coercive boundary value problems for regular degenerate differential operator equations abstract this study focuses on nonlocal boundary value problems bvp for degenerate elliptic differential operator equations doe that are defined in banach valued function spaces where boundary conditions contain a degenerate function and a principal part of the equation possess varying coefficients several conditions obtained that guarantee the maximal l p regularity and fredholmness these results are also applied to nonlocal bvp for regular degenerate partial differential equations on cylindrical domain to obtain the algebraic conditions that ensure the same properties

an isogeometric collocation approach for bernoulli euler beams and kirchhoff plates abstract in this paper iga collocation methods are for the first time introduced for the solution of thin structural problems described by the bernoulli euler beam and kirchhoff plate models in particular a precise description of the proposed methods of the relevant implementation details and of the strategy to efficiently deal with different combinations of boundary conditions is given finally several numerical experiments confirm that the proposed formulations represent an efficient and geometrically flexible tool for the simulation of thin structures

bootstrap critical values for testing homogeneity of covariance matrices abstract bartlett s modified likelihood ratio statistic a is often suggested in multivariate analysis for testing equality of covariance matrices unfortunately the 2 approximation to the null distribution of 2 log is useful only when the data is normally distributed this article presents a pooled bootstrap procedure that replaces the 2 approximation and makes bartlett s statistic a useful tool for data analysis this procedure also applies to most quadratic form test statistics

nonlinear isogeometric spatial bernoulli beam abstract a new element formulation of a geometrically nonlinear spatial curved beam assuming bernoulli theory including torsion without warping is proposed the element formulation is derived directly from the 3d continuum by means of nonlinear kinematics thus accounting for large displacements the geometric description of the proposed element is adapted from the spatial rod of greco and cuomo 2013 and extended to a nonlinear element formulation the proposed formulation can handle arbitrary orientations of the cross section along the beam in this publication nurbs are used as basis functions for discretization since they can easily provide the required c 1 continuity between elements the presented element formulation has four degrees of freedom three for displacements and one for the rotation around the center line in order to prove the accuracy of the developed spatial bernoulli beam several numerical examples are presented and compared to analytic solutions and other element formulations

optimal and reduced quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis abstract we continue the study initiated in hughes et al 2010 in search of optimal quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis these rules are optimal in the sense that there exists no other quadrature rule that can exactly integrate the elements of the given spline space with fewer quadrature points we extend the algorithm presented in hughes et al 2010 with an improved starting guess which combined with arbitrary precision arithmetic results in the practical computation of quadrature rules for univariate non uniform splines up to any precision explicit constructions are provided in sixteen digits of accuracy for some of the most commonly used uniform spline spaces defined by open knot vectors we study the efficacy of the proposed rules in the context of full and reduced quadrature applied to two and three dimensional diffusion reaction problems using tensor product and hierarchically refined splines and prove a theorem rigorously establishing the stability and accuracy of the reduced rules

nonlinear abstract boundary value problems in vector valued function spaces and applications abstract the nonlocal boundary value problems for linear and nonlinear differential operator equations of second order with dependent coefficients are studied the principal part of the differential operators generated by linear problems are nonself adjoint several conditions for the maximal regularity r positivity and the fredholmness in banach valued l p spaces are given by using these results the existence and uniqueness of the maximal regular solutions of nonlocal boundary value problems for nonlinear differential operator equations are established in applications nonlocal boundary value problems for nonlinear partial differential equations and their finite or infinite systems on cylindrical domains are studied

