reducing spurious dispersion anisotropy and reflection in finite element analysis of time harmonic acoustics abstract galerkin and stabilized galerkin least squares and galerkin gradient least squares finite element methods for solving problems of time harmonic acoustics are presented and analyzed the error of discretization is related to spurious representation of physical phenomena namely dispersion anisotropy and reflection all of which decrease with mesh refinement the performance of the stabilized methods in terms of dispersion and anisotropy is identical both are superior to the galerkin method relaxing wave resolution requirements further insight into the design of these methods is provided by the analyses the stabilized methods differ in the degree of spurious reflection that is engendered by transitions in mesh size the performance of galerkin gradient least squares deteriorates on non uniform meshes however galerkin least squares maintains its enhanced performance exhibiting low sensitivity to transitions in mesh size thereby reducing spurious dispersion anisotropy and reflection in finite element analysis of time harmonic acoustics guidelines for discretization pertaining to mesh orientation and wave resolution are presented

the sensitivity of muscle force predictions to changes in physiologic cross sectional area abstract the mechanical effects of a muscle are related in part to the size of the muscle and to its location relative to the joint it crosses for more than a century researchers have expressed muscle size by its physiological cross sectional area pcsa researchers mathematically calculating muscle and joint forces typically use some expression of a muscle s pcsa to constrain the solution to one which is reasonable i e a solution in which small muscles may not have large forces and large muscles have large forces when expected or when there is significant electromyographic activity it is obvious that muscle mass and therefore any expression of pcsa varies significantly from person to person even in individuals of similar weight and height since it is not practical to predict the pcsa of each muscle in a living subject s limb or trunk it is important to generally understand the sensitivity of muscle force solutions to possible variations in pcsa we used nonlinear optimization techniques to predict 47 muscle forces and hip contact forces in a living subject the pcsa volume muscle fiber length of each of 47 lower limb muscle elements from two cadaver specimens and the 47 pcsa s reported by pierrynowski were input into an optimization algorithm to create three solution sets the three solutions were qualitatively similar but at times a predicted muscle force could vary as much as two to eight times in contrast the joint force solutions were within 11 of each other and therefore much less variable when using optimization techniques to predict muscle forces it must be recognized that the solution is sensitive to many assumptions and variables such as pcsa the muscle force solutions are therefore best used to determine relative values i e trends in parametric studies on the other hand the joint force solutions are less sensitive to such variations and the absolute values are more reliable

finite element solution of the helmholtz equation with high wave number part i the h version of the fem abstract the paper addresses the properties of finite element solutions for the helmholtz equation the h version of the finite element method with piecewise linear approximation is applied to a one dimensional model problem new results are shown on stability and error estimation of the discrete model in all propositions assumptions are made on the magnitude of hk only where k is the wavelength and h is the stepwidth of the fe mesh previous analytical results had been shown with the assumption that k 2 h is small for medium and high wavenumber these results do not cover the meshsizes that are applied in practical applications the main estimate reveals that the error in h 1 norm of discrete solutions for the helmholtz equation is polluted when k 2 h is not small the error is then not quasioptimal i e the relation of the fe error to the error of best approximation generally depends on the wavenumber k it is noted that the pollution term in the relative error is of the same order as the phase lead of the numerical solution in the result of this analysis thorough and rigorous understanding of error behavior throughout the range of convergence is gained numerical results are presented that show sharpness of the error estimates and highlight some phenomena of the discrete solution behavior the h p version of the fem is studied in part ii

subgrid modeling in a galerkin method for the helmholtz equation abstract we improve the accuracy of finite element acoustic wave solutions without introducing additional degrees of freedom with physically inspired subgrid models the models explored here will not adversely impact system matrix storage or bandwidth can be used for structured or unstructured meshes do not require the solution of any auxiliary value problems and have minimal marginal overall computational cost one interpretation of the new models is as momentum transferred to and from modes at length scales below the local mesh dimension we show a method to approximate the effects of all subgrid modes on the grid scale solution and the significant improvements in local accuracy that the new models provide the new subgrid models also improve global or pollution accuracy through a reduction in the element dispersion error in addition we draw comparisons between this proposed method and much of the alternative and related work in this area

