spatiospectral concentration on a sphere we pose and solve the analogue of slepian s time frequency concentration problem on the surface of the unit sphere to determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of the sphere or alternatively of strictly spacelimited functions that are optimally concentrated in the spherical harmonic domain such a basis of simultaneously spatially and spectrally concentrated functions should be a useful data analysis and representation tool in a variety of geophysical and planetary applications as well as in medical imaging computer science cosmology and numerical analysis the spherical slepian functions can be found by solving either an algebraic eigenvalue problem in the spectral domain or a fredholm integral equation in the spatial domain the associated eigenvalues are a measure of the spatiospectral concentration when the concentration region is an axisymmetric polar cap the spatiospectral projection operator commutes with a sturm liouville operator this enables the eigenfunctions to be computed extremely accurately and efficiently even when their area bandwidth product or shannon number is large in the asymptotic limit of a small spatial region and a large spherical harmonic bandwidth the spherical concentration problem reduces to its planar equivalent which exhibits self similarity when the shannon number is kept invariant

a comparative study of different sets of variables for solving compressible and incompressible flows a globally conservative galerkin least squares formulation which attains correct shock structure is developed for any choice of variables only the choice of entropy variables satisfies exactly the discrete clausius duhem inequality without any dissipative mechanisms whereas for the rest of the variables artificial diffusion is required to guarantee entropy production the limit of the formulation is well defined for entropy variables and the primitive variables p u t leading to conservative incompressible formulations the approach is stable for any continuous interpolations both for compressible and incompressible flows a comparative study of different variables is performed indicating that entropy variables and the primitive variables p u t possess the most attributes for practical problem solving

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

slepian spatial spectral concentration problem on the sphere analytical formulation for limited colatitude longitude spatial region in this paper we develop an analytical formulation for the slepian spatial spectral concentration problem on the sphere for a limited colatitude longitude spatial region on the sphere defined as the cartesian product of a range of positive colatitudes and longitudes the solution of the slepian problem is a set of functions that are optimally concentrated and orthogonal within a spatial or spectral region these properties make them useful for applications where measurements are taken within a spatially limited region of the sphere and or a signal is only to be analyzed within a region of the sphere to support localized spectral spatial analysis and estimation and sparse representation of localized data in these applications we exploit the expansion of spherical harmonics in the complex exponential basis to develop an analytical formulation for the slepian concentration problem for a limited colatitude longitude spatial region we also extend the analytical formulation for spatial regions that are comprised of a union of rotated limited colatitude longitude subregions by exploiting various symmetries of the proposed formulation we design a computationally efficient algorithm for the implementation of the proposed analytical formulation such a reduction in computation time is demonstrated through numerical experiments we present illustrations of our results with the help of numerical examples and show that the representation of a spatially concentrated signal is indeed sparse in the slepian basis

incompressible flow past a circular cylinder dependence of the computed flow field on the location of the lateral boundaries the influence of the location of the lateral boundaries on 2d computation of unsteady incompressible flow past a circular cylinder is investigated the case of reynolds number 100 is used as a benchmark and several quantities characterizing the unsteady flow are obtained for a range of lateral boundary locations the computations are performed with two distinct finite element formulations space time velocity pressure formulation and velocity pressure stress formulation we conclude that the distance between the cylinder and the lateral boundaries can have a significant effect on the strouhal number and other flow quantities the minimum distance at which this influence vanishes has been found to be larger than what is commonly assumed

