theory and investigation of acoustic multiple input multiple output systems based on spherical arrays in a room spatial attributes of room acoustics have been widely studied using microphone and loudspeaker arrays however systems that combine both arrays referred to as multiple input multiple output mimo systems have only been studied to a limited degree in this context these systems can potentially provide a powerful tool for room acoustics analysis due to the ability to simultaneously control both arrays this paper offers a theoretical framework for the spatial analysis of enclosed sound fields using a mimo system comprising spherical loudspeaker and microphone arrays a system transfer function is formulated in matrix form for free field conditions and its properties are studied using tools from linear algebra the system is shown to have unit rank regardless of the array types and its singular vectors are related to the directions of arrival and radiation at the microphone and loudspeaker arrays respectively the formulation is then generalized to apply to rooms using an image source method in this case the rank of the system is related to the number of significant reflections the paper ends with simulation studies which support the developed theory and with an extensive reflection analysis of a room impulse response using the platform of a mimo system

parallel multilevel solution of nonlinear shell structures the analysis of large scale nonlinear shell problems asks for parallel simulation approaches one crucial part of effi cient and well scalable parallel fe simulations is the solver for the system of equations due to the inherent suitability for parallelization one is verymuch directed towards preconditioned iterative solvers however thin walled structures discretized byfinite elements lead to ill conditioned system matrices and therefore performance of iterative solvers is generallypoor this situation further deteriorates when the thickness change of the shell is taken into account a preconditioner for this challenging class of problems is presented combining two approaches in a parallel framework the first approach is a mechanicallymotivated improvement called scaled director conditioning sdc and is able to remove the extra ill conditioning that appears with three dimensional shell formulations as compared to formulations that neglect thickness change of the shell it is introduced at the element level and harmonizes well with the second approach utilizing a multilevel algorithm here a hierarchyof coarse grids is generated in a semi algebraic sense using an aggregation concept therebythe complicated and expensive explicit generation of course triangulations can be avoided the formulation of this combined preconditioning approach is given and the effects on the performance of iterative solvers is demonstrated via numerical examples

treating inhomogeneous essential boundary conditions in finite element methods and the calculation of boundary stresses finite element approximations of the stokes and navier stokes equations with in homogeneous essential boundary conditions are considered boundary conditions are enforced weakly by introducing lagrange multipliers optimal error estimates including some for the stress vector on the boundary are derived under minimal regularity assumptions on the data particular attention is paid to the analysis of a practical choice of finite element spaces for which the lagrange multiplier calculation uncouples from that for the velocity and pressure the results are also applicable to general second order elliptic systems

deconvolution for three dimensional acoustic source identification based on spherical harmonics beamforming abstract spherical harmonics beamforming shb with solid spherical arrays has become a particularly attractive tool for doing acoustic sources identification in cabin environments however it presents some intrinsic limitations specifically poor spatial resolution and severe sidelobe contaminations this paper focuses on overcoming these limitations effectively by deconvolution first and foremost a new formulation is proposed which expresses shb s output as a convolution of the true source strength distribution and the point spread function psf defined as shb s response to a unit strength point source additionally the typical deconvolution methods initially suggested for planar arrays deconvolution approach for the mapping of acoustic sources damas nonnegative least squares nnls richardson lucy rl and clean are adapted to shb successfully which are capable of giving rise to highly resolved and deblurred maps finally the merits of the deconvolution methods are validated and the relationships of source strength and pressure contribution reconstructed by the deconvolution methods vs focus distance are explored both with computer simulations and experimentally several interesting results have emerged from this study 1 compared with shb damas nnls rl and clean all can not only improve the spatial resolution dramatically but also reduce or even eliminate the sidelobes effectively allowing clear and unambiguous identification of single source or incoherent sources 2 the availability of rl for coherent sources is highest then damas and nnls and that of clean is lowest due to its failure in suppressing sidelobes 3 whether or not the real distance from the source to the array center equals the assumed one that is referred to as focus distance the previous two results hold 4 the true source strength can be recovered by dividing the reconstructed one by a coefficient that is the square of the focus distance divided by the real distance from the source to the array center 5 the reconstructed pressure contribution is almost not affected by the focus distance always approximating to the true one this study will be of great significance to the accurate localization and quantification of acoustic sources in cabin environments

super resolution on the sphere using convex optimization this paper considers the problem of recovering an ensemble of diracs on a sphere from its low resolution measurements the diracs can be located at any location on the sphere not necessarily on a grid we show that under a separation condition one can recover the ensemble with high precision by a three stage algorithm which consists of solving a semi definite program root finding and least square fitting the algorithm s computation time depends solely on the number of measurements and not on the required solution accuracy we also show that in the special case of non negative ensembles a sparsity condition is sufficient for recovery furthermore in the discrete setting we estimate the recovery error in the presence of noise as a function of the noise level and the super resolution factor

near field acoustic source localization and beamforming in spherical harmonics domain in this paper we address the issue of near field source localization using spherical microphone array the spherical array has been widely used for far field source localization due to ease of array processing in spherical harmonics domain various methods for far field source localization has been reformulated in spherical harmonics domain however near field source localization that involves joint estimation of range and bearing of the sources has hitherto not been investigated in this paper the near field data model is developed in spherical harmonics domain in particular three methods that jointly estimate the range and bearing of multiple sources in the spherical array framework are proposed two subspace based methods called the spherical harmonic multiple signal classification sh music and the spherical harmonics music group delay sh mgd for near field source localization are first presented in addition a method for near field source localization and beamforming using spherical harmonic mvdr sh mvdr is also formulated formulation and analysis of cramer rao bound for near field sources is presented in spherical harmonics domain various source localization experiments were conducted on simulated and signal acquired over spherical microphone array in an anechoic chamber root mean square error and probability of resolution are utilized as measures to evaluate the proposed methods the significance and practical application of the proposed methods is discussed using experiment on interference suppression the near field sh mvdr beamforming is utilized in this context