on the pollution effect in fe solutions of the 3d helmholtz equation we study convergence of the fem for a 3d problem of rigid scattering using separation of variables analytical results are presented for stability and error estimation for an h version galerkin fem with mesh refinement in radial direction we prove an upper bound that contains a pollution term similar to previous results in 1d and 2d this estimate is evaluated computationally using a 3d fem iem infinite elements implementation the tabulated and plotted errors show the theoretically predicted pollution effect in the fe error

validation of the greater trochanter method with radiographic measurements of frontal plane hip joint centers and knee mechanical axis angles and two other hip joint center methods several motion capture methods exist for predicting hip joint centers hjc these methods include regression models functional joints and projections from greater trochanters while regression and functional methods have been compared to imaging techniques the troch method has not been previously validated the purpose of this study was to compare frontal plane hjcs and knee mechanical axis angles estimated using the greater trochanter method with a regression bell and a functional method against those obtained using radiographs thirty five participants underwent a long standing anteroposterior radiograph and performed static and functional motion capture trials the bell functional and trochanter hjcs were constructed to predict mechanical axes and compare hjc locations one way repeated measures anovas were used to compare mechanical axes and hjc locations estimated by motion capture methods and measured using radiographs p 0 05 all methods overestimated mechanical axes compared to radiographs 2 but were not different mediolateral hjc locations and inter hjc widths were similar between methods however inter hjc widths were underestimated average 3 7 compared to radiographs the bell hjc was more superior and anterior to both functional and trochanter methods the trochanter hjc was more posterior to both methods the bell method outperformed the other methods in leg length predictions compared to radiographs although differences existed between methods all frontal plane hjc location differences were 1 7 cm this study validated the trochanter hjc prediction method mediolaterally and vertically with small respective correction factors therefore all hjc methods seem to be viable in predicting mechanical axes and frontal plane hjc locations compared with radiographs

a discontinuous hp finite element method for diffusion problems 1 d analysis abstract this paper presents the mathematical analysis of a new variant of the discontinuous galerkin method which is applicable to the numerical solution of diffusion problems not requiring auxiliary variables such as those used in mixed methods the focus of this study is on a class of linear second order boundary value problems for which we prove stability and a priori error estimates in both the finite and infinite dimensional spaces

evaluation of muscular moments at the lower limb joints by an on line processing of kinematic data and ground reaction abstract in order to analyse the muscular moments at the lower limb joints during human locomotion a new experimental technique is presented by using specially made instrumentation the images of the vector representing the ground reaction during its evolution are superimposed on line to the images showing the positions of the hip knee and ankle joint axes the sequence of superimposed images provides a direct representation of the muscular moments during the stance phase the time course values are obtained by multiplying the vector amplitude by its distance from the joints in each image the approximation of the computed values is evaluated by comparing the curves so obtained and those provided by a complete mathematical analysis of locomotion based on digital processing of the experimental data

statistical shape modelling versus linear scaling effects on predictions of hip joint centre location and muscle moment arms in people with hip osteoarthritis abstract marker based dynamic functional or regression methods are used to compute joint centre locations that can be used to improve linear scaling of the pelvis in musculoskeletal models although large errors have been reported using these methods this study aimed to investigate if statistical shape models could improve prediction of the hip joint centre hjc location the inclusion of complete pelvis imaging data from computed tomography ct was also explored to determine if free form deformation techniques could further improve hjc estimates mean euclidean distance errors were calculated between hjc from ct and estimates from shape modelling methods and functional and regression based linear scaling approaches the hjc of a generic musculoskeletal model was also perturbed to compute the root mean squared error rmse of the hip muscle moment arms between the reference hjc obtained from ct and the different scaling methods shape modelling without medical imaging data significantly reduced hjc location error estimates 11 4 3 3 mm compared to functional 36 9 17 5 mm p

consistent discontinuous finite elements in elastodynamics finite element discontinuities with respect to time have recently been extremely used in elastodynamic problems due to their natural utilization in combination with adaptive methods and their efficiency in discontinuity capturing techniques for non smooth problems in this work we present some theoretical aspects and numerical results concerning the use of spatial discontinuities in a consistent finite element method for the same class of problems we first review some formulations for the elastostatic problem and prove two korn like inequalities which are very useful for the derivation of convergence rates in sobolev norms next we present formulations for the dynamic case along with comments on their properties and estimates of convergence rates for smooth solutions followed by numerical investigations of a typically non smooth problem involving classical and emerging variational formulations we also show some numerical experiments with finite element spaces enriched by discontinuous functions other than piecewise lagrangian polynomials

