particle swarm optimization in electromagnetics the particle swarm optimization pso new to the electromagnetics community is a robust stochastic evolutionary computation technique based on the movement and intelligence of swarms this paper introduces a conceptual overview and detailed explanation of the pso algorithm as well as how it can be used for electromagnetic optimizations this paper also presents several results illustrating the swarm behavior in a pso algorithm developed by the authors at ucla specifically for engineering optimizations ucla pso also discussed is recent progress in the development of the pso and the special considerations needed for engineering implementation including suggestions for the selection of parameter values additionally a study of boundary conditions is presented indicating the invisible wall technique outperforms absorbing and reflecting wall techniques these concepts are then integrated into a representative example of optimization of a profiled corrugated horn antenna

a 3d mortar method for solid mechanics a version of the mortar method is developed for tying arbitrary dissimilar 3d meshes with a focus on issues related to large deformation solid mechanics issues regarding momentum conservation large deformations computational efficiency and bending are considered in particular a mortar method formulation that is invariant to rigid body rotations is introduced a scheme is presented for the numerical integration of the mortar surface projection integrals applicable to arbitrary 3d curved dissimilar interfaces here integration need only be performed at problem initialization such that coefficients can be stored and used throughout a quasi static time stepping process even for large deformation problems a degree of freedom reduction scheme exploiting the dual space interpolation method such that direct linear solution techniques can be applied without lagrange multipliers is proposed this provided a significant reduction in factorization times example problems which touch on the aforementioned solid mechanics related issues are presented published in 2003 by john wiley sons ltd

a viscosity adaption method for lattice boltzmann simulations abstract in this work we consider the limited fitness for practical use of the lattice boltzmann method for non newtonian fluid flows several authors have shown that the lbm is capable of correctly simulating those fluids however due to stability reasons the modeled viscosity range has to be truncated the resulting viscosity boundaries are chosen arbitrarily because the correct simulation mach number for the physical problem is unknown a priori this easily leads to corrupt simulation results a viscosity adaption method vam is derived which drastically improves the applicability of lbm for non newtonian fluid flows by adaption of the modeled viscosity range to the actual physical problem this is done through tuning of the global mach number to the solution dependent shear rate we demonstrate that the vam can be used to accelerate lbm simulations and improve their accuracy for both steady state and transient cases

the primal dual active set strategy as a semismooth newton method this paper addresses complementarity problems motivated by constrained optimal control problems it is shown that the primal dual active set strategy which is known to be extremely efficient for this class of problems and a specific semismooth newton method lead to identical algorithms the notion of slant differentiability is recalled and it is argued that the max function is slantly differentiable in lp spaces when appropriately combined with a two norm concept this leads to new local convergence results of the primal dual active set strategy global unconditional convergence results are obtained by means of appropriate merit functions

a primal formulation for imposing periodic boundary conditions on conforming and nonconforming meshes abstract a variational multiscale discontinuous galerkin vmdg method is developed for microscale modeling of domains containing conforming and non conforming meshes essentially the product of the applied volume average strain or macro strain and the domain diameter acts as an imposed displacement jump within the vmdg terms hence the method is suitable for modeling deformation of both block and truly self periodic representative volume elements rves the primal displacement field and macro strain are the only unknowns because the method eliminates the lagrange multiplier lm enforcement of the kinematic constraint rigorous derivation of the method provides a framework to accommodate either the macro stress or macro strain as the driver of the microscale boundary value problem the method is developed first for finite deformations and then specialized to small deformation kinematics algorithmic modifications to the method are also studied for their effects on tangent symmetry and convergence rate the results from numerical studies for isotropic and anisotropic materials show that the proposed method is robust accurate stable and variationally consistent for modeling complicated conforming and nonconforming rves

