adaptation from a lagrangian approach to an eulerian approach this paper proposes to use the metric properties of the distance function between two bodies in contact or gap function in simulations involving contact problems first the normal vectors which are involved in the formulation of the contact condition are defined through the gradient of this distance function this definition avoids to deal with the numerical penetration parameter which is generally introduced otherwise furthermore it allows the contact problem to be extended in a simple way to an eulerian formulation second this paper investigates two mesh adaptation strategies based on the properties of the distance function the first strategy consists in building a size map according to the values of this function in order to refine locally the mesh and consequently to improve the description of the contact surface the second strategy consists in adapting locally the mesh to the geometry of the contact surface this anisotropic adaptation is performed by constructing a metric map that allows the mesh size to be imposed in the direction of the distance function gradient a lot of elements are saved when compared with the isotropic case throughout this paper many numerical simulations are presented in the context of the forging process the deformable material is pressed between two rigid tools furthermore the algorithm used to calculate the signed distance to a surface mesh is detailed in appendix of this paper

immersed smoothed finite element method for two dimensional fluid structure interaction problems summary a novel method called immersed smoothed fem using three node triangular element is proposed for two dimensional fluid structure interaction fsi problems with largely deformable nonlinear solids placed within incompressible viscous fluid the fluid flows are solved using the semi implicit characteristic based split method smoothed fems are employed to calculate the transient responses of solids based on explicit time integration the fictitious fluid with two assumptions is introduced to achieve the continuous form of the fsi conditions the discrete formulations to calculate the fsi forces are obtained in terms of the characteristic based split scheme and the algorithm based on a set of fictitious fluid mesh is proposed for evaluating the fsi force exerted on the solid the accuracy stability and convergence properties of immersed smoothed fem are verified by numerical examples investigations on the mesh size ratio indicate that the stability is fairly independent of the wide range of the mesh size ratio no additional volume correction is required to satisfy the incompressible constraints copyright 2012 john wiley sons ltd

a lagrangian particle level set method we present a novel particle level set method for capturing interfaces the level set equation is solved in a lagrangian frame using particles that carry the level set information a key aspect of the method involves a consistent remeshing procedure for the regularization of the particle locations when the particle map gets distorted by the advection field the lagrangian description of the level set method is inherently adaptive and exact in the case of solid body motions the efficiency and accuracy of the method is demonstrated in several benchmark problems in two and three dimensions involving pure advection and curvature induced motion of the interface the simplicity of the particle description is shown to be well suited for real time simulations of surfaces involving cutting and reconnection as in virtual surgery environments

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

robust imposition of dirichlet boundary conditions on embedded surfaces summary we develop both stable and stabilized methods for imposing dirichlet constraints on embedded three dimensional surfaces in finite elements the stable method makes use of the vital vertex algorithm of bechet et al bechet et al 2009 int j numer meth engng 78 8 931 954 albeit with a modified set of discontinuous basis functions for the lagrange multiplier field on the embedded surface the stabilized method extends the work of dolbow and harari dolbow and harari 2009 int j numer meth engng 78 2 229 252 to three dimensional surfaces algorithmic and implementational details of both methods are provided several three dimensional benchmark problems are studied to compare and contrast the accuracy of the two approaches the results indicate that both methods yield optimal rates of convergence in various quantities of interest with the primary differences being in the surface flux the utility of the domain integral for extracting accurate surface fluxes is demonstrated for both techniques published by john wiley sons ltd copyright c 2000 john wiley sons ltd

eulerian formulation using stabilized finite element method for large deformation solid dynamics this paper describes an eulerian formulation for large deformation solid dynamics in the present eulerian approach an advective equation is solved using the stream upwind petrov galerkin finite element method the eulerian finite element method is applied to path dependent solid analyses such as impact bar and ductile necking problems these computational results using the eulerian finite element method are compared with the results obtained from using the lagrangian finite element method and an eulerian formulation based on a finite difference method copyright 2007 john wiley sons ltd