discontinuous galerkin methods for the helmholtz equation with large wave number this paper develops and analyzes some interior penalty discontinuous galerkin ipdg methods using piecewise linear polynomials for the helmholtz equation with the first order absorbing boundary condition in two and three dimensions it is proved that the proposed discontinuous galerkin methods are stable hence well posed without any mesh constraint for each fixed wave number k optimal order with respect to h error estimate in the broken h 1 norm and suboptimal order estimate in the l 2 norm are derived without any mesh constraint the latter estimate improves to optimal order when the mesh size h is restricted to the preasymptotic regime i e k 2 h gtrsim 1 numerical experiments are also presented to gauge the theoretical result and to numerically examine the pollution effect with respect to k in the error bounds the novelties of the proposed ipdg methods include the following first the methods penalize not only the jumps of the function values across the element edges but also the jumps of the normal and tangential derivatives second the penalty parameters are taken as complex numbers of positive imaginary parts so essentially and practically no constraint is imposed on the penalty parameters since the helmholtz problem is a non hermitian and indefinite linear problem as expected the crucial and the most difficult part of the whole analysis is to establish the stability estimates i e a priori estimates for the numerical solutions to this end the cruxes of our analysis are to establish and to make use of a local version of the rellich identity for the laplacian and to mimic the stability analysis for the pde solutions given in p cummings analysis of finite element based numerical methods for acoustic waves elastic waves and fluid solid interactions in the frequency domain ph d thesis the university of tennessee knoxville tn 2001 p cummings and x feng math models methods appl sci 16 2006 pp 139 160 u hetmaniuk commun math sci 5 2007 pp 665 678

regression with bivariate grouped data the problem of accounting for the grouping of continuous bivariate data in regression analyses is considered reasons why grouping must be taken seriously are advanced and a strategy for accounting for grouping is demonstrated the specific model asserts that in the absence of grouping the data would be bivariate normal this model is used to adjust estimates of parameters in a regression relating disease severity to a grouped exposure variable using data on pneumoconiosis in english coal miners ashford 1959 biometrics 15 573 581 the choice of computing methods is discussed and likelihood formulas are presented

finite element solution of the helmholtz equation with high wave number part ii the h p version of the fem in this paper which is part ii in a series of two the investigation of the galerkin finite element solution to the helmholtz equation is continued while part i contained results on the h version with piecewise linear approximation the present part deals with approximation spaces of order p ge 1 as in part i the results are presented on a one dimensional model problem with dirichlet robin boundary conditions in particular there are proven stability estimates both with respect to data of higher regularity and data that is bounded in lower norms the estimates are shown both for the continuous and the discrete spaces under consideration further there is proven a result on the phase difference between the exact and the galerkin finite element solutions for arbitrary p that had been previously conjectured from numerical experiments these results and further preparatory statements are then employed to show error estimates for the galerkin finite element method fem it becomes evident that the error estimate for higher approximation can with certain assumptions on the data be written in the same form as the piecewise linear case namely as the sum of the error of best approximation plus a pollution term that is of the order of the phase difference the paper is concluded with a numerical evaluation

effects of hip center location on the moment generating capacity of the muscles we have developed a three dimensional biomechanical model of the human lower extremity to study how the location of the hip center affects the moment generating capacity of four muscle groups the hip abductors adductors flexors and extensors the model computes the maximum isometric force and the resulting joint moments that each of 25 muscle tendon complexes develops at any body position abduction adduction flexion and extension moments calculated with the model correspond closely with isometric joint moments measured during maximum voluntary contractions we used the model to determine 1 the hip center locations that maximize and minimize the moment generating capacity of each muscle group and 2 the effects of superior inferior anterior posterior and medial lateral displacement of the hip center on the moment arms maximum isometric muscle forces and maximum isometric moments generated by each muscle group we found that superior inferior displacement of the hip center has the greatest effect on the force and moment generating capacity of the muscles a 2 cm superior displacement decreases abduction force 44 moment arm 12 and moment 49 while a 2 cm inferior displacement increases abduction force 20 moment arm 7 and moment 26 similarly a 2 cm superior displacement decreases flexion force 27 moment arm 6 and moment 22 while inferior displacement increases all three variables anterior posterior displacement alters the moment generating capacity of the flexors and extensors considerably primarily due to moment arm changes medial lateral displacement has a large effect on the moment generating capacity of the adductors only a 2 cm medial displacement decreases adduction moment arm 20 force 26 and moment 40 these results demonstrate that the force and moment generating capacities of the muscles are sensitive to the location of the hip center

