isogeometric analysis using t splines we explore t splines a generalization of nurbs enabling local refinement as a basis for isogeometric analysis we review t splines as a surface design methodology and then develop it for engineering analysis applications we test t splines on some elementary two dimensional and three dimensional fluid and structural analysis problems and attain good results in all cases we summarize the current status of t splines their limitations and future possibilities

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

subdivision surfaces a new paradigm for thin shell finite element analysis we develop a new paradigm for thin shell finite element analysis based on the use of subdivision surfaces for i describing the geometry of the shell in its undeformed configuration and ii generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the kirchhoff love theory of thin shells the particular subdivision strategy adopted here is loop s scheme with extensions such as required to account for creases and displacement boundary conditions the displacement fields obtained by subdivision are h2 and consequently have a finite kirchhoff love energy the resulting finite elements contain three nodes and element integrals are computed by a one point quadrature the displacement field of the shell is interpolated from nodal displacements only in particular no nodal rotations are used in the interpolation the interpolation scheme induced by subdivision is non local i e the displacement field over one element depend on the nodal displacements of the element nodes and all nodes of immediately neighbouring elements however the use of subdivision surfaces ensures that all the local displacement fields thus constructed combine conformingly to define one single limit surface numerical tests including the belytschko et al 10 obstacle course of benchmark problems demonstrate the high accuracy and optimal convergence of the method

renormalization theory in four dimensional scalar fields i we present a renormalization group approach to the renormalization theory of 44 using techniques that have been introduced and used in previous papers and that lead to very simple methods to bound the coefficients of the effective potential and of the schwinger functions the main aim of this paper is to show how one can in this way obtain then bounds

rotation free isogeometric thin shell analysis using pht splines this paper presents a novel approach for isogeometric analysis of thin shells using polynomial splines over hierarchical t meshes pht splines the method exploits the flexibility of t meshes for local refinement the main advantage of the pht splines in the context of thin shell theory is that it achieves c1 continuity so the kirchhoff love theory can be used in pristine form no rotational degrees of freedom are needed numerical results show the excellent performance of the present method

renormalization group in the local potential approximation in the local potential approximation renormalization group equations reduce to a semilinear parabolic partial differential equation we derive this equation and show the relation with the hierarchical model we construct a family of non trivial fixed points u 2n n 2 3 4 which have the form ofn well potentials and exist in the ranges of dimensions 2 d dn 2 2 n 1 asd dn u 2n tends to zero for the wilson fixed pointu 4 we give bounds on critical exponents in the case of dipole gas in this approximation we show that no non trivial fixed points exist

blowup and self similar solutions for two component drift diffusion systems abstract we discuss asymptotic properties of solutions of two component parabolic drift diffusion systems coupled through an elliptic equation in two space dimensions in particular conditions for finite time blowup versus the existence of forward self similar solutions are studied

isogeometric analysis for trimmed cad surfaces in this work an isogeometric analysis for trimmed cad surfaces in 2d linear elasticity problem is presented the main benefit of the proposed method is that no additional modeling for the analysis of the trimmed surface is necessary as a pioneering attempt to deal with the trimmed surfaces in isogeometric analysis the information on the trimming curves and trimmed surfaces exported from cad system is directly utilized for analysis for this trimmed elements are searched through using a projection scheme for the integration of trimmed elements nurbs enhanced integration scheme employed in nefem is adopted for the isogeometric analysis the construction of the stiffness matrix based on the spline basis function is presented in the formulation the information on the trimming curves is used not only for obtaining integration points but also for calculating the jacobian through error analyses of the verification examples the robustness and effectiveness of the proposed method are investigated it is observed that the proposed method gives the theoretical convergence rate multiple trimming curve problems which are difficult to analyze with conventional isogeometric analysis are easily treated with the proposed method an illuminating example is given in the same example t spline local refinement is also employed