fluid structure interaction with large structural displacements the calculation of viscous flows inside deformable structures faces major difficulties when enforcing the kinematic compatibility at the fluid structure interface and updating the geometry of the domain this paper proposes to overcome these problems by considering the fluid and the structure as a unique continuous medium to be studied in a fixed reference configuration the resulting problem is then split into a fluid and a structural part through an additive decomposition of the space of kinematically admissible test functions this approach treats the structure in a fully lagrangian way and uses an associated arbitrary lagrangian eulerian ale formulation for the fluid such a strategy has three advantages which are detailed in the present paper it can be discretised in time by implicit stable energy conserving time integration schemes and solved by simple iterative uncoupled algorithms the fluid and the structural problems can be approximated by independent finite element spaces the most recent geometrically exact nonlinear shell models can be used for the structures the full strategy has been implemented into an industrial cfd code results obtained in the simulation of industrial hydraulic shock absorbers are presented at the end of the paper

a computational approach to handle complex microstructure geometries in multiscale analysis of components there is usually a need to solve microstructures with complex geometries in this paper we use the extended finite element method x fem to solve scales involving complex geometries the x fem allows one to use meshes not necessarily matching the physical surface of the problem while retaining the accuracy of the classical finite element approach for material interfaces this is achieved by introducing a new enrichment strategy although the mesh does not need to conform to the physical surfaces it needs to be fine enough to capture the geometry of these surfaces a simple algorithm is described to adaptively refine the mesh to meet this geometrical requirement numerical experiments on the periodic homogenization of two phase complex cells demonstrate the accuracy and simplicity of the x fem c 2003 elsevier b v all rights reserved

residual free bubbles for embedded dirichlet problems abstract we examine a stabilized method employing residual free bubbles for enforcing dirichlet constraints on embedded finite element interfaces in particular we focus attention on problems where the underlying mesh is not explicitly fitted to the geometry of the interface the residual free bubble problem is derived for a simple case and extensions are discussed we show that under certain conditions stabilization only requires knowledge of the residual free bubble on the interface we then examine methods to approximate the residual free bubble a series of benchmark tests are used to demonstrate the accuracy and robustness of the method comparisons are made to nitsche s method employing an eigenvalue estimate for the global stability parameter particular emphasis is placed on the accuracy of flux evaluations on the interface finally we employ the method to simulate an evolving interface problem motivated by resin transfer molding

a fully eulerian formulation for fluid structure interaction problems in this work we present a fully eulerian framework for fluid structure interaction fsi problems coupling the incompressible navier stokes equations with a hyperelastic solid the fully eulerian framework is a monolithic implicit variational formulation for the coupled problem in contrast to the well established arbitrary lagrangian eulerian ale coordinates the fully eulerian framework formulates both subproblems fluid and solid in eulerian coordinates this concept circumvents various difficulties connected to ale coordinates since no artificial domain mapping is used the formulation is an interface capturing method and uses an extension of the solid s deformation the initial point set to detect the interface location by construction very large deformation as well as topology changes like contact of the solid to the domain boundary or other solid parts are possible

fully eulerian fluid structure interaction for time dependent problems abstract a fully eulerian framework formulation for solving time dependent fluid structure interaction problems is proposed in this work although some preliminary work on this approach exists for stationary configurations it remains to validate nonstationary processes the formulation is stated in an implicit monolithic frame of reference a finite difference scheme is used for temporal discretization whereas the spatial discretization is based on a galerkin finite element scheme the nonlinear problem is solved with a newton method and with analytical evaluation of the jacobian matrix in contrast to interface tracking methods for example the arbitrary lagrangian eulerian approach the interface must be captured which is similar to the level set method consequently the interface is allowed to intersect mesh cells which is a crucial difficulty of this method where appropriate treatment must be suggested the proposed formulation is substantiated by three numerical tests in which the performance of fully eulerian fluid structure interaction is demonstrated

modeling holes and inclusions by level sets in the extended finite element method a methodology to model arbitrary holes and material interfaces inclusions without meshing the internal boundaries is proposed the numerical method couples the level set method s osher j a sethian j comput phys 79 1 1988 12 to the extended finite element method x fem n moes j dolbow t belytschko int j numer methods engrg 46 1 1999 131 in the x fem the finite element approximation is enriched by additional functions through the notion of partition of unity the level set method is used for representing the location of holes and material interfaces and in addition the level set function is used to develop the local enrichment for material interfaces numerical examples in two dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique

time dependent subscales in the stabilized finite element approximation of incompressible flow problems abstract in this paper we analyze a stabilized finite element approximation for the incompressible navier stokes equations based on the subgrid scale concept the essential point is that we explore the properties of the discrete formulation that results allowing the subgrid scales to depend on time this apparently natural idea avoids several inconsistencies of previous formulations and also opens the door to generalizations

closed form expressions of some stochastic adapting equations for nonlinear adaptive activation function neurons in recent work we introduced nonlinear adaptive activation function fan artificial neuron models which learn their activation functions in an unsupervised way by information theoretic adapting rules we also applied networks of these neurons to some blind signal processing problems such as independent component analysis and blind deconvolution the aim of this letter is to study some fundamental aspects of fan units learning by investigating the properties of the associated learning differential equation systems

