designs for generalized linear models with random block effects via information matrix approximations summary the selection of optimal designs for generalized linear mixed models is complicated by the fact thatthefisherinformationmatrix onwhichmostoptimalitycriteriadepend iscomputationally expensive to evaluate we provide two novel approximations that reduce the computational cost of evaluating the information matrix by complete enumeration of response outcomes or monte carlo approximations thereof an asymptotic approximation that is accurate when there is strong dependence between observations in the same block and an approximation via kriging interpolators for logistic random intercept models we show how interpolation can be especially effective for finding pseudo bayesian designs that incorporate uncertainty in the values of the model parameters the new results are used to evaluate the efficiency for estimating conditional models of optimal designs from closed form approximations to the information matrix derived from marginal models correcting for the marginal attenuation of parameters in binary response models yields much improved designs typically with very high efficiencies however in some experiments exhibiting strong dependence designs for marginal models may still be inefficient forconditionalmodelling ourasymptoticresultsprovidesometheoreticalinsightsintowhysuch inefficiencies occur

an effective method for solving the hyper singular integral equations in 3 d acoustics the application of the boundary integral methods to the problem of acoustics exterior to a three dimensional surface suffers in general from the nonexistence of nonuniqueness of its solutions at frequencies that are characteristic of the associated interior problem the formulation that is most suitable for numerical implementation still appears to be that proposed by burton and miller proc r soc london ser a 323 201 210 1971 however the hypersingular kernels present in such a formulation render it computationally unattractive previous attempts to regularize such hypersingular kernels involved the use of double surface integrals or implicit use of tangential operators or closed form evaluations of hypersingular integrals the method of double surface integrals is computationally highly inefficient even though it allows higher order interpolation schemes on the surface the other two approaches are more conducive to the assumption of a constant value for each of the variables pressure a

numerical techniques for three dimensional steady state fluid structure interaction the application of a coupled finite element boundary integral approach to the analysis of vibrating elastic arbitrary shaped three dimensional structures in an infinite media is presented a feature of the methodologies implemented is the utilization of the isoparametric concept from finite element theory the same shape functions are used both to model the surface of the structure and to interpolate the acoustic variables over the radiating surface the boundary integral formulation used for the exterior acoustic field is a formulation that ensures uniqueness and existence of solutions for the entire frequency range an assessment of the accuracy was made after comparing the solutions attained for a vibrating submerged sphere for various excitation loads and frequencies with the exact solution

numerical modeling of acoustic radiation and scattering from thin bodies using a cauchy principal integral equation in this paper the helmholtz integral equation and its normal derivative are used for the numerical solution of acoustic radiation and scattering from thin bodies a regularized form of the normal derivative integral equation originally derived by maue is adopted to calculate the pressure jump across the thin body this regularized normal derivative integral equation converges in the cauchy principal value sense rather than only in the finite part sense the cauchy principal value integral can be further transformed into an integral that converges in the normal sense the c0 continuous isoparametric elements are used in the formulation so that the numerical model is compatible with other analysis tools such as the finite element method collocation points are placed inside each element to insure a unique normal direction and the c1 continuity condition the pressure jump is forced to be zero at the knife edge where the 1 r 1 2 singularity of the tangential velocities is modeled by the quarter point tec

on the numerical implementation of a cauchy principal value integral to insure a unique solution for acoustic radiation and scattering in this paper the boundary integral formulation proposed by burton and miller proc r soc london ser a 323 201 210 1971 to insure a unique solution for all frequencies is implemented in an isoparametric element environment a regularized normal derivative integral equation originally derived by maue z phys 126 601 618 1949 is used in the formulation to form a linear combination with the conventional helmholtz integral equation this regularized normal derivative integral equation converges in the cauchy principal value sense rather than only in the finite part sense the cauchy principal value integral can be further transformed into an integral that converges in the normal sense the c continuous isoparametric elements are used in the formulation collocation points are placed inside each element to insure a unique normal direction and continuity of tangential derivatives of the acoustic pressure through a systematic collocation point generation scheme the number of collocation point

