a recursive approach to local mesh refinement in two and three dimensions abstract the newest vertex strategy for local refinement in two dimensions is reviewed and discussed a recursive algorithm for local refinement of tetrahedral meshes in three dimensions based on similar bisection strategy is described the recursive approach requires certain restrictions on the initial mesh on the other hand under this condition the refinement process can be kept as local as needed and it can be fully inverted simple data structures and derefinement algorithms are also outlined

an efficient jacobi like algorithm for parallel eigenvalue computation a very fast jacobi like algorithm for the parallel solution of symmetric eigenvalue problems is proposed it becomes possible by not focusing on the realization of the jacobi rotation with a cordic processor but by applying approximate rotations and adjusting them to single steps of the cordic algorithm i e only one angle of the cordic angle sequence defines the jacobi rotation in each step this angle can be determined by some shift add and compare operations although only linear convergence is obtained for the most simple version of the new algorithm the overall operation count shifts and adds decreases dramatically a slow increase of the number of involved cordic angles during the runtime retains quadratic convergence

redundant cordic methods with a constant scale factor for sine and cosine computation proposes two redundant cordic coordinate rotation digital computer methods with a constant scale factor for sine and cosine computation called the double rotation method and the correcting rotation method in both methods the cordic is accelerated by the use of a redundant binary number representation as in the previously proposed redundant cordic in the proposed methods since the number of rotation extensions performed for each angle is a constant the scale factor is a constant independent of the operand hence one does not need to calculate the scale factor during the computation and can make a more efficient sine and cosine generator than that based on the previous redundant cordic

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

bkm a new hardware algorithm for complex elementary functions a new algorithm for computing the complex logarithm and exponential functions is proposed this algorithm is based on shift and add elementary steps and it generalizes some algorithms by briggs and de lugish 1970 as well as the cordic algorithm it can easily be used to compute the classical real elementary functions sin cos arctan ln exp this algorithm is more suitable for computations in a redundant number system than the cordic algorithm since there is no scaling factor when computing trigonometric functions

exact 3d boundary representation in finite element analysis based on cartesian grids independent of the geometry summary this paper proposes a novel immersed boundary method where the embedded domain is exactly described by using its computer aided design cad boundary representation with non uniform rational b splines nurbs or t splines the common feature with other immersed methods is that the current approach substantially reduces the burden of mesh generation in contrast the exact boundary representation of the embedded domain allows to overcome the major drawback of existing immersed methods that is the inaccurate representation of the physical domain a novel approach to perform the numerical integration in the region of the cut elements that is internal to the physical domain is presented and its accuracy and performance evaluated using numerical tests the applicability performance and optimal convergence of the proposed methodology is assessed by using numerical examples in three dimensions it is also shown that the accuracy of the proposed methodology is independent on the cad technology used to describe the geometry of the embedded domain copyright 2015 john wiley sons ltd

centred bimodules over prime rings closed submodules and applications to ring extensions let m be a centred bimodule over a prime ring r in this paper we define and study a very useful class of sub bimodules of m the class of closed sub bimodules there is a canonical torsion free extension of m to a q bimodule m which is always free over q where q is the complete ring of right quotients of r we prove that closed sub bimodules of m are in one to one correspondence with closed sub bimodules of m the results are applied to study the torsion free rank of a sub bimodule of m and to study non singular and strongly closed sub bimodules also the results are applied to study prime ideals in centred extensions and intermediate extensions in particular we complete and extend the results obtained in m ferrero j algebra 148 1992 1 16

cordic vectoring with arbitrary target value the computation of additional functions in the cordic module increases its flexibility we consider here the extension of the vectoring mode angle calculation so that the vector is rotated until one of the coordinates for instance y attains a target value t in contrast to the value 0 as in standard vectoring the main problem in the algorithm is that the modulus of the vector is scaled in each cordic iteration so that a direct comparison of y j with t does not assure convergence we present a scheme that overcomes this and in which the implementation consists of a standard cordic module plus a module to determine the direction of rotation this improves over a previous proposal in which more complex iterations are introduced as part of the cordic algorithm moreover an error analysis is performed to determine the datapath width required for convergence since this width is large we consider also the characteristics of the algorithm for a narrower datapath

adaptive simplification of huge sets of terrain grid data for geosciences applications we propose and discuss a new lepp surface method able to produce a small triangular approximation of huge sets of terrain grid data by using a two goal strategy that assures both small approximation error and well shaped 3d triangles this is a refinement method which starts with a coarse initial triangulation of the input data and incrementally selects and adds data points into the mesh as follows for the edge e having the highest error in the mesh one or two points close to one or two terminal edges associated with e are inserted in the mesh the edge error is computed by adding the triangle approximation errors of the two triangles that share e while each l 2 norm triangle error is computed by using a curvature tensor a good approximation of the surface at a representative point associated with both triangles the method produces triangular approximations that capture well the relevant features of the terrain surface by naturally producing well shaped triangles we compare our method with a pure l 2 norm optimization method