3d transient fixed point mesh adaptation for time dependent problems application to cfd simulations this paper deals with the adaptation of unstructured meshes in three dimensions for transient problems with an emphasis on cfd simulations the classical mesh adaptation scheme appears inappropriate when dealing with such problems hence another approach based on a new mesh adaptation algorithm and a metric intersection in time procedure suitable for capturing and track such phenomena is proposed more precisely the classical approach is generalized by inserting a new specific loop in the main adaptation loop in order to solve a transient fixed point problem for the mesh solution couple to perform the anisotropic metric intersection operation we apply the simultaneous reduction of the corresponding quadratic form regarding the adaptation scheme an anisotropic geometric error estimate based on a bound of the interpolation error is proposed the resulting computational metric is then defined using the hessian of the solution the mesh adaptation stage surface and volume is based on the generation by global remeshing of a unit mesh with respect to the prescribed metric a 2d model problem is used to illustrate the difficulties encountered then 2d and 3d complexes and representative examples are presented to demonstrate the efficiency of this method

a finite strain eulerian formulation for compressible and nearly incompressible hyperelasticity using high order b spline finite elements summary we present a numerical formulation aimed at modeling the nonlinear response of elastic materials using large deformation continuum mechanics in three dimensions this finite element formulation is based on the eulerian description of motion and the transport of the deformation gradient when modeling a nearly incompressible solid the transport of the deformation gradient is decomposed into its isochoric part and the jacobian determinant as independent fields a homogeneous isotropic hyperelastic solid is assumed and b splines based finite elements are used for the spatial discretization a variational multiscale residual based approach is employed to stabilize the transport equations the performance of the scheme is explored for both compressible and nearly incompressible applications the numerical results are in good agreement with theory illustrating the viability of the computational scheme copyright 2011 john wiley sons ltd

stabilized finite element method for incompressible flows with high reynolds number in the following paper we discuss the exhaustive use and implementation of stabilization finite element methods for the resolution of the 3d time dependent incompressible navier stokes equations the proposed method starts by the use of a finite element variational multiscale vms method which consists in here of a decomposition for both the velocity and the pressure fields into coarse resolved scales and fine unresolved scales this choice of decomposition is shown to be favorable for simulating flows at high reynolds number we explore the behaviour and accuracy of the proposed approximation on three test cases first the lid driven square cavity at reynolds number up to 50 000 is compared with the highly resolved numerical simulations and second the lid driven cubic cavity up to re 12 000 is compared with the experimental data finally we study the flow over a 2d backward facing step at re 42 000 results show that the present implementation is able to exhibit good stability and accuracy properties for high reynolds number flows with unstructured meshes

anisotropic mesh adaptation with optimal convergence for finite elements using embedded geometries this paper presents a numerical study of a recent technique that consists in modeling embedded geometries by a level set representation in combination with local anisotropic mesh refinement the local anisotropic mesh procedure is suitable for various orders p of finite element approximations this method proves beneficial in simulations involving complex geometries as it suppresses the need for the tedious process of body fitted mesh generation without altering the finite element formulation nor the prescription of boundary conditions the first part of the study deals with a simple laplace problem featuring a planar interface on which a dirichlet boundary condition is imposed it is shown that the appropriate amount of local isotropic refinement yields the optimal convergence rate for various finite element orders p unlike uniform refinement anisotropic refinement further ensures geometric convergence and limits the growth of the number of unknowns then we explain how to use metric based anisotropic adaptation to obtain nearly body fitted meshes with arbitrary geometries the optimal rate of convergence both for the solution and the geometry is demonstrated on 2d and 3d academic laplace problems involving curved boundaries finally applications in the field of fluid dynamics and material science are presented the results for these simulations successfully converge towards data from the literature analytical solutions or values obtained with body fitted meshes