a mortar segment to segment contact method for large deformation solid mechanics abstract contact modeling is still one of the most difficult aspects of non linear implicit structural analysis most 3d contact algorithms employed today use node on segment approaches for contacting dissimilar meshes two pass node on segment contact approaches have the well known deficiency of locking due to over constraint in this work we develop and demonstrate a segment to segment contact approach based on the mortar method by eliminating the over constraint this method appears to be much more robust than the node on segment approach furthermore node on segment approaches suffer when individual nodes slide out of contact at contact surface boundaries or when contacting nodes slide from facet to facet this causes jumps in the contact forces due to the discrete nature of the constraint enforcement and difficulties in convergence for implicit solution techniques these jumps in forces are avoided in the segment to segment approach since penetration is measured by the occluded weighted volume which varies smoothly with perturbations until now all mortar schemes have been developed for small deformation sliding and have mainly been applied on flat surfaces here we will present the integration scheme and the linearization approach used for handling the contact surface integrals in the event of large sliding the schemes are designed to conserve linear momentum and can be applied to arbitrarily curved 3d surfaces although expensive our numerical examples demonstrate that the approach is far more robust than even smoothed node on segment contact techniques that is problems previously not solvable with node on segment can now be solved with our segment to segment contact

a primal dual active set algorithm for three dimensional contact problems with coulomb friction in this paper efficient algorithms for contact problems with tresca and coulomb friction in three dimensions are presented and analyzed the numerical approximation is based on mortar methods for nonconforming meshes with dual lagrange multipliers using a nonsmooth complementarity function for the three dimensional friction conditions a primal dual active set algorithm is derived the method determines active contact and friction nodes and at the same time resolves the additional nonlinearity originating from sliding nodes no regularization and no penalization are applied and superlinear convergence can be observed locally in combination with a multigrid method it defines a robust and fast strategy for contact problems with tresca or coulomb friction the efficiency and flexibility of the method is illustrated by several numerical examples

improved robustness and consistency of 3d contact algorithms based on a dual mortar approach abstract mortar finite element methods have been successfully applied as discretization scheme to a wide range of contact and impact problems in recent years the 3d finite deformation contact formulation taken up and enhanced in this paper is based on a mortar approach using so called dual lagrange multipliers which substantially facilitate the treatment of interface constraints as compared with standard mortar techniques despite being quite well established in the meantime dual mortar methods may lack robustness or even consistency in certain situations e g when large curvatures occur in the contact zone or when one body slides off another at a sharp edge however since such scenarios are regularly appearing in engineering practice the present contribution provides several new extensions that completely resolve these issues and thus significantly improve the applicability of dual mortar formulations for challenging contact problems the proposed extensions include a consistent biorthogonalization procedure to obtain feasible dual lagrange multiplier shape functions close to boundaries of the contact surfaces an improved conditioning of the global linear system of equations by nodal scaling and a novel approach to unify the advantages of standard and dual mortar methods via a petrov galerkin type of lagrange multiplier interpolation several numerical examples demonstrate the achievable improvements in terms of consistency and robustness for 3d contact analysis including finite deformations

finite deformation frictional mortar contact using a semi smooth newton method with consistent linearization a two dimensional finite deformation frictional contact formulation with coulomb s law is presented the approach considers multibody contact and is based on a mortar formulation the enforcement of contact constraints is realized with dual lagrange multipliers these alternative multiplier spaces are constructed in a way that the multipliers can easily be eliminated from the global system of equations by static condensation such that the system size does not increase friction kinematic variables are formulated in an objective way and enter non smooth complementarity functions for expressing the contact constraints an active set strategy is derived by applying a semismooth newton method which treats contact nonlinearities material and geometrical nonlinearities in one single iterative scheme by further carrying out a consistent linearization for both normal and frictional contact forces and constraints a robust and highly efficient algorithm for linear and higher order quadratic interpolation is achieved efficiency of the proposed method and quality of results are demonstrated in serveral exemples

consistent treatment of boundaries with mortar contact formulations using dual lagrange multipliers abstract computational modelling of contact problems raises two basic questions which method should be used to enforce the contact conditions and how should this method be discretised the most popular enforcement methods are the lagrange multiplier method the penalty method and combinations of these two a frequently used discretisation method is the so called node to segment approach however this approach might lead to problems like jumps in contact forces loss of convergence or failure to pass the patch test thus in the last few years several segment to segment contact algorithms based on the mortar method were proposed combination of a mortar discretisation with a penalty based enforcement of the contact conditions leads to unphysical penetrations on the other hand a lagrange multiplier mortar method requires additional unknowns hence condensation of the lagrange multipliers is desirable to preserve the initial size of the system of equations this can be achieved by interpolating the lagrange multipliers with so called dual shape functions discretising two contacting bodies leads to opposed contact surface representations of finite element edges called slave and master elements respectively in current versions of dual lagrange multiplier mortar formulations an inconsistency at the boundary appears when only a part of a slave element instead of the entire element belongs to the contact area we present a modified definition of the dual shape functions in such slave elements the basic idea is to construct dual shape functions that fulfill the so called biorthogonality condition within the contact area this leads to consistent mortar matrices also in the boundary region to avoid ill conditioning of the stiffness matrix the modified mortar matrices are weighted with appropriate weighting factors in doing so the corresponding modified lagrange multiplier nodal values are of the same order as the unmodified ones various examples demonstrate the performance of the modified mortar contact algorithm