hierarchically refined and coarsened splines for moving interface problems with particular application to phase field models of prostate tumor growth abstract moving interface problems are ubiquitous in science and engineering to develop an accurate and efficient methodology for this class of problems we present algorithms for local h adaptivity of hierarchical b splines to be utilized in isogeometric analysis we extend bezier projection an efficient quadrature free local projection technique to the hierarchical setting in this case extraction operators may not be invertible to address this issue we develop a multi level reconstruction operator which maintains the locality properties of the projection we also introduce a balance parameter to control the overlap of hierarchical functions leading to improved numerical conditioning we apply our algorithms to the simulation of localized prostate cancer growth we model this disease using the phase field method and a set of diffusion reaction equations to account for the dynamics of nutrients and a key biomarker termed prostate specific antigen our results include examples on simple 2d and 3d domains and a more compelling tissue scale patient specific simulation which is run over a prostate anatomy extracted from medical images our methods for local h adaptivity efficiently capture the evolving interface between the tumor and the neighboring healthy tissue with remarkable accuracy in all cases

impact of geometric uncertainty on hemodynamic simulations using machine learning abstract in the cardiovascular system blood flow rates blood velocities and blood pressures can be modeled using the navier stokes equations inputs to the system are typically uncertain such as a the geometry of the arterial tree b clinically measured blood pressure and viscosity c boundary resistances among others due to a large number of such parameters efficient quantification of uncertainty in solution fields in this multi parameter space is challenging we use an adaptive stochastic collocation method to quantify the impact of uncertainty in geometry in patient specific models we develop a novel subdivision method to define the stochastic space of geometries to accelerate convergence and make the problem tractable we use a machine learning approach to approximate the simulation based solution towards this a reduced order model of the navier stokes equations is developed using a segmental resistance analog boundary conditions ratio of pressure to flow using an offline database of pre computed solutions we compute a map rule from the features to solution fields we achieve significant speed up of a few orders of magnitude by approximating the simulation based solution using a machine learning predictor a bootstrap aggregated decision tree was found to be the best predictor among many candidate regressors correlation coefficient of training set was 0 94 we demonstrate stochastic space convergence using the adaptive stochastic collocation method and also show robustness to the choice of geometry parameterization the sensitivities to geometry obtained using machine learning had a correlation coefficient of 0 92 with the values obtained using finite element simulations segments with significant disease in the larger arteries had the highest sensitivities terminal segments are more sensitive to dilation and proximal healthy segments are more sensitive to erosion sensitivity to geometry is highest when geometric resistance is comparable to net downstream resistance

improving stability of stabilized and multiscale formulations in flow simulations at small time steps abstract the objective of this paper is to show that use of the element vector based definition of stabilization parameters introduced in t e tezduyar computation of moving boundaries and interfaces and stabilization parameters int j numer methods fluids 43 2003 555 575 t e tezduyar y osawa finite element stabilization parameters computed from element matrices and vectors comput methods appl mech engrg 190 2000 411 430 circumvents the well known instability associated with conventional stabilized formulations at small time steps we describe formulations for linear advection diffusion and incompressible navier stokes equations and test them on three benchmark problems advection of an l shaped discontinuity laminar flow in a square domain at low reynolds number and turbulent channel flow at friction velocity reynolds number of 395

three dimensional simulation of unstable gravity driven infiltration of water into a porous medium infiltration of water in dry porous media is subject to a powerful gravity driven instability although the phenomenon of unstable infiltration is well known its description using continuum mathematical models has posed a significant challenge for several decades the classical model of water flow in the unsaturated flow the richards equation is unable to reproduce the instability here we present a computational study of a model of unsaturated flow in porous media that extends the richards equation and is capable of predicting the instability and captures the key features of gravity fingering quantitatively the extended model is based on a phase field formulation and is fourth order in space the new model poses a set of challenges for numerical discretizations such as resolution of evolving interfaces stiffness in space and time treatment of singularly perturbed equations and discretization of higher order spatial partial differential operators we develop a numerical algorithm based on isogeometric analysis a generalization of the finite element method that permits the use of globally smooth basis functions leading to a simple and efficient discretization of higher order spatial operators in variational form we illustrate the accuracy efficiency and robustness of our method with several examples in two and three dimensions in both homogeneous and strongly heterogeneous media we simulate for the first time unstable gravity driven infiltration in three dimensions and confirm that the new theory reproduces the fundamental features of water infiltration into a porous medium our results are consistent with classical experimental observations that demonstrate a transition from stable to unstable fronts depending on the infiltration flux

