dpoae group delays versus electrophysiological measures of cochlear delay in normal human ears group delays of 2 f1 f2 distortion product otoacoustic emissions dpoaes were determined using both f1 and f2 sweep paradigms in 24 normal hearing subjects these dpoae group delays were studied in comparison with cochlear delays estimated from derived band viiith nerve compound action potentials caps and auditory brainstem responses abrs in the same subjects the center frequencies of the derived bands in the electrophysiological experiment were matched with the f2 frequencies in the dpoae recording to ensure that dpoaes and derived caps and abrs were generated at the same places along the cochlear partition thus allowing for a direct comparison the degree to which dpoae group delays are larger in the f2 than in the f1 sweep paradigm is consistent with a theoretical analysis of the so called wave fixed model both dpoae group delays are highly correlated with cap and abr derived measures of cochlear delay the principal result of this study is that roundtrip dpoae group delay in the f1 sweep

an immersed boundary method with direct forcing for the simulation of particulate flows we present an improved method for computing incompressible viscous flow around suspended rigid particles using a fixed and uniform computational grid the main idea is to incorporate peskin s regularized delta function approach acta numerica 11 2002 1 into a direct formulation of the fluid solid interaction force in order to allow for a smooth transfer between eulerian and lagrangian representations while at the same time avoiding strong restrictions of the time step this technique was implemented in a finite difference and fractional step context a variety of two and three dimensional simulations are presented ranging from the flow around a single cylinder to the sedimentation of 1000 spherical particles the accuracy and efficiency of the current method are clearly demonstrated

uniform preconditioners for a parameter dependent saddle point problem with application to generalized stokes interface equations we consider an abstract parameter dependent saddle point problem and present a general framework for analyzing robust schur complement preconditioners the abstract analysis is applied to a generalized stokes problem which yields robustness of the cahouet chabard preconditioner motivated by models for two phase incompressible flows we consider a generalized stokes interface problem application of the general theory results in a new schur complement preconditioner for this class of problems the robustness of this preconditioner with respect to several parameters is treated results of numerical experiments are given that illustrate robustness properties of the preconditioner

an adaptive finite element moreau yosida based solver for a coupled cahn hilliard navier stokes system an adaptive a posteriori error estimator based finite element method for the numerical solution of a coupled cahn hilliard navier stokes system with a double obstacle homogenous free interfacial energy density is proposed a semi implicit euler scheme for the time integration is applied which results in a system coupling a quasi stokes or oseen type problem for the fluid flow to a variational inequality for the concentration and the chemical potential according to the cahn hilliard model 16 a moreau yosida regularization is employed which relaxes the constraints contained in the variational inequality and thus enables semi smooth newton solvers with locally superlinear convergence in function space moreover upon discretization this yields a mesh independent method for a fixed relaxation parameter for the finite dimensional approximation of the concentration and the chemical potential piecewise linear and globally continuous finite elements are used and for the numerical approximation of the fluid velocity taylor hood finite elements are employed the paper ends by a report on numerical examples showing the efficiency of the new method

multicomponent acoustic distortion product otoacoustic emission phase in humans ii implications for distortion product otoacoustic emissions generation phase characteristics and latency of 2f1 f2 3f1 2f2 and 2f2 f1 acoustic distortion product otoacoustic emissions dpoaes recorded in normally hearing adults have been described in a companion paper moulin and kemp multicomponent acoustic distortion product otoacoustic emission phase in humans i general characteristics j acoust soc am 100 1617 1639 1996 phase versus frequency functions pff have been recorded using two methods depending whether f1 or f2 was swept in frequency defining respectively an f1 sweep and an f2 sweep method the present study compares 2f1 f2 3f1 2f2 4f1 3f2 and 2f2 f1 dpoaes phase characteristics and latencies obtained by these two methods for lower sideband dpoaes the f2 sweep gave consistently longer latencies than the f1 sweep method whereas no difference was obtained for the 2f2 f1 dpoae this suggests that the lower sideband dpoaes and the 2f2 f1 dpoae do not come from the same aspect of the traveling wave the longer delay obtained with an f2 sweep is suggested to be due to an additional delay added by the proximity of the peak of the f2 traveling wave the place fixed and the wave fixed models of dpoae generation are discussed and an intermediate model of dpoae generation is introduced to explain such additional delay and the existence of phase irregularities which were observed in the pff the ratio of the latencies obtained by the two sweep methods is frequency dependent and a relation to cochlear frequency selectivity is suggested finally analysis of the differences in latency of the different lower sideband dpoae components allowed an estimation of the return latency of dpoaes

multigrid methods for saddle point problems stokes and lame systems we develop new multigrid methods for a class of saddle point problems that include the stokes system in fluid flow and the lame system in linear elasticity as special cases the new smoothers in the multigrid methods involve optimal preconditioners for the discrete laplace operator we prove uniform convergence of the w w cycle algorithm in the energy norm and present numerical results for w w cycle and v v cycle algorithms

a temporal discretization scheme to compute the motion of light particles in viscous flows by an immersed boundary method the paper introduces a time scheme for an immersed boundary method which enables the efficient phase resolving simulation of very light particles in viscous flow a simple modification of the time scheme of the method detailed in kempe and frohlich 2012 34 is proposed to extend the range of applicability to particle to fluid density ratios as they occur with bubbles in liquids this modification is termed virtual mass approach it is shown for the generic test case of a sphere moving under stokes flow conditions that the approach can be used in conjunction with several time integration schemes without altering the order of convergence of the base scheme the new scheme is rigorously validated for the three dimensional case of a sphere rising or settling at finite reynolds number as well as for the rotation of a sphere in viscous flow

