cutfem topology optimization of 3d laminar incompressible flow problems abstract this paper studies the characteristics and applicability of the cutfem approach of burman et al 2014 as the core of a robust topology optimization framework for 3d laminar incompressible flow and species transport problems at low reynolds numbers r e 200 cutfem is a methodology for discretizing partial differential equations on complex geometries by immersed boundary techniques in this study the geometry of the fluid domain is described by an explicit level set method where the parameters of a discretized level set function are defined as functions of the optimization variables the fluid behavior is modeled by the incompressible navier stokes equations species transport is modeled by an advection diffusion equation the governing equations are discretized in space by a generalized extended finite element method face oriented ghost penalty terms are added for stability reasons and to improve the conditioning of the system the boundary conditions are enforced weakly via nitsche s method the emergence of isolated volumes of fluid surrounded by solid during the optimization process leads to a singular analysis problem an auxiliary indicator field is modeled to identify these volumes and to impose a constraint on the average pressure numerical results for 3d steady state and transient problems demonstrate that the cutfem analyses are sufficiently accurate and the optimized designs agree well with results from prior studies solved in 2d or by density approaches

bubbling solutions for an anisotropic planar elliptic problem with exponential nonlinearity abstract let be a bounded domain in r 2 with smooth boundary we study the following anisotropic elliptic problem a x a x e s 1 h x in 0 on where a x is a positive smooth function h c 0 s 0 is a large parameter and 1 is a positive first eigenfunction of the problem a x a x under dirichlet boundary condition in we construct solutions of this problem which exhibit multiple concentration behavior around maximum points of a x 1 in the domain as s

on nontrivial solutions of a dirichlet problem whose jumping nonlinearity crosses a multiple eigenvalue let be a bounded domain in rn n 2 with smooth boundary let p r r be a continuous function such that p 0 0 and limt p t t p exist we discuss the existence of nontrivial solutions of the dirichlet problem u p u in u 0 on our hypotheses relate the position of the point p p in the plane with the extended spectrum of they seem to allow noticeably greater freedom for the numbers p than is usually found in the literature in the sense that the interval with end points p is here permitted to contain in its interior an eigenvalue of arbitrarily multiplicity of it also appears that we significantly weaken some technical conditions on p of another paper which treats the crossing of a simple eigenvalue

open loop optimal control of a flapping wing using an adjoint lattice boltzmann method abstract we present the usage of an adjoint lattice boltzmann method lbm for open loop control of two dimensional flapping wing motion movement of the wing is parametrised with periodic b splines while the wing interacts with the surrounding flow via an immersed boundary ib method multi objective optimisation is performed using a gradient optimisation algorithm for which sensitivities are calculated with an adjoint method the objectives selected were the mean lift force and mechanical power to achieve performance suitable for optimisation we also present an efficient gpu implementation of the lbm and adjoint lbm the immersed boundary approach employed for the lbm is verified against results from the literature while for the flapping case it is compared with two different finite volume method fvm approaches the obtained pareto front of optimal designs shows a clear discrepancy between the power consumption and the mean lift force a significant improvement of the basic wing design is demonstrated and highlights the applicability of adjoint lbm simulations in complex open loop control problems

on the convergence of the inverses of toeplitz matrices and its applications many issues in signal processing involve the inverses of toeplitz matrices one widely used technique is to replace toeplitz matrices with their associated circulant matrices based on the well known fact that toeplitz matrices asymptotically converge to their associated circulant matrices in the weak sense this often leads to considerable simplification however it is well known that such a weak convergence cannot be strengthened into strong convergence it is this fact that severely limits the usefulness of the close relation between toeplitz matrices and circulant matrices observing that communication receiver design often needs to seek optimality in regard to a data sequence transmitted within finite duration we define the finite term strong convergence regarding two families of matrices we present a condition under which the inverses of a toeplitz matrix converges in the strong sense to a circulant matrix for finite term quadratic forms this builds a critical link in the application of the convergence theorems for the inverses of toeplitz matrices since the weak convergence generally finds its usefulness in issues associated with minimum mean squared error and the finite term strong convergence is useful in issues associated with the maximum likelihood or maximum a posteriori principles