optimum waveform signal sets with amplitude and energy constraints it is desirable to choose the waveforms making up a signaling alphabet so that they are maximally separated one from another this problem is considered in the space of square integrable functions for signals which have finite duration and are constrained in the ranges of their values as well as in energy corresponding to each of the following cases we establish sharp bounds for the minimum distance and for the average distance between elements of a fixed size signal set and construct sets of signals that attain both bounds simultaneously begin list item em case a energy constraint only the average energy of the waveforms in the signal set is at most sigma where 0 leq sigma item em case b energy and peak amplitude constraints the average energy of the waveforms in the signal set is leq sigma 0 leq sigma and the absolute value of each waveform is at most 1 item em case c energy and value constraints the average energy of the waveforms in the signal set is at most b 2 sigma a 2 1 sigma and each waveform takes values in the set a b where 0 leq a and 0 leq sigma leq 1 end list cases a and b are applicable to signal design for communication in channels with additive noise say gaussian and case c is applicable to signal design for optical channels where the signal represents the intensity of a photon stream the general character of the results is that the minimum distance behaves like gamma sigma in cases a and b and like gamma sigma 1 sigma in case c with gamma a suitable constant

stability of semidiscrete formulations for parabolic problems at small time steps solutions of direct time integration schemes that converge in time to conventional semidiscrete formulations may be polluted at small time steps by spurious spatial oscillations along with attendant overshoot in time this degradation is not an artifact of the time marching scheme but rather a property of the solution of the semidiscrete formulation itself a critical time step for the onset of spatial oscillations is derived by analogy to singularly perturbed elliptic problems we then propose a simple procedure of spatial stabilization to remove this pathology from implicit time integration schemes without affecting unconditional temporal stability spatially stabilized implicit time integration is free of spurious spatial oscillations at small time steps and numerical experience points to improved temporal accuracy as well

isogeometric analysis of free surface flow abstract this paper presents the first application of isogeometric analysis a new computational technology built on higher order and higher continuity basis functions employed in computer aided design and computer graphics to the computation of free surface phenomena described using the level set approach the method is based on the variational framework that is suitable for discretization by standard finite elements as well as the basis functions employed in isogeometric analysis the underlying numerical formulation globally conserves mass and preserves a sharp air water interface for the entire length of the simulation the numerical tests indicate that the proposed methodology gives an accurate description of the free surface behavior in both quasi steady and dynamic regimes furthermore very good per degree of freedom accuracy is obtained when higher order and higher continuity isogeometric discretizations are employed in free surface computations

variable kinematic modelling of laminated composite plates a displacement based variable kinematic global local finite element model is developed using hierarchical multiple assumed displacement fields at two different levels 1 at the element level and 2 at the mesh level the displacement field hierarchy contains both a conventional plate expansion 2 d and a full layerwise 3 d expansion depending on the accuracy desired the variable kinematic element can use various terms from the composite displacement field thus creating a hierarchy of different elements having a wide range of kinematic complexity and representing a number of different mathematical models the vkfe is then combined with the mesh superposition technique to further increase the computational efficiency and robustness of the computational algorithm these models are used to analyse a number of laminated composite plate problems that contain localized subregions where significant 3 d stress fields exist e g free edge effects

