sufficiency and duality in nonsmooth multiobjective optimization involving generalized f α π d type i functions in this paper new classes of generalized f a p d type i functions are introduced for a nonsmooth multiobjective programming problem based upon these generalized functions sufficient optimality conditions are established weak strong and strict converse duality theorems are also derived for wolfe and mond weir type multiobjective dual programs in order to relate the efficient and weak efficient solutions of primal and dual problems

generalized fictitious methods for fluid structure interactions analysis and simulations we present a new fictitious pressure method for fluid structure interaction fsi problems in incompressible flow by generalizing the fictitious mass and damping methods we published previously in 1 the fictitious pressure method involves modification of the fluid solver whereas the fictitious mass and damping methods modify the structure solver we analyze all fictitious methods for simplified problems and obtain explicit expressions for the optimal reduction factor convergence rate index at the fsi interface 2 this analysis also demonstrates an apparent similarity of fictitious methods to the fsi approach based on robin boundary conditions which have been found to be very effective in fsi problems we implement all methods including the semi implicit robin based coupling method in the context of spectral element discretization which is more sensitive to temporal instabilities than low order methods however the methods we present here are simple and general and hence applicable to fsi based on any other spatial discretization in numerical tests we verify the selection of optimal values for the fictitious parameters for simplified problems and for vortex induced vibrations viv even at zero mass ratio for ever resonance we also develop an empirical a posteriori analysis for complex geometries and apply it to 3d patient specific flexible brain arteries with aneurysms for very large deformations we demonstrate that the fictitious pressure method enhances stability and convergence and is comparable or better in most cases to the robin approach or the other fictitious methods

partitioning strategies for the interaction of a fluid with a poroelastic material based on a nitsche s coupling approach abstract we develop a computational model to study the interaction of a fluid with a poroelastic material the coupling of stokes and biot equations represents a prototype problem for these phenomena which feature multiple facets on one hand it shares common traits with fluid structure interaction on the other hand it resembles the stokes darcy coupling for these reasons the numerical simulation of the stokes biot coupled system is a challenging task the need of large memory storage and the difficulty to characterize appropriate solvers and related preconditioners for the equations at hand are typical shortcomings of classical discretization methods applied to this problem such as the finite element method for spatial discretization and finite differences for time stepping the application of loosely coupled time advancing schemes mitigates these issues because it allows to solve each equation of the system independently with respect to the others at each time step in this work we develop and thoroughly analyze a loosely coupled scheme for stokes biot equations the scheme is based on nitsche s method for enforcing interface conditions once the interface operators corresponding to the interface conditions have been defined time lagging allows us to build up a loosely coupled scheme with good stability properties the stability of the scheme is guaranteed provided that appropriate stabilization operators are introduced into the variational formulation of each subproblem the error of the resulting method is also analyzed showing that splitting the equations pollutes the optimal approximation properties of the underlying discretization schemes in order to restore good approximation properties while maintaining the computational efficiency of the loosely coupled approach we consider the application of the loosely coupled scheme as a preconditioner for the monolithic approach both theoretical insight and numerical results confirm that this is a promising way to develop efficient solvers for the problem at hand

an unusual stabilized finite element method for a generalized stokes problem an unusual stabilized finite element is presented and analyzed herein for a generalized stokes problem with a dominating zeroth order term the method consists in subtracting a mesh dependent term from the formulation without compromising consistency the design of this mesh dependent term as well as the stabilization parameter involved are suggested by bubble condensation stability is proven for any combination of velocity and pressure spaces under the hypotheses of continuity for the pressure space optimal order error estimates are derived for the velocity and the pressure using the standard norms for these unknowns numerical experiments confirming these theoretical results and comparisons with previous methods are presented

finite element approximation of transmission conditions in fluids and solids introducing boundary subgrid scales terms involving jumps of stresses on boundaries are proposed for the finite element approximation of the stokes problem and the linear elasticity equations these terms are designed to improve the transmission conditions between subdomains at three different levels namely between the element domains between the interfaces in homogeneous domain interaction problems and at the interface between the fluid and the solid in fluid structure interaction problems the benefits in each case are respectively the possibility of using discontinuous pressure interpolations in a stabilized finite element approximation of the stokes problem a stronger enforcement of the stress continuity in homogeneous domain decomposition problems and a considerable improvement of the behavior of iterative schemes to couple the fluid and the solid in fluid structure integration algorithms the motivation to introduce these terms stems from a decomposition of the unknown into a conforming and a non conforming part a hybrid formulation for the latter and a simple approximation for the unknowns involved in the hybrid problem copyright 2011 john wiley sons ltd

quasi newton methods for implicit black box fsi coupling abstract in this paper we introduce a new multi vector update quasi newton mvqn method for implicit coupling of partitioned transient fsi solvers the new quasi newton method facilitates the use of black box field solvers and under certain circumstances can be demonstrated to provide newton like convergence behaviour for strongly coupled fsi benchmark problems we demonstrate the superior convergence behaviour and robust nature of the mvqn method compared to other well known quasi newton coupling schemes including the least squares reduced order modelling ibqn ls scheme the classical rank 1 update broyden s method and fixed point iterations with dynamic relaxation the quasi newton methods are analysed on a suite of strongly coupled fsi problems including but not limited to internal incompressible flow through a flexible tube where the solid density is an order of magnitude lower than the fluid density