an abstract theorem in nonlinear analysis and two applications abstract we prove abstract multiplicity theorems for a class of nonlinear equations on the hilbert space l 2 then we use these theorems to deduce new results for two different types of nonlinear boundary value problems

le nombre de solutions de certains problemes semi lineaires elliptiques abstract in this paper we compute the exact number of solutions for certain semi linear elliptic problems in the first part we derive some complementary results to a theorem of ambrosetti and prodi the global behaviour of bifurcating branches is then studied for some classes of problems in the context of a concave or a convex nonlinearity in the second part we consider the branch of positive solutions lastly in the third part in dimension one for an autonomous equation we obtain a precise description of all the solutions to these problems the proofs rely on simple eigenvalue comparison arguments

sequence estimation and synchronization from nonsynchronized samples the authors study the problem of maximum likelihood sequence estimation and synchronization from samples of the output of a matched filter taken at integer multiples of the symbol rate which is assumed perfectly known by the receiver a general analysis is presented of sampled receivers that handle arbitrary baseband pulse shapes and arbitrary sampling rates it is observed that the optimal processing of the matched filter samples consists of digital interpolation followed by symbol by symbol decoding when sampling is at or above the nyquist rate or viterbi decoding when sampling is below the nyquist rate performance is studied through the cramer rao bound on mean square estimation error and a lower bound on error probability

solving fluid flow domain identification problems with adjoint lattice boltzmann methods a novel strategy towards solving fluid flow domain identification problems for incompressible newtonian fluids is proposed and investigated in this paper the resulting numerical approach is of great importance for academic studies as well as for medical and industrial applications for example it can be used in combination with phase contrast mri measurements to characterise flow dynamics as well as flow domains highly accurately the problem is formulated as a optimisation problem which minimised the distance between a given and a simulated flow field whereby the latter one is the solution of a parameterised porous media bgk boltzmann model the parameter represents the porosity distributed in the domain and its distribution is obtained as the final result of the optimisation problem the proposed gradient based solution strategy makes use of an adjoint lattice boltzmann method albm due to their similar structure to lattice boltzmann methods lbm they also show excellent parallelisation behaviour in this preliminary work first validation results are presented as well as performance results and improvements for both single core and parallel implementation in particular with a simple domain identification test case a cube is being identified by position and shape inside a wind tunnel in only few optimisation steps even with only partial flow data being available

depth averaged lattice boltzmann and finite element methods for single phase flows in fractures with obstacles abstract we use lattice boltzmann method lbm mrt and cumulant schemes to study the performance and accuracy of single phase flow modeling for propped fractures the simulations are run using both the two and three dimensional stokes equations and a 2 5d stokes brinkman approximate model the lbm results are validated against finite element method fem simulations and an analytical solution to the stokes brinkman flow around an isolated circular obstacle both lbm and fem 2 5d stokes brinkman models are able to reproduce the analytical solution for an isolated circular obstacle in the case of 2d stokes and 2 5d stokes brinkman models the differences between the extrapolated fracture permeabilities obtained with lbm and fem simulations for fractures with multiple obstacles are below 1 the differences between the fracture permeabilities computed using 3d stokes lbm and fem simulations are below 8 the differences between the 3d stokes and 2 5 stokes brinkman results are less than 7 for fem study and 8 for the lbm case the velocity perturbations that are introduced around the obstacles are not fully captured by the parabolic velocity profile inherent to the 2 5d stokes brinkman model