semidiscrete finite element approximations of a linear fluid structure interaction problem semidiscrete finite element approximations of a linear fluid structure interaction problem are studied first results concerning a divergence free weak formulation of the interaction problem are reviewed next semidiscrete finite element approximations are defined and the existence of finite element solutions is proved with the help of an auxiliary discretely divergence free formulation a discrete inf sup condition is verified and the existence of a finite element pressure is established strong a priori estimates for the finite element solutions are also derived then by passing to the limit in the finite element approximations the existence of a strong solution is demonstrated and semidiscrete error estimates are obtained

dolph chebyshev beampattern design for spherical arrays spherical arrays with array processing based on spherical harmonics have been recently studied for a wide range of applications that require three dimensional beamforming in this correspondence a dolph chebychev beampattern design widely used in array processing due to the direct control over main lobe width and maximum sidelobe level is developed for spherical arrays within the spherical harmonics framework we show that due to the similarity between the legendre polynomials that define the spherical array beampattern and the chebyshev polynomials that define the desired dolph chebyshev beampattern spherical array weights can be computed directly and accurately given desired main lobe width or sidelobe level

galerkin finite element methods with symmetric pressure stabilization for the transient stokes equations stability and convergence analysis we consider the stability and convergence analysis of pressure stabilized finite element approximations of the transient stokes equation the analysis is valid for a class of symmetric pressure stabilization operators but also for standard inf sup stable velocity pressure spaces without stabilization provided the initial data are chosen as a specific method dependent ritz projection we get unconditional stability and optimal convergence for both pressure and velocity approximations in natural norms for arbitrary interpolations of the initial data a condition between the space and time discretization parameters has to be verified in order to guarantee pressure stability

convergence analysis of a projection semi implicit coupling scheme for fluid structure interaction problems in this paper we provide a convergence analysis of a projection semi implicit scheme for the simulation of fluid structure systems involving an incompressible viscous fluid the error analysis is performed on a fully discretized linear coupled problem a finite element approximation and a semi implicit time stepping strategy are respectively used for space and time discretization the fluid is described by the stokes equations the structure by the classical linear elastodynamics equations linearized elasticity plate or shell models and all changes of geometry are neglected we derive an error estimate in finite time and we prove that the time discretization error for the coupling scheme is at least sqrt delta t finally some numerical experiments that confirm the theoretical analysis are presented

a coupled momentum method for modeling blood flow in three dimensional deformable arteries abstract blood velocity and pressure fields in large arteries are greatly influenced by the deformability of the vessel moreover wave propagation phenomena in the cardiovascular system can only be described considering wall deformability since blood is usually described as an incompressible fluid however computational methods for simulating blood flow in three dimensional models of arteries have either considered a rigid wall assumption for the vessel or significantly simplified or reduced geometries computing blood flow in deformable domains using standard techniques like the ale method remains a formidable problem for large realistic anatomic and physiologic models of the cardiovascular system we have developed a new method to simulate blood flow in three dimensional deformable models of arteries the method couples the equations of the deformation of the vessel wall at the variational level as a boundary condition for the fluid domain we consider a strong coupling of the degrees of freedom of the fluid and the solid domains and a linear membrane model enhanced with transverse shear for the vessel wall the effect of the vessel wall boundary is therefore added in a monolithic way to the fluid equations resulting in a remarkably robust scheme we present here the mathematical formulation of the method and discuss issues related to the fluid solid coupling membrane formulation time integration method and boundary and initial conditions implementation is discussed and results with simple geometries as well as large subject specific models are presented

a loosely coupled scheme for the interaction between a fluid elastic structure and poroelastic material abstract we model the interaction between an incompressible viscous fluid thin elastic structure and a poroelastic material the poroelastic material is modeled using the biot s equations of dynamic poroelasticity the fluid elastic structure and the poroelastic material are fully coupled giving rise to a nonlinear moving boundary problem with novel energy estimates we present a modular loosely coupled scheme where the original problem is split into the fluid sub problem elastic structure sub problem and poroelasticity sub problem an energy estimate associated with the stability of the scheme is derived in the case where one of the coupling parameters is equal to zero we present numerical tests where we investigate the effects of the material properties of the poroelastic medium on the fluid flow our findings indicate that the flow patterns highly depend on the storativity of the poroelastic material and cannot be captured by considering fluid structure interaction only

numerical analysis of a linearised fluid structure interaction problem this paper describes the numerical analysis of a time dependent linearised fluid structure interaction problems involving a very viscous fluid and an elastic shell in small displacements for simplicity all changes of geometry are neglected a single variational formulation is proposed for the whole problem and generic discretisation strategies are introduced independently on the fluid and on the structure more precisely the space approximation of the fluid problem is realized by standard mixed finite elements the shell is approximated by dkt finite elements and time derivatives are approximated either by midpoint rules or by backward difference formula using fundamental energy estimates on the continuous problem written in a proper functional space on its discrete equivalent and on an associated error evolution equation we can prove that the proposed variational problem is well posed and that its approximation in space and time converges with optimal order to the continuous solution

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

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

a stable partitioned fsi algorithm for incompressible flow and deforming beams an added mass partitioned amp algorithm is described for solving fluid structure interaction fsi problems coupling incompressible flows with thin elastic structures undergoing finite deformations the new amp scheme is fully second order accurate and stable without sub time step iterations even for very light structures when added mass effects are strong the fluid governed by the incompressible navier stokes equations is solved in velocity pressure form using a fractional step method large deformations are treated with a mixed eulerian lagrangian approach on deforming composite grids the motion of the thin structure is governed by a generalized euler bernoulli beam model and these equations are solved in a lagrangian frame using two approaches one based on finite differences and the other on finite elements the key amp interface condition is a generalized robin mixed condition on the fluid pressure this condition which is derived at a continuous level has no adjustable parameters and is applied at the discrete level to couple the partitioned domain solvers special treatment of the amp condition is required to couple the finite element beam solver with the finite difference based fluid solver and two coupling approaches are described a normal mode stability analysis is performed for a linearized model problem involving a beam separating two fluid domains and it is shown that the amp scheme is stable independent of the ratio of the mass of the fluid to that of the structure a traditional partitioned tp scheme using a dirichlet neumann coupling for the same model problem is shown to be unconditionally unstable if the added mass of the fluid is too large a series of benchmark problems of increasing complexity are considered to illustrate the behavior of the amp algorithm and to compare the behavior with that of the tp scheme the results of all these benchmark problems verify the stability and accuracy of the amp scheme results for one benchmark problem modeling blood flow in a deforming artery are also compared with corresponding results available in the literature