higher radix square rooting a general discussion on nonrestoring square root algorithms is presented showing bounds and constraints delimiting the space of feasible algorithms for all the choices of radix digit set and representation of the partial remainder two classes of algorithms are then derived from the general discussion and it is shown how it is possible to determine two parameters with a relevant impact on the implementation the number of radicand bits to be inspected in order to obtain a starting value and the number of partial remainder bits to be examined for digit selection the algorithms for the specific case of radix 4 digit set 2 1 0 1 2 and partial remainder represented in carry save form are derived in order to show that the algorithms introduced can lead to better results than those obtained with algorithms previously presented

injectivity of b spline biquadratic maps abstract the application of isogeometric analysis requires a full parametrization map of the physical domain this map is suitable for the analysis only if it is injective in this paper we give a necessary condition for the injectivity of a b spline biquadratic map moreover sufficient injectivity conditions which are easy to check in the practice are introduced a method for parametrizing planar regions using a biquadratic map is also proposed the method is simpler than others reported in the literature since it is based on the solution of an optimization problem without restrictions and only requires the construction of a quadrilateral mesh with optimal geometric properties finally we show that the proposed method can be successfully used to obtain high quality parametrizations of simply connected planar regions with irregular boundary

three dimensional isogeometrically enriched finite elements for frictional contact and mixed mode debonding abstract we present an isogeometric enrichment technique for three dimensional finite element computations applied to frictional contact and mixed mode debonding this is an extension of previous work that focused on two dimensional and frictionless problems to offer a more complete view of the enriched element s performance a comparison of the results to tri variate isogeometric discretizations and standard lagrangian elements is also included here the enrichment is applied by discretizing parts of the surface that require higher accuracy with isogeometric basis functions while the rest of the body uses lagrangian shape functions by using an isogeometric surface representation the higher continuity across element boundaries and higher order of interpolation can be exploited at the same time the generation of tri variate isogeometric meshes is avoided a convergence study without any surface effects involving only volume integrals shows that the enriched elements can also be beneficial for these problems the major advantage of the isogeometric element enrichment over standard tri linear elements is demonstrated in contact problems including normal and tangential tractions for both mixed mode cohesive debonding and frictional contact the enrichment increases robustness and leads to more accurate results than standard linear lagrangian elements all computations are also compared to results using tri variate isogeometric discretizations to give a complete picture of the element s performance it is also shown that the proposed enrichment formulation has advantages in mesh generation

computing functions cos sup 1 and sin sup 1 using cordic an extension of the cordic coordinate rotation digital computer algorithm that makes it possible to compute the functions cos sup 1 sin sup 1 square root 1 t sup 2 sinh sup 1 cosh sup 1 and square root 1 t sup 2 is presented the algorithms are suitable for vlsi implementation and require only a slight modification of the original cordic algorithm

mapped b spline basis functions for shape design and isogeometric analysis over an arbitrary parameterization abstract it is well known that b spline surfaces are defined by a regular array of control vertices in case of models with arbitrary topology it is extremely difficult to maintain continuity conditions among neighboring surfaces the scenario is also true for applications in isogeometric analysis iga this paper presents a novel method for shape design and isogeometric analysis from a quadrilateral control mesh of arbitrary topology using mapped b spline basis functions based on an arbitrary input quadrilateral control mesh a global parameterization of the final surface is first defined through a gravity center method gcm a re parameterization method is then applied to map a b spline basis function to others that are explicitly defined and are tailored to each of the control vertices which can be either regular or extraordinary ones the final surface is defined by all the input control vertices with their corresponding mapped basis functions for practical implementation the surface can be evaluated patch by patch depending on the order of the b spline basis function used for mapping to others the global continuity of the resulting surface including at extraordinary points can be arbitrary higher order in the present paper a uniform cubic b spline basis function is used and the resulting surface is globally c 2 continuous several numerical examples are provided to demonstrate the proposed method for both shape design and isogeometric analysis

weighted t splines with application in reparameterizing trimmed nurbs surfaces abstract to facilitate isogeometric analysis this paper presents a new type of t spline named the weighted t spline which introduces a new weighting idea to t spline basis functions weighted t spline basis functions satisfy partition of unity and are linearly independent in addition we apply the bicubic weighted t splines to reparameterize trimmed nurbs surface patches edge interval extension is performed to reconstruct the trimming curve on the t spline surface and the trimming curve can be exactly preserved comparisons with standard t splines show that the weighted t splines can decrease the required number of control points and t mesh elements the surface error introduced by weighted t spline basis functions is bounded within 0 5 and the error introduced by the trimming curve is constrained within its three ring neighboring elements weighted t spline models are also applied to solve the linear elasticity problems and poisson s equation demonstrating that they can be used in isogeometric analysis