adjoint based fluid flow control and optimisation with lattice boltzmann methods a lattice boltzmann lb framework to solve fluid flow control and optimisation problems numerically is presented problems are formulated on a mesoscopic basis in a side condition the dynamics of a newtonian fluid is described by a family of simplified boltzmann like equations namely bgk boltzmann equations which are linked to an incompressible navier stokes equation it is proposed to solve the non linear optimisation problem by a line search algorithm the needed derivatives are obtained by deriving the adjoint equations referred to as adjoint bgk boltzmann equations the primal equations are discretised by standard lattice boltzmann methods lbm while for the adjoint equations a novel discretisation strategy is introduced the approach follows the main ideas behind lbm and is therefore referred to as adjoint lattice boltzmann methods albm the corresponding algorithm retains most of the basic features of lb algorithms in particular it enables a highly efficient parallel implementation and thus solving large scale fluid flow control and optimisation problems the overall solution strategy the derivation of a prototype adjoint bgk boltzmann equation the novel albm and its parallel realisation as well as its validation are discussed in detail in this article numerical and performance results are presented for a series of steady state distributed control problems with up to approximately 1 6 million unknown control parameters obtained on a high performance computer with up to 256 processing units

discrete adjoint sensitivity analysis for fluid flow topology optimization based on the generalized lattice boltzmann method abstract a discrete adjoint sensitivity analysis for fluid flow topology optimization based on the lattice boltzmann method lbm with multiple relaxation times mrt is developed the lattice boltzmann fluid solver is supplemented by a porosity model using a darcy force the continuous transition from fluid to solid facilitates a gradient based optimization process of the design topology of fluidic channels the adjoint lbm equation which is used to compute the gradient of the optimization objective with respect to the design variables is derived in moment space and found to be as simple as the original lbm the moment based spatial momentum derivatives used to express the discrete objective functional cost function have the advantage that the local stress tensor is a local quantity avoiding the numerical computation of gradients of the discrete velocity field this is particularly useful if dissipation is a design criterion as demonstrated in this paper the method is validated by a detailed comparison with results obtained by borrvall et al for stokes flow while their approach is only valid for stokes flow i e very low reynolds numbers our approach in its present form can in principle be applied for flows of different reynolds numbers just like the navier stokes equation based approaches this point is demonstrated with a bending pipe example for various reynolds numbers

multiple solutions for a semilinear boundary value problem a computational multiplicity proof abstract we prove the first genuine partial differential equation result on a conjecture concerning the number of solutions of second order elliptic boundary value problems with a nonlinearity which grows superlinearly at the proof makes massive use of computer assistance after approximate solutions have been computed by a numerical mountain pass algorithm combined with a newton iteration to improve accuracy a fixed point argument is used to show the existence of exact solutions close to the approximations

a counterexample to the lazer mckenna conjecture on donne un contre exemple complet a une conjecture de lazer et mckenna si f r r est c 1 si f 1 y quand y si 1 si l et si contient au moins k 1 valeurs propres de sur alors l equation u f u t 1 v dans u 0 sur a au moins 2 k 1 solutions pour t positif grand

a stable discretization of the lattice boltzmann equation for simulation of incompressible two phase flows at high density ratio a stable discretization of the lattice boltzmann equation lbe for non ideal gases is presented for simulation of incompressible two phase flows having high density and viscosity ratios the stiffness of the discretized forcing terms in lbe for non ideal gases is known to trigger severe numerical instability and restrict practical application of the lbe method use of a proper pressure updating scheme is also crucial to the stability of the lbe method because of non negligible pressure variation across the phase interface to deal with these issues we propose a stable discretization scheme which assumes the low mach number approximation and utilizes the stress and potential forms of the surface tension force the incompressible transformation and the consistent discretization of the intermolecular forcing terms the proposed stable discretization scheme is applied to simulate 1 d advection equation with a source term a stationary droplet droplet oscillation and droplet splashing and deposition on a thin film at a density ratio of 1000 with varying reynolds numbers the numerical solutions of stationary and oscillatory droplets agree well with analytic solutions including the laplace s law the time history of the spread factor of the liquid sheet emitted after the droplet impact also follows the known spreading power law

sign changing semi classical solutions of the brezis nirenberg problems with jump nonlinearities in high dimensions abstract in this paper we consider the following elliptic equation e 2 u u u u p 2 u u 2 2 u in u 0 on where r n n 4 is a bounded domain u max u 0 0 are constants e 0 is a small parameter and 2 p 2 2 n n 2 we obtain a least energy sign changing solution to this problem for e 0 that is sufficiently small by means of the variational method furthermore by combining the elliptic and local energy estimates we study the concentration behavior of this least energy sign changing solution and the location of the positive and negative spikes as e 0 our results partially complete the studies in 6 2011 in the sense that due to sobolev embedding only subcritical cases are considered in that paper