outflow boundary conditions for three dimensional finite element modeling of blood flow and pressure in arteries flow and pressure waves emanate from the heart and travel through the major arteries where they are damped dispersed and reflected due to changes in vessel caliber tissue properties and branch points as a consequence solutions to the governing equations of blood flow in the large arteries are highly dependent on the outflow boundary conditions imposed to represent the vascular bed downstream of the modeled domain the most common outflow boundary conditions for three dimensional simulations of blood flow are prescribed constant pressure or traction and prescribed velocity profiles however in many simulations the flow distribution and pressure field in the modeled domain are unknown and cannot be prescribed at the outflow boundaries an alternative approach is to couple the solution at the outflow boundaries of the modeled domain with lumped parameter or one dimensional models of the downstream domain we previously described a new approach to prescribe outflow boundary conditions for simulations of blood flow based on the dirichlet to neumann and variational multiscale methods this approach termed the coupled multidomain method was successfully applied to solve the non linear one dimensional equations of blood flow with a variety of models of the downstream domain this paper describes the extension of this method to three dimensional finite element modeling of blood flow and pressure in the major arteries outflow boundary conditions are derived for any downstream domain where an explicit relationship of pressure as a function of flow rate or velocities can be obtained at the coupling interface we developed this method in the context of a stabilized semi discrete finite element method flow rate and pressure distributions are shown for different boundary conditions to illustrate the dramatic influence of alternative boundary conditions on these quantities

a new family of projection schemes for the incompressible navier stokes equations with control of high frequency damping abstract a simple spatially discrete model problem consisting of mass points and dash pots is presented which allows for the assessment of the properties of different projection schemes for the solution of the incompressible navier stokes equations in particular the temporal accuracy the stability and the numerical damping are investigated the present study suggests that it is not possible to formulate a second order accurate projection pressure correction scheme which possesses any high frequency damping motivated by this observation two new families of projection schemes are proposed which are developed from the generalised midpoint rule and from the generalised method respectively and offer control over high frequency damping both schemes are investigated in detail on the basis of the model problem and subsequently implemented in the context of a finite element formulation for the incompressible navier stokes equations comprehensive numerical studies of the flow in a lid driven cavity and the flow around a cylinder are presented the observations made are in agreement with the conclusions drawn from the model problem

isogeometric spline forests in this paper we present isogeometric spline forests an isogeometric spline forest is a hierarchical spline representation capable of representing surfaces or volumes of arbitrarily complex geometry and topological genus spline forests can accomodate arbitrary degree and smoothness in the underlying hierarchical basis as well as non uniform knot interval configurations we describe adaptive h refinement and coarsening algorithms for isogeometric spline forests and develop a bezier extraction framework which provides a simple and efficient single level finite element description of the complex multi level unstructured hierarchical spline basis we then demonstrate the potential of spline forests as a basis for analysis in the context of transient advection diffusion problems where fully integrated adaptivity is demonstrated for the first time in an isogeometric simulation in all cases the adaptive process remains local even in the case of moving fronts and preserves exact geometry at the coarsest level of the discretization the accuracy and robustness of the approach is demonstrated in all cases

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

uncertainty quantification of simulated biomechanical stimuli in coronary artery bypass grafts coronary artery bypass graft surgery cabg is performed on more than 400 000 patients annually in the u s however saphenous vein grafts svgs implanted during cabg exhibit poor patency compared to arterial grafts with failure rates up to 40 within 10 years after surgery differences in mechanical stimuli are known to play a role in driving maladaptation and have been correlated with endothelial damage and thrombus formation as these quantities are difficult to measure in vivo multi scale coronary models offer a way to quantify them while accounting for complex coronary physiology however prior studies have primarily focused on deterministic evaluations without reporting variability in the model parameters due to uncertainty this study aims to assess confidence in multi scale predictions of wall shear stress and wall strain while accounting for uncertainty in peripheral hemodynamics and material properties boundary condition distributions are computed by assimilating uncertain clinical data while spatial variations of vessel wall stiffness are obtained through approximation by a random field we developed a stochastic submodeling approach to mitigate the computational burden of repeated multi scale model evaluations to focus exclusively on the bypass grafts this produces a two level decomposition of quantities of interest into submodel contributions and full model submodel discrepancies we leverage these two levels in the context of forward uncertainty propagation using a previously proposed multi resolution approach the time and space averaged wall shear stress is well estimated with a coefficient of variation of 35 but ignorance about the spatial distribution on the wall elastic modulus and thickness lead to large variations in an objective measure of wall strain with coefficients of variation up to 100 sensitivity analysis reveals how the interactions between the flow and material parameters contribute to output variability