a stabilised immersed boundary method on hierarchical b spline grids for fluid rigid body interaction with solid solid contact abstract an accurate efficient and robust numerical scheme is presented for the simulation of the interaction between flexibly supported rigid bodies and incompressible fluid flow with topology changes and solid solid contact the solution of the incompressible navier stokes equations is approximated by employing a stabilised formulation on cartesian grids discretised with hierarchical b splines the solid is modelled as a rigid body and represented by linear segments along its boundary kinematic conditions along the fluid rigid body interface are enforced weakly using nitsche s method while ghost penalty operators are employed to avoid excessive ill conditioning of the system matrix arising from small cut cells a staggered scheme is used for resolving the coupled fluid rigid body interaction the contact between moving or moving and fixed solid bodies is modelled with lagrange multipliers the excellent performance and wide range of applicability of the proposed scheme are demonstrated in a number of benchmark tests as well as industrially relevant model problems the examples cover the galloping phenomena particulate flow hydraulic check valves and a model turbine

combined interface boundary condition method for fluid rigid body interaction abstract this research is motivated by the recent work which has presented a new loosely coupled partitioned algorithm for fluid structure interaction fsi r jaiman p geubelle e loth x jiao combined interface boundary condition method for unsteady fluid structure interaction comput methods appl mech engrg 200 2011 27 39 the loosely coupled partitioned algorithm is intrinsically exposed to the notorious time lag effect whose remedy promotes the combined interface boundary condition cibc method in this method correction terms for velocity and traction are introduced at two sequential time steps with a coupling parameter that plays an important part in the stability and accuracy of the coupled system the structural traction ratio that appears explicitly in the traction correction is estimated based on the solution of the structural subsystem this handling asks for the structural traction before it is corrected by the cibc method in this paper a new formulation for the cibc method is developed to repair the aforementioned inconvenience after simple manipulation the structural traction ratio is removed in constructing the traction correction therefore the structural traction is no more needed in cibc correction terms meantime the ratio t is employed to tune the interfacial corrections instead of the coupling parameter an arbitrary lagrangian eulerian finite element method is used to analyze fsi the characteristic based split cbs scheme is employed to solve incompressible navier stokes equations while the equation for rigid body dynamics is solved by newmark method a numerical technique called moving submesh approach is performed for the mesh deformation for respecting geometric conservation law a mass source term is implanted into the cbs scheme on the moving mesh several numerical examples are tested to validate the proposed methodology for fluid rigid body interaction the obtained results are in agreement with the existing data and some famous features of flow phenomena have been detected successfully

space time finite element techniques for computation of fluid structure interactions we describe the space time finite element techniques we developed for computation of fluid structure interaction fsi problems among these techniques are the deforming spatial domain stabilized space time dsd sst formulation and its special version and the mesh update methods including the solid extension mesh moving technique semmt also among these techniques are the block iterative quasi direct and direct coupling methods for the solution of the fully discretized coupled fluid and structural mechanics equations we present some test computations for the mesh moving techniques described we also present numerical examples where the fluid is governed by the navier stokes equations of incompressible flows and the structure is governed by the membrane and cable equations overall we demonstrate that the techniques we have developed have increased the scope and accuracy of the methods used in computation of fsi problems 2005 elsevier b v all rights reserved

incremental displacement correction schemes for incompressible fluid structure interaction in this paper we introduce a class of incremental displacement correction schemes for the explicit coupling of a thin structure with an incompressible fluid these methods enforce a specific robin neumann explicit treatment of the interface coupling we provide a general stability and convergence analysis that covers both the incremental and the non incremental variants their stability properties are independent of the added mass effect the superior accuracy of the incremental schemes with respect to the original non incremental variant is highlighted by the error estimates and then confirmed in a benchmark by numerical experiments

stabilized finite element methods for the velocity pressure stress formulation of incompressible flows abstract formulated in terms of velocity pressure and the extra stress tensor the incompressible navier stokes equations are discretized by stabilized finite element methods the stabilized methods proposed are analyzed for a linear model and extended to the navier stokes equations the numerical tests performed confirm the good stability characteristics of the methods these methods are applicable to various combinations of interpolation functions including the simplest equal order linear and bilinear elements

curvilinear immersed boundary method for simulating fluid structure interaction with complex 3d rigid bodies the sharp interface curvib approach of ge and sotiropoulos l ge f sotiropoulos a numerical method for solving the 3d unsteady incompressible navier stokes equations in curvilinear domains with complex immersed boundaries journal of computational physics 225 2007 1782 1809 is extended to simulate fluid structure interaction fsi problems involving complex 3d rigid bodies undergoing large structural displacements the fsi solver adopts the partitioned fsi solution approach and both loose and strong coupling strategies are implemented the interfaces between immersed bodies and the fluid are discretized with a lagrangian grid and tracked with an explicit front tracking approach an efficient ray tracing algorithm is developed to quickly identify the relationship between the background grid and the moving bodies numerical experiments are carried out for two fsi problems vortex induced vibration of elastically mounted cylinders and flow through a bileaflet mechanical heart valve at physiologic conditions for both cases the computed results are in excellent agreement with benchmark simulations and experimental measurements the numerical experiments suggest that both the properties of the structure mass geometry and the local flow conditions can play an important role in determining the stability of the fsi algorithm under certain conditions the fsi algorithm is unconditionally unstable even when strong coupling fsi is employed for such cases however combining the strong coupling iteration with under relaxation in conjunction with the aitken s acceleration technique is shown to effectively resolve the stability problems a theoretical analysis is presented to explain the findings of the numerical experiments it is shown that the ratio of the added mass to the mass of the structure as well as the sign of the local time rate of change of the force or moment imparted on the structure by the fluid determine the stability and convergence of the fsi algorithm the stabilizing role of under relaxation is also clarified and the upper bound of the under relaxation coefficient required for stability is derived