a two point boundary value problem with a rapidly oscillating solution some numerical methods are developed for a two point boundary value problem with a rapidly oscillating solution the two point boundary value problem is chosen to model some of the difficulties that may be expected to occur in solving the reduced wave equation at moderately high frequencies

a fourth order compact scheme for the helmholtz equation alpha interpolation of fem and fdm stencils we propose a fourth order compact scheme on structured meshes for the helmholtz equation given by r f x 2 0 the scheme consists of taking the alpha interpolation of the galerkin finite element method and the classical central finite difference method in 1d this scheme is identical to the alpha interpolation method j comput appl math 1982 8 1 15 19 and in 2d making the choice 0 5 we recover the generalized fourth order compact pade approximation j comput phys 1995 119 252 270 comput meth appl mech engrg 1998 163 343 358 therein using the parameter 2 we follow siam rev 2000 42 3 451 484 comput meth appl mech engrg 1995 128 325 359 for the analysis of this scheme and its performance on square meshes is compared with that of the quasi stabilized fem comput meth appl mech engrg 1995 128 325 359 in particular we show that the relative phase error of the numerical solution and the local truncation error of this scheme for plane wave solutions diminish at the rate o l 4 where l represent the wavenumber and the mesh size respectively an expression for the parameter is given that minimizes the maximum relative phase error in a sense that will be explained in section 4 5 convergence studies of the error in the l2 norm the h1 semi norm and the l euclidean norm are done and the pollution effect is found to be small copyright 2010 john wiley sons ltd

a least squares method for the helmholtz equation abstract we investigate the use of least squares methods to approximate the helmholtz equation the basis used in the discrete method consists of solutions of the helmholtz equation either consisting of plane waves or bessel functions on each element of a finite element grid unlike previous methods of this type we do not use polynomial based finite elements the use of small elements and relatively few basis functions per element allows us to prove convergence theorems for the method and to some extent control the conditioning of the resulting linear sy stem numerical results show the efficiency of the new method and suggest that it may be possible to obtain accurate results with a coarser grid than is usual for standard finite element methods

a discontinuous finite element formulation for helmholtz equation abstract a discontinuous finite element formulation for helmholtz problems is presented with c 0 continuity across inter element boundaries enforced in a weak sense depending on two parameters and whose choice is crucial for the performance of the proposed method these parameters are chosen through one dimension numerical experiments aiming at minimizing the pollution error optimal values of these parameters are then adopted in more general situations the accuracy and stability of the proposed formulation for linear and bilinear shape functions are demonstrated in several numerical examples in one and two dimensions

a galerkin least squares finite element method for the two dimensional helmholtz equation in this paper a galerkin least squares gls finite element method in which residuals in least squares form are added to the standard galerkin variational equation is developed to solve the helmholtz equation in two dimensions an important feature of gls methods is the introduction of a local mesh parameter that may be designed to provide accurate solutions with relatively coarse meshes previous work has accomplished this for the one dimensional helmholtz equation using dispersion analysis in this paper the selection of the gls mesh parameter for two dimensions is considered and leads to elements that exhibit improved phase accuracy for any given direction of wave propagation an optimal gls mesh parameter is determined using two dimensional fourier analysis in general problems the direction of wave propagation will not be known a priori in this case an optimal gls parameter is found which reduces phase error for all possible wave vector orientations over elements the optimal gls parameters are derived for both consistent and lumped mass approximations several numerical examples are given and the results compared with those obtained from the galerkin method the extension of gls to higher order quadratic interpolations is also presented

rounding error in regression the appropriateness of sheppard s corrections abstract we consider three simple approaches to rounding error in least squares regression the first treats the rounded data as if they were unrounded the second adds an adjustment to the diagonal of the covariance matrix of the variables and the third subtracts an adjustment from the diagonal the third sheppard s corrections can be motivated as maximum likelihood with small rounding error and either 1 joint normal data or 2 normal residuals regular independent variables and large samples although an example and theory suggest that the third approach is usually preferable to the first two a generally satisfactory attack on rounding error in regression requires the specification of the full distribution of variables and convenient computational methods for this problem are not currently available author