the expectation maximization algorithm for symbol unsynchronized sequence detection the expectation maximization em algorithm for maximizing likelihood functions combined with the viterbi algorithm is applied to the problem of sequence detection when symbol timing information is not present although the em algorithm is noncausal results obtained using the algorithm on the problem of nonsynchronized sequence detection indicate that it converges most of the time in three iterations making it both of theoretical and of practical interest a practical algorithm based on the em algorithm is introduced it reduces the computational burden and improves performance by making use of timing estimates in previous observation windows

on the maximum of solutions for a semilinear elliptic problem on etudie certaines proprietes d un probleme aux valeurs propres semilineaires elliptique avec second membre non defini on montre que chaque solution doit avoir son maximum dans un intervalle specifie j

level set based topology optimization of transient flow using lattice boltzmann method considering an oscillating flow condition abstract topology optimization is widely applied to various design problems in both structure and fluid dynamics engineering specifically the development of energy dissipation devices with vibration control remains a key consideration the aim of this study is to improve devices that maximize the absorption or dissipation of the vibration of an oscillating object and propose an approach in which the level set based topology optimization of transient flow using the lattice boltzmann method is simultaneously applied to forward and reverse direction flows to deal with oscillating flows in real world engineering designs although several studies have examined topology optimization to minimize dissipated kinetic energy this study introduces an objective function for maximizing the dissipated kinetic energy in time varying fluid flows via velocity gradients

topology optimization using the lattice boltzmann method incorporating level set boundary expressions this paper presents a topology optimization method for fluid dynamics problems based on the level set method and using the lattice boltzmann method lbm in this optimization method the optimization problems are formulated based on the original boltzmann equation and the design sensitivities are precisely obtained without the time consuming numerical operations encountered when dealing with a large scale asymmetric matrix in contrast to previous research in which the lbm uses the lattice boltzmann equation lbe for the formulations of optimization problems and the derivation of their adjoint equations that is we newly derive sensitivity formulations from the original boltzmann equation not the lbe that can be said to be an approximated equation and these formulations yield strictly correct sensitivities that are error free based on the above formulations we construct a level set based topology optimization method incorporating a fictitious interface energy for the design of a fluid channel that minimizes flow friction furthermore two and three dimensional numerical examples are provided to confirm the validity and utility of the presented method

a cascaded phase field lattice boltzmann model for the simulation of incompressible immiscible fluids with high density contrast abstract in this work a conservative phase field model for the simulation of immiscible multiphase flows is developed using an incompressible velocity based cascaded lattice boltzmann method clbm extensions are made to the lattice boltzmann lb equations for interface tracking and incompressible hydrodynamics proposed by fakhari et al 1 by performing relaxation operations in central moment space this was motivated by the work of fei et al 2 3 where promising results from such a transformation were observed the relaxation of central moments is defined in a reference frame moving with the fluid while the existing multiple relaxation time 4 5 scheme performs collision in a fixed frame of reference moreover the derivations make use of continuous maxwellian distribution functions as a result the clbm enhances the galilean invariance and stability of the method when high lattice mach numbers are evident the cascaded scheme has been previously used in the literature to simulate multiphase flows based on the pseudo potential model where it allowed for high density and viscosity contrasts to be captured 6 7 here the clbm is implemented within the phase field framework and is verified through the analysis of a layered poiseuille flow the performance of the clbm is then investigated in terms of spurious currents galilean invariance and computational efficiency finally the work of fakhari et al 1 is extended by validating the model s ability to capture the relation between surface tension and the rise velocity of a planar taylor bubble in both stagnant and flowing fluids new counter current results indicate that the rise velocity model of ha ngoc and fabre 8 also applies in this regime