a weighted residual formulation for the chief method in acoustics in this article the combined helmholtz integral equation formulation chief proposed by schenck is greatly improved so that it will alleviate the annoying nodal surface problem the constraint provided by each chief equation and its first order derivatives is enforced in a weighted residual sense over a small interior region rather than only at a single point consequently chief blocks rather than chief points are used in the numerical implementation although the corresponding interior problem may have nodal surfaces at characteristic frequencies it has no such things as nodal blocks therefore the chief block chief b method is expected to work even if all of the chief blocks fall on the intersection of several nodal surfaces this new formulation is implemented in an isoparametric element environment numerical examples in spherical radiation and scattering at intermediate frequencies are given to test the new formulation

iterative solution of high order boundary element method for acoustic impedance boundary value problems abstract a high order boundary element method for time harmonic acoustic impedance boundary value problems is presented the method is based on the galerkin type formulation of the burton miller integral equation bmie with high order polynomial basis and testing functions this formulation has several important advantages it is free of the interior resonance problem the hypersingular integral operator of the traditional bmie formulation can be avoided it leads to faster convergence in terms of the number of unknowns than the low order methods and it shows a good performance with iterative solvers to avoid the numerical difficulties associated to the implementation of the singular surface integral equations the singularity extraction technique is applied to evaluate the integrals in the singular and near singular cases the resulting matrix equation is solved iteratively with the generalized minimal residual method gmres and a simple preconditioner based on the incomplete lu factorization is applied to expedite the convergence numerical results indicate that the bmie formulation with galerkin method and high order basis functions has good convergence properties for various geometries and boundary conditions on a wide frequency range when the gmres method is applied to solve the matrix equation iteratively this in turn indicates that the formulation is well suited for an efficient application of fast solution procedures such as the fast multipole method

a comparison of techniques for overcoming non uniqueness of boundary integral equations for the collocation partition of unity method in two dimensional acoustic scattering the partition of unity method has become an attractive approach for extending the allowable frequency range for wave simulations beyond that available using piecewise polynomial elements the non uniqueness of solution obtained from the conventional boundary integral equation cbie is well known the cbie derived through green s identities suffers from a problem of non uniqueness at certain characteristic frequencies two of the standard methods of overcoming this problem are the so called combined helmholtz integral equation formulation chief method and that of burton and miller the latter method introduces a hypersingular integral which may be treated in various ways in this paper we present the collocation partition of unity boundary element method pubem for the helmholtz problem and compare the performance of chief against a burton miller formulation regularised using the approach of li and huang

a method to overcome computational difficulties in the exterior acoustics problem when the boundary integral equation method is applied to exterior acoustics problems singularities occur in the resulting algebraic equations at various frequencies associated with the eigenvalues of an interior problem these frequencies are referred to as forbidden and various methods have been devised to overcome the computational difficulties presented at these frequencies the work presented here is an extension to the chief method in that higher derivatives in addition to the function itself are constrained to be zero at selected points in the interior domain whereas the relative success of either method depends on the quantity and selection of interior points the superchief method requires fewer interior points and is less sensitive to point selection resulting in improved robustness without a significant increase in computational complexity

a boundary node method for airfoils based on the dirichlet condition abstract a nonsingular integral equation is developed for thin airfoils with the dirichlet boundary condition both singular and near singular kernels which accompany the original integral equation are flattened out after such regularizations the difficulty in the numerical quadrature is greatly reduced a program with an arbitrary order integral formulation becomes available in the present approach two kinds of airfoils the van de vooren and joukowski airfoils are analyzed for demonstration in this paper in comparison with the results from constant doublet methods the results from the proposed methods are shown to match the analytic solutions excellently

a novel technique in boundary integral equations for analyzing acoustic radiation from axisymmetric bodies a novel technique is suggested to avoid singular integrals of boundary integral equations bie for exterior sound radiation problems the technique reproduction of diagonal terms rdt utilizes special solutions of some monopole sources which give the distribution of theoretical surface pressure and velocity to reproduce diagonal terms in the bie matrices it is proposed to employ three monopole sources in reproduction of diagonal terms in both pressure and velocity matrices although the interior points are applied to generate monopole solutions the concept is basically different from that of general interior helmholtz equations so the present technique is different from those traditional methods to improve bie method through added interior helmholtz equations several examples are presented to demonstrate the effectiveness of the proposed technique for closed axisymmetric surfaces numerical results show that the technique of rdt can improve the accuracy of the solution up to 10 times compared to the conventional techniques such as shf chief shf