a weighted point based formulation for isogeometric contact abstract in the context of isogeometric contact analysis surfaces of objects can be described smoothly due to the high continuity of the involved shape functions this facilitates construction of a continuous normal field which may be beneficial for modeling of contact problems this property allows for stable collocation of the virtual contact work using considerable less evaluation points than numerical integration while the approximation quality of the computational results is almost the same in this context a weighted point based method pts is introduced as an extension of the point to segment method pts proposed previously by matzen et al 2013 the weights enable transmission of contact stresses instead of contact forces along the contact surfaces in normal direction the non penetration condition is enforced by the lagrange multiplier method combined with the penalty method in tangential direction corresponding to the collocation weights a constant or nurbs lagrange multiplier field is introduced a comparison between the collocation based contact formulations pts pts and a mortar method is drawn showing that weighted collocation is able to achieve almost the same accuracy as the integration based mortar formulation

discrete lattice effects on the forcing term in the lattice boltzmann method we show that discrete lattice effects must be considered in the introduction of a force into the lattice boltzmann equation a representation of the forcing term is then proposed with the representation the navier stokes equation is derived from the lattice boltzmann equation through the chapman enskog expansion several other existing force treatments are also examined

higher order mortar finite element methods in 3d with dual lagrange multiplier bases mortar methods with dual lagrange multiplier bases provide a flexible efficient and optimal way to couple different discretization schemes or nonmatching triangulations here we generalize the concept of dual lagrange multiplier bases by relaxing the condition that the trace space of the approximation space at the slave side with zero boundary condition on the interface and the lagrange multiplier space have the same dimension we provide a new theoretical framework within this relaxed setting which opens a new and simpler way to construct dual lagrange multiplier bases for higher order finite element spaces as examples we consider quadratic and cubic tetrahedral elements and quadratic serendipity hexahedral elements numerical results illustrate the performance of our approach

efficient simulation of multi body contact problems on complex geometries a flexible decomposition approach using constrained minimization we consider the numerical simulation of non linear multi body contact problems in elasticity on complex three dimensional geometries in the case of warped contact boundaries and non matching finite element meshes particular emphasis has to be put on the discretization of the transmission of forces and the non penetration conditions at the contact interface we enforce the discrete contact constraints by means of a non conforming domain decomposition method which allows for optimal error estimates here we develop an efficient method to assemble the discrete coupling operator by computing the triangulated intersection of opposite element faces in a locally adjusted projection plane but carrying out the required quadrature on the faces directly our new element based algorithm does not use any boundary parameterizations and is also suitable for isoparametric elements the emerging non linear system is solved by a monotone multigrid method of optimal complexity several numerical examples in 3d illustrate the effectiveness of our approach copyright 2008 john wiley sons ltd

unilateral non linear dynamic contact of thin walled structures using a primal dual active set strategy the efficient modelling of three dimensional contact problems is still a challenge in non linear implicit structural analysis we use a primal dual active set strategy siam j optim 2003 13 865 888 based on dual lagrange multipliers siam j numer anal 2000 38 989 1012 to handle the non linearity of the contact conditions this allows us to enforce the contact constraints in a weak integral sense without any additional parameter due to the biorthogonality condition of the basis functions the lagrange multipliers can be locally eliminated we perform a static condensation to achieve a reduced system for the displacements the lagrange multipliers representing the contact pressure can be easily recovered from the displacements in a variationally consistent way for the application to thin walled structures we adapt a three dimensional non linear shell formulation including the thickness stretch of the shell to contact problems a reparametrization of the geometric description of the shell body gives us a surface oriented shell element which allows the application of contact conditions directly to nodes lying on the contact surface shell typical locking phenomena are treated with the enhanced assumed strain method and the assumed natural strain method the discretization in time is done with the implicit generalized method j appl mech 1993 60 371 375 and the generalized energy momentum method comp methods appl mech eng 1999 178 343 366 to compare the development of energies within a frictionless contact description in order to conserve the total energy within the discretized frictionless contact framework we follow an approach from laursen and love int j numer methods eng 2002 53 245 274 who introduced a discrete contact velocity to update the velocity field in a post processing step various examples show the good performance of the primal dual active set strategy applied to the implicit dynamic analysis of thin walled structures