simultaneous untangling and smoothing of tetrahedral meshes abstract the quality improvement in mesh optimisation techniques that preserve its connectivity are obtained by an iterative process in which each node of the mesh is moved to a new position that minimises a certain objective function the objective function is derived from some quality measure of the local submesh that is the set of tetrahedra connected to the adjustable or free node although these objective functions are suitable to improve the quality of a mesh in which there are non inverted elements they are not when the mesh is tangled this is due to the fact that usual objective functions are not defined on all r 3 and they present several discontinuities and local minima that prevent the use of conventional optimisation procedures otherwise when the mesh is tangled there are local submeshes for which the free node is out of the feasible region or this does not exist in this paper we propose the substitution of objective functions having barriers by modified versions that are defined and regular on all r 3 with these modifications the optimisation process is also directly applicable to meshes with inverted elements making a previous untangling procedure unnecessary this simultaneous procedure allows to reduce the number of iterations for reaching a prescribed quality to illustrate the effectiveness of our approach we present several applications where it can be seen that our results clearly improve those obtained by other authors

x inner automorphisms of semi commutative quantum algebras abstract many important quantum algebras such as quantum symplectic space quantum euclidean space quantum matrices q analogs of the heisenberg algebra and the quantum weyl algebra are semi commutative in addition enveloping algebras u l of even lie color algebras are also semi commutative in this paper we generalize work of montgomery and examine the x inner automorphisms of such algebras the theorems and examples in our paper show that for algebras r of this type the non identity x inner automorphisms of r tend to have infinite order thus if g is a finite group of automorphisms of r then the action of g will be x outer and this immediately gives useful information about crossed products r t g

c2 interpolation t splines abstract in this work we construct a class of c 2 interpolation t spline called it spline basis functions over regular t meshes a new rule for determining the local knot vectors of the it spline basis functions is designed the resulting it spline basis functions are always linearly independent for regular t meshes in order to guarantee the partition of unity and compact support properties of the it spline basis functions several modified schemes are developed an iteration adjustment algorithm for adjusting the points on it spline surface to the targeted points is proposed some applications of the new it spline basis functions in fitting bivariate functions and open 3d meshes solving numerical pdes and iga are given

isogeometric analysis for csg models abstract the iga isogeometric analysis was developed as a bridge between cad and cae with its highly precise geometry representation however iga can only do little with the models that cad systems generated in csg constructive solid geometry manner because the trimmed domain exists this paper presents a method named constructive solid isogeometric analysis csiga to work for csg models that are composed of primitive solids with union subtraction and intersection operators first this work decomposes the csg models into several primitive solids represented by nurbs separately then cuts the primitives with their adjacent ones to produce a set of trimmed tri variable nurbs primitives and finally uses boolean operators to compose them as to the single trimmed solid an integration scheme is presented meanwhile a combination scheme has been developed to deal with the union of multiple trimmed solids by using a mortar method the formulation is verified by applying the isogeometric analysis on several solids which have theoretical solutions such as elliptic cylinder and combined brick and some tests on multiple trimmed solids are done too it is shown that the csiga method can deal with csg models efficiently

iterative superlinear convergence svd beamforming algorithm and vlsi architecture for mimo ofdm systems in this paper we propose a singular value decomposition svd algorithm with superlinear convergence rate which is suitable for the beamforming mechanism in mimo ofdm channels with short coherent time or short training sequence the proposed superlinear convergence svd sl svd algorithm has the following features 1 superlinear convergence rate 2 the ability of being extended smaller numbers of transmit and receive antennas 3 being insensitive to dynamic range problems during the iterative process in hardware implementations and 4 low computational cost we verify the proposed design by using the vlsi implementation with cmos 90 nm technology the post layout result of the design has the feature of 0 48 core area and 18 mw power consumption our design can achieve 7 m channel matrices s and can be extended to deal with different transmit and receive antenna sets

redundant and on line cordic for unitary transformations two sided unitary transformations of arbitrary 2 spl times 2 matrices are needed in parallel algorithms based on jacobi like methods for eigenvalue and singular value decompositions of complex matrices this paper presents a two sided unitary transformation structured to facilitate the integrated evaluation of parameters and application of the typically required transformations using only the primitives afforded by cordic thus enabling significant speedup in the computation of these transformations on special purpose processor array architectures implementing jacobi like algorithms we discuss implementation in nonredundant cordic to motivate and lead up to implementation in the redundant and on line enhancements to cordic both variable and constant scale factor redundant cfr cordic approaches are detailed and it is shown that the transformations may be computed in 10n spl delta time where n is the data precision in bits and spl delta is a constant accounting for accumulated on line delays a more area intensive approach using a novel on line cordic encoded angle summation difference scheme reduces computation time to 6n spl delta the area time complexities involved in the various approaches are detailed