well posedness regularity and convergence analysis of the finite element approximation of a generalized robin boundary value problem in this paper we propose the mathematical and finite element analysis of a second order partial differential equation endowed with a generalized robin boundary condition which involves the laplace beltrami operator by introducing a function space h 1 omega gamma of h 1 omega functions with h 1 gamma traces where gamma subseteq partial omega based on a variational method we prove that the solution of the generalized robin boundary value problem possesses a better regularity property on the boundary than in the case of the standard robin problem we numerically solve generalized robin problems by means of the finite element method with the aim of validating the theoretical rates of convergence of the error in the norms associated to the space h 1 omega gamma

galerkin free model reduction for fluid structure interaction using proper orthogonal decomposition abstract a galerkin free model reduction approach for fluid structure interaction fsi is presented in this article the reduced order model rom is based on proper orthogonal decomposition pod where a reduced basis is formed using energy dominant pod modes the reduced basis also consists of characteristics pod time modes that are derived from the pod time modes coefficients by using their periodicity in addition to flow variables the solution state vector comprises the mesh deformation taking into account the structural deformation in fsi a rom solution is obtained by performing a linear interpolation of the reduced basis for changing operating control parameters the proposed galerkin free pod rom approach is demonstrated in terms of two test cases a canonical case study of vortex induced vibration viv of a cylinder at reynolds number r e 100 where simulations are performed for various structural to fluid mass ratios and a shock wave boundary layer induced panel flutter for the second case we use previously computed high fidelity simulations considering only the effect of panel thickness on the aeroelastic coupling between the flexible panel and shock wave boundary layer interaction swbli the inflow is at mach 2 and reynolds number based on panel length r e a 50000 the presented galerking free rom procedure is clean and robust for large mesh deformations in addition to a significantly lower cost of computation compared to the fsi high fidelity simulations

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

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

flow rate boundary problems for an incompressible fluid in deformable domains formulations and solution methods in this paper we consider the numerical solution of the interaction of an incompressible fluid and an elastic structure in a truncated computational domain as well known in this case there is the problem of prescribing realistic boundary data on the artificial sections when only partial data are available this problem has been investigated extensively for the rigid case in this work we start considering the compliant case by focusing on the flow rate conditions for the fluid we propose three formulations of this problem different algorithms for its numerical solution and carry out several 2d numerical simulations with the aim of comparing the performances of the different algorithms

novel modal methods for transient analysis with a reduced order model based on enhanced craig bampton formulation abstract for transient analysis of structural dynamics with reduced order model rom data recovery procedures that use modal methods such as the classical mode acceleration ma and modal displacement md methods are an important step in order to increase the convergence and accuracy of the solution in this work we propose novel ma and md methods for highly accurate transient analysis with a reduced order model based on enhanced craig bampton ecb formulation which is an extension of the classical craig bampton cb method that is a way to reduce the size of a finite element fe model the performance of the proposed data recovery approach is demonstrated with two numerical examples we also investigate the relation between the proposed and classical ma and md methods

generalized sampling expansion for functions on the sphere functions on the sphere appear in several applications including geodesics imaging and acoustics sampling of these functions may result in aliasing if the sampling condition is not met the generalized sampling expansion introduced by papoulis enables the reconstruction of a band limited function sampled at a frequency lower than the nyquist frequency using the outputs of several linear time invariant systems this paper formulates the generalized sampling expansion for functions on the sphere using spherical harmonics decomposition facilitating sub nyquit sampling without aliasing error an analysis of linear systems on the sphere and the aliasing phenomenon in the spherical harmonics domain is presented examples demonstrating the performance of the method and its limitations are studied

a three dimensional computational method for blood flow in the heart 1 immersed elastic fibers in a viscous incompressible fluid abstract this paper describes the numerical solution of the 3 dimensional equations of motion of a viscous incompressible fluid that contains an immersed system of elastic fibers implementation details such as vectorization and the efficient use of external memory are discussed the method is applied to the damped vibrations of a fiber wound toroidal tube and empirical evidence of convergence is presented

a partitioned scheme for fluid composite structure interaction problems we present a benchmark problem and a loosely coupled partitioned scheme for fluid structure interaction with composite structures the benchmark problem consists of an incompressible viscous fluid interacting with a structure composed of two layers a thin elastic layer with mass which is in contact with the fluid and modeled by the koiter membrane shell equations and a thick elastic layer with mass modeled by the equations of linear elasticity an efficient modular partitioned operator splitting scheme is proposed to simulate solutions to the coupled nonlinear fsi problem without the need for sub iterations at every time step an energy estimate associated with unconditional stability is derived for the fully nonlinear fsi problem defined on moving domains two instructive numerical benchmark problems are presented to test the performance of numerical fsi schemes involving composite structures it is shown numerically that the proposed scheme is at least first order accurate both in time and space this work reveals a new physical property of fsi problems involving thin interfaces with mass the inertia of the thin fluid structure interface regularizes solutions to the full fsi problem

an effective fluid structure interaction formulation for vascular dynamics by generalized robin conditions in this work we focus on the modeling and numerical simulation of the fluid structure interaction mechanism in vascular dynamics we first propose a simple membrane model to describe the deformation of the arterial wall which is derived from the koiter shell equations and is applicable to an arbitrary geometry secondly we consider a reformulation of the fluid structure problem in which the newly derived membrane model thanks to its simplicity is embedded into the fluid equations and will appear as a generalized robin boundary condition the original problem is then reduced to the solution of subsequent fluid equations defined on a moving domain and may be achieved with a fluid solver only we also derive a stability estimate for the resulting numerical scheme finally we propose new outflow absorbing boundary conditions which are easy to implement and allow us to reduce significantly the spurious pressure wave reflections that typically appear in artificially truncated computational domains we present several numerical results showing the effectiveness of the proposed approaches