a stable fluid structure interaction solver for low density rigid bodies using the immersed boundary projection method dispersion of low density rigid particles with complex geometries is ubiquitous in both natural and industrial environments we show that while explicit methods for coupling the incompressible navier stokes equations and newton s equations of motion are often sufficient to solve for the motion of cylindrical particles with low density ratios for more complex particles such as a body with a protrusion they become unstable we present an implicit formulation of the coupling between rigid body dynamics and fluid dynamics within the framework of the immersed boundary projection method similarly to previous work on this method the resulting matrix equation in the present approach is solved using a block lu decomposition each step of the block lu decomposition is modified to incorporate the rigid body dynamics we show that our method achieves second order accuracy in space and first order in time third order for practical settings only with a small additional computational cost to the original method our implicit coupling yields stable solution for density ratios as low as 10 4 we also consider the influence of fictitious fluid located inside the rigid bodies on the accuracy and stability of our method

fluid structure interaction by means of variational multiscale reduced order models this is the peer reviewed version of the following article tello a codina r baiges j fluid structure interaction by means of variational multiscale reduced order models int j numer methods eng 2020 121 2601 2625 https doi org 10 1002 nme 6321 which has been published in final form at https onlinelibrary wiley com doi abs 10 1002 nme 6321 this article may be used for non commercial purposes in accordance with wiley terms and conditions for self archiving

stabilization of explicit coupling in fluid structure interaction involving fluid incompressibility abstract in this work we propose a stabilized explicit coupling scheme for fluid structure interaction problems involving a viscous incompressible fluid the coupled discrete formulation is based on nitsche s method with a time penalty term giving l 2 control on the fluid pressure variations at the interface for a linear model problem we prove that the scheme is stable in the energy norm irrespectively of the so called added mass effect namely the fluid structure density ratio and the geometry of the domain numerical experiments in the linear and non linear case show that optimal time accuracy can be obtained by performing one defect correction iteration

parallel embedded boundary methods for fluid and rigid body interaction abstract the implementations of an updated body fitted and a non body fitted method to deal with the interaction of a fluid and a rigid body are described the physics of the fluid is modeled by the incompressible navier stokes equations a parallel fluid solver based on the vms variational multiscale finite element method serves as the basis for the implementation for the rigid body movement the newton euler equations are solved numerically to account for the interaction the force that the fluid exerts on the rigid body is determined on the one hand on the other hand the velocity of the rigid body is imposed as a dirichlet boundary condition on the fluid a fixed eulerian mesh discretizes the fluid domain except for nodes in the vicinity of the rigid body boundary for the case of the updated body fitted approach the wet boundary of the rigid body is embedded in the fluid mesh and tracked by a moving surface mesh it is a distinctive characteristic of the updated body fitted strategy that in order to impose velocities on the interface some of the nodes near the body surface are moved by using a local r adaptivity algorithm to conform with this surface by contrast the non body fitted approach uses kriging interpolation for velocity prescription over the fluid on the interface given that fluid nodes can become solid nodes and vice versa due to the rigid body movement we have adopted the fmale approach a variation of the ale method to keep the fluid mesh fixed algorithms to ensure high performance like skd trees to determine if a given spatial point is currently inside the solid are also used all these ingredients constitute two approaches that are both computationally efficient and accurate numerical experiments are presented to assess their performance comparatively

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

explicit robin neumann schemes for the coupling of incompressible fluids with thin walled structures abstract we introduce a class of explicit coupling schemes for the numerical solution of fluid structure interaction problems involving a viscous incompressible fluid and a general thin walled structure e g including damping and non linear behavior the fundamental ingredient in these methods is a parameter free explicit robin interface condition for the fluid which enables the fluid solid splitting through appropriate extrapolations of the solid velocity and fluid stress on the interface the resulting solution procedures are genuinely partitioned stability and error estimates are provided for all the variants depending on the extrapolations using energy arguments within a representative linear setting in particular we show that one of them simultaneously yields added mass free unconditional stability and optimal first order time accuracy a comprehensive numerical study involving different examples from the literature supports the theory

a stable second order partitioned iterative scheme for freely vibrating low mass bluff bodies in a uniform flow abstract we present a stable partitioned iterative scheme for solving fluid body interaction problems at low structure to fluid mass ratio the scheme relies on the so called nonlinear interface force correction based on aitken s extrapolation process to stabilize the coupled partitioned system employing an arbitrary lagrangian eulerian finite element framework approximate interface force correction is constructed through subiterations to account for the missing effects of off diagonal jacobian terms in the partitioned staggered scheme through the generalized aitken s geometric extrapolation process with a dynamic stabilization parameter the interface corrections allow to satisfy the force equilibrium with arbitrary accuracy while expanding the scope of partitioned iterative schemes for fluid structure interaction with strong added mass effects to assess the proposed iterative scheme against the standard strong coupling effects of mass ratio are investigated for a freely vibrating circular cylinder we show that our second order scheme is stable for low mass density ratio and hence is able to handle strong added mass effects the numerical stability and robustness of the scheme is then demonstrated for a new application of tandem square cylinder undergoing complex wake induced vibration and galloping