a low latency pipelined 2d and 3d cordic processors the unfolded and pipelined cordic is a high performance hardware element that produces a wide variety of one and two argument functions with high throughput the reduction in delay power and area cost are of significant interest regarding this module due to its high demand for resources the linear approximation to rotation has been proposed to achieve such reductions however the schemes for rotation multiplication and vectoring division complicate the implementation in a single unit in this work we improve the linear approximation scheme leading to a unified implementation for rotation and vectoring where fully parallel tree multipliers are used instead of the second half of cordic iterations we also combine the linear approximation to rotation with the scale factor compensation so that the compensation is concurrently performed with the rotation process we then extend the method to 3d cordic such an extension is not straightforward due to the lack of existing analytical expressions for the convergence of the algorithm a comparison using a rough area time model and synthesis results shows that our proposals may achieve significant reductions in delay with no increase in area in actual implementations

isogeometric triangular bernstein bezier discretizations automatic mesh generation and geometrically exact finite element analysis isogeometric analysis iga was introduced as a way to bypass the design to analysis bottleneck inherent in the traditional computer aided design cad through finite element analysis fea paradigm however an outstanding problem in the field of iga is that of surface to volume parameterization in cad packages solid objects are represented by a collection of nurbs or t spline bounding surfaces but to perform engineering analysis on real world problems we must find a way to parameterize the volumes of these objects as well this has proven to be difficult using traditional iga as the tensor product nature of trivariate nurbs and t splines limit their ability to create analysis suitable parameterizations of arbitrarily complex volumes to overcome the limitations of trivariate nurbs and t splines we propose the use of rational bernstein bezier tetrahedra to create analysis suitable volumetric parameterizations for isogeometric analysis in this paper which is part one of a two part series we present the methodology for discretizing two dimensional geometries using rational bernstein bezier triangles in addition to presenting finite element analysis methodologies based on rational bernstein bezier triangles we also introduce two new mesh generation strategies for automatically creating high quality geometrically exact curvilinear meshes we assess the quality of our mesh generation schemes using a suite of challenging two dimensional geometries and we verify the accuracy of our proposed numerical discretization approach using the method of manufactured solutions

an on line square root algorithm in this correspondence a systematic derivation of an on line square root algorithm is presented the algorithm operates on variables represented in the normalized radix r floating point system in a digit by digit fashion with an on line delay of 1 the approach used in deriving the square root algorithm is described in detail the basic characteristics of hardware level implementation are also discussed

a remark on reducing iteration time when result digit is zero for radix 2 srt division and square root with redundant remainders in a previous paper by p montuschi and l ciminiera ibid vol 42 no 2 p239 246 feb 1993 an architecture for shared radix 2 division and square root has been presented whose main characteristic is the ability to avoid any addition subtraction when the digit 0 has been selected here we emphasize the characteristics of the digit selection mechanism used by montuschi and ciminiera by presenting a small modification of the digit selection hardware which has the benefit to further reduce the computation delay with respect to the time estimated in that work

x inner automorphisms of enveloping rings abstract in this paper we determine the x inner automorphisms of the smash product r u l of a prime ring r by the universal enveloping algebra u l of a characteristic 0 lie algebra l specifically we show that any such automorphism stabilizing r can be written as a product 1 2 where 1 is induced by conjugation by a unit of q3 r the symmetric martindale ring of quotients of r and 2 is induced by conjugation by a unit of q3 t here s ql r is the left martindale ring of quotients of r and t is the centralizer of s in s u l r u l one of the subtleties of the proof is that we must work in several unrelated overrings of r u l

redundant and on line cordic application to matrix triangularization and svd several modifications to the cordic method of computing angles and performing rotations are presented 1 the use of redundant carry free addition instead of a conventional carry propagate one 2 a representation of angles in a decomposed form to reduce area and communication bandwidth 3 the use of on line addition left to right digit serial addition to replace shifters by delays and 4 the use of online multiplication square root and division to compute scaling factors and perform the scaling operations the modifications improve the speed and the area of cordic implementations the proposed scheme uses efficiently floating point representations the application of the modified cordic method to matrix triangularization by givens rotations and to the computation of the singular value decomposition svd are discussed

a unified and division free cordic argument reduction method with unlimited convergence domain including inverse hyperbolic functions one of the main problems of the cordic algorithm is the limited convergence domain in which the functions can be calculated two different approaches can be employed to overcome this constraint first an argument reduction method and second an expansion of the cordic convergence domain while the first approach requires significant processing overhead due to the need for divisions especially for tanh sup 1 the second technique achieves an increased but still limited convergence domain only in this brief contribution we present a unified division free argument reduction method and a regular pipeline array architecture for floating point or fixed point implementations which results in savings of computation time in contrast to previous methods we avoid extra cordic arithmetic for realization of argument reduction