liquid vapor transformations with surfactants phase field model and isogeometric analysis surfactants are compounds that find energetically favorable to be located at the boundaries between fluids they are able to modify the properties of those interfaces for example reducing surface tension here we propose a new model for liquid vapor flows with surfactants which captures the dynamics of the surfactant and accounts for phase transformations in the fluid the aforementioned model is derived from a free energy functional by using a coleman noll approach the proposed theory emanates from the isothermal navier stokes korteweg equations which describe single component two phase flow and naturally allow for phase transformations we believe that our model has significant potential to study the influence of surfactants in vaporization and condensation processes from a numerical point of view the proposed model poses significant challenges to existing discretization methods including stiffness in space and time internal and boundary layers as well as higher order partial differential operators to overcome these challenges we propose algorithms based on isogeometric analysis which permit an accurate and efficient discretization finally we illustrate the viability of the theoretical framework and the effectiveness of our algorithms by solving several numerical problems in two and three dimensions

tensor based cortical surface morphometry via weighted spherical harmonic representation we present a new tensor based morphometric framework that quantifies cortical shape variations using a local area element the local area element is computed from the riemannian metric tensors which are obtained from the smooth functional parametrization of a cortical mesh for the smooth parametrization we have developed a novel weighted spherical harmonic spharm representation which generalizes the traditional spharm as a special case for a specific choice of weights the weighted spharm is shown to be the least squares approximation to the solution of an isotropic heat diffusion on a unit sphere the main aims of this paper are to present the weighted spharm and to show how it can be used in the tensor based morphometry as an illustration the methodology has been applied in the problem of detecting abnormal cortical regions in the group of high functioning autistic subjects

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

provably unconditionally stable second order time accurate mixed variational methods for phase field models we introduce provably unconditionally stable mixed variational methods for phase field models our formulation is based on a mixed finite element method for space discretization and a new second order accurate time integration algorithm the fully discrete formulation inherits the main characteristics of conserved phase dynamics namely mass conservation and nonlinear stability with respect to the free energy we illustrate the theory with the cahn hilliard equation but our method may be applied to other phase field models we also propose an adaptive time stepping version of the new time integration method we present some numerical examples that show the accuracy stability and robustness of the new method

linear transforms for fourier data on the sphere application to high angular resolution diffusion mri of the brain this paper presents a novel family of linear transforms that can be applied to data collected from the surface of a 2 sphere in three dimensional fourier space this family of transforms generalizes the previously proposed funk radon transform frt which was originally developed for estimating the orientations of white matter fibers in the central nervous system from diffusion magnetic resonance imaging data the new family of transforms is characterized theoretically and efficient numerical implementations of the transforms are presented for the case when the measured data is represented in a basis of spherical harmonics after these general discussions attention is focused on a particular new transform from this family that we name the funk radon and cosine transform fract based on theoretical arguments it is expected that fract based analysis should yield significantly better orientation information e g improved accuracy and higher angular resolution than frt based analysis while maintaining the strong characterizability and computational efficiency of the frt simulations are used to confirm these theoretical characteristics and the practical significance of the proposed approach is illustrated with real diffusion weighted mri brain data these experiments demonstrate that in addition to having strong theoretical characteristics the proposed approach can outperform existing state of the art orientation estimation methods with respect to measures such as angular resolution and robustness to noise and modeling errors

a new finite element formulation for computational fluid dynamics x the compressible euler and navier stokes equations a space time element method is presented for solving the compressible euler and navier stokes equations the proposed formulation includes the variational equation predictor multi corrector algorithms and boundary conditions the variational equation is based on the time discontinuous galerkin method in which the physical entropy variables are employed a least squares operator and a discontinuity capturing operator are added resulting in a high order accurate and unconditionally stable method implicit explicit predictor multi corrector algorithms applicable to steady as well as unsteady problems are presented techniques are developed to enhance their efficiency implementation of boundary conditions is addressed in particular a technique is introduced to satisfy nonlinear essential boundary conditions and a consistent method is presented to calculate boundary fluxes numerical results are presented to demonstrate the performance of the method