a matrix free implicit incompressible fractional step algorithm for fluid structure interaction applications in this paper we detail a fast fully coupled partitioned fluid structure interaction fsi scheme for the incompressible fluid new fractional step algorithms are proposed which make possible the fully implicit but matrix free parallel solution of the entire coupled fluid solid system these algorithms include artificial compressibility pressure poisson solution in conjunction with upwind velocity stabilisation as well as simplified pressure stabilisation for improved computational efficiency a dual timestepping approach is proposed where a jacobi method is employed for the momentum equations while the pressures are concurrently solved via a matrix free preconditioned gmres methodology this enables efficient sub iteration level coupling between the fluid and solid domains parallelisation is effected for distributed memory systems the accuracy and efficiency of the developed technology is evaluated by application to benchmark problems from the literature the new schemes are shown to be efficient and robust with the developed preconditioned gmres solver furnishing speed ups ranging between 50 and 80

on mathematical modeling of fluid structure interactions with nonlinear effects in this paper the numerical simulation of aeroelastic interactions of flexibly supported two degrees of freedom 2 dof airfoil in two dimensional 2d incompressible viscous turbulent flow subjected to a gust sudden change of flow conditions is considered the flow is modeled by reynolds averaged navier stokes equations rans and by k turbulence model the considered flow problem is discretized in space using the fully stabilized finite element fe method implemented in the developed in house program which allows to solve interaction problems in order to treat the time dependent inlet boundary condition the standard stabilization procedure was modified further the under relaxation procedure was introduced in order to overcome the artificial instability of the coupling algorithm the aeroelastic response to a sudden gust is numerically analyzed with the aid of the developed fe code

fixed grid fluid structure interaction in two dimensions based on a partitioned lattice boltzmann and p fem approach over the last decade the lattice boltzmann method which was derived from the kinetic gas theory has matured as an efficient approach for solving navier stokes equations the p fem approach has proved to be highly efficient for a variety of problems in the field of structural mechanics our goal is to investigate the validity and efficiency of coupling the two approaches to simulate transient bidirectional fluid structure interaction problems with geometrically non linear structural deflections a benchmark configuration of self induced large oscillations for a flag attached to a cylinder can be accurately and efficiently reproduced within this setting we describe in detail the force evaluation techniques displacement transfers and the algorithm used to couple these completely different solvers as well as the results and compare them with a benchmark reference solution computed by a monolithic finite element approach copyright 2009 john wiley sons ltd

robust controllability for linear uncertain descriptor systems in this paper under assumptions that the linear nominal descriptor system is regular and controllable some sufficient conditions are proposed to preserve the assumed properties when both structured elemental and unstructured norm bounded parameter uncertainties are added into the nominal descriptor system besides another sufficient conditions are also presented to preserve the assumed properties for a class of linear descriptor systems having structured uncertainties in the structure information matrix as well as having both structured and unstructured parameter uncertainties in the system matrix and the input matrix simultaneously the corresponding results for the dual observability robustness problems are straightforward extensions three numerical examples are given to illustrate the applications of the proposed sufficient conditions and it is shown that the proposed sufficient conditions could be less conservative than the existing ones reported recently in the literature

inexact accurate partitioned algorithms for fluid structure interaction problems with finite elasticity in haemodynamics in this paper we consider the numerical solution of the three dimensional fluid structure interaction problem in haemodynamics in the case of real geometries physiological data and finite elasticity vessel deformations we study some new inexact schemes obtained from semi implicit approximations which treat exactly the physical interface conditions while performing just one or few iterations for the management of the interface position and of the fluid and structure non linearities we show that such schemes allow to improve the efficiency while preserving the accuracy of the related exact implicit scheme to do this we consider both a simple analytical test case and two real cases of clinical interest in haemodynamics we also provide an error analysis for a simple differential model problem when a bdf method is considered for the time discretization and only few newton iterations are performed at each temporal instant

explicit strategies for incompressible fluid structure interaction problems nitsche type mortaring versus robin robin coupling we discuss explicit coupling schemes for fluid structure interaction problems where the added mass effect is important in this paper we show the close relation between coupling schemes using nitsche s method and a robin robin type coupling in the latter case the method may be implemented either using boundary integrals of the stresses or the more conventional discrete lifting operators recalling the explicit method proposed in comput methods appl mech engrg 198 5 8 766 784 2009 we make the observation that this scheme is stable under a hyperbolic type cfl condition but that optimal accuracy imposes a parabolic type cfl conditions due to the splitting error two strategies to enhance the accuracy of the coupling scheme under the hyperbolic cfl condition are suggested one using extrapolation and defect correction and one using a penalty free non symmetric nitsche method finally we illustrate the performance of the proposed schemes on some numerical examples in two and three space dimensions

a weakly compressible hybridizable discontinuous galerkin formulation for fluid structure interaction problems abstract a scheme for the solution of fluid structure interaction fsi problems with weakly compressible flows is proposed in this work a novel hybridizable discontinuous galerkin hdg method is derived for the discretization of the fluid equations while the standard continuous galerkin cg approach is adopted for the structural problem the chosen hdg solver combines robustness of discontinuous galerkin dg approaches in advection dominated flows with higher order accuracy and efficient implementations two coupling strategies are examined in this contribution namely a partitioned dirichlet neumann scheme in the context of hybrid hdg cg discretizations and a monolithic approach based on nitsche s method exploiting the definition of the numerical flux and the trace of the solution to impose the coupling conditions numerical experiments show optimal convergence of the hdg and cg primal and mixed variables and superconvergence of the postprocessed fluid velocity the robustness and the efficiency of the proposed weakly compressible formulation in comparison to a fully incompressible one are also highlighted on a selection of two and three dimensional fsi benchmark problems