dual quadratic mortar finite element methods for 3d finite deformation contact mortar finite element methods allow for a flexible and efficient coupling of arbitrary nonconforming interface meshes and are by now quite well established in nonlinear contact analysis in this pa

accuracy of non newtonian lattice boltzmann simulations this work deals with the accuracy of non newtonian lattice boltzmann simulations previous work for newtonian fluids indicate that depending on the numerical value of the dimensionless collision frequency additional artificial viscosity is introduced which negatively influences the accuracy since the non newtonian fluid behavior is incorporated through appropriate modeling of the dimensionless collision frequency a dependent error e is introduced and its influence on the overall error is investigated here simulations with the srt and the mrt model are carried out for power law fluids in order to numerically investigate the accuracy of non newtonian lattice boltzmann simulations a goal of this accuracy analysis is to derive a recommendation for an optimal choice of the time step size and the simulation mach number respectively for the non newtonian case an error estimate for e in the form of a functional is derived on the basis of a series expansion of the lattice boltzmann equation this functional can be solved analytically for the case of the hagen poiseuille channel flow of non newtonian fluids with the help of the error functional the prediction of the global error minimum of the velocity field is excellent in regions where the e error is the dominant source of error with an optimal simulation mach number the simulation is about one order of magnitude more accurate additionally for both collision models a detailed study of the convergence behavior of the method in the non newtonian case is conducted the results show that the simulation mach number has a major impact on the convergence rate and second order accuracy is not preserved for every choice of the simulation mach number

truncation error analysis of lattice boltzmann methods a truncation error analysis is performed for models based on the lattice boltzmann lb equation this analysis involves two steps the recursive application of the lb equation and a taylor series expansion unlike previous analytical studies of lb methods the present work does not assume an asymptotic relationship between the temporal and spatial discretization parameters or between the probability distribution function f and its equilibrium distribution feq effective finite difference stencils are derived for both the distribution function and the primitive variables i e density and velocity the governing partial differential equations are also recovered the associated truncation errors are derived and the results are validated by numerical simulation of analytic flows analysis of the truncation errors elucidates the roles of the kinetic theory relaxation parameter and the discretization parameters x and t the effects of initial and boundary conditions are also addressed and are shown to significantly affect the overall accuracy of the method

a mortar based frictional contact formulation for large deformations using lagrange multipliers abstract in this work a lagrange multiplier method is proposed to solve 2d coulomb frictional contact problems in the context of large deformations as the proposed formulation is based on the mortar method the constraints are imposed in a weak integral sense along the contact surface in order to compute the contact integrals we use a numerical integration based on the definition of the kinematical variables gap slip and their variations at the quadrature points the linearization of non linear equations virtual work and contact constraints is developed in order to apply a newton s method the examples show that the numerical integration still preserves the optimal rate of convergence of the finite element solution

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

stable lagrange multipliers for quadrilateral meshes of curved interfaces in 3d for the discretization of coupled problems by means of mortar finite elements the choice of the discrete lagrange multiplier space is of crucial importance for the performance of the resulting numerical scheme dual lagrange multipliers offer several advantages since they can be locally eliminated in this paper the lowest order dual lagrange multipliers are extended to arbitrary quadrilateral or triangular surface grids in a first step two alternatives are provided for the case of planar interfaces for the approximation of vector fields two more modifications are given for use on curvilinear interfaces a priori results are obtained and several numerical examples are shown