isogeometric analysis for phase field models of geometric pdes and high order pdes on stationary and evolving surfaces abstract in this paper we present an isogeometric analysis iga for phase field models of three different yet closely related classes of partial differential equations pdes geometric pdes high order pdes on stationary surfaces and high order pdes on evolving surfaces the latter can be a coupling of the former two classes in the context of geometric pdes we consider mean curvature flow and willmore flow problems and their corresponding phase field approximations which yield second order and fourth order nonlinear parabolic pdes through some numerical examples we study the convergence behavior of isogeometric analysis for these equations using the method of manufactured solutions moreover we study numerically the convergence of these phase field approximations to the sharp interface solutions as for the high order pdes on stationary surfaces we consider a model problem which is the cahn hilliard equation on a unit sphere where the surface is modeled using a diffuse interface approach finally as a model problem for high order pdes on evolving surfaces we consider a phase field model of a deforming multicomponent vesicle which couples the vesicle shape changes with the phase separation process on the vesicle surface the model consists of two fourth order nonlinear pdes which their direct finite element formulation in a galerkin framework necessitates smooth basis functions with at least global c 1 continuity a condition that can be easily satisfied using spline bases in iga we solve the coupled equations both in two dimensions where the vesicle is a curve and in three dimensions where the vesicle is a surface the simulation results agree with the numerical and experimental results from the literature

a generalized α method for integrating the filtered navier stokes equations with a stabilized finite element method abstract a generalized method is developed and analyzed for linear first order systems the method is then extended to the filtered navier stokes equations within the context of a stabilized finite element method the formulation is studied through the application to laminar flow past a circular cylinder and turbulent flow past a long transverse groove the method is formulated to obtain a second order accurate family of time integrators whose high frequency amplification factor is the sole free parameter such an approach allows the replication of midpoint rule zero damping gear s method maximal damping or anything in between

a stabilized finite element method for computing turbulence abstract for many flows reynold averaged navier stokes simulation ranss techniques do not give an acceptable description of the flow in these cases a more detailed simulation of the turbulence is required one such detailed simulation technique large eddy simulation les has matured to the point of application to complex flows historically these simulations have been carried out with structured grids which suffer from two major difficulties the extension to higher reynolds numbers leads to an impractical number of grid points and most real world flows are rather difficult to represent geometrically with structured grids unstructured grid methods offer a release from both of these constraints herein we describe the development and validation of a massively parallel stabilized finite element method for les

degrees of freedom in multiple antenna channels a signal space approach multiple antenna systems that are limited by the area and geometry of antenna arrays are considered given these physical constraints the limit on the available number of spatial degrees of freedom is derived the commonly used statistical multiple input multiple output mimo model is inadequate antenna theory is applied to take into account the area and geometry constraints and to define the spatial signal space so as to interpret experimental channel measurements in an array independent but manageable description of the physical environment based on these modeling strategies for a spherical array of effective aperture a in a physical environment of angular spread spl omega in solid angle the number of spatial degrees of freedom is shown to be a spl omega for uni polarized antennas and 2a spl omega for tri polarized antennas together with the 2wt degrees of freedom for a system of bandwidth w transmitting in an interval t the total degrees of freedom of a multiple antenna channel is therefore 4wta spl omega