a finite element formulation for the stokes problem allowing equal velocity pressure interpolation abstract in this paper we study a variational formulation of the stokes problem that accommodates the use of equal velocity pressure finite element interpolations the motivation of this method relies on the analysis of a class of fractional step methods for the navier stokes equations for which it is known that equal interpolations yield good numerical results the reason for this turns out to be the difference between two discrete laplacian operators computed in a different manner the formulation of the stokes problem considered here aims to reproduce this effect from the analysis of the finite element approximation of the problem we obtain stability and optimal error estimates using velocity pressure interpolations satisfying a compatibility condition much weaker than the inf sup condition of the standard formulation in particular this condition is fulfilled by the most common equal order interpolations

on finite element approximations of problems having inhomogeneous essential boundary conditions abstract the analysis and implementation of finite element methods for problems with inhomogeneous essential boundary conditions are considered the results are given for linear second order elliptic partial differential equations and for the nonlinear stationary navier stokes equations for certain easily implemented boundary treatments optimal error estimates and numerical examples are provided for problems posed on polyhedral domains

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

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

fluid structure interaction in blood flow capturing non zero longitudinal structure displacement we present a new model and a novel loosely coupled partitioned numerical scheme modeling fluid structure interaction fsi in blood flow allowing non zero longitudinal displacement arterial walls are modeled by a linearly viscoelastic cylindrical koiter shell model capturing both radial and longitudinal displacement fluid flow is modeled by the navier stokes equations for an incompressible viscous fluid the two are fully coupled via kinematic and dynamic coupling conditions our numerical scheme is based on a new modified lie operator splitting that decouples the fluid and structure sub problems in a way that leads to a loosely coupled scheme which is unconditionally stable this was achieved by a clever use of the kinematic coupling condition at the fluid and structure sub problems leading to an implicit coupling between the fluid and structure velocities the proposed scheme is a modification of the recently introduced kinematically coupled scheme for which the newly proposed modified lie splitting significantly increases the accuracy the performance and accuracy of the scheme were studied on a couple of instructive examples including a comparison with a monolithic scheme it was shown that the accuracy of our scheme was comparable to that of the monolithic scheme while our scheme retains all the main advantages of partitioned schemes such as modularity simple implementation and low computational costs

an efficient interface capturing method for a large collection of interacting bodies immersed in a fluid an efficient method to capture an arbitrary number of fluid structure interfaces in a level set framework is built following ideas introduced for contour capturing in image analysis using only three label maps and two distance functions we succeed in locating and evolving the bodies independently in the whole domain and get the distance between the closest bodies in order to apply a collision force whatever the number of cells is the method is applied to rigid solid bodies in order to compare to the results available in the literature in that case a global penalization model uses the label maps to follow the solid bodies all together without a separate computation of each body velocity numerical simulations are performed in two and three dimensions an application to immersed vesicles is also proposed and shows the capability and efficiency of the method to handle numerical contacts between elastic bodies at low resolution two dimensional simulations of vesicles under various flow conditions are presented

multi point taylor expansions of analytic functions taylor expansions of analytic functions are considered with respect to several points allowing confluence of any of them cauchy type formulas are given for coefficients and remainders in the expansions and the regions of convergence are indicated it is explained how these expansions can be used in deriving uniform asymptotic expansions of integrals the method is also used for obtaining laurent expansions in several points as well as taylor laurent expansions

continuous interior penalty finite element method for oseen s equations in this paper we present an extension of the continuous interior penalty method of douglas and dupont interior penalty procedures for elliptic and parabolic galerkin methods in computing methods in applied sciences lecture notes in phys 58 springer verlag berlin 1976 pp 207 216 to oseen s equations the method consists of a stabilized galerkin formulation using equal order interpolation for pressure and velocity to counter instabilities due to the pressure velocity coupling or due to a high local reynolds number we add a stabilization term giving l2 control of the jump of the gradient over element faces edges in two dimensions to the standard galerkin formulation boundary conditions are imposed in a weak sense using a consistent penalty formulation due to nitsche we prove energy type a priori error estimates independent of the local reynolds number and give some numerical examples recovering the theoretical results

fluid structure partitioned procedures based on robin transmission conditions in this article we design new partitioned procedures for fluid structure interaction problems based on robin type transmission conditions the choice of the coefficient in the robin conditions is justified via simplified models the strategy is effective whenever an incompressible fluid interacts with a relatively thin membrane as in hemodynamics applications we analyze theoretically the new iterative procedures on a model problem which represents a simplified blood vessel system in particular the robin neumann scheme exhibits enhanced convergence properties with respect to the existing partitioned procedures the theoretical results are checked using numerical experimentation

modular vs non modular preconditioners for fluid structure systems with large added mass effect in this article we address the numerical simulation of fluid structure interaction fsi problems featuring large added mass effect we analyze different preconditioners for the coupled system matrix obtained after space time discretization and linearization of the fsi problem the classical dirichlet neumann preconditioner has the advantage of modularity because it allows to reuse existing fluid and structure codes with minimum effort simple interface communication unfortunately its performance is very poor in case of large added mass effects alternatively we consider two non modular approaches the first one consists in preconditioning the coupled system with a suitable diagonal scaling combined with an ilut preconditioner the system is then solved by a krylov method the drawback of this procedure is that the combination of fluid and structure codes to solve the coupled system is not straightforward the second non modular approach we consider is a splitting technique based on an inexact block lu factorization of the linear fsi system the resulting algorithm computes the fluid velocity separately from the coupled pressure structure system at each iteration reducing the computational cost independently of the preconditioner the efficiency of semi implicit algorithms i e those that treat geometric and fluid nonlinearities in an explicit way is highlighted and their performance compared to the one of implicit algorithms all the methods are tested on three dimensional blood vessel systems the algorithm combining the non modular ilut preconditioner with krylov methods proved to be the fastest