asymptotic analysis of the lattice boltzmann equation in this article we analyze the lattice boltzmann equation lbe by using the asymptotic expansion technique we first relate the lbe to the finite discrete velocity model fdvm of the boltzmann equation with the diffusive scaling the analysis of this model directly leads to the incompressible navier stokes equations as opposed to the compressible navier stokes equations obtained by the chapman enskog analysis with convective scaling we also apply the asymptotic analysis directly to the fully discrete lbe as opposed to the usual practice of analyzing a continuous equation obtained through the taylor expansion of the lbe this leads to a consistency analysis which provides order by order information about the numerical solution of the lbe the asymptotic technique enables us to analyze the structure of the leading order errors and the accuracy of numerically derived quantities such as vorticity it also justifies the use of richardson s extrapolation method as an example a two dimensional taylor vortex flow is used to validate our analysis the numerical results agree very well with our analytic predictions

biorthogonal splines for optimal weak patch coupling in isogeometric analysis with applications to finite deformation elasticity abstract a new construction of biorthogonal splines for isogeometric mortar methods is proposed the biorthogonal basis has a local support and at the same time optimal approximation properties which yield optimal results with mortar methods we first present the univariate construction which has an inherent crosspoint modification the multivariate construction is then based on a tensor product for weighted integrals whereby the important properties are inherited from the univariate case numerical results including large deformations confirm the optimality of the newly constructed biorthogonal basis

constrained pareto optimization of wide band and steerable concentric ring arrays a multi objective evolutionary algorithm that explicitly introduces the management of a single or multiple constraints on the solutions of an electromagnetic problem is presented in this paper the proposed strategy is based upon a modified genetic algorithm which evaluates the strength of a solution by considering both the match to the desired performance objectives as well as the satisfaction of specific requirements imposed to the design constraints the key issue is represented by the adaptive constraints management and its influence on the selective pressure of the genetic algorithm the procedure is applied to the optimization of concentric ring arrays several design examples of steerable and wideband arrays are provided to prove the flexibility and reliability of the approach a particular emphasis is given to the changes in array performance when the same objectives are requested but different kinds of constraints are forced

formulation and comparison of algorithms for frictional contact problems this paper presents two algorithms for solving the discrete quasi static small displacement linear elastic contact problem with coulomb friction the algorithms are adoptions of a newton method for solving b differentiable equations and an interior point method for solving smooth constrained equations for the application of the former method the contact problem is formulated as a system of b differentiable equations involving the projection operator onto sets with simple structure for the application of the latter method the contact problem is formulated as a system of smooth equations involving complementarity conditions and with the non negativity of variables treated as constraints the two algorithms are numerically tested for two dimensional problems containing up to 100 contact nodes and up to 100 time increments results show that at the present stage of development the newton method is superior both in robustness and speed additional comparison is made with a commercial finite element code

a segment to segment mortar contact method for quadratic elements and large deformations abstract this paper describes a new extension of mortar based segment to segment algorithms for large deformation contact analysis permitting their use when quadratic interpolations are used in the underlying finite element method the work builds upon results previously described by puso and laursen m a puso t a laursen a mortar segment to segment contact method for large deformation solid mechanics comput methods appl mech engrg 193 2004 601 629 m a puso t a laursen a mortar segment to segment frictional contact method for large deformations comput methods appl mech engrg 193 2004 601 629 where methods were developed for quasistatic and implicit dynamic analysis in the context of linear element interpolations here we see that many algorithmic ideas from the linear case can be adopted for use with quadratic elements along with different alternative interpolations of the mortar contact multipliers the result is a class of methods appropriate for use for either mesh tying true large sliding simulation frictionless or frictional and readily admits mixing of element types several numerical examples are given to demonstrate the effectiveness of the approach

a finite deformation mortar contact formulation using a primal dual active set strategy in recent years nonconforming domain decomposition techniques and in particular the mortar method have become popular in developing new contact algorithms here we present an approach for two dimensional frictionless multibody contact based on a mortar formulation and using a primal dual active set strategy for contact constraint enforcement we consider linear and higher order quadratic interpolations throughout this work so called dual lagrange multipliers are introduced for the contact pressure but can be eliminated from the global system of equations by static condensation thus avoiding an increase in system size for this type of contact formulation we provide a full linearization of both contact forces and normal non penetration and tangential frictionless sliding contact constraints in the finite deformation frame the necessity of such a linearization in order to obtain a consistent newton scheme is demonstrated by further interpreting the active set search as a semi smooth newton method contact nonlinearity and geometrical and material nonlinearity can be resolved within one single iterative scheme this yields a robust and highly efficient algorithm for frictionless finite deformation contact problems numerical examples illustrate the efficiency of our method and the high quality of results