a 2d finite element scheme for fluid solid acoustic interactions and its application to human phonation abstract we present a recently developed approach for the modeling of fluid solid acoustic interaction problems for the efficient numerical solution of the coupled three field problem we apply the finite element method the mechanical and the acoustic fields are approximated by a standard galerkin scheme a residual based stabilization method is chosen for the fluid field the interaction of the eulerian fluid field with the lagrangian mechanical field is based on the arbitrary lagrangian eulerian ale method and is iteratively coupled in a strong sense the solid acoustic interaction is based on continuum mechanics and the fluid acoustic coupling on lighthill s analogy the new steps of our scheme are verified through validation examples finally a fluid solid acoustic simulation of the human phonation process is presented based on a realistic model

a penalty projection algorithm for a monolithic fluid structure interaction solver in this paper we propose a new iterative penalty projection algorithm for a monolithic fluid structure interaction solver projection methods that split the computation of the velocity from the pressure are very popular in fluid dynamics since the boundary errors generated by the projection method are localized mainly near the boundary layers where the incorrect pressure boundary conditions are imposed however when solid regions are taken into account the pressure projected field cannot satisfy fully coupled boundary constraints imposed on external solid surfaces such as stress free conditions and due to the rigidity of the medium the boundary errors propagate deeply in the interior in order to reduce the projection errors we propose a one step penalty projection method in the fluid domain and an iterative penalty projection method in the solid region this technique decouples the pressure velocity degrees of freedom and as a consequence the computational cost in order to verify the accuracy and robustness of the proposed method we compare the results between this splitting velocity pressure algorithm and the coupled one these numerical results show stability and robustness of the proposed algorithm with a strong reduction of the computational effort a new penalty projection algorithm for a monolithic fsi solver is proposed projection method error is localized where pressure boundary conditions are imposed a one step penalty together with an iterative projection algorithm is used this technique reduces the problem degrees of freedom and the computational cost numerical results show stability and reduction of cpu effort for large problems

pressure bubbles stabilization features in the stokes problem abstract the standard finite element approximation using equal order linear continuous velocity pressure variables is enriched with velocity and pressure bubble functions to model the stokes problem we show by static condensation that these bubble functions give rise to a stabilized method involving least squares forms of the momentum and of the continuity equations in particular pressure bubbles play a key role in explaining the addition of the least squares form of the continuity equation in a stabilized method for stokes

necessary and sufficient conditions in constrained optimization additional conditions are attached to the kuhn tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization under appropriate constraint qualifications necessary and sufficient conditions are also given for optimality of the dual problem duality and converse duality are treated accordingly

analysis of the block gauss seidel solution procedure for a strongly coupled model problem with reference to fluid structure interaction the block gauss seidel procedure is widely used for the resolution of the strong coupling in the computer simulation of fluid structure interaction based on a simple model problem this work presents a detailed analysis of the convergence behaviour of the method in particular the model problem is used to highlight some aspects that arise in the context of the application of the block gauss seidel method to fsi problems thus the effects of the time integration schemes chosen of relaxation techniques of physical constraints and non linearities on the convergence of the iterations are investigated

sufficiency and duality in nondifferentiable multiobjective programming involving generalized type i functions abstract recently hachimi and aghezzaf defined generalized f d type i functions a new class of functions that unifies several concepts of generalized type i functions in this paper the generalized f d type i functions are extended to nondifferentiable functions by utilizing the new concepts we obtain several sufficient optimality conditions and prove mixed type and mond weir type duality results for the nondifferentiable multiobjective programming problem

analysis and optimization of robin robin partitioned procedures in fluid structure interaction problems in the solution of fluid structure interaction fsi problems partitioned procedures are modular algorithms that involve separate fluid and structure solvers that interact in an iterative framework through the exchange of suitable transmission conditions at the fs interface in this work we study using fourier analysis the convergence of partitioned algorithms based on robin transmission conditions we derive for different models of the fluid and the structure a frequency dependent reduction factor at each iteration of the partitioned algorithm which is minimized by choosing optimal values of the coefficients in the robin transmission conditions two dimensional numerical results are also reported which highlight the effectiveness of the optimization procedure

bubble functions prompt unusual stabilized finite element methods a second order linear scalar differential equation including a zero th order term is approximated using first the standard galerkin method enriched with bubble functions static condensation of the bubbles suggest an unusual stabilized finite element method for which we establish a convergence study and obtain successful numerical simulations the method is generalized to allow for a convection operator in the equation this work may be employed as a starting point for simulation of nonlinear equations governing turbulence phenomena flows with chemical reactions and other important problems

on sufficiency of the kuhn tucker conditions if all the functions fo x f x f x are convex on c then these conditions are also sufficient various classes of functions have been defined for the purpose of weakening this limitation of convexity in mathematical programming mangasarian 11 has speculated that pseudo convexity of x and quasiconvexity off x are the weakest conditions that can be imposed so that the above conditions are sufficient for optimality it will be shown that there are other wide classes of functions for which the conditions are sufficient 545

fluid structure interaction problems with strong added mass effect in this paper the so called added mass effect is investigated from a different point of view of previous publications the monolithic fluid structure problem is partitioned using a static condensation of the velocity terms following this procedure the classical stabilized projection method for incompressible fluid flows is introduced the procedure allows obtaining a new pressure segregated scheme for fluid structure interaction problems which has good convergent characteristics even for biomechanical application where the added mass effect is strong the procedure reveals its power when it is shown that the same projection technique must be implemented in staggered fsi methods copyright 2009 john wiley sons ltd