fast formation and assembly of finite element matrices with application to isogeometric linear elasticity abstract recently a new formation and assembly strategy was proposed in 1 which resulted in significant speedups in the formation and assembly time of the galerkin mass matrix in isogeometric analysis the strategy relies on three key ingredients 1 assembly row by row instead of element by element and an efficient formation strategy based on 2 sum factorization and 3 weighted quadrature that is applied to each specific row of the matrix compared to traditional element procedures applied to three dimensional problems the computational complexity is lowered from o p 9 per degree of freedom to o p 4 where p is the order of polynomials this is close to the theoretical minimum of o p 3 attained by for example collocation consequently this type of formation and assembly scales favorably with polynomial degree which opens the way for high order isogeometric analysis employing k refinement that is use of maximally smooth higher order splines in this work we discuss various important details for the practical implementation of the weighted quadrature formation strategy proposed in 1 specifically we extend the weighted quadrature scheme to accurately integrate the elements of the stiffness matrix in linear elasticity and propose a means of distributing quadrature points for non uniform mixed continuity spline spaces furthermore we discuss efficient access and assignment into the prevalent sparse matrix data structures namely compressed sparse row csr and compressed sparse column csc in particular row by row or column by column assembly allows matrix rows or columns respectively to be formed contiguously in the storage order of the sparse matrix thereby minimizing the memory overhead and eliminating the addition assignment operation on sparse matrices several three dimensional benchmark problems illustrate the efficiency and efficacy of the proposed formation and assembly technique applied to isogeometric linear elasticity we show that the accuracy of full gauss quadrature is maintained while the computational burden of forming the matrix equations is significantly reduced

duality and unified analysis of discrete approximations in structural dynamics and wave propagation comparison of p method finite elements with k method nurbs we study the discretization behavior of classical finite element and nurbs approximations on problems of structural vibrations and wave propagation we find that on the basis of equal numbers of degrees of freedom and bandwidth nurbs have superior approximation properties in fact we observe that the high mode behavior of classical finite elements is divergent with the order of approximation a surprisingly negative result on the other hand nurbs offer almost spectral approximation properties and all modes converge with increasing order of approximation

an integrated fitting and fairing approach for object reconstruction using smooth nurbs curves and surfaces abstract this paper presents a new approach for object reconstruction by means of smooth nurbs curves and surfaces compared to the common object reconstruction algorithms that first fit a curve or surface to a dataset and then try to make it smooth in a post processing fairing stage this article proposes to apply the fitting and fairing procedures simultaneously to achieve desirable results in the integrated fitting and fairing approach the respective fitting and fairing objectives are met in a multi objective optimization process in the developed methodology the structure of the reconstructed curves and surfaces e g the arrangement of the knot vectors and location of control points is optimized in such a way that the desired fairness will be locally achieved in every segment of the reconstructed object the functionality of the developed method is investigated by some industrial case studies

multi dimensional nurbs model for predicting maximum free surface oscillation in swaying rectangular storage tanks abstract in this paper a multi dimensional non uniform rational b spline nurbs model is presented aiming at predicting the maximum free surface oscillation mfso in the swaying rectangular storage tanks the accuracy and clear mathematical meaning of the nurbs formulation make it attractive for the purpose in this regard a numerical model is developed to simulate the liquid sloshing phenomenon in a rectangular tank by means of coupling the reynolds averaged navier stokes rans solver and the volume of fluid vof technique the rans equations are discretized and solved using the staggered grid finite difference smac method in order to validate the model a rectangular tank with specified width and water depth is exposed to a presumed horizontal periodic sway motion and the results of the numerical analysis are compared to a well established example in the next step the numerical model is used to simulate the sloshing phenomenon in the rectangular storage tanks with different widths and water depths under different harmonic excitations finally a multi dimensional nurbs hyper surface is employed to fit a multivariate function to the sloshing results based on the numerical data as a result a new mathematical relationship is suggested by this article to estimate the mfso in the swaying rectangular storage tanks so that practitioners may benefit more when they try to apply the presented methodology to their real world problems

nonlocal problems for boussinesq equations abstract in this paper the existence and uniqueness of solution of the integral boundary value problem for abstract boussinesq equations are obtained