iterative techniques for time dependent stokes problems abstract in this paper we consider solving the coupled systems of discrete equations which arise from implicit time stepping procedures for the time dependent stokes equations using a mixed finite element spatial discretization at each time step a two by two block system corresponding to a perturbed stokes problem must be solved although there are a number of techniques for iteratively solving this type of block system to be effective they require a good preconditioner for the resulting pressure operator schur complement in contrast to the time independent stokes equations where the pressure operator is well conditioned the pressure operator for the perturbed system becomes more ill conditioned as the time step is reduced and or the reynolds number is increased in this paper we shall describe and analyze preconditioners for the resulting pressure systems these preconditioners give rise to iterative rates of convergence which are independent of both the mesh size h as well as the time step and reynolds number parameter k

imposing the free slip condition with a continuous forcing immersed boundary method the numerical simulation of spherical and ellipsoidal bubbles in purified fluids requires the imposition of the free slip boundary condition at the bubble surface this paper describes a numerical method for the implementation of free slip boundary conditions in the context of immersed boundary methods in contrast to other numerical approaches for multiphase flows the realization is not straightforward the reason is that the immersed boundary method treats the liquid as well as the gas phase as a field of constant density and viscosity with a fictitious fluid inside the bubble the motion of the disperse phase is computed explicitly by solving the momentum balance for each of its elements and is coupled to the continuous phase via additional source terms in the navier stokes equations the paper starts with illustrating that an ad hoc method is unsuccessful on this basis a new method is proposed employing appropriate direct forcing at the bubble surface a central finding is that with common ratios between the step size of the grid and the bubble diameter curvature terms need to be accounted for to obtain satisfactory results the new method is first developed for spherical objects and then extended to generally curved interfaces this is done by introducing a local coordinate system which approximates the surface in the vicinity of a lagrangian marker with the help of the two principal curvatures of the surface at this point the numerical scheme is then validated for spherical and ellipsoidal objects with or without prescribed constant angular velocity it is shown that the proposed method achieves similar convergence behavior as the method for no slip boundaries the results are compared to analytical solutions for creeping flow around a sphere and to numerical reference data obtained on a body fitted grid the numerical tests confirm the excellent performance of the proposed method

effective preconditioning of uzawa type schemes for a generalized stokes problem the schur complement of a model problem is considered as a preconditioner for the uzawa type schemes for the generalized stokes problem the stokes problem with the additional term alpha boldmath u in the motion equation the implementation of the preconditioned method requires for each iteration only one extra solution of the poisson equation with neumann boundary conditions for a wide class of 2d and 3d domains a theorem on its convergence is proved in particular it is established that the method converges with a rate that is bounded by some constant independent of alpha some finite difference and finite element methods are discussed numerical results for finite difference mac scheme are provided

a discontinuous galerkin reduced basis numerical homogenization method for fluid flow in porous media we present a new conservative multiscale method for stokes flow in heterogeneous porous media the method couples a discontinuous galerkin finite element method dg fem at the macroscopic scale for the solution of an effective darcy equation with a stokes solver at the pore scale to recover effective permeabilities at macroscopic quadrature points to avoid costly computation of numerous stokes problems throughout the macroscopic computational domain the pore geometry is parametrized and a model order reduction algorithm is used to select representative microscopic geometries accurate stokes solutions and related permeabilities are obtained for these representative geometries in an offline stage in an online stage the dg fem is computed with permeabilities recovered at the desired macroscopic quadrature points from the precomputed stokes solutions the multiscale method is shown to be mass conservative at the macro scale and the computational cost for the online stage is similar to the cost of solving a single scale darcy problem numerical experiments for two and three dimensional problems illustrate the efficiency and the performance of the proposed method

fast iterative solvers for discrete stokes equations we consider saddle point problems that result from the finite element discretization of stationary and nonstationary stokes equations three efficient iterative solvers for these problems are treated namely the preconditioned conjugate gradient method introduced by bramble and pasciak the preconditioned minres method and a method due to bank et al we give a detailed overview of algorithmic aspects and theoretical convergence results for the method of bank et al a new convergence analysis is presented a comparative study of the three methods for a three dimensional stokes problem discretized by the hood taylor p2 p1 finite element pair is given

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

an immersed boundary finite volume method for simulations of flow in complex geometries abstract a new immersed boundary method for simulating flows over or inside complex geometries is developed by introducing a mass source sink as well as a momentum forcing the present method is based on a finite volume approach on a staggered mesh together with a fractional step method both momentum forcing and mass source are applied on the body surface or inside the body to satisfy the no slip boundary condition on the immersed boundary and also to satisfy the continuity for the cell containing the immersed boundary in the immersed boundary method the choice of an accurate interpolation scheme satisfying the no slip condition on the immersed boundary is important because the grid lines generally do not coincide with the immersed boundary therefore a stable second order interpolation scheme for evaluating the momentum forcing on the body surface or inside the body is proposed three different flow problems decaying vortices and flows over a cylinder and a sphere are simulated using the immersed boundary method proposed in this study and the results agree very well with previous numerical and experimental results verifying the accuracy of the present method

a decoupled augmented iim strategy for incompressible two phase flows with interfaces on irregular domains a decoupled augmented immersed interface method for solving incompressible two phase flows involving both irregular domains and interfaces is presented in order to impose the prescribed velocity at the boundary of the irregular domain singular force as one set of augmented variables is introduced the velocity components at the two fluid interface as another set of augmented variables are introduced to satisfy the continuity condition of the velocity across the interface so that the jump conditions for the velocity and pressure are decoupled across the interface the augmented variables and or the forces along the interface boundary are related to the jumps in both pressure and velocity and the jumps in their derivatives across the interface boundary and applied to the fluid through jump conditions the resulting augmented equation is a couple system of these two sets of augmented variables and the direct application of the gmres is impractical due to larger iterations in this work the novel decoupling of two sets of the augmented variables is proposed and the decoupled augmented equation is then solved by the lu or the gmres method the stokes equations are discretized via the finite difference method with the incorporation of jump contributions on a staggered cartesian grid and solved by the conjugate gradient uzawa type method the numerical results show that second order accuracy for the velocity is confirmed the present method has also been applied to solve for incompressible two phase navier stokes flow with interfaces on irregular domains copyright 2011 john wiley sons ltd

a smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations the effects of complex boundary conditions on flows are represented by a volume force in the immersed boundary methods the problem with this representation is that the volume force exhibits non physical oscillations in moving boundary simulations a smoothing technique for discrete delta functions has been developed in this paper to suppress the non physical oscillations in the volume forces we have found that the non physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions it has been shown that the smoothed discrete delta functions constructed in this paper have one order higher derivative than the regular ones moreover not only the smoothed discrete delta functions satisfy the first two discrete moment conditions but also their derivatives satisfy one order higher moment condition than the regular ones the smoothed discrete delta functions are tested by three test cases a one dimensional heat equation with a moving singular force a two dimensional flow past an oscillating cylinder and the vortex induced vibration of a cylinder the numerical examples in these cases demonstrate that the smoothed discrete delta functions can effectively suppress the non physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations

efficient preconditioning of the linearized navier stokes equations for incompressible flow we outline a new class of robust and efficient methods for solving subproblems that arise in the linearization and operator splitting of navier stokes equations we describe a very general strategy for preconditioning that has two basic building blocks a multigrid v cycle for the scalar convection diffusion operator and a multigrid v cycle for a pressure poisson operator we present numerical experiments illustrating that a simple implementation of our approach leads to an effective and robust solver strategy in that the convergence rate is independent of the grid robust with respect to the time step and only deteriorates very slowly as the reynolds number is increased

fast iterative solution of stabilised stokes systems part ii using general block preconditioners mixed finite element approximation of the classical stokes problem describing slow viscous incompressible flow gives rise to symmetric indefinite systems for the discrete velocity and pressure variables iterative solution of such indefinite systems is feasible and is an attractive approach for large problems part i of this work described a conjugate gradient like method the method of preconditioned conjugate residuals which is applicable to symmetric indefinite problems a j wathen and d j silvester siam j numer anal 30 1993 pp 630 649 using simple arguments estimates for the eigenvalue distribution of the discrete stokes operator on which the convergence rate of the iteration depends are easily derived part i discussed the important case of diagonal preconditioning scaling this paper considers the more general class of block preconditioners where the partitioning into blocks corresponds to the natural partitioning into the velocity and pressure variables it is shown that provid

a class of iterative methods for solving saddle point problems we consider the numerical solution of indefinite systems of linear equations arising in the calculation of saddle points we are mainly concerned with sparse systems of this type resulting from certain discretizations of partial differential equations we present an iterative method involving two levels of iteration similar in some respects to the uzawa algorithm we relate the rates of convergence of the outer and inner iterations proving that under natural hypotheses the outer iteration achieves the rate of convergence of the inner iteration the technique is applied to finite element approximations of the stokes equations

analysis of semi staggered finite difference method with application to bingham flows abstract in this paper a finite difference scheme for incompressible flow problems is treated the scheme uses non staggered grid for velocity approximation a special stabilization is introduced to ensure the well posedness and optimal approximation properties of the scheme the stability estimate is proved in the form of a mesh independent bound for the norm of discrete operator inverse the finite difference method is particularly suitable for problems in which velocity vector is involved in additional quantities that enter the system of flow equations as for example in the bingham problem we describe this application in the paper in some detail results of numerical experiments are included that confirm the applicability and optimality of the method

navier stokes simulation with constraint forces finite difference method for particle laden flows and complex geometries building on an idea of fogelson and peskin j comput phys 79 50 1988 we describe the implementation and verification of a simulation technique for systems of non brownian particles in fluids at reynolds numbers up to about 20 on the particle scale this direct simulation technique fills a gap between simulations in the viscous regime and high reynolds number modeling it also combines sufficient computational accuracy with numerical efficiency and allows studies of several thousand in principle arbitrarily shaped extended and hydrodynamically interacting particles on regular work stations we verify the algorithm in two and three dimensions for i single falling particles and ii a fluid flowing through a bed of fixed spheres in the context of sedimentation we compute the volume fraction dependence of the mean sedimentation velocity the results are compared with experimental and other numerical results both in the viscous and inertial regime and we find very satisfactory agreement

a second order accurate immersed boundary method for fully resolved simulations of particle laden flows an immersed boundary method ibm with second order spatial accuracy is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles the method is based on the computationally efficient direct forcing method of uhlmann m uhlmann an immersed boundary method with direct forcing for simulation of particulate flows j comput phys 209 2005 448 476 that is embedded in a finite volume pressure correction method the ibm consists of two grids a fixed uniform eulerian grid for the fluid phase and a uniform lagrangian grid attached to and moving with the particles a regularized delta function is used to communicate between the two grids and proved to be effective in suppressing grid locking without significant loss of efficiency the original method is improved by 1 a better approximation of the no slip no penetration ns np condition on the surface of the particles by a multidirect forcing scheme 2 a correction for the excess in the effective particle diameter by a slight retraction of the lagrangian grid from the surface towards the interior of the particles with a fraction of the eulerian grid spacing and 3 an enhancement of the numerical stability for particle fluid mass density ratios near unity by a direct account of the inertia of the fluid contained within the particles the new ibm contains two new parameters the number of iterations n s of the multidirect forcing scheme and the retraction distance r d the effect of n s and r d on the accuracy is investigated for five different flows the results show that r d has a strong influence on the effective particle diameter and little influence on the error in the ns np condition while exactly the opposite holds for n s a novel finding of this study is the demonstration that r d has a strong influence on the order of grid convergence it is found that for spheres the choice of r d 0 3 dx yields second order accuracy compared to first order accuracy of the original method that corresponds to r d 0 finally n s 2 appears optimal for reducing the error in the ns np condition and maintaining the computational efficiency of the method