virtual bubbles and galerkin least squares type methods ga l s abstract the equivalence between stabilized finite element methods or galerkin least squares tyoe methods ga l s and the standard galerkin method with bubble functions is established in an abstract framework the results are applicable to various finite element spaces including high order elements and applications to the advective diffusive model and to the stokes problem are presented illustrating the potential of the abstract theory introduced here

optimality and duality for the multiobjective fractional programming with the generalized f ρ convexity abstract a class of multiobjective fractional programmings mfp are first formulated where the involved functions are local lipschitz and clarke subdifferentiable in order to deduce our main results we give the definitions of the generalized f convex class about the clarke subgradient under the above generalized convexity assumption the alternative theorem is obtained and some sufficient and necessary conditions for optimality are also given related to the properly efficient solution for the problems finally we formulate the two dual problems md and md1 corresponding to mfp and discuss the week strong and reverse duality

artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows this note investigates the so called arti cial added mass e ect which is responsible for devastating instabilities within sequentially staggered fluid structure interaction fsi simulations where incompressible fluids are considered a discrete representation of the added mass operatorma is given and instability conditions are evaluated for different temporal discretisation schemes it is proven that for every sequentially staggered scheme and given spatial discretisation of a problem a mass ratio between fluid and structural mass density can be found at which the coupled system becomes unstable the analysis is quite general and does not depend upon the particular spatial discretisation schemes used however here special attention is put on stabilised finite elements employed on the fluid partition numerical investigations further highlight the results

on sufficiency and duality for nonsmooth multiobjective programming problems involving generalized v r invex functions abstract in this paper a class of nonsmooth multiobjective programming problems with inequality constraints is considered we introduce the concepts of v r pseudo invex strictly v r pseudo invex and v r quasi invex functions in which the involved functions are locally lipschitz based upon these generalized v r invex functions sufficient optimality conditions for a feasible point to be an efficient or a weakly efficient solution are derived appropriate duality theorems are proved for a mond weir type dual program of a nonsmooth multiobjective programming under the aforesaid functions

multi level quasi newton coupling algorithms for the partitioned simulation of fluid structure interaction abstract in partitioned fluid structure interaction simulations the flow equations and the structural equations are solved separately coupling iterations between the flow calculation and the structural calculation can be used to enforce the equilibrium conditions on the fluid structure interface low wave number fourier modes of the difference between the correct interface displacement and the interface displacement during gauss seidel coupling iterations are typically unstable for strongly coupled problems with a dirichlet neumann decomposition using interface quasi newton iterations with an approximation for the inverse of the jacobian from a least squares model iqn ils these unstable modes are automatically detected and stabilized as the unstable modes have a low wave number and can hence be resolved on coarser grids the new multi level iqn ils ml iqn ils technique first constructs the approximation for the inverse of the jacobian on coarser grid levels and then uses it and improves it further on the original finest grid level this multi level approach reduces the number of coupling iterations on the finest grid level and can also be applied to the interface block quasi newton ibqn ls technique one dimensional and three dimensional numerical results demonstrate that this new class of multi level quasi newton coupling techniques can reduce the duration of a partitioned fluid structure interaction simulation

a strongly coupled immersed boundary formulation for thin elastic structures we present a strongly coupled immersed boundary method for flowstructure interaction problems involving thin deforming bodies the method is stable for arbitrary choices of solid to fluid mass ratios and for large body motions as with many strongly coupled immersed boundary methods our method requires the solution of a nonlinear algebraic system at each time step the system is solved through iteration where the iterates are obtained by linearizing the system and performing a block lu factorization this restricts all iterations to small dimensional subsystems that scale with the number of discretization points on the immersed surface rather than on the entire flow domain moreover the iteration procedure we propose does not involve heuristic regularization parameters and has converged in a small number of iterations for all problems we have considered we derive our method for general deforming surfaces and verify the method with two dimensional test problems of geometrically nonlinear flags undergoing large amplitude flapping behavior

some vector optimization problems in banach spaces with generalized convexity abstract in this paper we consider a vector optimization problem where all functions involved are defined on banach spaces new classes of generalized type i functions are introduced for functions between banach spaces based upon these generalized type i functions we obtain a few sufficient optimality conditions and prove some results on duality

explicit synchronous partitioned algorithms for interface problems based on lagrange multipliers abstract traditional explicit partitioned schemes exchange boundary conditions between subdomains and can be related to iterative solution methods for the coupled problem as a result these schemes may require multiple subdomain solves acceleration techniques or optimized transmission conditions to achieve sufficient accuracy and or stability we present a new synchronous partitioned method derived from a well posed mixed finite element formulation of the coupled problem we transform the resulting differential algebraic equation dae to a hessenberg index 1 form in which the algebraic equation defines the lagrange multiplier as an implicit function of the states using this fact we eliminate the multiplier and reduce the dae to a system of explicit odes for the states explicit time integration both discretizes this system in time and decouples its equations as a result the temporal accuracy and stability of our formulation are governed solely by the accuracy and stability of the explicit scheme employed and are not subject to additional stability considerations as in traditional partitioned schemes we establish sufficient conditions for the formulation to be well posed and prove that classical mortar finite elements on the interface are a stable choice for the lagrange multiplier we show that in this case the condition number of the schur complement involved in the elimination of the multiplier is bounded by a constant the paper concludes with numerical examples illustrating the approach for two different interface problems

an extended finite element method lagrange multiplier based approach for fluid structure interaction abstract this paper presents a new fixed grid fluid structure interaction scheme that can be applied to the interaction of most general structures with incompressible flow it is based on an extended finite element method xfem based strategy the extended eulerian fluid field and the lagrangian structural field are partitioned and iteratively coupled using lagrange multiplier techniques for non matching grids the approach allows the simulation of the interaction of thin and bulky structures exhibiting large deformations finally qualitative examples and a benchmark computation demonstrate key features and accuracy of the method