parametric mesh regularization for interpolatory shape design and isogeometric analysis over a mesh of arbitrary topology abstract isogeometric analysis iga over a mesh of arbitrary topology is a challenging task since the concept of iga was proposed in the literature one can find some results in iga over an irregular mesh based on approximating schemes while little work is reported so far using interpolatory schemes this paper presents a parametric mesh regularization pmr method for iga using mapped interpolatory basis functions over a mesh of arbitrary topology given a geometric model defined over a mesh of arbitrary topology a global parametric mesh is first defined from the given control mesh using a gravity center method gcm yuan and ma 2014 the resulting parametric mesh is further regularized such that it ensures absolute interpolatory modeling with mapped interpolatory basis functions necessary geometric rules are developed for the regularization process while maintaining the same mesh topological structure the interpolatory basis function used in this paper is a kind of truncated interpolatory basic function tibf studied in our early work yuan and ma 2013 it can also be applied to other mapped interpolatory basis functions in addition to the capability of interpolatory modeling the proposed pmr method can also be applied to approximating schemes which further enriches the capability of such schemes in both modeling and isogeometric analysis of some models in a more appropriate and convenient manner the proposed pmr method has also the potential in achieving higher order continuity at extraordinary vertices using higher order mapped interpolatory basis functions

higher radix square root with prescaling a scheme for performing higher radix square root based on prescaling of the radicand is presented to reduce the complexity of the result digit selection the scheme requires several steps namely multiplication for prescaling the radicand square root multiplication for prescaling for the division and division online algorithms are used to reduce the overall time and pipelining to reuse the different modules an estimate of the execution time for a radix 256 unit for double precision square root and a comparison with other implementations indicate that the proposed approach is an alternative to consider when designing a square root unit

a new approach to solid modeling with trivariate t splines based on mesh optimization abstract we present a new method to construct a trivariate t spline representation of complex genus zero solids for the application of isogeometric analysis the proposed technique only demands a surface triangulation of the solid as input data the key of this method lies in obtaining a volumetric parameterization between the solid and the parametric domain the unitary cube to do that an adaptive tetrahedral mesh of the parametric domain is isomorphically transformed onto the solid by applying a mesh untangling and smoothing procedure the control points of the trivariate t spline are calculated by imposing the interpolation conditions on points sited both on the inner and on the surface of the solid the distribution of the interpolating points is adapted to the singularities of the domain in order to preserve the features of the surface triangulation

parallel singular value decomposition of complex matrices using multidimensional cordic algorithms the singular value decomposition svd of complex matrices is computed in a highly parallel fashion on a square array of processors using kogbetliantz s analog of jacobi s eigenvalue decomposition method to gain further speed new algorithms for the basic svd operations are proposed and their implementation as specialized processors is presented the algorithms are 3 d and 4 d extensions of the cordic algorithm for plane rotations when these extensions are used in concert with an additive decomposition of 2 spl times 2 complex matrices which enhances parallelism and with low resolution rotations early on in the svd process which reduce operation count a fivefold speedup can be achieved over the fastest alternative approach

isogeometric analysis suitable trivariate nurbs models from standard b rep models abstract this paper presents an effective method to automatically construct trivariate spline models of complicated geometry and arbitrary topology required for nurbs based isogeometric analysis the input is a triangulation of the solid model s boundary the boundary surface is decomposed into a set of cuboids in two steps pants decomposition and cuboid decomposition the novelty of our method is the pants to cuboids decomposition algorithm the algorithm is completely automatic and very robust even for low quality and noisy meshes the set of cuboids composes a generalized polycube approximating very roughly the input model s geometry while faithfully replicating its topology due to its regular structure the polycube is suitable for serving as the parametric domain for the tensor product spline representation based on a discrete harmonic mapping between the cuboids boundary and the polycube s boundary surface and volume parameterizations are generated in order to fit the trivariate splines the efficiency and the robustness of the proposed approach are illustrated by several examples

actions of divided power hopf algebras abstract we study prime ideals in enveloping algebra smash products and use a duality construction to obtain results on prime ideals in rings on which divided power hopf algebras act these actions correspond to higher derivations first we consider chains of prime ideals in an enveloping algebra smash product over an arbitrary ring where the lie algebra is assumed to be finite dimensional abelian over a field of positive characteristic we give a bound on the length of such a chain where the ideals all have the same intersection with the coefficient ring then using an explicit construction of a duality theorem of blattner and montgomery in this context we are able to apply results on enveloping algebra smash products to study the invariant ideals of prime ideals in a ring under a locally nilpotent divided power hopf algebra action

classical localizability in solvable enveloping algebras and poincare birkhoff witt extensions abstract in several classes of noncommutative noetherian rings jategaonkar s intersection conditions are verified for finite unions of cliques of prime ideals and it follows that these finite unions of cliques are classically localizable if they satisfy incomparability among the rings in question are the enveloping algebra of any finite dimensional solvable lie algebra g over any field k of characteristic zero any twisted smash product r u g where r is a commutative noetherian k algebra and g acts on r via k linear derivations and certain iterated differential operator rings over r in contrast to previously verified cases k is allowed to be countable one tool used here a lying over theorem for cliques has some independent interest namely if r s is a flat finite centralizing extension of noetherian rings satisfying the second layer condition and if x is a clique in spec r there exists a clique y in spec s such that p r p y x