a mortar method for energy momentum conserving schemes in frictionless dynamic contact problems summary in the present work the mortar method is applied to planar large deformation contact problems without friction in particular the proposed form of the mortar contact constraints is invariant under translations and rotations these invariance properties lay the foundation for the design of energy momentum timestepping schemes for contact impact problems the iterative solution procedure is embedded into an active set algorithm lagrange multipliers are used to enforce the mortar contact constraints the solution of generalized saddle point systems is circumvented by applying the discrete null space method numerical examples demonstrate the robustness and enhanced numerical stability of the newly developed energymomentum scheme copyright q 2008 john wiley sons ltd

parallel particle swarm optimization and finite difference time domain pso fdtd algorithm for multiband and wide band patch antenna designs this paper presents a novel evolutionary optimization methodology for multiband and wide band patch antenna designs the particle swarm optimization pso and the finite difference time domain fdtd are combined to achieve the optimum antenna satisfying a certain design criterion the antenna geometric parameters are extracted to be optimized by pso and a fitness function is evaluated by fdtd simulations to represent the performance of each candidate design the optimization process is implemented on parallel clusters to reduce the computational time introduced by full wave analysis two examples are investigated in the paper first the design of rectangular patch antennas is presented as a test of the parallel pso fdtd algorithm the optimizer is then applied to design e shaped patch antennas it is observed that by using different fitness functions both dual frequency and wide band antennas with desired performance are obtained by the optimization the optimized e shaped patch antennas are analyzed fabricated and measured to validate the robustness of the algorithm the measured less than 18 db return loss for dual frequency antenna and 30 5 bandwidth for wide band antenna exhibit the prospect of the parallel pso fdtd algorithm in practical patch antenna designs

a multi level optimization method using pso for the optimal design of an l shaped folded monopole antenna array this study presents a multi level optimization mlo method applied in particle swarm optimization pso to solve a 3 objective optimization problem for an antenna array design consisting of two l shaped folded monopole antennas lfmas operating in the ieee 802 11 b g wlan band 2400 2484 mhz the method incorporates a simple concept whereby three sub objective functions representing the reflection coefficient s 11 the mutual coupling s 21 and the entire antenna volume of the lfma array are minimized one by one in the pso to obtain an optimal lfma array configuration that provides reduced size and higher antenna performance the advantages of the proposed method both in terms of deriving appropriate optimization results and reducing computational cost for the optimization problem are demonstrated by comparing its performance with that of a conventional weighted aggregation cwa method and a method using the concept of pareto dominance pd the optimal lfma array configuration obtained by the proposed method has a 10 resonant bandwidth s 11 10 db for 2 32 2 57 ghz s 21 reduced to less than 15 db in this band and an antenna volume that was markedly decreased to 28 5 of that of the original design

lattice boltzmann simulations of blood flow non newtonian rheology and clotting processes the numerical simulation of thrombosis in stented aneurysms is an important issue to estimate the efficiency of a stent in this paper we consider a lattice boltzmann lb approach to bloodflow modeling and we implement a non newtonian correction in order to reproduce more realistic flow profiles we obtain a good agreement between simulations and casson s model of blood rheology in a simple geometry finally we discuss how by using a passive scalar suspension model with aggregation on top of the lb dynamics we can describe the clotting processes in the aneurysm

a second order accurate lattice boltzmann non newtonian flow model a second order accurate lattice boltzmann model is presented for non newtonian flow the non newtonian nature of the flow is implemented using a power law model this is used to enable the accuracy of the model to be assessed and is not a limitation of the model the second order accuracy is demonstrated for a range of power law model parameter values representing shear thinning and shear thickening fluids these results are compared with those of gabbanelli et al 2006 phys rev e 72 046312 and it is noted that a higher order of accuracy and greater computational efficiency are achieved these results demonstrate the suitability of the lbm for shear dependent non newtonian flow simulations

a mortar finite element method using dual spaces for the lagrange multiplier the mortar finite element method allows the coupling of different discretization schemes and triangulations across subregion boundaries in the original mortar approach the matching at the interface is realized by enforcing an orthogonality relation between the jump and a modified trace space which serves as a space of lagrange multipliers in this paper this lagrange multiplier space is replaced by a dual space without losing the optimality of the method the advantage of this new approach is that the matching condition is much easier to realize in particular all the basis functions of the new method are supported in a few elements the mortar map can be represented by a diagonal matrix in the standard mortar method a linear system of equations must be solved the problem is considered in a positive definite nonconforming variational as well as an equivalent saddle point formulation