an adaptive version of the immersed boundary method a computational setting for the immersed boundary method employing an adaptive mesh refinement is presented enhanced accuracy for the method is attained locally by covering an immersed boundary vicinity with a sequence of nested progressively finer rectangular grid patches which dynamically follow the immersed boundary motion the set of equations describing the interaction between a non stationary viscous incompressible fluid and an immersed elastic boundary is solved by coupling a projection method specially designed for locally refined meshes to an implicit formulation of the immersed boundary method the main contributions of this work concern the formulation and the implementation of a multilevel self adaptive version of the immersed boundary method on locally refined meshes this approach is tested for a particular two dimensional model problem for which no significant difference is found between the solutions obtained on a mesh refined locally around the immersed boundary and on the associated uniform mesh built with the resolution of the finest level

multigrid methods for saddle point problems oseen system abstract we develop and analyze multigrid methods for the oseen system in fluid flow we show that the w cycle algorithm is a uniform contraction if the number of smoothing steps is sufficiently large numerical results that illustrate the performance of the methods are also presented

an efficient solver for the incompressible navier stokes equations in rotation form we consider preconditioned iterative methods applied to discretizations of the linearized navier stokes equations in two and three dimensional bounded domains both unsteady and steady flows are considered the equations are linearized by picard iteration we make use of the rotation form of the momentum equations which has several advantages from the linear algebra point of view we focus on a preconditioning technique based on the hermitian skew hermitian splitting of the resulting nonsymmetric saddle point matrix we show that this technique can be implemented efficiently when the rotation form is used we study the performance of the solvers as a function of mesh size reynolds number time step and algorithm parameters our results indicate that fast convergence independent of problem parameters is achieved in many cases the preconditioner appears to be especially attractive in the case of low viscosity and for unsteady problems

an immersed boundary method for the simulation of bubbles with varying shape the paper presents a numerical method for the simulation of bubbles with variable shape in the framework of an immersed boundary method the liquid gas interface is described analytically by a series expansion in spherical harmonics such a representation of the interface is very accurate and robust and the error of the computed surface curvature is substantially smaller compared to a discrete representation of the surface by grid points the shape of the bubble is computed by minimizing the local displacement energy of pressure and surface tension forces and is coupled to the continuous phase by adapting the lagrangian surface mesh in each time step this is done with the constraint of constant bubble volume exactly implemented as a first step the bubbles are restricted to axisymmetric shapes the resulting algorithm is thoroughly validated by several numerical tests and finally applied to freely rising bubbles with stationary and oscillatory shape as well the computed bubble shapes are in very good agreement with experimental and numerical reference data

multi grid methods for stokes and navier stokes equations in the present paper we introduce transforming iterations an approach to construct smoothers for indefinite systems this turns out to be a convenient tool to classify several well known smoothing iterations for stokes and navier stokes equations and to predict their convergence behaviour epecially in the case of high reynolds numbers using this approach we are able to construct a new smoother for the navier stokes equations based on incomplete lu decompositions yielding a highly effective and robust multi grid method besides some qualitative theoretical convergence results we give large numerical comparisons and tests for the stokes as well as for the navier stokes equations for a general convergence theory we refer to 29

robust preconditioners for the high contrast stokes equation we consider the stokes equation with high contrast viscosity coefficients we construct a preconditioner that is robust with respect to contrast size and mesh size simultaneously based on the preconditioner proposed by aksoylu et al 2008 we examine the performance of our preconditioner against multigrid and provide a comparative study reflecting the effect of the underlying discretization and the aspect ratio of the mesh we address the rigorous justification of the solver methods p uzawa and p minres used in aksoylu and unlu 2013 and compare the results with additional solver method schur complement reduction scr we observe that our preconditioner is only contrast size robust under the p scr solver the inexact p uzawa solver remains to be the best choice for the most effective performance of our preconditioner as we observe contrast size and mesh size robustness simultaneously in this case as the contrast size grows asymptotically we prove and numerically demonstrate that the inexact p uzawa solver converges to the exact one finally we show that our preconditioner is contrast size and mesh size robust under p minres when the schur complement solve is accurate enough

a reduced basis finite element heterogeneous multiscale method for stokes flow in porous media a reduced basis darcy stokes finite element heterogeneous multiscale method rb ds fe hmm is proposed for the stokes problem in porous media the multiscale method is based on the darcy stokes finite element heterogeneous multiscale method ds fe hmm introduced in abdulle and budac 2015 that couples a darcy equation solved on a macroscopic mesh with missing permeability data extracted from the solutions of stokes micro problems at each macroscopic quadrature point to overcome the increasingly growing cost of repeatedly solving the stokes micro problems as the macroscopic mesh is refined we parametrize the microscopic solid geometry and approximate the infinite dimensional manifold of parameter dependent solutions of stokes problems by a low dimensional space this low dimensional reduced basis space is obtained in an offline stage by a greedy algorithm and used in an online stage to compute the effective darcy permeability at a cost independent of the microscopic mesh the discretization of the parametrized stokes problems relies on a petrov galerkin formulation that allows for a stable and fast online evaluation of the required permeabilities a priori and a posteriori estimates of the rb ds fe hmm are derived and a residual based adaptive algorithm is proposed two and three dimensional numerical experiments confirm the accuracy of the rb ds fe hmm and illustrate the speedup compared to the ds fe hmm c 2016 elsevier b v all rights reserved

an improved immersed boundary method with direct forcing for the simulation of particle laden flows an efficient approach for the simulation of finite size particles with interface resolution was presented by uhlmann m uhlmann an immersed boundary method with direct forcing for the simulation of particulate flows j comput phys 209 2005 448 476 the present paper proposes several enhancements of this method which considerably improve the results and extend the range of applicability an important step is a simple low cost iterative procedure for the euler lagrange coupling yielding a substantially better imposition of boundary conditions at the interface even for large time steps furthermore it is known that the basic method is restricted to ratios of particle density and fluid density larger than some critical value above 1 hence excluding for example non buoyant particles this can be remedied by an efficient integration step for the artificial flow field inside the particles to extend the accessible density range down to 0 3 this paper also shows that the basic scheme is inconsistent when moving surfaces are allowed to approach closer than twice the step size a remedy is developed based on excluding from the force computation all surface markers whose stencil overlaps with the stencil of a marker located on the surface of a collision partner the resulting algorithm is throughly validated and is demonstrated to substantially improve upon the original method