prime ideals in differential operator rings and crossed products of infinite groups abstract we use a version of the martindale ring of quotients to study prime ideals in extensions of a ringr corresponding to two cases ifg is a group of automorphisms ofr we form the crossed product r g if g is a lie algebra of derivations of r we have the twisted differential operator ring denoted byr g sometimes known as the twisted smash product r t u g we obtain analogues of incomparability for crossed products of nilpotent groups and differential operator rings of solvable lie algebras in the case of crossed products the incomparability result of d s passman and m lorenz for the infinite cyclic group also proved by g bergman is generalized

linear independence of the t spline blending functions associated with some particular t meshes based on the local refinement algorithm addressed in sederberg et al 2004 17 we analyze the linear independence of the bi cubic t spline blending functions corresponding to particular t meshes

efficient construction of multi block volumetric spline parameterization by discrete mask method isogeometric analysis attempts to unify the mathematical languages in design and analysis to realize the seamless integration of cad and cae in three dimensional isogeometric analysis parametric volume is employed as the computational domain for a given set of boundary information in this paper we propose a discrete mask method for the efficient construction of multi block volumetric parameterization based on a set of given boundary spline surfaces given the block partition information of a model the interior control points can be obtained efficiently by solving a sparse linear system the existence and uniqueness of the solution for the linear system are also proved after performing a pre process on the non compatible boundary surfaces the discrete coons mask is generalized to a unified form which provides more choices for the construction of inner control points the proposed method is not only suitable for the multi block case with c 1 continuity but can also be used for the case in which the boundary surfaces are of different degrees and with different number of control points and knot vectors several examples are presented to illustrate the effectiveness of the proposed method

discrete basis and computation of elementary functions we give necessary and sufficient conditions in order that the infinite product or sum of the terms of a positive decreasing sequence generates the reals in a given interval

efficient r adaptive isogeometric analysis with winslow s mapping and monitor function approach abstract motivated by the moving mesh method in conventional finite element analysis in this paper we propose an r adaptive isogeometric analysis framework by winslow s mapping and monitor function approach we construct a new monitor function based on the absolute curvature metric of the isogeometric solution surface in the proposed r adaptive framework the redistribution of the inner control points is performed to increase the density of control points in the regions where curvature based or error based monitor functions are maximum the new locations of the inner control points are obtained by solving governing pdes using isogeometric collocation method which is more efficient in solving large scale problems by employing winslow s mapping we ensure that the generated r adaptive parameterization is valid for isogeometric analysis and can be used as optimal initial grid for subsequent h refinements multiple two dimensional heat conduction examples are solved which confirm the effectiveness of the proposed method

sparse iteration 4d cordic algorithms for multiplying quaternions novel 4d cordic algorithms and hardware architecture for multiplying quaternions are presented aimed at constant coefficient multipliers in our solution microrotations are multiplications by hypercomplex numbers with only one non zero imaginary part such transformations can be described using sparse matrices and implemented using less hardware resources than the iteration of the known quaternion cordic algorithm chip area can be saved because sparse microrotations can be computed using a permutation network and two operand adders without four operand additions which are necessary in the known solution the obtainable area savings depend on the implementation technology and the architectures of adders and bit shifters but can be as large as 45 and 25 percent for asic and fpga circuits respectively the circuitry simplifications come at the cost of slowing down computations our approach improves the area delay product and a single sparse iteration can be executed up to 15 percent faster than the conventional one but more microrotations are usually necessary to achieve the required accuracy on the other hand a sparse 4d iteration can be identified with microrotations of two 2d cordics which work in parallel this makes convergence analysis easier than in the previous 4d solution as it is sufficient to consider only two dimensions

prime ideals in enveloping rings let l be a lie algebra over the field k of characteristic 0 and let u l denote its universal enveloping algebra if r is a k algebra and l acts on r as derivations then there is a natural ring generated by r and u l which is denoted by r u l and called the smash product of r by u l the aim of this paper is to describe the prime ideals of this algebra when it is noetherian specifically we show that there exists a twisted enveloping algebra u x on which l acts and a precisely defined one to one correspondence between the primes p of r u l with p n r 0 and the l stable primes of u x here x is a lie algebra over some field c 2 k let l be a lie algebra over the field k and let u l denote its universal envelop ing algebra if r is a k algebra and l acts on r as derivations then this action determines in a natural manner a ring generated by rand u l which is denoted by r u l and called the smash product of r by u l the aim of this paper is to study the prime ideals p of r u l disjoint from r that is with p n r o the main result here describes these primes when char k 0 and r u l is right noetherian when dealing with smash products it is frequently necessary to study more general objects for example if x is a lie ideal of l then r u l is determined by its subalgebra r u x and the quotient u lj x indeed