discontinuous finite element formulations applied to cracked elastic domains the solutions of boundary value problems defined on cracked domains are usually non smooth in the surroundings of the crack in this work we formulate the elasticity problem of a body with such geometric characteristic in a number of equivalent variational alternatives and show that we can take advantage of the theory of discontinuous finite elements in order to approximate its solution in an interesting way at little higher programming cost in comparison with the classical galerkin method the idea consists in splitting the global domain into a number of regions in which local mesh refinements are undertaken independently producing irregular meshes with non matching elements that are suitable to be used in discontinuous finite element methods this strategy seems to be attractive to be employed in situations that we know in advance where the critical regions of the domain are located as well as in adaptive techniques

dispersion analysis and error estimation of galerkin finite element methods for the helmholtz equation when applying numerical methods for the computation of stationary waves from the helmholtz equation one obtains numerical waves that are dispersive also in non dispersive media the numerical wave displays a phase velocity that depends on the parameter k of the helmholtz equation in dispersion analysis the phase difference between the exact and the numerical solutions is investigated in this paper the authors recent result on the phase difference for one dimensional problems is numerically evaluated and discussed in the context of other work directed to this topic it is then shown that previous error estimates in h1 norm are of nondispersive character but hold for medium or high wavenumber on extremely refined mesh only on the other hand recently proven error estimates for constant resolution contain a pollution term with certain assumptions on the exact solution this term is of the order of the phase difference thus a link is established between the results of dispersion analysis and the results of numerical analysis throughout the paper the presentation and discussion of theoretical results is accompanied by numerical evaluation of several model problems special attention is given to the performance of the galerkin method with a higher order of polynomial approximation p h p version

ignorability and coarse data we present a general statistical model for data coarsening which includes as special cases rounded heaped censored partially categorized and missing data formally with coarse data observations are made not in the sample space of the random variable of interest but rather in its power set grouping is a special case in which the degree of coarsening is known and nonstochastic we establish simple conditions under which the possible stochastic nature of the coarsening mechanism can be ignored when drawing bayesian and likelihood inferences and thus the data can be validly treated as grouped data the conditions are that the data be coarsened at random a generalization of the condition missing at random and that the parameters of the data and the coarsening process be distinct applications of the general model and the ignorability condition are illustrated in a numerical example and described briefly in a variety of special cases

a discontinuous hp finite element method for convection diffusion problems this paper presents a new method which exhibits the best features of both finite volume and finite element techniques special attention is given to the issues of conservation flexible accuracy and stability the method is elementwise conservative the order of polynomial approximation can be adjusted element by element and the stability is not based on the introduction of artificial diffusion but on the use of a very particular finite element formulation with discontinuous basis functions the method supports h p and hp approximations and can be applied to any type of meshes including non matching grids a priori error estimates and numerical experiments on representative model problems indicate that the method is robust and capable of delivering high accuracy

least squares trefftz type elements for the helmholtz equation trefftz type elements or t elements are finite elements the internal field of which fulfills the governing differential equations of the problem a priori whereas the prescribed boundary conditions and the interelement continuity must be enforced by some suitable method in this paper the relevant matching is achieved by means of a least squares procedure the so called frameless or least squares t elements for helmholtz s equation related to the scattering of waves by offshore structures in 2 d are developed and studied the required accuracy of the solution can be obtained by increasing the number of either the subdomains or t functions which can be regarded as the h or p type approach respectively convergence studies are performed with much attention to the use of special purpose elements for a doubly connected domain with a circular hole and for an angular corner subdomain the most attractive features of the presented formulation are its simplicity and robustness the matrix of the resulting linear system is always hermitian and positive definite 1998 john wiley sons ltd

a generalized finite element method for solving the helmholtz equation in two dimensions with minimal pollution when using the galerkin fem for solving the helmholtz equation in two dimensions the error of the corresponding solution differs substantially from the error of the best approximation and this effect increases with higher wave number k in this paper we will design a generalized finite element method gfem for the helmholtz equation such that the pollution effect is minimal

two level finite element method and its application to the helmholtz equation a two level finite element method is introduced and its application to the helmholtz equation is considered the method retains the desirable features of the galerkin method enriched with residual free bubbles while it is not limited to discretizations using elements with simple geometry the method can be applied to other equations and to irregular shaped domains