linear and nonlinear abstract equations with parameters abstract this paper focuses on nonlocal boundary value problems for linear and nonlinear abstract elliptic equations in banach spaces here equations and boundary conditions contain certain parameters the uniform separability of the linear problem and the existence and uniqueness of maximal regular solution of nonlinear problem are obtained in l p spaces for linear case the discreteness of spectrum of corresponding parameter dependent differential operator is obtained the behavior of solution when the parameter approaches zero and its smoothness with respect to the parameter is established moreover we show the estimate for analytic semigroups in terms of interpolation spaces this fact can be used to obtain maximal regularity properties for abstract boundary value problems

discrete dispersion relation for hp version finite element approximation at high wave number the dispersive properties of high order finite element schemes are analyzed in the setting of the helmholtz equation and an explicit form of the discrete dispersion relation is obtained for elements of arbitrary order it is shown that the numerical dispersion displays three different types of behavior depending on the size of the order of the method relative to the mesh size and the wave number quantitative estimates are obtained for the behavior and rates of decay of the dispersion error in the differing regimes all estimates are fully explicit and are shown to be sharp limits are obtained where transitions between the different regimes occur and used to provide guidelines for the selection of the mesh size and the polynomial order in terms of the wave number so that the dispersion error is controlled

operator valued fourier multiplier theorems and maximal l_p regularity we prove a mihlin type multiplier theorem for operator valued multiplier functions on umd spaces the essential assumption is r boundedness of the multiplier function as an application we give a characterization of maximal l p regularity for the generator of an analytic semigroup t t in terms of the r boundedness of the resolvent of a or the semigroup t t

linear and nonlinear degenerate differential operators and applications abstract the boundary value and mixed value problems for linear and nonlinear singular degenerate abstract elliptic and parabolic equations are studied the linear problems involve some parameters the uniform l p separability properties of linear problems and the optimal regularity results for nonlinear problems are obtained the equations include linear operators defined in banach spaces in which by choosing the spaces and operators we can obtain numerous classes of problems for singular degenerate differential equations which occur in a wide variety of physical systems

on the application of isogeometric finite volume method in numerical analysis of wet steam flow through turbine cascades abstract the isogeometric finite volume analysis is utilized in this research to numerically simulate the two dimensional viscous wet steam flow between stationary cascades of a steam turbine for the first time in this approach the analysis suitable computational mesh with curved boundaries is generated for the fluid flow by employing a non uniform rational b spline nurbs surface that describes the cascade geometry and the governing equations are then discretized by the nurbs representation thanks to smooth and accurate geometry representation of the nurbs formulation the employed isogeometric framework not only resolves issues concerning the conventional mesh generation techniques of the finite volume method in steam turbine problems but also as validated against well established experiments significantly improves the accuracy of the numerical solution in addition the shock location in the cascade is predicted and tracked with a sufficient accuracy

a nonmetric approach to linear discriminant analysis abstract a new nonmetric linear discriminant analysis approach is proposed that is based on the maximization of an index of separation differing from that used by the classical method the possibility of choosing between fisher s classical discriminant function and the one proposed here enables us to reduce the number of misclassifications for given data the method is exemplified on empirical data and various simulations and is compared with the classical linear discriminant analysis

dea and the discriminant analysis of ratios for ranking units the purpose of this study is to develop a new method which provides for given inputs and outputs the best common weights for all the units that discriminate optimally between the efficient and inefficient units as pregiven by the data envelopment analysis dea in order to rank all the units on the same scale this new method discriminant data envelopment analysis of ratios dr dea presents a further post optimality analysis of dea for organizational units when their multiple inputs and outputs are given we construct the ratio between the composite output and the composite input where their common weights are computed by a new non linear optimization of goodness of separation between the two pregiven groups a practical use of dr dea is that the common weights may be utilized for ranking the units on a unified scale dr dea is a new use of a two group discriminant criterion that has been presented here for ratios rather than the traditional discriminant analysis which applies to a linear function moreover non parametric statistical tests are employed to verify the consistency between the classification from dea efficient and inefficient units and the post classification as generated by dr dea