analysis of the inexact uzawa algorithm for saddle point problems in this paper we consider the so called inexact uzawa algorithm for iteratively solving linear block saddle point problems such saddle point problems arise for example in finite element and finite difference discretizations of stokes equations the equations of elasticity and mixed finite element discretization of second order problems we consider both the linear and nonlinear variants of the inexact uzawa iteration we show that the linear method always converges as long as the preconditioners defining the algorithm are properly scaled bounds for the rate of convergence are provided in terms of the rate of convergence for the preconditioned uzawa algorithm and the reduction factor corresponding to the preconditioner for the upper left hand block in the case of nonlinear iteration the inexact uzawa algorithm is shown to converge provided that the nonlinear process approximating the inverse of the upper left hand block is of sufficient accuracy bounds for the nonlinear iteration are given in terms of this accuracy parameter and the rate of convergence of the preconditioned linear uzawa algorithm applications to the stokes equations and mixed finite element discretization of second order elliptic problems are discussed and finally the results of numerical experiments involving the algorithms are presented

sources of distortion product otoacoustic emissions revealed by suppression experiments and inverse fast fourier transforms in normal ears primary and secondary sources combine to produce the 2f1 f2 distortion product otoacoustic emission dpoae measured in the ear canals of humans dpoaes were obtained in nine normal hearing subjects using a fixed f2 paradigm in which f1 was varied the f2 was 2 or 4 khz and absolute and relative primary levels were varied data were obtained with and without a third tone f3 placed 15 6 hz below 2f1 f2 the level of f3 was varied in order to suppress the stimulus frequency otoacoustic emission sfoae coming from the 2f1 f2 place these data were converted from the complex frequency domain into an equivalent time representation using an inverse fast fourier transform ifft iffts of unsuppressed dpoae data were characterized by two or more peaks relative amplitudes of these peaks depended on overall primary level and on primary level differences the suppressor eliminated later peaks but early peaks remained relatively unaltered results are interpreted to mean that the dpoae measured in humans includes components from the f2 place intermodulation distortion and dp place in the form of a sfoae these findings build on previous work by providing evidence that multiple peaks in the ifft are due to a secondary source at the dp place

estimating bone conduction transfer functions using otoacoustic emissions a technique for estimating the nonparametric bone conduction transfer function using distortion product otoacoustic emissions dpoaes is presented individual transfer functions were obtained using dpoaes recorded from a single ear of five normal hearing adults repeatability of the technique was investigated by performing measurements on at least three dates functions were reasonably repeatable and were unique to each individual as expected from subjective measurements input force and dpoae measurements were made for each individual and a model of the auditory periphery representative of an average person was employed the technique is objective and requires only passive cooperation but robust dpoaes are needed and the measurement time can be onerous for a wide frequency band or fine frequency resolution with appropriate adjustments to the model of the auditory periphery the method could be applied with animal models

simultaneous latency estimations for distortion product otoacoustic emissions and envelope following responses the purpose of this research was to simultaneously estimate processing delays in the cochlea and brainstem using the same acoustic stimuli apparent latencies were estimated from ear canal measurements of 2f1 f2 distortion product otoacoustic emissions dpoaes and scalp recordings of the f2 f1 envelope following response efr the stimuli were equal level tone pairs 65db spl with the upper tone f2 set at either 900 or 1800hz to fix the initiation site of the dpoae and efr the frequency of f1 was swept continuously between frequency limits chosen to keep the efr response between 150 and 170hz the average dpoae latencies were 9 6 and 6 2ms for f2 900 and 1800hz and the corresponding efr latencies were 12 4 and 8 8ms in a control condition a third suppressor tone was added near the dpoae response frequency to evaluate whether the potential source at fdp was contributing significantly to the measured emission dpoae latency is the sum of both inward and outward cochlear delays the efr apparent la

a non iterative immersed boundary method for spherical particles of arbitrary density ratio in this paper an immersed boundary method with semi implicit fluidsolid coupling for mobile particles of arbitrary density ratio is developed the new scheme does not require any iterations to balance fluid forces and particle forces at the interface a new formulation of the particle equations of motion is proposed which not only accounts for the particle itself but also for a lagrangian layer surrounding the particle surface furthermore it is shown by analytical considerations that the six equations for the linear and angular velocity of the spherical particle decouple which allows their sequential solution on this basis a new time integration scheme is obtained which is unconditionally stable for all fluidsolid density ratios and enables large time steps with courant numbers around unity the new scheme is extensively validated for various test cases and its convergence is assessed an appealing issue is that compared to existing immersed boundary methods the new scheme only alters coefficients in the particle equations and the order of the steps making it easy to implement in present codes with explicit coupling this substantially extends the field of application of such methods an extremely efficient semi implicit ibm for mobile particles of arbitrary density ratio is developed unconditional stability is achieved without any iterative coupling to balance fluid and particle forces at the interface the new scheme only alters coefficients in the particle equations and the sequence of the operations in each time step extensive validation for various test cases including buoyant particles with zero mass