application of an ultra weak variational formulation of elliptic pdes to the two dimensional helmholtz problem a new technique to solve elliptic linear pdes called ultra weak variational formulation uwvf in this paper is introduced in b despres c r acad sci paris 318 1994 pp 939 944 this paper is devoted to an evaluation of the potentialities of this technique it is applied to a model wave problem the two dimensional helmholtz problem the new method is presented in three parts following the same style of presentation as the classical one of the finite elements method even though they are definitely conceptually different methods the first part is committed to the variational formulation and to the continuous problem the second part defines the discretization process using a galerkin procedure the third part actually studies the efficiency of the technique from the order of convergence point of view this is achieved using theoretical proofs and a series of numerical experiments in particular it is proven and shown the order of convergence is lower bounded by a linear function of the number of degrees of freedom an application to scattering problems is presented in a fourth part

a new parametric approach for modeling hip forces during gait an analytical parametric model was developed to estimate the natural biological variations in muscle forces and their effect on the hip forces subject only to physiological constraints and not predefined optimization criterion force predictions are based on the joint kinematics and kinetics of each subject a previously published muscle model and physiological constraints on the muscle force distributions the model was used to determine the hip contact forces throughout the stance phase of gait of a subject with a total hip replacement thr the parametrically modeled peak hip force without antagonistic muscle activity varied from 2 7 to 3 2 body weights mean 2 9 body weights which agreed well with published in vivo measurements from instrumented thrs in other subjects for every 10 increase in antagonistic activity the mean peak hip force increased by 0 2 body weights the parametric model allows one to examine the effect of specific muscle weaknesses or increased antagonistic muscle activity on the hip forces the model also provides a tool for studying the effect of gait adaptations on hip forces as predictions are based on each individual s gait data differences in peak forces between subjects can then be evaluated relative to the uncertainty in not knowing the precise muscle force distributions

adaptive numerical solution of a discontinuous galerkin method for a helmholtz problem in low frequency regime we develop an a posteriori error analysis for helmholtz problem using the local discontinuous galerkin ldg for short approach for the sake of completeness we give a description of the main a priori results of this method indeed under some assumptions on regularity of the solution of an adjoint problem we prove that a the corresponding indefinite discrete scheme is well posed b the approach is convergent with the expected convergence rates as long as the meshsize h is small enough we give precise information on how small h has to be in terms of the size of the wave number and its distance to the set of eigenvalues for the same boundary value problem for the laplacian after that we present a reliable and efficient a posteriori error estimator with detailed information on the dependence of the constants on the wave number we finish presenting extensive numerical experiments which illustrate the theoretical results proven in this paper and suggest that stability and convergence may occur under less restrictive assumptions than those taken in the present work we derive an a posteriori error estimator that is reliable and locally quasi efficient the efficiency and reliability constants have been characterized with respect to the physical parameter we include numerical examples that validate our theoretical results recognizing singularities and inner layers for moderate values of

a residual based finite element method for the helmholtz equation a new residual based finite element method for the scalar helmholtz equation is developed this method is obtained from the galerkin approximation by appending terms that are proportional to residuals on element interiors and inter element boundaries the inclusion of residuals on inter element boundaries distinguishes this method from the well known galerkin least squares method and is crucial to the resulting accuracy of this method in two dimensions and for regular bilinear quadrilateral finite elements it is shown via a dispersion analysis that this method has minimal phase error numerical experiments are conducted to verify this claim as well as test and compare the performance of this method on unstructured meshes with other methods it is found that even for unstructured meshes this method retains a high level of accuracy copyright 2000 john wiley sons ltd

preasymptotic error analysis of cip fem and fem for helmholtz equation with high wave number part ii hp version in this paper which is the second in a series of two the preasymptotic error analysis of the continuous interior penalty finite element method cip fem and the fem for the helmholtz equation in two and three dimensions is continued while part i contained results on the linear cip fem and fem the present part deals with approximation spaces of order p ge 1 by using a modified duality argument preasymptotic error estimates are derived for both methods under the condition of frac kh p le c 0 frac p k frac 1 p 1 where k is the wave number h is the mesh size and c 0 is a constant independent of k h p and the penalty parameters it is shown that the pollution errors of both methods in h 1 norm are o k 2p 1 h 2p if p o 1 and are o frac k p 2 frac kh sigma p 2p if the exact solution u in h 2 omega which coincide with existent dispersion analyses for the fem on cartesian grids here sigma is a constant independent of k h p and the penalty par