optimality and duality in nonsmooth multiobjective optimization involving generalized type i functions abstract a nonsmooth multiobjective optimization problem involving generalized type i vectorvalued functions is considered karush kuhn tucker type necessary and sufficient optimality conditions are obtained for a feasible point to be an efficient or properly efficient solution duality theorems are proved for wolfe type and mond weir type duals under the generalized type i assumptions

an accelerated fully coupled parallel 3d hybrid finite volume fluid structure interaction scheme abstract in this paper we propose a fast parallel 3d fully coupled partitioned hybrid unstructured finite volume fluid structure interaction fsi scheme spatial discretisation is effected via a vertex centred finite volume method where a hybrid nodal elemental strain procedure is employed for the solid in the interest of accuracy for the incompressible fluid a split step algorithm is presented which allows the entire fluid solid system to be solved in a fully implicit yet matrix free manner the algorithm combines a preconditioned gmres solver for implicit integration of pressures with dual timestepping on the momentum equations thereby allowing strong coupling of the system to occur through the inner solver iterations further acceleration is provided at little additional cost by applying lu sgs relaxation to the viscous and advective terms the solver is parallelised for distributed memory systems using mpi and its scaling efficiency evaluated the developed modelling technology is evaluated by application to two 3d fsi problems the advanced matrix free solvers achieve reductions in overall cpu time of up to 50 times while preserving close to linear parallel computing scaling using up to 128 cpus for the problems considered

optimality and duality in nondifferentiable multiobjective optimization involvingd type i and related functions abstract in this paper new classes of functions namely d type i d quasitype i and d pseudo type i are defined for a multiobjective nondifferentiable programming problem kuhn tucker type necessary and sufficient optimality conditions are obtained for a feasible point to be a weak minimum for this problem two duals are formulated and various duality results are given by using the above defined classes of functions considering the concept of a weak minimum

optimality criteria in nonlinear programming involving nonconvex functions abstract in this paper a new class of functions called convex quasiconvex and pseudoconvex are defined and a number of sufficient optimality criteria are obtained for nonlinear programming problems involving these functions

a projection semi implicit scheme for the coupling of an elastic structure with an incompressible fluid we address the numerical simulation of fluid structure systems involving an incompressible viscous fluid this issue is particularly difficult to face when the fluid added mass acting on the structure is strong as it happens in hemodynamics for example indeed several works have shown that in such situations implicit coupling seems to be necessary in order to avoid numerical instabilities although significant improvements have been achieved during the last years solving implicit coupling often exhibits a prohibitive computational cost in this work we introduce a semi implicit coupling scheme which remains stable for a reasonable range of the discretization parameters the first idea consists in treating implicitly the added mass effect whereas the other contributions geometrical non linearities viscous and convective effects are treated explicitly the second idea relies on the fact that this kind of explicit implicit splitting can be naturally performed using a chorin temam projection scheme in the fluid we prove conditional stability of the scheme for a fully discrete formulation several numerical experiments point out the efficiency of the present scheme compared to several implicit approaches

on an improved unusual stabilized finite element method for theadvective reactive diffusive equation an improved unusual finite element method is studied herein for a second order linear scalar differential equation including a zero order term the method consists in subtracting from the standard galerkin method a mesh dependent term suggested by static condensation of the bubbles based on this idea a new stabilized parameter is constructed which improves accuracy of the solution several numerical tests attest the efficiency of the present method and an error analysis is perfomed

truly monolithic algebraic multigrid for fluid structure interaction the coupling of flexible structures to incompressible fluids draws a lot attention during the last decade many different solution schemes have been proposed in this contribution we concentrate on strong coupling fluid structure interaction by means of monolithic solution schemes therein a newton krylov method is applied to the monolithic set of nonlinear equations such schemes require good preconditioning to be efficient we propose two preconditioners that apply algebraic multigrid techniques to the entire fluid structure interaction system of equations the first is based on a standard block gauss seidel approach where approximate inverses of the individual field blocks are based on a algebraic multigrid hierarchy tailored for the type of the underlying physical problem the second is based on a monolithic coarsening scheme for the coupled system that makes use of prolongation and restriction projections constructed for the individual fields the resulting nonsymmetric monolithic algebraic multigrid method therefore involves coupling of the fields on coarse approximations to the problem yielding significantly enhanced performance

kinematic splitting algorithm for fluid structure interaction in hemodynamics abstract in this paper we study a kinematic splitting algorithm for fluid structure interaction problems this algorithm belongs to the class of loosely coupled fluid structure interaction schemes we will present stability analysis for a coupled problem of non newtonian shear dependent fluids in moving domains with viscoelastic boundaries fluid flow is described by the conservation laws with nonlinearities in convective and diffusive terms for simplicity of presentation the structure is modelled by the generalized string equation but the results presented in the paper may be generalized to more complex structure models the arbitrary lagrangian eulerian approach is used in order to take into account moving computational domain numerical experiments including numerical error analysis and comparison of hemodynamic parameters for newtonian and non newtonian fluids demonstrate reliability of the proposed scheme