lattice boltzmann method for 3 d flows with curved boundary in this work we investigate two issues that are important to computational efficiency and reliability in fluid dynamic applications of the lattice boltzmann equation lbe 1 computational stability and accuracy of different lattice boltzmann models and 2 the treatment of the boundary conditions on curved solid boundaries and their 3 d implementations three athermal 3 d lbe models q15d3 q19d3 and q27d3 are studied and compared in terms of efficiency accuracy and robustness the boundary treatment recently developed by filippova and hanel 1998 j comp phys 147 219 and mei et al 1999 j comp phys 155 307 in 2 d is extended to and implemented for 3 d the convergence stability and computational efficiency of the 3 d lbe models with the boundary treatment for curved boundaries were tested in simulations of four 3 d flows 1 fully developed flows in a square duct 2 flow in a 3 d lid driven cavity 3 fully developed flows in a circular pipe and 4 a uniform flow over a sphere we found that while the 15 velocity 3 d q15d3 model is more prone to numerical instability and the q27d3 is more computationally intensive the q19d3 model provides a balance between computational reliability and efficiency through numerical simulations we demonstrated that the boundary treatment for 3 d arbitrary curved geometry has second order accuracy and possesses satisfactory stability characteristics

incompressible limits of lattice boltzmann equations using multiple relaxation times lattice boltzmann equations using multiple relaxation times are intended to be more stable than those using a single relaxation time the additional relaxation times may be adjusted to suppress non hydrodynamic modes that do not appear directly in the continuum equations but may contribute to instabilities on the grid scale if these relaxation times are fixed in lattice units as in previous work solutions computed on a given lattice are found to diverge in the incompressible small mach number limit this non existence of an incompressible limit is analysed for an inclined one dimensional jet an incompressible limit does exist if the non hydrodynamic relaxation times are not fixed but scaled by the mach number in the same way as the hydrodynamic relaxation time that determines the viscosity

a dual mortar approach for 3d finite deformation contact with consistent linearization in this paper an approach for three dimensional frictionless contact based on a dual mortar formulation and using a primal dual active set strategy for direct constraint enforcement is presented we focus on linear shape functions but briefly address higher order interpolation as well the study builds on previous work by the authors for two dimensional problems first and foremost the ideas of a consistently linearized dual mortar scheme and of an interpretation of the active set search as a semi smooth newton method are extended to the 3d case this allows for solving all types of nonlinearities i e geometrical material and contact within one single newton scheme owing to the dual lagrange multiplier approach employed this advantage is not accompanied by an undesirable increase in system size as the lagrange multipliers can be condensed from the global system of equations moreover it is pointed out that the presented method does not make use of any regularization of contact constraints numerical examples illustrate the efficiency of our method and the high quality of results in 3d finite deformation contact analysis

a primal dual active set strategy for non linear multibody contact problems abstract non conforming domain decomposition methods provide a powerful tool for the numerical approximation of partial differential equations for the discretization of a non linear multibody contact problem we use the mortar approach with a dual lagrange multiplier space to handle the non linearity of the contact conditions we apply a primal dual active set strategy to find the actual contact zone the algorithm can be easily generalized to multibody contact problems a suitable basis transformation guarantees the same algebraic structure in the multibody situation as in the one body case using an inexact primal dual active set strategy in combination with a multigrid method yields an efficient iterative solver different numerical examples for one and multibody contact problems illustrate the performance of the method

lattice boltzmann method for non newtonian power law fluids we study an ad hoc extension of the lattice boltzmann method that allows the simulation of non newtonian fluids described by generalized newtonian models we extensively test the accuracy of the method for the case of shear thinning and shear thickening truncated power law fluids in the parallel plate geometry and show that the relative error compared to analytical solutions decays approximately linear with the lattice resolution finally we also tested the method in the reentrant flow geometry in which the shear rate is no longer a scalar and the presence of two singular points requires high accuracy in order to obtain satisfactory resolution in the local stress near these points in this geometry we also found excellent agreement with the solutions obtained by standard finite element methods and the agreement improves with higher lattice resolution