error analysis of some galerkin least squares methods for the elasticity equations the recent technique of stabilizing mixed finite element methods by augmenting the galerkin formulation with least squares terms calculated separately on each element is considered the error analysis is performed in a unified manner yielding improved results for some methods introduced earlier in addition a new formulation is introduced and analyzed method is used within two different contexts the first is in connection with the plain strain or three dimensional problems near the incompressible limit for which the poisson ratio equals one half it is well known that for these problems a standard lower order displacement finite element method will break down by now it is also well known how a working method can be obtained a new unknown the pressure is introduced and discretized with a finite element space different from that used for the displacements the finite element method obtained falls into the class of saddlepoint problems for which there is a general theory developed by brezzi and babuska 5 7 the application of this theory shows that the method converges optimally if the discrete spaces for the displacement and pressure satisfy a stability condition for a particular choice of displacement and pressure approximations it can be a difficult task to verify this babuska brezzi or inf sup condition during the last decade this problem has been intensively studied and the performances of many combinations are now known cf 18 and 23 26 for some recent extensions in addition there exists a general technique utilizing bubble functions by which a stable method can

spatial aliasing in spherical microphone arrays performance of microphone arrays at the high frequency range is typically limited by aliasing which is a result of the spatial sampling process this paper presents analysis of aliasing for spherical microphone arrays which have been recently studied for a range of applications the paper presents theoretical analysis of spatial aliasing for various sphere sampling configurations showing how high order spherical harmonic coefficients are aliased into the lower orders spatial antialiasing filters on the sphere are then introduced and the performance of spatially constrained filters is compared to that of the ideal antialiasing filter a simulation example shows how the effect of aliasing on the beam pattern can be reduced by the use of the antialiasing filters

finite element approximations of the nonstationary navier stokes problem part iv error estimates for second order time discretization this paper provides an error analysis for the crank nicolson method of time discretization applied to spatially discrete galerkin approximations of the nonstationary navier stokes equations second order error estimates are proven locally in time under realistic assumptions about the regularity of the solution for approximations of an exponentially stable solution these local error estimates are extended uniformly in time as text t to infty

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

a new partitioned staggered scheme for flexible multibody interactions with strong inertial effects abstract in generic flexible multibody interaction problems the differences in the mass damping and stiffness of the bodies can be very large of particular interest is a small change in the higher mass structure which triggers relatively large inertial effects on the lower mass structure in this work a new partitioned staggered time integration scheme is developed and its applicability is extended to the problems involving low mass ratios in coupled multibody problems the equation of motion of body with larger inertia is integrated by implicit newmark method whereas the smaller inertia is solved using a robust self starting explicit integration procedure the coupled formulation includes explicit correction terms that adjusts the amount of interfacial velocity which plays a key role in the stability and accuracy of the simulations a wide range of mass 10 6 10 1 damping and stiffness 10 3 10 3 ratios are chosen to assess the stability and accuracy characteristics of the proposed scheme the closed form expressions for the coupling parameter have been constructed for both matching and non matching time stepping through the godunov ryabenkii normal mode analysis the stability of the proposed method is observed as a function of the relative properties and temporal discretisation of the coupled system the time step of the heavier body significantly influences the stability more than the lighter body to maintain the staggering error minimal an optimal range of the coupling parameter is identified the error computed with uniform variation in the time step revealed that the present method is more accurate than the existing methods the partitioned method is an energy preserving integration method for the dynamic analysis of multibody systems as a potential application of this scheme flexible multibody problems in the field of offshore engineering viz wave energy converter and floater mooring systems are presented and validated with experimental measurements

fluid structure algorithms based on steklov poincare operators in this paper we review some classical algorithms for fluid structure interaction problems and we propose an alternative viewpoint mutuated from the domain decomposition theory this approach yields preconditioned richardson iterations on the steklov poincare nonlinear equation at the fluid structure interface

stable loosely coupled type algorithm for fluid structure interaction in blood flow we introduce a novel loosely coupled type algorithm for fluid structure interaction between blood flow and thin vascular walls this algorithm successfully deals with the difficulties associated with the added mass effect which is known to be the cause of numerical instabilities in fluid structure interaction problems involving fluid and structure of comparable densities our algorithm is based on a time discretization via operator splitting which is applied in a novel way to separate the fluid sub problem from the structure elastodynamics sub problem in contrast with traditional loosely coupled schemes no iterations are necessary between the fluid and structure sub problems this is due to the fact that our novel splitting strategy uses the added mass effect to stabilize rather than to destabilize the numerical algorithm this stabilizing effect is obtained by employing the kinematic lateral boundary condition to establish a tight link between the velocities of the fluid and of the structure in each sub problem the stability of the scheme is discussed on a simplified benchmark problem and we use energy arguments to show that the proposed scheme is unconditionally stable due to the crucial role played by the kinematic lateral boundary condition the proposed algorithm is named the kinematically coupled scheme

a new approach to numerical solution of defective boundary value problems in incompressible fluid dynamics we consider the incompressible navier stokes equations where on a part of the boundary flow rate and mean pressure boundary conditions are prescribed there are basically two strategies for solving these defective boundary problems the variational approach see j heywood r rannacher and s turek internat j numer methods fluids 22 1996 pp 325 352 and the augmented formulation see l formaggia j f gerbeau f nobile and a quarteroni siam j numer anal 40 2002 pp 376 401 and a veneziani and c vergara internat j numer methods fluids 47 2005 pp 803 816 however both of these approaches present some drawbacks for the flow rate problem the former resorts to nonstandard functional spaces which are quite difficult to discretize on the other hand for the mean pressure problem it yields exact solutions only in very special cases the latter is applicable only to the flow rate problem since for the mean pressure problem it provides unfeasible boundary conditions in this paper we propose a new strategy based on a reformulation of the problems at hand in terms of the minimization of an appropriate functional this approach allows us to treat the two kinds of problems flow rate and mean pressure successfully within the same framework which can be useful in view of a mixed problem where the two conditions are simultaneously prescribed on different artificial boundaries moreover it is more versatile being prone to be extended to other kinds of defective conditions we analyze the problems obtained with this approach and propose some algorithms for their numerical solution several numerical results are presented supporting the effectiveness of our approach