a method for the automatic evaluation of the dynamic relaxation parameters abstract dynamic relaxation a vector iteration method which belongs to the family of methods under the title of three term recursive formulae is described with viscous and kinetic damping an automatic procedure is developed for the evaluation of the iteration parameters thus avoiding any trial run or any eigenvalue analysis of the modified stiffness matrix starting values for the maximum eigenvalue could be obtained from the gershgorin bound and for the minimum eigenvalue any positive number less than the estimated maximum eigenvalue the method is applied to geometrically and material nonlinear problems and comparisons are made with an improved conjugate gradient method and a direct stiffness method

isogeometric collocation methods for the reissner mindlin plate problem abstract within the general framework of isogeometric methods collocation schemes have been recently proposed as a viable and promising low cost alternative to standard isogeometric galerkin approaches in this paper isogeometric collocation methods for the numerical approximation of reissner mindlin plate problems are proposed for the first time locking free primal and mixed formulations are herein considered and the potential of isogeometric collocation as a geometrically flexible and computationally efficient simulation tool for shear deformable plates is shown through the solution of several numerical tests

construction of the hierarchical φ4 trajectory we study the invariant unstable manifold of the trivial renormalization group fixed point tangent to the 4 vertex in the hierarchical approximation we parametrize it by a running 4 coupling with linear step function the manifold is studied as a fixed point of the renormalization group composed with a flow of the running coupling we present a rigorous construction of it beyond perturbation theory by means of a contraction mapping starting from a perturbative approximant of order seven we obtain a convergent representation in dimensions 2 d 28 9 with certain restrictions the perturbative approximant is logarithmically divergent in d 3 dimensions

existence of stiffness matrix integrals for singularly parameterized domains in isogeometric analysis abstract isogeometric analysis is a numerical simulation method which uses the nurbs based representation of cad models nurbs stands for non uniform rational b splines and is a generalization of the concept of b splines the isogeometric method uses the tensor product structure of 2 or 3 dimensional nurbs functions to parameterize domains which are structurally equivalent to a rectangle or a hexahedron the special case of singularly parameterized nurbs surfaces and nurbs volumes is used to represent non quadrangular or non hexahedral domains without splitting which leads to a very compact and convenient representation if the parameterization of the physical domain is available the test functions for the isogeometric analysis are obtained by composing the inverse of the domain parameterization with the nurbs basis functions in the case of singular parameterizations however some of the resulting test functions are not well defined at the singular points and they do not necessarily satisfy the required integrability assumptions consequently the stiffness matrix integrals which occur in the numerical discretizations may not exist after summarizing the basics of the isogeometric method we discuss the existence of the stiffness matrix integrals for 1 2 and 3 dimensional second order elliptic partial differential equations we consider several types of singularities of nurbs parameterizations and derive conditions which guarantee the existence of the required integrals in addition we present cases with diverging integrals and show how to modify the test functions in these situations

isogeometric finite element data structures based on bezier extraction of t splines we develop finite element data structures for t splines based on bezier extraction generalizing our previous work for nurbs as in traditional finite element analysis the extracted bezier elements are defined in terms of a fixed set of polynomial basis functions the so called bernstein basis the bezier elements may be processed in the same way as in a standard finite element computer program utilizing exactly the same data processing arrays in fact only the shape function subroutine needs to be modified while all other aspects of a finite element program remain the same a byproduct of the extraction process is the element extraction operator this operator localizes the topological and global smoothness information to the element level and represents a canonical treatment of t junctions referred to as hanging nodes in finite element analysis and a fundamental feature of t splines a detailed example is presented to illustrate the ideas copyright 2011 john wiley sons ltd

the hierarchicalφ4 trajectory by perturbation theory in a running coupling and its logarithmby perturbation theory in a running coupling and its logarithm we compute the hierarchical 4 in terms of perturbation theory in a running coupling in the three dimensional case we resolve a singularity due to resonance of power counting factors in terms of logarithms of the running coupling numerical data are presented and the limits of validity explored we also compute moving eigenvalues and eigenvectors on the trajectory as well as their fusion rules