an interactive geometry modeling and parametric design platform for isogeometric analysis in this paper an interactive parametric design through analysis platform is proposed to help design engineers and analysts make more effective use of isogeometric analysis iga to improve their product design and performance we develop several rhinoceros rhino plug ins to take input design parameters through a user friendly interface generate appropriate surface and or volumetric models perform mechanical analysis and visualize the solution fields all within the same computer aided design cad program as part of this effort we propose and implement graphical generative algorithms for iga model creation and visualization based on grasshopper a visual programming interface to rhino the developed platform is demonstrated on two structural mechanics examples an actual wind turbine blade and a model of an integrally bladed rotor ibr in the latter example we demonstrate how the rhino functionality may be utilized to create conforming volumetric models for iga

closed and prime ideals in free centred extensions prime ideals in ring extensions r g s have extensively been studied in the last years for example when the extension s is finite and generated by a set of r centralizing elements s is called a liberal extension 15 161 a normalizing extension is again a finite extension which is generated by a set of r normalizing elements e g 8 121 also prime ideals in more general types of extensions not necessarily finite have been considered e g l 2 13 141 on the other hand the author in 4 studied prime ideals in polynomial rings r x actually a more general class of ideals called the principal closed ideals are defined and considered in 4 and the results on prime ideals are obtained as applications of the general results a main tool in that paper is the representation of closed ideals by using manic polynomials in c x where c is the extended centroid of the prime ring r closed ideals have also been used to study prime ideals in ore extensions c3 61 the purpose of this paper is to extend the results in 4 to free centred extensions the ring s is said to be a free centred extension of r if s is free as an r module and there exists a basis e ei rer of r centralizing elements such that the common identity 1 of r and s is in e there are several usual examples of free centred extensions namely a group or even a semigroup ring rg in particular a polynomial ring in any set of either commuting or non commuting indeterminates also a matrix ring even a ring of infinite matrices provided that every matrix in the ring has a finite number of non zero entries and the identity is adjoined finally a tensor product s r gl k where l is a field and r and k are l algebras

solid t spline construction from boundary representations for genus zero geometry abstract this paper describes a novel method to construct solid rational t splines for complex genus zero geometry from boundary surface triangulations we first build a parametric mapping between the triangulation and the boundary of the parametric domain a unit cube after that we adaptively subdivide the cube using an octree subdivision project the boundary nodes onto the input triangle mesh and at the same time relocate the interior nodes via mesh smoothing this process continues until the surface approximation error is less than a pre defined threshold t mesh is then obtained by pillowing the subdivision result one layer on the boundary and its quality is improved templates are implemented to handle extraordinary nodes and partial extraordinary nodes in order to get a gap free t mesh the obtained solid t spline is c 2 continuous except for the local region around each extraordinary node and partial extraordinary node the boundary surface of the solid t spline is c 2 continuous everywhere except for the local region around the eight nodes corresponding to the eight corners of the parametric cube finally a bezier extraction technique is used to facilitate t spline based isogeometric analysis the obtained bezier mesh is analysis suitable with no negative jacobians several examples are presented in this paper to show the robustness of the algorithm

computing the symmetric ring of quotients abstract we discuss and compute the symmetric martindale ring of quotients for various classes of prime rings in particular we consider free algebras and group algebras

algebraic mesh quality metrics quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics the theory based on the jacobian and related matrices provides a means of constructing classifying and evaluating mesh quality metrics the jacobian matrix is factored into geometrically meaningful parts a nodally invariant jacobian matrix can be defined for simplicial elements using a weight matrix derived from the jacobian matrix of an ideal reference element scale and orientation invariant algebraic mesh quality metrics are defined the singular value decomposition is used to study relationships between metrics equivalence of the element condition number and mean ratio metrics is proved the condition number is shown to measure the distance of an element to the set of degenerate elements algebraic measures for skew length ratio shape volume and orientation are defined abstractly with specific examples given two combined metrics shape volume and shape volume orientation are algebraically defined and examples of such metrics are given algebraic mesh quality metrics are extended to nonsimplicial elements a series of numerical tests verifies the theoretical properties of the metrics defined

ideals and quotients in crossed products of hopf algebras let h be a hopf algebra over a field k acting on the k algebra r with action twisted by a cocycle t such that the crossed product algebra r h can be constructed this paper is concerned with the relationship between the ideals of r hand those of r and with computing the extended cen ter and symmetric quotient ring of r h in terms of the extended center c and symmetric quotient ring q of r our best results are obtained when h is an irreducible hopf algebra or more generally when h is of the form k kg where k is irreducible and kg is the group algebra of a group g some examples of irreducible hopf algebras are enveloping algebras of lie algebras u l along with their restricted counterparts u l in characteristic

parallel vlsi matrix pencil algorithm for high resolution direction finding algorithms to find the directions of arrival doas of multiple signals from measurements on an array of antenna doublets esprit method and their parallel vlsi implementation are discussed in particular algorithms that allow large scale pipelining and use only robust unitary transformations are identified this problem is solved by a matrix pencil approach in which the generalized eigenvalues of a pair of data matrices are determined a modified stewart jacobi approach is used for which convergence is improved and parameter computations are simplified the resulting architecture is a two layer jacobi array that can handle all the subproblems two qr factorizations two svds and a single generalized schur decomposition the mapping of the subproblems on a single parallel array of cordic processors is considered