the effect of stimulus frequency ratio on distortion product otoacoustic emission components a detailed measurement of distortion product otoacoustic emission dpoae fine structure was used to extract estimates of the two major components believed to contribute to the overall dpoae level in the ear canal a fixed ratio paradigm was used to record dpoae fine structure from three normal hearing ears over a range of 400 hz for 12 different stimulus frequency ratios between 1 053 and 1 36 and stimulus levels between 45 and 75 db spl inverse fourier transforms of the amplitude and phase data were filtered to extract the early component from the generator region of maximum stimulus overlap and the later component reflected from the characteristic frequency region of the dpoae after filtering the data were returned to the frequency domain to evaluate the impact of the stimulus frequency ratio and stimulus level on the relative levels of the components although there were significant differences between data from different ears some consistent patterns could be detected the component from the overlap region of the stimulus tones exhibits a bandpass shape with the maximum occurring at a ratio of 1 2 the mean data from the dpoae characteristic frequency region also exhibits a bandpass shape but is less sharply tuned and exhibits greater variety across ears and stimulus levels the component from the dpoae characteristic frequency region is dominant at ratios narrower than approximately 1 1 the transition varies between ears the relative levels of the two components are highly variable at ratios greater than 1 3 and highly dependent on the stimulus level the reflection component is larger at all ratios at the lowest stimulus level tested 45 45 db spl we discuss the factors shaping dpoae component behavior and some cursory implications for the choice of stimulus parameters to be used in clinical protocols

distortion product otoacoustic emission delay measurement in human ears the measurement of distortion product otoacoustic emission dpoae delay using the phase gradient method is discussed a short f2 sweep paradigm is described its merits are discussed and comparisons made with other methods using sweeps of less than 4 consistent and reliable measurements were obtained from 12 normal ears except for a few isolated measurements investigation of these apparent anomalies indicated that the short f2 sweep method was sensitive to the localized effects of narrow distortion product intensity notches and spontaneous emissions it is possible that middle ear pressure instability or some local change in the cochlea sometimes compounded the situation the intersubject range 63 of the mean of dpoae delay values was greater than the range of values observed due to measurement variability 5 6 of the mean or intrasubject variability 8 5 of the mean demonstrating that the method can detect real differences between ears however comparison with previous work shows that caution is needed in interpreting these data as all dpoae phase methods provide only partial latency values the physical interpretation depends on both the stimulus sweep used and the origin of dpoaes our data shows that f1 sweep derived latency is lower than f2 sweep data by more than 20 caution also needs to be exercised when comparing cochlear traveling wave delay as inferred from electrophysiological data with that obtained from dpoae delay measurements

level set methods an overview and some recent results the level set method was devised by s osher and j a sethian 1988 j comput phys 79 12 49 as a simple and versatile method for computing and analyzing the motion of an interface in two or three dimensions bounds a possibly multiply connected region the goal is to compute and analyze the subsequent motion of under a velocity field v this velocity can depend on position time the geometry of the interface and the external physics the interface is captured for later time as the zero level set of a smooth at least lipschitz continuous function x t i e t x x t 0 is positive inside negative outside and is zero on t topological merging and breaking are well defined and easily performed in this review article we discuss recent variants and extensions including the motion of curves in three dimensions the dynamic surface extension method fast methods for steady state problems diffusion generated motion and the variational level set approach we also give a user s guide to the level set dictionary and technology and couple the method to a wide variety of problems involving external physics such as compressible and incompressible possibly reacting flow stefan problems kinetic crystal growth epitaxial growth of thin films vortex dominated flows and extensions to multiphase motion we conclude with a discussion of applications to computer vision and image processing

group delays of distortion product otoacoustic emissions relating delays measured with f1 and f2 sweep paradigms a theoretical analysis is presented of group delays of distortion product otoacoustic emissions dpoaes measured with the phase gradient method the aim of the analysis is to clarify the differences in group delays d1 and d2 obtained using the f1 and the f2 sweep paradigms respectively and the dependence of group delays on the order of the dpoae two models are considered the place fixed and the wave fixed models while in the former model the generation place is assumed to be invariant with both f1 and f2 sweeps in the latter model the shift of generation place is fully accounted for by making a simple local approximation of the cochlear scale invariance a mathematical conversion from phase place to phase frequency gradients is incorporated in the wave fixed model under the assumption that the dpoae as recorded at the best f2 f1 ratio is dominated by the contribution from the generation site and not by e g reflection components the analysis leads to simple expressions for the ratio and difference between d1 and d2 validation of the models against experimental data indicates that lower sideband dpoaes 2f1 f2 3f1 2f2 4f1 3f2 are most consistent with the wave fixed model upper sideband components 2f2 f1 in contrast are not properly described by either the place fixed or the wave fixed model independent whether dpoae generation is assumed to originate at the f2 or at the more basally located f dp characteristic place

a preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems this paper provides a preconditioned iterative technique for the solution of saddle point problems these problems typically arise in the numerical approximation of partial differential equations by lagrange multiplier techniques and or mixed methods the saddle point problem is reformulated as a symmetric positive definite system which is then solved by conjugate gradient iteration applications to the equations of elasticity and stokes are discussed and the results of numerical experiments are given

analysis of iterative methods for saddle point problems a unified approach in this paper two classes of iterative methods for saddle point problems are considered inexact uzawa algorithms and a class of methods with symmetric preconditioners in both cases the iteration matrix can be transformed to a symmetric matrix by block diagonal matrices a simple but essential observation which allows one to estimate the convergence rate of both classes by studying associated eigenvalue problems the obtained estimates apply for a wider range of situations and are partially sharper than the known estimates in literature a few numerical tests are given which confirm the sharpness of the estimates

an efficient numerical method for the two fluid stokes equations with a moving immersed boundary we consider the immersed boundary problem in which the boundary separates two very viscous fluids with differing viscosities the moving elastic boundary may exert a force on the local fluid the model solution is obtained using the immersed interface method which computes second order accurate approximations by incorporating known jumps in the solution or its derivatives into a finite difference method these jump conditions become coupled when the fluid viscosity has a jump across the boundary and this coupling renders the application of the immersed interface method challenging we present a method that first uses boundary integral equations to reduce the two fluid stokes problem to the single fluid case and then solves the single fluid problem using the immersed interface method using this method we assess through two numerical examples how the fluid dynamics are affected by differing viscosities in the two fluid regions we also propose an implicit algorithm and a fractional step algorithm for advancing the boundary position because both algorithms make use of the integral form of the solution neither one requires the solution of a large system of coupled nonlinear equations as is traditionally the case numerical results suggest that for sufficiently stiff problems the fractional time stepping algorithm is the most efficient in the sense that it allows the largest time interval between subsequent updates of global model solutions