existence and multiplicity of solutions for elliptic equations with jumping nonlinearities abstract in this paper we are concerned with a semilinear elliptic dirichlet problem with jumping nonlinearity and using a completely variational method we show that the number of solutions may be arbitrarily large provided the number of jumped eigenvalues is large enough in order to prove this fact we show that for every positive integer k when a suitable parameter is large enough there exists a solution which presents k peaks under the assumptions we consider in this paper new unexpected phenomena are observed in the study of this problem and new methods are required to construct the k peaks solutions and describe their asymptotic behavior weak limits of the rescaled solutions localization of the concentration points of the peaks asymptotic profile of the rescaled peaks etc

remarks and generalizations related to a recent multiplicity result of a lazer and p mckenna we will show here that this result has a natural generalization to the case that u 5 ai to state the result we consider the model problem lu au autel 2 where 0 0 and set t 0 we have a nonlinear eigenvalue problem lu yu au 4 the following proposition is known cf fueik 3 dancer 2 and also lo where the result appears in the formulation given below

lazer mckenna conjecture the critical case abstract we consider an elliptic problem of ambrosetti prodi type involving critical sobolev exponent on a bounded smooth domain of dimension six or higher by constructing solutions with many sharp peaks near the boundary of the domain but not on the boundary we prove that the number of solutions for this problem is unbounded as the parameter tends to infinity thereby proving the lazer mckenna conjecture in the critical case

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

a bpsk qpsk timing error detector for sampled receivers a simple algorithm for detection of timing error of a synchronous band limited bpsk or qpsk data stream is proposed the algorithm requires only two samples per symbol for its operation one of the two samples is also used for the symbol decision derivation of the s curve reveals a sinusoidal shape

on the superlinear ambrosetti prodi problem l et be a smooth bounded domain in r n we consider the semilinear elliptic boundary value problem

on the performance limits of data aided synchronization this paper addresses data aided da synchronization in which the reference parameter acquisition is aided by a training sequence known to the receiver the cramer rao lower bound crb for the da timing and or carrier phase recovery is presented for da parameter estimation the crb typically varies with the training sequence this indicates that different training sequences offer fundamentally different performance in the literature the widely cited closed form crb for timing and carrier phase recovery was derived under the assumption that the training sequence is independent and identically distributed i i d and sufficiently long we derive a closed form crb for timing and carrier phase recovery with respect to an arbitrary training sequence and pulse shaping function for the over and under sampling cases it turns out that the crb is a weighted summation of the aperiodic correlation of the training sequence and the weighting factor is determined by the pulse shaping filter therefore this paper reveals the fundamental link between a training sequence and its corresponding performance limit

the exact number of solutions for a class of ordinary differential equations through morse index computation we consider a class of second order ordinary differential equations with jumping nonlinearities that cross the first k eigenvalues under zero boundary conditions and by means of a morse index computation show the existence of exactly 2 k solutions

on the superlinear lazer mckenna conjecture abstract we prove the lazer mckenna conjecture for a superlinear elliptic problem of ambrosetti prodi type by constructing solutions with sharp peaks

the method of moving asymptotes a new method for structural optimization a new method for non linear programming in general and structural optimization in particular is presented in each step of the iterative process a strictly convex approximating subproblem is generated and solved the generation of these subproblems is controlled by so called moving asymptotes which may both stabilize and speed up the convergence of the general process

adjoint lattice boltzmann for topology optimization on multi gpu architecture in this paper we present a topology optimization technique applicable to a broad range of flow design problems we propose also a discrete adjoint formulation effective for a wide class of lattice boltzmann methods lbm this adjoint formulation is used to calculate sensitivity of the lbm solution to several type of parameters both global and local the numerical scheme for solving the adjoint problem has many properties of the original system including locality and explicit time stepping thus it is possible to integrate it with the standard lbm solver allowing for straightforward and efficient parallelization overcoming limitations typical for the discrete adjoint solvers this approach is successfully used for the channel flow to design a free topology mixer and a heat exchanger both resulting geometries being very complex maximize their objective functions while keeping viscous losses at acceptable level