a variational multiscale method with subscales on the element boundaries for the helmholtz equation summary in this paper we apply the variational multiscale method with subgrid scales on the element boundaries to the problem of solving the helmholtz equation with low order finite elements the expression for the subscales is obtained by imposing the continuity of fluxes across the interelement boundaries the stabilization parameter is determined by performing a dispersion analysis yielding the optimal values for the different discretizations and finite element mesh configurations the performance of the method is compared with that of the standard galerkin method and the classical galerkin least squares method with very satisfactory results some numerical examples illustrate the behavior of the method copyright 2012 john wiley sons ltd

residual free bubbles for the helmholtz equation the galerkin method enriched with residual free bubbles is considered for approximating the solution of the helmholtz equation two dimensional tests demonstrate the improvement over the standard galerkin method and the galerkin least squares method using piecewise bilinear interpolations

an edge based smoothed finite element method es fem for analyzing three dimensional acoustic problems abstract it is well known that one key issue of solving the helmholtz equation using finite element method fem is the accuracy deterioration in the solution with increasing wave number due to the numerical dispersion error such a numerical dispersion error is essentially caused by the overly stiff nature of the fem model to overcome this problem this paper presents an edge based smoothed finite element method es fem for analyzing acoustic problems using linear triangular and tetrahedron elements that can be generated automatically respectively for complicated two dimensional and three dimensional domains the discretized linear system equations for es fem are established using the smoothed galerkin weak form with smoothing domains associated with the edges of the triangles or surfaces of the tetrahedrons the edge based gradient smoothing operation provides proper softening effect makes the es fem model much softer than the overly stiff fem model and hence significantly reduces the numerical dispersion error numerical examples including a 2d problem of acoustic pressure distribution in a vehicle passenger compartment and a 3d problem about the acoustic pressure distribution in an engine chamber have been studied using the present es fem the results demonstrate that the es fem possesses the following advantages compared with the standard fem using the same meshes first es fem achieves similar convergence rate but better accuracy especially at high frequency second es fem is less sensitive to the mesh distortion meaning that the quality of mesh has less effect on the solution of es fem third it works well for triangular types of meshes and thus for the problems with complicated geometry

a discontinuous galerkin method with lagrange multipliers for the solution of helmholtz problems in the mid frequency regime we present a discontinuous galerkin method dgm for the solution of the helmholtz equation in the mid frequency regime our approach is based on the discontinuous enrichment method in which the standard polynomial field is enriched within each finite element by a non conforming field that contains free space solutions of the homogeneous partial differential equation to be solved hence for the helmholtz equation the enrichment field is chosen here as the superposition of plane waves we enforce a weak continuity of these plane waves across the element interfaces by suitable lagrange multipliers preliminary results obtained for two dimensional model problems discretized by uniform meshes reveal that the proposed dgm enables the development of elements that are far more competitive than both the standard linear and the standard quadratic galerkin elements for the discretization of helmholtz problems

a discontinuous finite element based domain decomposition method in this work we introduce a somewhat unconventional finite element based nonoverlapping domain decomposition method the convenient space decomposition method csd for parallel computers that can be applied to a wide class of boundary value problems and which can only be implemented efficiently exclusively with primal variables by means of the use of discontinuous elements interesting aspects and properties are pointed out along with proofs for the most relevant results numerical experiments for purely diffusion problems are also presented in order to evaluate the effectiveness of the proposed scheme and to confirm the validity of the related theoretical results

inference from coarse data via multiple imputation with application to age heaping abstract multiple imputation is applied to a demographic data set with coarse age measurements for tanzanian children the heaped ages are multiply imputed with plausible true ages using a a simple naive model and b a new relatively complex model that relates true age to the observed values of heaped age sex and anthropometric variables the imputed true ages are used to create valid inferences under the models and compare inferences across models thereby revealing sensitivity of inferences to prior specifications from naive to complex in addition diagnostic analyses applied to the imputed data are used to suggest which models appear most appropriate because it is not clear just what set of heaping intervals should be used the models are applied under various assumptions about the heaping rounding to the nearest year or half year versus a combination of rounding and truncation as practiced in the united states and medium versus wide heaping interval sizes the most striking conclusions ar

a discontinuoushpfinite element method for diffusion problems we present an extension of the discontinuous galerkin method which is applicable to the numerical solution of diffusion problems the method involves a weak imposition of continuity conditions on the solution values and on fluxes across interelement boundaries within each element arbitrary spectral approximations can be constructed with different orderspin each element we demonstrate that the method is elementwise conservative a property uncharacteristic of high order finite elements for clarity we focus on a model class of linear second order boundary value problems and we developpriorierror estimates convergence proofs and stability estimates the results of numerical experiments onh andp convergence rates for representative two dimensional problems suggest that the method is robust and capable of delivering exponential rates of convergence