asymptotic stability of a two species chemotaxis system with non diffusive chemoattractant abstract we study the behavior of two biological populations u and v attracted by the same chemical substance whose behavior is described in terms of second order parabolic equations the model considers a logistic growth of the species and the interactions between them are relegated to the chemoattractant production the system is completed with a third equation modeling the evolution of chemical we assume that the chemical w is a non diffusive substance and satisfies an ode more precisely u t u u 1 w w 1 u 1 u x t 0 v t v v 2 w w 2 v 1 v x t 0 w t h u v w x t 0 under appropriate boundary and initial conditions in an n dimensional open and bounded domain we consider the cases of positive chemo sensitivities not necessarily constant elements the chemical production function h increases as the concentration of the species u and v increases we first study the global existence and uniform boundedness of the solutions by using an iterative approach the asymptotic stability of the homogeneous steady state is a consequence of the growth of h i and the size of i finally some examples of the theoretical results are presented for particular functions h and i

running coupling expansion for the renormalized φ 4 4 trajectory from renormalization invariance we formulate a renormalized running coupling expansion for the function and the potential of the renormalized 4 trajectory on four dimensional euclidean space time renormalization invariance is used as a first principle no reference is made to bare quantities the expansion is proved to be finite to all orders of perturbation theory the proof includes a large momentum bound on the connected free propagator amputated vertices

form finding with dynamic relaxation and isogeometric membrane elements a method for form finding with dynamic relaxation and non uniform rational b splines nurbs based isogeometric membrane elements has been implemented and studied regarding the influence of the discretization and element shape on the form finding the procedure allows for rapid form finding since nurbs describe the curved geometry well and it is shown that the form finding can be performed using a coarse mesh however to minimize the bending strain energy a fine mesh is needed using smaller elements is more advantageous than increasing the degree of the basis functions keeping the number of integration points few and converging at a lesser number of iterations using isogeometric analysis iga simplifies further studies since the form found shape can be exactly represented with a shell element formulation the method is suitable to be used in computer aided design environments such as rhinoceros 3d during design stages where the form finding can be evaluated together with other studies in a design context

avoiding shear locking for the timoshenko beam problem via isogeometric collocation methods in this work we study isogeometric collocation methods for the timoshenko beam problem considering both mixed and displacement based formulations in particular we show that locking free solutions are obtained for mixed methods independently on the approximation degrees selected for the unknown fields moreover several numerical tests are provided in order to support our theoretical results and to show the good behavior and the flexibility of isogeometric collocation methods in this context

adaptive isogeometric analysis by local h refinement with t splines isogeometric analysis based on non uniform rational b splines nurbs as basis functions preserves the exact geometry but suffers from the drawback of a rectangular grid of control points in the parameter space which renders a purely local refinement impossible this paper demonstrates how this difficulty can be overcome by using t splines instead t splines allow the introduction of so called t junctions which are related to hanging nodes in the standard fem obeying a few straightforward rules rectangular patches in the parameter space of the t splines can be subdivided and thus a local refinement becomes feasible while still preserving the exact geometry furthermore it is shown how state of the art a posteriori error estimation techniques can be combined with refinement by t splines numerical examples underline the potential of isogeometric analysis with t splines and give hints for further developments

an extended isogeometric thin shell analysis based on kirchhoff love theory abstract an extended isogeometric element formulation xiga for analysis of through the thickness cracks in thin shell structures is developed the discretization is based on non uniform rational b splines nurbs the proposed xiga formulation can reproduce the singular field near the crack tip and the discontinuities across the crack it is based on the kirchhoff love theory where c 1 continuity of the displacement field is required this condition is satisfied by the nurbs basis functions hence the formulation eliminates the need of rotational degrees of freedom or the discretization of the director field facilitating the enrichment strategy the performance and validity of the formulation is tested by several benchmark examples

on the renormalization group transformation for scalar hierarchical models we give a new proof for the existence of a non gaussian hierarchical renormalization group fixed point using what could be called a beta function for this problem we also discuss the asymptotic behavior of this fixed point and the connection between the hierarchical models of dyson and gallavotti