interrelations among distortion product phase gradient delays their connection to scaling symmetry and its breaking distortion product otoacoustic emission dpoae phase versus frequency functions and corresponding phase gradient delays have received considerable attention because of their potential for providing information about mechanisms of emission generation cochlear wave latencies and characteristics of cochlear tuning the three measurement paradigms in common use fixed f1 fixed f2 and fixed f2 f1 yield significantly different delays suggesting that they depend on qualitatively different aspects of cochlear mechanics in this paper theory and experiment are combined to demonstrate that simple phenomenological arguments which make no detailed mechanistic assumptions concerning the underlying cochlear mechanics predict relationships among the delays that are in good quantitative agreement with experimental data obtained in guinea pigs to understand deviations between the simple theory and experiment a general equation is found that relates the three delays for any deterministic model of dpoae generation both model independent and exact the general relation provides a powerful consistency check on the measurements and a useful tool for organizing and understanding the structure in dpoae phase data e g for interpreting the relative magnitudes and intensity dependencies of the three delays analysis of the general relation demonstrates that the success of the simple phenomenological approach can be understood as a consequence of the mechanisms of emission generation and the approximate local scaling symmetry of cochlear mechanics the general relation is used to quantify deviations from scaling manifest in the measured phase gradient delays the results indicate that deviations from scaling are typically small and that both linear and nonlinear mechanisms contribute significantly to these deviations intensity dependent mechanisms contributing to deviations from scaling include cochlear reflection and wave interference effects associated with the mixing of distortion and reflection source emissions as in dpoae fine structure finally the ratio of the fixed f1 and fixed f2 phase gradient delays is shown to follow from the choice of experimental paradigm and in the scaling limit contains no information about cochlear physiology whatsoever these results cast considerable doubt on the theoretical basis of recent attempts to use relative dpoae phase gradient delays to estimate the bandwidths of peripheral auditory filters

group delays of distortion product otoacoustic emissions in the guinea pig this paper presents a comprehensive set of experimental data on group delays of distortion product otoacoustic emissions dpoaes in the guinea pig group delays of the dpoaes with frequencies 2f1 f2 3f1 2f2 4f1 3f2 and 2f2 f1 were measured with the phase gradient method both the f1 and the f2 sweep paradigm were used differences between the two sweep paradigms were investigated for the four dpoaes as well as the group delay differences between the dpoaes analysis revealed larger group delays with the f2 sweep paradigm but only for the lower sideband dpoaes with fdp f1 f2 for the lower sideband cubic distortion product 2f1 f2 the f2 sweep delays were a factor of 1 17 1 54 larger than the f1 sweep delays depending on frequency the upper sideband dpoae 2f2 f1 showed no significant difference between f1 and f2 sweep group delays except for the highest and lowest f2 frequencies comparing the group delays of the dpoaes for each sweep paradigm separately equal group delays were found for all four dpoaes measured with the f1 sweep with the f2 sweep paradigm on the other hand the group delays of the three lower sideband dpoaes occurred to be larger than the group delays of the upper sideband dpoae 2f2 f1 a tentative interpretation of the data in the context of proposed explanatory hypotheses on dpoae group delays is given

an immersed interface method for stokes flows with fixed moving interfaces and rigid boundaries we present an immersed interface method for solving the incompressible steady stokes equations involving fixed moving interfaces and rigid boundaries irregular domains the fixed moving interfaces and rigid boundaries are represented by a number of lagrangian control points in order to enforce the prescribed velocity at the rigid boundaries singular forces are applied on the fluid at these boundaries the strength of singular forces at the rigid boundary is determined by solving a small system of equations for the deformable interfaces the forces that the interface exerts on the fluid are calculated from the configuration position of the deformed interface the jumps in the pressure and the jumps in the derivatives of both pressure and velocity are related to the forces at the fixed moving interfaces and rigid boundaries these forces are interpolated using cubic splines and applied to the fluid through the jump conditions the positions of the deformable interfaces are updated implicitly using a quasi newton method bfgs within each time step in the proposed method the stokes equations are discretized via the finite difference method on a staggered cartesian grid with the incorporation of jump contributions and solved by the conjugate gradient uzawa type method numerical results demonstrate the accuracy and ability of the proposed method to simulate incompressible stokes flows with fixed moving interfaces on irregular domains

sources of dpoaes revealed by suppression experiments inverse fast fourier transforms and sfoaes in impaired ears dpoae sources are modeled by intermodulation distortion generated near the f2 place and a reflection of this distortion near the dp place in a previous paper inverse fast fourier transforms iffts of dpoae filter functions in normal ears were consistent with this model konrad martin et al j acoust soc am 109 2862 2879 2001 in the present article similar measurements were made in ears with specific hearing loss configurations it was hypothesized that hearing loss at f2 or dp frequencies would influence the relative contributions to the dpoae from the corresponding basilar membrane places and would affect the relative magnitudes of sfoaes at frequencies equal to f2 and fdp dpoaes were measured with f2 4 khz f1 varied and a suppressor near fdp l2 was 25 55 db spl l1 l2 10 db sfoaes were measured at f2 and at 2 7 khz the average fdp produced by the f1 sweep for stimulus levels of 20 60 db spl sfoae results supported predictions of the pattern of amplitude differences between sfoaes

improved volume conservation in the computation of flows with immersed elastic boundaries this paper introduces a recipe for the construction of a finite difference divergence operator the coefficients of which are completely determined once an interpolation scheme has been chosen substitution of this divergence operator for the previously used divergence based on central differences makes a dramatic improvement in the overall volume conservation that is observed in an immersed boundary computation this improvement is particularly important for computations in which an elastic boundary separates chambers containing fluid at substantially different pressures a situation which is prominent in cardiac fluid dynamics during the contraction of the ventricles