solving the hypersingular boundary integral equation in three dimensional acoustics using a regularization relationship regularization of the hypersingular integral in the normal derivative of the conventional helmholtz integral equation through a double surface integral method or regularization relationship has been studied by introducing the new concept of discretized operator matrix evaluation of the double surface integrals is reduced to calculate the product of two discretized operator matrices such a treatment greatly improves the computational efficiency as the number of frequencies to be computed increases the computational cost of solving the composite helmholtz integral equation is comparable to that of solving the conventional helmholtz integral equation in this paper the detailed formulation of the proposed regularization method is presented the computational efficiency and accuracy of the regularization method are demonstrated for a general class of acoustic radiation and scattering problems the radiation of a pulsating sphere an oscillating sphere and a rigid sphere insonified by a plane acoustic wave are solved using the new method with curvilinear quadrilateral isoparametric elements it is found that the numerical results rapidly converge to the corresponding analytical solutions as finer meshes are applied

acoustic scattering by a hard or soft body across a wide frequency range by the helmholtz integral equation method in this paper the acoustic scattering by an obstacle across a wide frequency range of sound waves is investigated on the basis of the helmholtz integral formulation to overcome the nonuniqueness difficulties the methods proposed by burton npl report nac 30 jan 1973 and by burton and miller proc r soc london ser a 323 201 210 1971 are adopted for the dirichlet and neumann problems respectively the aim of this paper is twofold the first is to bring together completely regular formulations of the helmholtz integral equation and its normal derivative the second is to extend these formulations to treat the higher frequency problems the weakly singular integrals are regularized by subtracting out one term and adding it back depending on the problem concerned the additional integral can finally be expressed in an explicit form or results in solving a surface source distribution of the equipotential body the hypersingular kernels are regularized by the method of using some properties of the associated laplace equation originally proposed by chien et al j acoust soc am 88 918 937 1990 the completely regularized integral equations are amenable to computation by direct use of the standard quadrature methods to study the acoustic scattering due to higher frequency waves filon s quadrature method proc r soc edinburgh 49 38 47 1928 is extended to treat the rapidly oscillatory integrands numerical examples consist of acoustic scattering from a hard or soft sphere of radius a across a wide spectrum of wave numbers ka 20 comparisons of the numerical results with the exact solutions demonstrate the validity and efficiency of the implementation

a boundary integral equation method for two dimensional acoustic scattering problems this work formulates the singularity free integral equations to study 2 d acoustic scattering problems to avert the nonuniqueness difficulties burton s and burton and miller s methods are employed to solve the dirichlet and neumann problems respectively the surface helmholtz integral equations and their normal derivative equations in bounded form are derived the weakly singular integrals are desingularized by subtracting a term from the integrand and adding it back with an exact value depending on the relevant problem the additional integral can finally be either expressed in an explicit form or transformed to form a surface source distribution of the related equipotential body the hypersingular kernel is desingularized further using some properties of an interior laplace problem the new formulations are advantageous in that they can be computed by directly using standard quadrature formulas also discussed is the contour a unique feature of 2 d problems instead of dividing the boundary surface into several small elements a parametric representation of a 2 d boundary curve is further proposed to facilitate a global numerical implementation calculations consist of acoustic scattering by a hard and a soft circular cylinder respectively comparing the numerical results with the exact solutions demonstrates the proposed method s effectiveness

a comparative study of different discretizations for solving bivariate aggregation population balance equation in this work a comparative study on how the solution of a pure bivariate aggregation population balance equation depends on different structured grids is presented numerical results obtained using the most commonly used cell average and fixed pivot techniques on four different types of structured grids are compared with the exact solutions as expected the cell average technique predicts more accurate solution than the fixed pivot technique for all different grids moreover the results predicted using the cell average technique using x type grid with logarithmic scale in the radial direction provide solutions of high quality among all other grids