modeling viscoelastic behavior of arterial walls and their interaction with pulsatile blood flow fluid structure interaction describing wave propagation in arteries driven by the pulsatile blood flow is a complex problem whenever possible simplified models are called for one dimensional models are typically used in arterial sections that can be approximated by the cylindrical geometry allowing axially symmetric flows although a good first approximation to the underlying problem the one dimensional model suffers from several drawbacks the model is not closed an ad hoc velocity profile needs to be prescribed to obtain a closed system and the model equations are quasi linear hyperbolic oversimplifying the viscous fluid dissipation typically producing shock wave solutions not observed in healthy humans in this manuscript we derived a simple closed reduced model that accounts for the viscous fluid dissipation to the leading order the resulting fluid structure interaction system is of hyperbolic parabolic type arterial walls were modeled by a novel linearly viscoelastic cylindrical koiter shell model and the flow of blood by the incompressible viscous navier stokes equations kelvin voigt type viscoelasticity was used to capture the hysteresis behavior observed in the measurements of the arterial stress strain response using the a priori estimates obtained from an energy inequality together with the asymptotic analysis and ideas from homogenization theory for porous media flows we derived an effective model which is an 2 approximation to the three dimensional axially symmetric problem whereis the aspect ratio of the cylindrical arterial section our model shows two interesting features of the underlying problem bending rigidity often times neglected in the arterial wall models plays a nonnegligible role in the 2 approximation of the original problem and the viscous fluid dissipation imparts long term viscoelastic memory effects on the motion of the arterial walls this does not to the leading order influence the hysteresis behavior of arterial walls the resulting model although two dimensional is in the form that allows the use of one dimensional finite element method techniques producing fast numerical solutions we devised a version of the douglas rachford time splitting algorithm to solve the underlying hyperbolic parabolic problem the results of the numerical simulations were compared with the experimental flow measurements performed at the texas heart institute and with the data corresponding to the hysteresis of the human femoral artery and the canine abdominal aorta excellent agreement was observed

large degree asymptotics of generalized bernoulli and euler polynomials abstract asymptotic expansions are given for large values of n of the generalized bernoulli polynomials b n z and euler polynomials e n z in a previous paper lopez and temme 1999 these polynomials have been considered for large values of with n fixed in the literature no complete description of the large n asymptotics of the considered polynomials is available we give the general expansions summarize known results of special cases and give more details about these results we use two point taylor expansions for obtaining new type of expansions the analysis is based on contour integrals that follow from the generating functions of the polynomials

deconvolution for the localization of sound sources using a circular microphone array during the last decade the aeroacoustic community has examined various methods based on deconvolution to improve the visualization of acoustic fields scanned with planar sparse arrays of microphones these methods assume that the beamforming map in an observation plane can be approximated by a convolution of the distribution of the actual sources and the beamformer s point spread function defined as the beamformer s response to a point source by deconvolving the resulting map the resolution is improved and the side lobes effect is reduced or even eliminated compared to conventional beamforming even though these methods were originally designed for planar sparse arrays in the present study they are adapted to uniform circular arrays for mapping the sound over 360 this geometry has the advantage that the beamforming output is practically independent of the focusing direction meaning that the beamformer s point spread function is shift invariant this makes it possible to apply computationally efficient deconvolution algorithms that consist of spectral procedures in the entire region of interest such as the deconvolution approach for the mapping of the acoustic sources 2 the fourier based non negative least squares and the richardson lucy this investigation examines the matter with computer simulations and measurements

numerical treatment of defective boundary conditions for the navier stokes equations we present a formulation for accommodating defective boundary conditions for the incompressible navier stokes equations where only averaged values are prescribed on measurable portions of the boundary in particular we consider the case where the flow rate is imposed on several domain sections this methodology has an interesting application in the numerical simulation of flow in blood vessels when only a reduced set of boundary data are generally available for the upstream and downstream sections

edge stabilization for the generalized stokes problem a continuous interior penalty method in this note we introduce and analyze a stabilized finite element method for the generalized stokes equation stability is obtained by adding a least squares penalization of the gradient jumps acro

nitsche xfem for the coupling of an incompressible fluid with immersed thin walled structures abstract in this paper we introduce a nitsche xfem method for fluid structure interaction problems involving a thin walled elastic structure lagrangian formalism immersed in an incompressible viscous fluid eulerian formalism the fluid domain is discretized with an unstructured mesh not fitted to the solid mid surface mesh weak and strong discontinuities across the interface are allowed for the velocity and pressure respectively the fluid solid coupling is enforced consistently using a variant of nitsche s method with cut elements robustness with respect to arbitrary interface intersections is guaranteed through suitable stabilization several coupling schemes with different degrees of fluid solid time splitting implicit semi implicit and explicit are investigated a series of numerical test in 2d involving static and moving interfaces illustrates the performance of the different methods proposed

splitting methods based on algebraic factorization for fluid structure interaction we discuss in this paper the numerical approximation of fluid structure interaction fsi problems dealing with strong added mass effect we propose new semi implicit algorithms based on inexact block lu factorization of the linear system obtained after the space time discretization and linearization of the fsi problem as a result the fluid velocity is computed separately from the coupled pressure structure velocity system at each iteration reducing the computational cost we investigate explicit implicit decomposition through algebraic splitting techniques originally designed for the fsi problem this approach leads to two different families of methods which extend to fsi the algebraic pressure correction method and the yosida method two schemes that were previously adopted for pure fluid problems furthermore we have considered the inexact factorization of the fluid structure system as a preconditioner the numerical properties of these methods have been tested on a model problem representing a blood vessel system

an overview of projection methods for incompressible flows a series of numerical issues related to the analysis and implementation of fractional step methods for incompressible flows are addressed in this paper these methods are often referred to in the literature as projection methods and can be classified into three classes namely the pressure correction methods the velocity correction methods and the consistent splitting methods for each class of schemes theoretical and numerical convergence results available in the literature are reviewed and open questions are discussed the essential results are summarized in a table which could serve as a useful reference to numerical analysts and practitioners published by elsevier b v msc 65n35 65n22 65f05 35j05