level of subject specific detail in musculoskeletal models affects hip moment arm length calculation during gait in pediatric subjects with increased femoral anteversion biomechanical parameters of gait such as muscle s moment arm length mal and muscle tendon length are known to be sensitive to anatomical variability nevertheless most studies rely on rescaled generic models rgmo constructed from averaged data of cadaveric measurements in a healthy adult population as an alternative deformable generic models dgmo have been proposed these models integrate a higher level of subject specific detail by applying characteristic deformations to the musculoskeletal geometry in contrast musculoskeletal models based on magnetic resonance mr images mrmo reflect the involved subject s characteristics in every level of the model this study investigated the effect of the varying levels of subject specific detail in these three model types on the calculated hip mal during gait in a pediatric population of seven cerebral palsy subjects presenting aberrant femoral geometry our results show large percentage differences in calculated mal between rgmo and mrmo furthermore the use of dgmo did not uniformly reduce inter model differences in calculated mal the magnitude of these percentage differences stresses the need to take these effects into account when selecting the level of subject specific detail one wants to integrate in musculoskeletal furthermore the variability of these differences between subjects and between muscles makes it very difficult to a priori estimate their importance for a biomechanical analysis of a certain muscle in a given subject

continuous discontinuous galerkin methods applied to elasticity problems abstract a new family of coupled continuous discontinuous galerkin formulations is presented and analyzed in this paper these formulations have some distinguishing properties support to all boundary conditions without differentiating whether the condition is dirichlet or not the continuous part of the formulations can use the discontinuous part to have better accuracy and robustness properties and the discontinuous part has the same stabilized properties of common discontinuous galerkin methods a new promising stability parameter is introduced and its effects analyzed in the numerical experiments some important results related to the stability of the formulations associated with the polynomial degree adopted for the continuous component are also shown

on accuracy conditions for the numerical computation of waves abstract the helmholtz equation k 2 n 2 u f with a variable index of refraction n and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems such problems can be solved numerically by first truncating the given unbounded domain imposing a suitable outgoing radiation condition on an artificial boundary and then solving the resulting problem on the bounded domain by direct discretization for example using a finite element method in practical applications the mesh size h and the wave number k are not independent but are constrained by the accuracy of the desired computation it will be shown that the number of points per wavelength measured by kh 1 is not sufficient to determine the accuracy of a given discretization for example the quantity k 3 h 2 is shown to determine the accuracy in the l 2 norm for a second order discretization method applied to several propagation models

a two level domain decomposition method for the iterative solution of high frequency exterior helmholtz problems summary we present a lagrange multiplier based two level domain decomposition method for solving iteratively large scale systems of equations arising from the finite element discretization of high frequency exterior helmholtz problems the proposed method is essentially an extension of the regularized feti finite element tearing and interconnecting method to indefinite problems its two key ingredients are the regularization of each subdomain matrix by a complex interface lumped mass matrix and the preconditioning of the interface problem by an auxiliary coarse problem constructed to enforce at each iteration the orthogonality of the residual to a set of carefully chosen planar waves we show numerically that the proposed method is scalable with respect to the mesh size the subdomain size and the wavenumber we report performance results for a submarine application that highlight the efficiency of the proposed method for the solution of high frequency acoustic scattering problems discretized by finite elements

the discontinuous enrichment method we propose a finite element based discretization method in which the standard polynomial field is enriched within each element by a nonconforming field that is added to it the enrichment contains free space solutions of the homogeneous differential equation that are not represented by the underlying polynomial field continuity of the enrichment across element interfaces is enforced weakly by lagrange multipliers in this manner we expect to attain high coarse mesh accuracy without significant degradation of conditioning assuring good performance of the computation at any mesh resolution examples of application to acoustics and advection diffusion are presented

solution of helmholtz equation by trefftz method the application of the trefftz method for calculating wave forces on offshore structures is presented indirect and direct formulations using complete and non singular systems of trefftz functions for the helmholtz equation are posed in this paper an effective technique using different interpolation functions for the velocity potential and wave force are suggested to improve the computational accuracy of the wave force the numerical examples show that the present method is highly efficient and accurate