hypersingular boundary integral equations for exterior acoustic problems a bounded form of the hypersingular helmholtz integral equation for 3 d acoustic problems is developed in this paper all integrals with singular kernels are regularized within each regular surface element in the sense of kellogg with twice continuous differentiability the standard gaussian quadrature formula is applied without any special treatment for all the computational points the collocation points are chosen to be the gauss legendre nodes and no interpolation function is assumed for acoustic variables

an investigation into integral equation methods involving nearly singular kernels for acoustic scattering this work presents a numerical means of investigating the acoustic scattering by disk shaped bodies on the basis of burton and miller s method the singularity free formulations of helmholtz integral equation and its normal derivative are used to form a composite equation a triangle polar co ordinate transformation method is further applied to treat the nearly singular kernels arising from a situation in which the field points and source points are very close together numerical simulations consist of the acoustic scattering by a short circular cylinder and a thin circular disk respectively for the latter case with zero thickness the corresponding analytical solutions involving angular and radial oblate spheroidal wave functions are evaluated as well comparing the numerical results with the experimental data and analytical solutions demonstrates the effectiveness of the proposed method

a finite volume preserving scheme on nonuniform meshes and for multidimensional coalescence in this paper we present a deterministic numerical approximation of the coalescence or smoluchowski equation the proposed numerical scheme conserves the first order momentum and deals with nonuniform grids the generalization to a multidimensional framework is also described we validate the scheme considering some classical tests in both one and two dimensions and discuss its behavior when gelation occurs our numerical results and code are compared with those already existent in the literature

fft based evaluation of multivariate aggregation integrals in population balance equations on uniform tensor grids abstract we consider the numerical solution of the multivariate aggregation population balance equation on a uniform tensor grid we introduce a multidimensional fast fourier transformation for the efficient evaluation of the aggregation integrals leading to a reduction in the complexity order of the algorithm compared to the direct evaluation approach we illustrate the new evaluation algorithm for two discretizations an fem approach as well as the sectional method we discuss the conservation of moments for these methods and provide numerical comparisons illustrating the superior performance of fft based algorithms we also discuss and numerically illustrate their potential for parallelization

acoustic isogeometric boundary element analysis an isogeometric boundary element method based on t splines is used to simulate acoustic phenomena we restrict our developments to low frequency problems to establish the fundamental properties of the proposed approach using t splines the computer aided design cad and boundary element analysis are integrated without recourse to geometry clean up or mesh generation a regularized burton miller formulation is used resulting in integrals which are at most weakly singular we employ a collocation based approach to generate the linear system of equations the method is verified against closed form solutions and direct comparisons are made with conventional lagrangian discretizations it is demonstrated that the superior accuracy of the isogeometric approach emanates from the exact geometric description encapsulated in the t spline the method is then applied to a real world application to illustrate the potential for integrated engineering design and analysis

non singular boundary integral formulations for plane interior potential problems in this article a non singular formulation of the boundary integral equation is developed to solve smooth and non smooth interior potential problems in two dimensions the subtracting and adding back technique is used toregularize the singularity of green s function and to simplify the calculation of the normal derivative of green s function after that a global numerical integration is directly applied at the boundary and those integration points are also taken as collocation points to simplify the algorithm of computation the result indicates that this simple method gives the convergence speed of order n 3 in the smooth boundary cases for both dirichlet and mix type problems for the non smooth cases the convergence speed drops at o n 1 2 for the dirichlet problems

a boundary integral method for acoustic radiation and scattering in this article a computational method is proposed for computing the helmholtz integral equation for acoustic radiation and scattering problems with a three dimensional body shape unlike the previous boundary element method the integration of acoustic properties is based on the global body surface instead of local elements the approximation function of body geometry and the weighting function of numerical integration are independently chosen when the singular kernels of helmholtz equation are regularized as bounded discontinuous functions the order of integration polynomials for acoustic properties can be arbitrarily chosen therefore the accuracy and efficiency of computation can be increased