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

a fictitious domain method for external incompressible viscous flow modeled by navier stokes equations abstract in this article we discuss a fictitious domain method for the numerical solutions of three dimensional elliptic problems with dirichlet boundary conditions and also of the navier stokes equations modeling incompressible viscous flow the methodology for the navier stokes equations described here takes a systematic advantage of time discretization by operator splitting in order to treat separately advection imbedding and incompressibility due to the decoupling fast elliptic solvers can be used to treat the incompressibility condition even if the original problem is taking place on a nonregular geometry the resulting methodology is applied to two dimensional unsteady external incompressible viscous flow problems and three dimensional stokes problems

continuous interior penalty finite element method for the time dependent navier stokes equations space discretization and convergence this paper focuses on the numerical analysis of a finite element method with stabilization for the unsteady incompressible navier stokes equations incompressibility and convective effects are both stabilized adding an interior penalty term giving l 2 control of the jump of the gradient of the approximate solution over the internal faces using continuous equal order finite elements for both velocities and pressures in a space semi discretized formulation we prove convergence of the approximate solution the error estimates hold irrespective of the reynolds number and hence also for the incompressible euler equations provided the exact solution is smooth

an approximate method for solving incompressible navier stokes problems with flow rate conditions we consider the incompressible navier stokes problem with flow rate boundary conditions this problem has been investigated in j heywood r rannacher s turek artificial boundaries and flux and pressure conditions for the incompressible navier stokes equations int j numer methods fluids 22 1996 325 352 l formaggia j f gerbeau f nobile a quarteroni numerical treatment of defective boundary conditions for the navier stokes equation siam j numer anal 40 1 2002 376 401 a veneziani c vergara flow rate defective boundary conditions in haemodynamics simulations int j numer methods fluids 47 2005 803 816 in the latter two papers a feasible numerical formulation of this problem based on a lagrange multiplier approach has been investigated this approach has the drawback of high computational costs in this paper we propose an approximate formulation of this problem yielding a strong reduction of the computational costs the error analysis shows that the error introduced by this approximate formulation is confined in a small region of the boundary this is confirmed by the numerical simulations

plane wave decomposition of the sound field on a sphere by spherical convolution spherical microphone arrays have been recently studied for sound analysis and sound recordings which have the advantage of spherical symmetry facilitating three dimensional analysis this paper complements the recent microphone array design studies by presenting a theoretical analysis of plane wave decomposition given the sound pressure on a sphere the analysis uses the spherical fourier transform and the spherical convolution where it is shown that the amplitudes of the incident plane waves can be calculated as a spherical convolution between the pressure on the sphere and another function which depends on frequency and the sphere radius the spatial resolution of plane wave decomposition given limited bandwidth in the spherical fourier domain is formulated and ways to improve the computation efficiency of plane wave decomposition are introduced the paper concludes with a simulation example of plane wave decomposition

quadratic variational framework for signal design on the 2 sphere this paper introduces a quadratic variational framework for solving a broad class of signal design problems on the 2 sphere the functional to be extremized combines energy concentration measures using a weighting function in the spatial domain multiplicative weights in the spectral domain and a total energy constraint this leads to two formulations of the signal design problem on the 2 sphere one a fredholm integral equation in the spatial domain and the other an infinite matrix equation in the spectral domain the framework is illustrated by deriving the key equations for the two classical spatio spectral concentration problems on the 2 sphere and for an isotropic filter design that maximizes the filtered energy in addition using the proposed framework we formulate a joint 3 d beamforming application which achieves optimal directivity and spatial resolution simultaneously

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

comparisons between reduced order models and full 3d models for fluid structure interaction problems in haemodynamics when modelling the cardiovascular system the effect of the vessel wall on the blood flow has great relevance arterial vessels are complex living tissues and three dimensional specific models have been proposed to represent their behaviour the numerical simulation of the 3d 3d fluid structure interaction fsi coupled problem has high computational costs in terms of required time and memory storage even if many possible solutions have been explored to speed up the resolution of such problem we are far from having a 3d 3d fsi model that can be solved quickly in 3d 3d fsi models two of the main sources of complexity are represented by the domain motion and the coupling between the fluid and the structural part nevertheless in many cases we are interested in the blood flow dynamics in compliant vessels whereas the displacement of the domain is small and the structure dynamics is less relevant in these situations techniques to reduce the complexity of the problem can be used one consists in using transpiration conditions for the fluid model as surrogate for the wall displacement thus allowing problem s solution on a fixed domain another strategy consists in modelling the arterial wall as a thin membrane under specific assumptions figueroa et al 2006 nobile and vergara 2008 instead of using a more realistic but more computationally intensive 3d elastodynamic model using this strategy the dynamics of the vessel motion is embedded in the equation for the blood flow combining the transpiration conditions with the membrane model assumption we obtain an attractive formulation in fact instead of solving two different models on two moving physical domains we solve only a navier stokes system in a fixed fluid domain where the structure model is integrated as a generalized robin condition in this paper we present a general formulation in the boundary conditions which is independent of the time discretization scheme choice and on the stress strain constitutive relation adopted for the vessel wall structure our aim is first to write a formulation of a reduced order model with zero order transpiration conditions for a generic time discretization scheme then to compare a 3d 3d fsi model and a reduced fsi one in two realistic patient specific cases a femoropopliteal bypass and an aorta in particular we are interested in comparing the wall shear stresses in fact this quantity can be used as a risk factor for some pathologies such as atherosclerosis or thrombogenesis more in general we want to assess the accuracy and the computational convenience to use simpler formulations based on reduced order models in particular we show that in the case of small displacements using a 3d 3d fsi linear elastic model or the correspondent reduced order one yields many similar results