an adaptive fixed mesh ale method for free surface flows in this work we present a fixed mesh ale method for the numerical simulation of free surface flows capable of using an adaptive finite element mesh covering a background domain this mesh is successively refined and unrefined at each time step in order to focus the computational effort on the spatial regions where it is required some of the main ingredients of the formulation are the use of an arbitrary lagrangian eulerian formulation for computing temporal derivatives the use of stabilization terms for stabilizing convection stabilizing the lack of compatibility between velocity and pressure interpolation spaces and stabilizing the ill conditioning introduced by the cuts on the background finite element mesh and the coupling of the algorithm with an adaptive mesh refinement procedure suitable for running on distributed memory environments algorithmic steps for the projection between meshes are presented together with the algebraic fractional step approach used for improving the condition number of the linear systems to be solved the method is tested in several numerical examples the expected convergence rates both in space and time are observed smooth solution fields for both velocity and pressure are obtained as a result of the contribution of the stabilization terms finally a good agreement between the numerical results and the reference experimental data is obtained

unified lagrangian formulation for elastic solids and incompressible fluids application to fluid structure interaction problems via the pfem abstract we present a general lagrangian formulation for treating elastic solids and quasi fully incompressible fluids in a unified form the formulation allows to treat solid and fluid subdomains in a unified manner in fluid structure interaction fsi situations in our work the fsi problem is solved via the particle finite element method pfem the pfem is an effective technique for modeling complex interactions between floating and submerged bodies and free surface flows accounting for splashing of waves large motions of the bodies and frictional contact conditions applications of the unified lagrangian formulation to a number of fsi problems are given

generalized robin neumann explicit coupling schemes for incompressible fluid structure interaction stability analysis and numerics we introduce a new class of explicit coupling schemes for the numerical solution of fluid structure interaction problems involving a viscous incompressible fluid and an elastic structure these methods generalize the arguments reported in 13 10 to the case of the coupling with thick walled structures the basic idea lies in the derivation of an intrinsic interface robin consistency at the space semi discrete level using a lumped mass approximation in the structure the fluid solid splitting is then performed through appropriate extrapolations of the solid velocity and stress on the interface based on these methods a new parameter free robin neumann iterative procedure is also proposed for the partitioned solution of implicit coupling a priori energy estimates guaranteeing the added mass free stability of the schemes and the convergence of the iterative procedure are established the accuracy and robustness of the methods are illustrated in several numerical examples

unified computational framework for the efficient solution of n field coupled problems with monolithic schemes abstract in this paper we propose and evaluate the performance of a unified computational framework for preconditioning systems of linear equations resulting from the solution of coupled problems with monolithic schemes the framework is composed by promising application specific preconditioners presented previously in the literature with the common feature that they are able to be implemented for a generic coupled problem involving an arbitrary number of fields and to be used to solve a variety of applications the first selected preconditioner is based on a generic block gauss seidel iteration for uncoupling the fields and standard algebraic multigrid amg methods for solving the resulting uncoupled problems the second preconditioner is based on the semi implicit method for pressure linked equations simple which is extended here to deal with an arbitrary number of fields and also results in uncoupled problems that can be solved with standard amg finally a more sophisticated preconditioner is considered which enforces the coupling at all amg levels in contrast to the other two techniques which resolve the coupling only at the finest level our purpose is to show that these methods perform satisfactory in quite different scenarios apart from their original applications to this end we consider three very different coupled problems thermo structure interaction fluid structure interaction and a complex model of the human lung numerical results show that these general purpose methods are efficient and scalable in this range of applications

robin robin preconditioned krylov methods for fluid structure interaction problems in this work we propose a robin robin preconditioner combined with krylov iterations for the solution of the interface system arising in fluid structure interaction fsi problems it can be seen as a partitioned fsi procedure and in this respect it generalizes the ideas introduced in s badia f nobile c vergara j comput phys 227 2008 7027 7051 we analyze the convergence of gmres iterations with the robin robin preconditioner on a model problem and compare its efficiency with some existing algorithms the method is shown to be very efficient for many challenging fluid structure interaction problems such as those characterized by a large added mass effect or by enclosed fluids in particular the possibility to solve balloon type problems without any special treatment makes this algorithm very appealing compared to the computationally intensive existing approaches c 2009 elsevier b v all rights reserved

an analysis of a new stable partitioned algorithm for fsi problems part i incompressible flow and elastic solids stable partitioned algorithms for fluid structure interaction fsi problems are developed and analyzed in this two part paper part i describes an algorithm for incompressible flow coupled with compressible elastic solids while part ii discusses an algorithm for incompressible flow coupled with structural shells importantly these new added mass partitioned amp schemes are stable and retain full accuracy with no sub iterations per time step even in the presence of strong added mass effects e g for light solids the numerical approach described here for bulk compressible solids extends the scheme of banks et al 1 2 for inviscid compressible flow and uses robin mixed boundary conditions with the fluid and solid solvers at the interface the basic amp robin conditions involving a linear combination of velocity and stress are determined from the outgoing solid characteristic relation normal to the fluid solid interface combined with the matching conditions on the velocity and traction two alternative forms of the amp conditions are then derived depending on whether the fluid equations are advanced with a fractional step method or not the stability and accuracy of the amp algorithm is evaluated for linearized fsi model problems the full nonlinear case being left for future consideration a normal mode analysis is performed to show that the new amp algorithm is stable for any ratio of the solid and fluid densities including the case of very light solids when added mass effects are large in contrast it is shown that a traditional partitioned algorithm involving a dirichlet neumann coupling for the same fsi problem is formally unconditionally unstable for any ratio of densities exact traveling wave solutions are derived for the fsi model problems and these solutions are used to verify the stability and accuracy of the corresponding numerical results obtained from the amp algorithm for the cases of light medium and heavy solids