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

optimally space localized band limited wavelets on s q 1 the localization of a function can be analyzed with respect to different criteria in this paper we focus on the uncertainty relation on spheres introduced by goh and goodman uncertainty principles and asymptotic behavior appl comput harmon anal 16 2004 69 89 where the localization of a function is measured in terms of the product of two variances the variance in space domain and the variance in frequency domain after deriving an explicit formula for the variance in space domain of a function in the space wn qs of spherical polynomials of degree at most n s which are orthogonal to all spherical polynomials of degree at most n we are able to identify up to rotation and multiplication by a constant the polynomial in wn qs with minimal variance in space domain or in other words to determine the optimally space localized polynomial in wn qs

weighted fourier series representation and its application to quantifying the amount of gray matter we present a novel weighted fourier series wfs representation for cortical surfaces the wfs representation is a data smoothing technique that provides the explicit smooth functional estimation of unknown cortical boundary as a linear combination of basis functions the basic properties of the representation are investigated in connection with a self adjoint partial differential equation and the traditional spherical harmonic spharm representation to reduce steep computational requirements a new iterative residual fitting irf algorithm is developed its computational and numerical implementation issues are discussed in detail the computer codes are also available at http www stat wisc edu mchung softwares weighted spharm weighted spharm html as an illustration the wfs is applied in quantifying the amount of gray matter in a group of high functioning autistic subjects within the wfs framework cortical thickness and gray matter density are computed and compared

optimal filters on the sphere we derive optimal filters on the sphere in the context of detecting compact objects embedded in a stochastic background process the matched filter and the scale adaptive filter are derived on the sphere in the most general setting allowing for directional template profiles and filters the performance and relative merits of the two optimal filters are discussed the application of optimal filter theory on the sphere to the detection of compact objects is demonstrated on simulated data a naive detection strategy is adopted with an initial aim of illustrating the application of the new filter theory derived on the sphere nevertheless this simple object detection strategy is demonstrated to perform well even at low signal to noise ratio

spherical diffusion for 3d surface smoothing a diffusion based approach to surface smoothing is presented surfaces are represented as scalar functions defined on the sphere the approach is equivalent to gaussian smoothing on the sphere and is computationally efficient since it does not require iterative smoothing furthermore it does not suffer from the well known shrinkage problem evolution of important shape features parabolic curves under diffusion is demonstrated a nonlinear modification of the diffusion process is introduced in order to improve smoothing behavior of elongated and poorly centered objects

efficient computation of slepian functions for arbitrary regions on the sphere in this paper we develop a new method for the fast and memory efficient computation of slepian functions on the sphere slepian functions which arise as the solution of the slepian concentration problem on the sphere have desirable properties for applications where measurements are only available within a spatially limited region on the sphere and or a function is required to be analyzed over the spatially limited region slepian functions are currently not easily computed for large band limits for an arbitrary spatial region due to high computational and large memory storage requirements for the special case of a polar cap the symmetry of the region enables the decomposition of the slepian concentration problem into smaller subproblems and consequently the efficient computation of slepian functions for large band limits by exploiting the efficient computation of slepian functions for the polar cap region on the sphere we develop a formulation supported by a fast algorithm for the approximate computation of slepian functions for an arbitrary spatial region to enable the analysis of modern datasets that support large band limits for the proposed algorithm we carry out accuracy analysis of the approximation computational complexity analysis and review of memory storage requirements we illustrate through numerical experiments that the proposed method enables faster computation and has smaller storage requirements while allowing for sufficiently accurate computation of the slepian functions

intrinsic limits of dimensionality and richness in random multipath fields we study the dimensions or degrees of freedom of farfield multipath that is observed in a limited source free region of space the multipath fields are studied as solutions to the wave equation in an infinite dimensional vector space we prove two universal upper bounds on the truncation error of fixed and random multipath fields a direct consequence of the derived bounds is that both fixed and random multipath fields have an effective finite dimension for circular and spherical spatial regions we show that this finite dimension is proportional to the radius and area of the region respectively we use the karhunen loegraveve kl expansion of random multipath fields to quantify the notion of multipath richness the multipath richness is defined as the number of significant eigenvalues in the kl expansion that achieve 99 of the total multipath energy we establish a lower bound on the largest eigenvalue this lower bound quantifies to some extent the well known reduction of multipath richness with reducing the angular power spread of multipath angular power spectrum