a fast iterative algorithm for elliptic interface problems a fast second order accurate iterative method is proposed for the elliptic equation grad cdot beta x y grad u f x y in a rectangular region omega in two space dimensions we assume that there is an irregular interface across which the coefficient beta the solution u and its derivatives and or the source term f may have jumps we are especially interested in the cases where the coefficients beta are piecewise constant and the jump in beta is large the interface may or may not align with an underlying cartesian grid the idea in our approach is to precondition the differential equation before applying the immersed interface method proposed by leveque and li siam j numer anal 4 1994 pp 1019 1044 in order to take advantage of fast poisson solvers on a rectangular region an intermediate unknown function the jump in the normal derivative across the interface is introduced our discretization is equivalent to using a second order difference scheme for a corresponding poisson equation in the region and a second order discretization for a neumann like interface condition thus second order accuracy is guaranteed a gmres iteration is employed to solve the schur complement system derived from the discretization a new weighted least squares method is also proposed to approximate interface quantities from a grid function numerical experiments are provided and analyzed the number of iterations in solving the schur complement system appears to be independent of both the jump in the coefficient and the mesh size

a bayesian analysis of simultaneous equation models by combining recursive analytical and numerical approaches abstract inference on simultaneous equation models using a bayesian approach is still far from a routine procedure serious numerical problems may occur in most practical situations in this paper a unifying framework is proposed using recent analytical see steel 1988 and well documented poly t based methods in order to reduce the dimension of the final monte carlo integration different integration sequences are examined and the implications for various model and prior assumptions are tabulated an application to klein s model i clearly illustrates the computational feasibility and numerical stability of the hybrid method proposed

stabilized continuous and discontinuous galerkin techniques for darcy flow we design stabilized methods based on the variational multiscale decomposition of darcy s problem a model for the subscales is designed by using a heuristic fourier analysis this model involves a characteristic length scale that can go from the element size to the diameter of the domain leading to stabilized methods with different stability and convergence properties these sta bilized methods mimic the different possible functional settings of the continuous problem the optimal method depends on the velocity and pressure approximation order they also involve a subgrid projector that can be either the identity when applied to finite element residuals or can have an image orthogonal to the finite element space in pa rticular we have designed a new stabilized method that allows the use of piecewise constant pressures we consider a general setting in which velocity and pressure can be approximated by either continuous or discontinuous approximations all these methods have been analyzed proving stability and convergence results in some cases duality arguments have been used to obtain error bounds in the l 2 norm

bayesian estimation of common parameters from multiresponse data with missing observations new relations are derived for bayesian estimation of parameters in nonlinear multiresponse models modal and interval estimates are provided for the parameter vector of a multiresponse expectation model and for the covariance matrix of a multivariate normal error distribution incomplete observation sets are handled directly two chemical examples are analyzed

stabilized finite element approximation of transient incompressible flows using orthogonal subscales abstract in this paper we present a stabilized finite element method to solve the transient navier stokes equations based on the decomposition of the unknowns into resolvable and subgrid scales the latter are approximately accounted for so as to end up with a stable finite element problem which in particular allows to deal with convection dominated flows and the use of equal velocity pressure interpolations three main issues are addressed the first is a method to estimate the behavior of the stabilization parameters based on a fourier analysis of the problem for the subscales secondly the way to deal with transient problems discretized using a finite difference scheme is discussed finally the treatment of the nonlinear term is also analyzed a very important feature of this work is that the subgrid scales are taken as orthogonal to the finite element space in the transient case this simplifies considerably the numerical scheme

multiresponse estimation with special application to linear systems of differential equations we present a multiresponse estimation procedure for parameters of systems described by as the procedure features a generalized gauss newton algorithm for optimizing the determinant criterion efficient evaluation of the expectation function and its derivatives directly from the reaction network or compartment diagram automatic determination of starting values and eficient computational procedures for handling linear constraints on the responses

an asymptotic property of model selection criteria probability models are estimated by use of penalized log likelihood criteria related to akaike 1973 information criterion aic and minimum description length mdl the accuracies of the density estimators are shown to be related to the tradeoff between three terms the accuracy of approximation the model dimension and the descriptive complexity of the model classes the asymptotic risk is determined under conditions on the penalty term and is shown to be minimax optimal for some cases as an application we show that the optimal rate of convergence is simultaneously achieved for log densities in sobolev spaces w sub 2 sup s u without knowing the smoothness parameter s and norm parameter u in advance applications to neural network models and sparse density function estimation are also provided