combined immersed boundary finite difference methods for three dimensional complex flow simulations a second order accurate highly efficient method is developed for simulating unsteady three dimensional incompressible flows in complex geometries this is achieved by using boundary body forces that allow the imposition of the boundary conditions on a given surface not coinciding with the computational grid the governing equations therefore can be discretized and solved on a regular mesh thus retaining the advantages and the efficiency of the standard solution procedures two different forcings are tested showing that while the quality of the results is essentially the same in both cases the efficiency of the calculation strongly depends on the particular expression a major issue is the interpolation of the forcing over the grid that determines the accuracy of the scheme this ranges from zeroth order for the most commonly used interpolations up to second order for an ad hoc velocity interpolation the present scheme has been used to simulate several flows whose results have been validated by experiments and other results available in the literature finally in the last example we show the flow inside an ic piston cylinder assembly at high reynolds number to our knowledge this is the first example in which the immersed boundary technique is applied to a full three dimensional complex flow with moving boundaries and with a reynolds number high enough to require a subgrid scale turbulence model

interpretation of distortion product otoacoustic emission measurements i two stimulus tones the interpretation of common but poorly understood observed characteristics of distortion product emissions is assisted by the development of a simple model this model essentially includes only saturation of the cochlear amplifier with emissions arising naturally from the same nonlinear processes which cause the saturation the model provides useful physical explanations of emission behavior particularly considered as a function of the stimulus intensities of the two primaries i e behavior with fixed stimulus frequencies it is assumed that emission generation consists of two main components which are always present in the total emission but which most often have approximately opposite i e canceling phases one component arises in a small region centered about the peak of the emission generation function while the other arises from the region basal to this peak at low stimulus levels with normal cochlear amplifier operation the peak of the emission generation function is sharp so the emission from the peak region dominates the total emission this peak emission has typically been characterized as the active emission at high stimulus levels where saturation is important or at all levels when the gain of the cochlear amplifier is reduced the summed basal component dominates the total emission the characteristics of this basal emission are similar to and continuous with the characteristics of the truly passive emission i e the emission observed when the cochlear amplifier gain is identically zero under circumstances when the emissions from the peak and basal components are approximately equal there is seen a sharp notch characteristic of phase cancellation the simple model produces emission distributions as a function of independent variation of the two stimulus amplitudes which are in good agreement with observation it is shown that the furosemide assay provides a good estimate of cochlear amplifier gain when a correction factor of about 10 db is added however when using two stimulus tones neither absolute emission amplitudes or emission input output functions or the furosemide assay can adequately distinguish between cases of moderate versus poor cochlear amplifier dysfunction when the cochlear amplifier gains are in the range from about half normal to zero

efficient numerical method for the direct numerical simulation of the flow past a single light moving spherical body in transitional regimes an efficient numerical method for solving the coupled system of navier stokes equations and equations of motion of a single spherical particle is presented it combines a spectral spectral element spatial discretization in a cylindrical domain moving translationally with the free particle and particle equations of motion involving hydrodynamic forces integrated on the particle surface the time discretization is semi implicit with a third order accurate explicit treatment of the advective terms and a fully implicit treatment of the remaining linear problem consisting in stokes like equations coupled with the particle equations of motion it is shown that the fully implicit approach is the only way to account for very light spheres moreover no reduction of the time step is necessary the particle equations of motion are re formulated as a simple system of six linear equations for six unknowns using the fact that the six components combining the hydrodynamic forces and torques depend linearly on particle translation and angular velocities they are solved directly and are thus exactly satisfied at each time step numerical tests show that the increase of computing costs needed to account for the free sphere degrees of freedom remains within about 20 per time step the accuracy and resolution independence of the solution are tested at the primary instability threshold and for a strongly supercritical zigzagging trajectory a partial validation using available experimental results is also presented very satisfactory accuracy is shown to be obtained with only a very limited number of azimuthal modes

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

fast iterative solution of stabilised stokes systems part i using simple diagonal preconditioners mixed finite element approximation of the classical stokes problem describing slow viscous incompressible flow gives rise to symmetric indefinite systems for the discrete velocity and pressure variables iterative solution of such indefinite systems is feasible and is an attractive approach for large problems the use of stabilisation methods for convenient but unstable mixed elements introduces stabilisation parameters we show how these can be chosen to obtain rapid iterative convergence we propose a conjugate gradient like method the method of preconditioned conjugate residuals which is applicable to symmetric indefinite problems describe the effects of stabilisation on the algebraic structure of the discrete stokes operator and derive estimates of the eigenvalue spectrum of this operator on which the convergence rate of the iteration depends here we discuss the simple case of diagonal preconditioning our results apply to both locally and globally stabilised mixed elements as well as to elements which are inherently stable we demonstrate that convergence rates comparable to that achieved using the diagonally scaled conjugate gradient method applied to the discrete laplacian are approachable for the stokes problem

a jacobian free based iim for incompressible flows involving moving interfaces with dirichlet boundary conditions in this paper a finite difference marker and cell mac scheme is presented for the steady stokes equations with moving interfaces and dirichlet boundary condition the moving interfaces are represented by lagrangian control points and their position is updated implicitly using a jacobian free approach within each time step the forces at the moving interfaces are calculated from the position of the interfaces and interpolated using cubic splines and then applied to the fluid through the related jump conditions the proposed jacobian free newton generalized minimum residual gmres method avoids the need to form and store the matrix explicitly in the computation of the inverse of the jacobian and betters numerical stability the stokes equations are discretized on a mac grid via a second order finite difference scheme with the incorporation of jump contributions and the resulting saddle point system is solved by the conjugate gradient uzawa type method numerical results demonstrate very well the accuracy and effectiveness of the proposed method the present algorithm has been applied to solve incompressible navier stokes flows with moving interfaces copyright 2010 john wiley sons ltd