fully decoupled time marching schemes for incompressible fluid thin walled structure interaction in this paper we introduce a class of fully decoupled time marching schemes velocity pressure displacement splitting for the coupling of an incompressible fluid with a thin walled elastic or viscoelastic structure the time splitting combines a projection method in the fluid with a specific robin neumann treatment of the interface coupling a priori energy estimates guaranteeing unconditional stability are established for some of the schemes the accuracy and performance of the methods proposed are illustrated by a thorough numerical study

existence of a solution to a fluid multi layered structure interaction problem abstract we study a nonlinear unsteady moving boundary fluid structure interaction fsi problem in which the structure is composed of two layers a thick layer and a thin layer which serves as a fluid structure interface with mass the fluid flow which is driven by the time dependent dynamic pressure data is modeled by the navier stokes equations for an incompressible viscous fluid defined on a 2d cylinder the elastodynamics of the cylinder wall is governed by the 1d linear wave equation modeling the thin structural layer and by the 2d equations of linear elasticity modeling the thick structural layer we prove existence of a weak solution to this nonlinear fsi problem as long as the cylinder radius is greater than zero the spaces of weak solutions presented in this manuscript reveal a striking new feature the presence of a thin fluid structure interface with mass regularizes solutions of the coupled problem

a second order in time approximation of fluid structure interaction problem we propose and analyze a novel second order in time partitioned method for the interaction between an incompressible viscous fluid and a thin elastic structure the proposed numerical method is based on the crank nicolson discretization scheme which is used to decouple the system into a fluid subproblem and a structure subproblem the scheme is loosely coupled and therefore at every time step each subproblem is solved only once energy and error estimates for a fully discretized scheme using finite element spatial discretization are derived we prove that the scheme is stable under a cfl condition second order convergent in time and optimally convergent in space numerical examples support the theoretically obtained results and demonstrate the applicability of the method to realistic simulations of blood flow

symbolic evaluation of coefficients in airy type asymptotic expansions computer algebra algorithms are developed for evaluating the coefficients in airy type asymptotic expansions that are obtained from integrals with a large parameter the coefficients are defined from recursive schemes obtained from integration by parts an application is given for the weber parabolic cylinder function

large degree asymptotics of generalized bessel polynomials abstract asymptotic expansions are given for large values of n of the generalized bessel polynomials y n z the analysis is based on integrals that follow from the generating functions of the polynomials a new simple expansion is given that is valid outside a compact neighborhood of the origin in the z plane new forms of expansions in terms of elementary functions valid in sectors not containing the turning points z i n are derived and a new expansion in terms of modified bessel functions is given earlier asymptotic expansions of the generalized bessel polynomials by wong and zhang 1997 and dunster 2001 are discussed

functional delay and sum beamforming for three dimensional acoustic source identification with solid spherical arrays abstract solid spherical arrays have become particularly attractive tools for doing acoustic sources identification in cabin environments spherical harmonics beamforming shb is the popular conventional algorithm regrettably its results suffer from severe sidelobe contaminations and the existing solutions are incapable of removing these contaminations both significantly and efficiently this paper focuses on conquering these problems by creating a novel functional delay and sum fdas algorithm first and foremost a new delay and sum das algorithm is established and for which the point spread function psf is derived the determination principle of the truncated upper limit of the spherical harmonics degree is explored and the performance is examined as well as compared with that of shb next the fdas algorithm is created by combining das and the functional beamforming fb approach initially suggested for planar arrays and its merits are demonstrated additionally performances of das and fdas are probed into under the situation that the source is not at the focus point several interesting results have emerged 1 the truncated upper limit of the spherical harmonics degree capable of making das meet fb s requirement exists and its minimum value depends only on the wave number and the array radius 2 das can accurately locate and quantify the single source and the incoherent or coherent sources and its comprehensive performance is not inferior to that of shb 3 for single source or incoherent sources fdas can not only accurately locate and quantify the source but also significantly and efficiently attenuate sidelobes effectively detect weak sources and acquire somewhat better spatial resolution in contrast to that for coherent sources fdas is not available 4 das can invariably quantify the source accurately irrespectively of the focus distance whereas fdas is burdened with a quantification deviation growing with the increase of the exponent parameter when the focus distance is unequal to the distance from the source to the array center or the focus directions do not embrace the source direction fortunately the deviation can be commendably compensated for by the introduced scale and integrate method this study will be of great significance to the accurate and quick localization and quantification of acoustic sources in cabin environments

existence of a weak solution to a nonlinear fluid structure interaction problem modeling the flow of an incompressible viscous fluid in a cylinder with deformable walls we study a nonlinear unsteady moving boundary fluid structure interaction fsi problem arising in modeling blood flow through elastic and viscoelastic arteries the fluid flow which is driven by the time dependent pressure data is governed by two dimensional incompressible navier stokes equations while the elastodynamics of the cylindrical wall is modeled by the one dimensional cylindrical koiter shell model two cases are considered the linearly viscoelastic and the linearly elastic koiter shell the fluid and structure are fully coupled two way coupling via the kinematic and dynamic lateral boundary conditions describing continuity of velocity the no slip condition and the balance of contact forces at the fluid structure interface we prove the existence of weak solutions to the two fsi problems the viscoelastic and the elastic case as long as the cylinder radius is greater than zero the proof is based on a novel semi discrete operator splitting numerical scheme known as the kinematically coupled scheme introduced in guidoboni et al j comput phys 228 18 6916 6937 2009 to numerically solve the underlying fsi problems the backbone of the kinematically coupled scheme is the well known marchuk yanenko scheme also known as the lie splitting scheme we effectively prove convergence of that numerical scheme to a solution of the corresponding fsi problem