an adaptive level set method with enhanced volume conservation for simulations in multiphase domains while implicit interface methods such as the level set method have the main advantage of avoiding explicit interface meshing they raise important volume conservation issues that can be handled by local mesh refinement this refinement is then performed multiple times throughout the simulation in order to follow the interface nevertheless mesh adaptation itself is a process that generates a volume conservation problem due to field transfer in this work multiphase simulations are addressed using a new lagrangian level set method that relies on an automatic mesh motion and topological mesh adaptation procedure remeshing is hence activated only when element flipping is detected this procedure is extended in order to take into account local phase distributions during remeshing so that volume conservation can be controlled 2 this method relies on a robust level set reinitialization technique also developed in this work 1 this constraint on volume conservation is automatically relaxed when necessary in order to take into account complex topological events such as apperance disappearance and coalescence of objects during the simulation numerical results show that the proposed method is competitive in terms of cost and accuracy with respect to standard eulerian and lagrangian level set methods while still enabling large displacements and deformations some examples concerning the modeling of evolutive microstructures will be detailed references 1 m shakoor b scholtes p o bouchard and m bernacki an efficient and parallel level set reinitialization method application to micromechanics and microstructural evolutions applied mathematical modelling 39 23 24 7291 7302 2015 2 m shakoor p o bouchard and m bernacki an adaptive level set method with enhanced volume conservation for simulations in multiphase domains international journal for numerical methods in engineering volume 109 issue 4 27 january 2017 555 576

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

multiresponse parameter estimation with a new and noninformative prior summary a noninformative prior distribution for the covariance matrix of a normal distribution is derived from a data relocated likelihood function this new prior distribution also follows from jeffreys s rule resulting modifications of current formulae for multiresponse parameter estimation are summarized

an information maximization approach to blind separation and blind deconvolution we derive a new self organizing learning algorithm that maximizes the information transferred in a network of nonlinear units the algorithm does not assume any knowledge of the input distributions and is defined here for the zero noise limit under these conditions information maximization has extra properties not found in the linear case linsker 1989 the nonlinearities in the transfer function are able to pick up higher order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation this enables the network to separate statistically independent components in the inputs a higher order generalization of principal components analysis we apply the network to the source separation or cocktail party problem successfully separating unknown mixtures of up to 10 speakers we also show that a variant on the network architecture is able to perform blind deconvolution cancellation of unknown echoes and reverberation in a speech signal finally we derive dependencies of information transfer on time delays we suggest that information maximization provides a unifying framework for problems in blind signal processing

a symmetric positive definite formulation for monolithic fluid structure interaction in this paper we consider a strongly coupled monolithic fluid structure interaction framework for incompressible flow as opposed to a loosely coupled partitioned method this requires solving a single linear system that combines the unknown velocities of the structure with the unknown pressures of the fluid in our previous work we were able to obtain a symmetric formulation of this coupled system however it was also indefinite making it more difficult to solve in fact in practice there have been cases where we have been unable to invert the system in this paper we take a novel approach that consists of factoring the damping matrix of deformable structures and show that this can be used to obtain a symmetric positive definite system at least to the extent that the uncoupled systems were symmetric positive definite we use a traditional mac grid discretization of the fluid and a fully lagrangian discretization of the structures for the sake of exposition noting that our procedure can be generalized to other scenarios for the special case of rigid bodies where there are no internal damping forces we exactly recover the system of batty et al 2007 4

finite element approximation of the three field formulation of the stokes problem using arbitrary interpolations the stress displacement pressure formulation of the elasticity problem may suffer from two types of numerical instabilities related to the finite element interpolation of the unknowns the first is the classical pressure instability that occurs when the solid is incompressible whereas the second is the lack of stability in the stresses to overcome these instabilities there are two options the first is to use different interpolation for all the unknowns satisfying two inf sup conditions whereas there are several displacement pressure interpolations that render the pressure stable less possibilities are known for the stress interpolation the second option is to use a stabilized finite element formulation instead of the plain galerkin approach if this formulation is properly designed it is possible to use arbitrary interpolation for all the unknowns the purpose of this paper is precisely to present one of such formulations in particular it is based on the decomposition of the unknowns into their finite element component and a subscale which will be approximated and whose goal is to yield a stable formulation a singular feature of the method to be presented is that the subscales will be considered orthogonal to the finite element space we describe the design of the formulation and present the results of its numerical analysis