finite element and nurbs approximations of eigenvalue boundary value and initial value problems abstract we study the spectral approximation properties of finite element and nurbs spaces from a global perspective we focus on eigenfunction approximations and discover that the l 2 norm errors for finite element eigenfunctions exhibit pronounced spikes about the transition points between branches of the eigenvalue spectrum this pathology is absent in nurbs approximations by way of the pythagorean eigenvalue error theorem we determine that the squares of the energy norm errors of the eigenfunctions are the sums of the eigenvalue errors and the squares of the l 2 norm eigenfunction errors the spurious behavior of the higher eigenvalues for standard finite elements is well known and therefore inherited by the energy norm errors along with the spikes in the l 2 norm of the eigenfunction errors the eigenvalue pathology is absent for nurbs the implications of these results to the corresponding elliptic boundary value problem and parabolic and hyperbolic initial value problems are discussed

effects of parameterization and knot placement techniques on primal and mixed isogeometric collocation formulations of spatial shear deformable beams with varying curvature and torsion abstract we present a displacement based and a mixed isogeometric collocation iga c formulation for free form three dimensional shear deformable beams with high and rapidly varying curvature and torsion when such complex shapes are concerned the approach used to build the iga geometric model becomes relevant although iga c has been so far successfully applied to a wide range of problems the effects that different parameterization and knot placement techniques may have on the accuracy of collocation based formulations is still an unexplored field to fill this gap primal and mixed formulations are used combining two parameterization methods chord length and equally spaced with two knot placement techniques uniformly spaced and de boor with respect to the space varying frenet local frame we derive the strong form of the governing equations in a compact form through the definition of two matrix operators conveniently used to perform first and second order derivatives of the vector fields involved in the formulations this approach is very efficient and easy to implement within a collocation based scheme several challenging numerical experiments allow to test the different considered parameterizations and knot placement techniques revealing in particular that with the primal formulation an equally spaced parameterization is definitively the most recommended choice and it should always be used with an approximation degree of at least p 6 although some caution must be adopted when very high jacobians and small curvatures occur the same holds for the mixed formulation with the difference that p 4 is enough to yield accurate results

on the closedness of the sum of two closed operators o t t 1 where e g a is the infinitesimal generator of an analytic semigroup in a complex banach space x we find that in general it is false that for every fe lp 0 t x problem 1 has a solution uewi p o t x c lp o t a usually it is necessary to impose some further regularity conditions on f consider for instance the way in which problem 1 is studied in the paper 8 and compare th 3 7 and 3 14 which are applied in w 4 of the same paper to solve problem 1 we find that in general we have only strong solutions while in the hilbert space setting we have strict solutions this corresponds to the fact that in general the operator a b where b u u is only closable while in a hilbert space it is closed this remark suggests that the better result may depend on the nicer geometric properties of a hilbert space with respect to a general banach space and it is natural to ask which conditions should be imposed on the banach space to force the sum of two suitable closed opera tors to be closed the above considerations motivate the manifold aim of the present paper a to find conditions on a banach space x and on closed linear operators a and b acting in x which ensure that a b is closed b to apply the result of a to problem 1 it seems that the convenient property for the banach space x is convexity or otherwise stated the umd condition for information about these equiva lent conditions we refer to 4 in which it is also proved that if x is convex and l p oe then the hilbert transform is continuous from lp r x into lp r x on the other hand it is also known see 2 that if there exists pe 1 oe such that the hilbert transform is continuous from lp r x into itself

scaling units via the canonical correlation analysis in the dea context abstract this paper deals with the evaluation of decision making units which have multiple inputs and outputs a new method cca dea is developed where the canonical correlation analysis cca is utilized to provide a full rank scaling for all the units rather than a categorical classification for efficient and inefficient units as done by the data envelopment analysis dea the cca dea approach is an attempt to bridge the gap between the frontier approach of dea and the average tendencies of statistics econometrics nonparametric statistical tests are employed to validate the consistency between the classification from the dea and the postclassification that was generated by the cca dea