a globally convergent matrix free algorithm for implicit time marching schemes arising in finite element analysis in fluids a solution procedure for solving nonlinear time marching problems is presented the nonsymmetric systems of equations arising from a newton type linearization of these time marching problems are solved using an iterative strategy based on the generalized minimal residual gmres algorithm matrix free techniques leading to reduction in storage are presented incorporation of a linesearch algorithm in the newton gmres scheme is discussed an automatic time increment control strategy is developed to increase the stability of the time marching process high speed flow computations demonstrate the effectiveness of these algorithms

a unified approach to compressible and incompressible flows abstract we present a finite element formulation for solving the compressible navier stokes equations which accommodates the use of any set of variables if primitive variables p u t or entropy variables are used the incompressible limit is well behaved therefore one formulation can be used to solve both compressible and incompressible flows

a hybrid variational collocation immersed method for fluid structure interaction using unstructured t splines summary we present a hybrid variational collocation immersed and fully implicit formulation for fluid structure interaction fsi using unstructured t splines in our immersed methodology we define an eulerian mesh on the whole computational domain and a lagrangian mesh on the solid domain which moves arbitrarily on top of the eulerian mesh mathematically the problem reduces to solving three equations namely the linear momentum balance mass conservation and a condition of kinematic compatibility between the lagrangian displacement and the eulerian velocity we use a weighted residual approach for the linear momentum and mass conservation equations but we discretize directly the strong form of the kinematic relation deriving a hybrid variational collocation method we use t splines for both the spatial discretization and the information transfer between the eulerian mesh and the lagrangian mesh t splines offer us two main advantages against non uniform rational b splines they can be locally refined and they are unstructured the generalized method is used for the time discretization we validate our formulation with a common fsi benchmark problem achieving excellent agreement with the theoretical solution an example involving a partially immersed solid is also solved the numerical examples show how the use of t junctions and extraordinary nodes results in an accurate efficient and flexible method copyright 2015 john wiley sons ltd

a computational framework for fluid structure interaction finite element formulation and applications abstract this work is concerned with the modelling of the interaction of fluid flow with flexibly supported rigid bodies the fluid flow considered is governed by the incompressible navier stokes equations and modelled by employing stabilised low order velocity pressure finite elements the motion of the fluid domain is accounted for by an arbitrary lagrangian eulerian ale strategy the rigid body motion excited by the fluid flow is restricted by the elastic and damping properties of the supports for the temporal discretisation the discrete implicit generalised method is employed the resulting strongly coupled set of nonlinear equations is solved by means of a novel partitioned solution procedure which is based on the newton raphson methodology and incorporates full linearisation of the overall incremental problem the strong coupling is resolved and optimal convergence of the residuals is achieved several numerical examples are presented to demonstrate the robustness and efficiency of the methodology the examples clearly capture the phenomena of vortex induced oscillations and galloping

time dependent subgrid scales in residual based large eddy simulation of turbulent channel flow the present study investigates the effect of taking into account the time dependency of the fine subgrid scales in a residual based variational multiscale approach for large eddy simulation the residual based variational multiscale method with time dependent dynamic subgrid scales is presented and the impact of the time dependency is studied for the well known test case of turbulent channel flow results are presented from computations for various values of the reynolds number namely ret 180 ret 395 and ret 590 and several time step sizes a generalized a time integration scheme is employed results from our numerical experiments with dynamic subgrid scales are compared to results obtained with an approximation not explicitly taking the time dependency of the subgrid scales into account for all re t values and time step sizes under consideration results for resolved quantities computed by both approaches are very similar this statement applies to both mean streamwise velocity and root mean square velocity fluctuations however it provides a model for the subgrid scales not depend ing on the time step size and enabling a more robust representation of unresolved scales thus we conclude that the time dependent subgrid scale approximation is not capable of producing more accurate results for this type of flow if the time step size is chosen within an optimal range however we expect it to be more advantageous for more complex problems since our results indicate that it provides a more reliable representation of unresolved scales

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100