spline parameterization method for 2d and 3d geometries based on t mesh optimization abstract we present a method to obtain high quality spline parameterization of 2d and 3d geometries for their use in isogeometric analysis as input data the proposed method demands a boundary representation of the domain and it constructs automatically a spline transformation between the physical and parametric domains parameterization of the interior of the object is obtained by deforming isomorphically an adapted parametric t mesh onto the physical domain by applying a t mesh untangling and smoothing procedure which is the key of the method mesh optimization is based on the mean ratio shape quality measure the spline representation of the geometry is calculated by imposing interpolation conditions using the data provided by one to one correspondence between the meshes of the parametric and physical domains we give a detailed description of the proposed technique and show some examples also we present some examples of the application of isogeometric analysis in geometries parameterized with our method

error analysis and reduction for angle calculation using the cordic algorithm in this paper we consider the errors appearing in angle computations with the cordic algorithm circular and hyperbolic coordinate systems using fixed point arithmetic we include errors arising not only from the finite number of iterations and the finite width of the data path but also from the finite number of bits of the input we show that this last contribution is significant when both operands are small and that the error is acceptable only if an input normalization stage is included making unsatisfactory other previous proposals to reduce the error we propose a method based on the prescaling of the input operands and a modified cordic recurrence and show that it is a suitable alternative to the input normalization with a smaller hardware cost this solution can also be used in pipelined architectures with redundant carry save arithmetic

calf a cordic adaptive lattice filter calf is a cordic processor implementation of the adaptive lattice filter unlike previously reported results which simply use the cordic processor to implement the lattice algorithm formulated for conventional multiply and accumulate type arithmetic units a novel adaptive normalized lattice algorithm which directly updates the rotation angles rather than the reflection coefficients is reported thus this angle updating lattice algorithm is derived specifically for implementation with a vlsi cordic processor moreover this algorithm was further modified to a sign sign algorithm to take advantage of the fact that the cordic processors only rotate a finite number of distinct rotation angles computer simulation results showed good converging properties even at rather coarsely quantized angles

constructing iga suitable planar parameterization from complex cad boundary by domain partition and global local optimization abstract in this paper we propose a general framework for constructing iga suitable planar b spline parameterizations from given complex cad boundaries instead of the computational domain bounded by four b spline curves planar domains with high genus and more complex boundary curves are considered firstly some pre processing operations including bezier extraction and subdivision are performed on each boundary curve in order to generate a high quality planar parameterization then a robust planar domain partition framework is proposed to construct high quality patch meshing results with few singularities from the discrete boundary formed by connecting the end points of the resulting boundary segments after the topology information generation of quadrilateral decomposition the optimal placement of interior bezier curves corresponding to the interior edges of the quadrangulation is constructed by a global optimization method to achieve a patch partition with high quality finally after the imposition of c 1 g 1 continuity constraints on the interface of neighboring bezier patches with respect to each quad in the quadrangulation the high quality bezier patch parameterization is obtained by a local optimization method to achieve uniform and orthogonal iso parametric structures while keeping the continuity conditions between patches the efficiency and robustness of the proposed method are demonstrated by several examples which are compared to results obtained by the skeleton based parameterization approach

simplification of surface mesh using hausdorff envelope this paper presents a new method for surface mesh simplification given an initial surface mesh denoted as reference mesh the goal is to reduce the number of mesh elements while preserving the geometric approximation as well as the shape quality of the resulting mesh two tolerance areas with respect to the reference mesh have been introduced to preserve the geometry of the surface the reference mesh is then simplified and optimized in terms of shape quality so that the resulting mesh belongs to these tolerance areas several examples of surface meshes are provided regarding different application areas in order to assess the efficiency of the simplification method

the extended centroid and x inner automorphisms of ore extensions for the ore extension r t s d where r is a prime ring we determine the center the extended centroid and the x inner automorphisms the results depend on the structure of ideals of r t s d

square rooting algorithms for high speed digital circuits two binary algorithms for the square rooting of a number or of a sum of two numbers are presented they are based on the classical nonrestoring method the main difference lies in the replacement of subtractions and additions by a parallel reduction f three summands which may be positive and negative to two summands to eliminate the carry propagation two of three summands form the successive partial remainder their most significant bit triples sometimes together with a sign bit of the earlier partial remainder are used to determine digits 1 0 1 of a redundant square root notation these digits are transformed during the square rooting process into the conventional notation square root bits which are next used in further square rooting steps to form the third reduced summands

triangular processor array for computing singular values a triangular processor array for computing the singular values of an m n m n matrix is proposed a jacobi type algorithm is used to first triangularize the given matrix and then diagonalize the resultant triangular form the requirements are 14n2 o n processors and o m ns time where s denotes the number of sweeps the triangular array can be extended to a rectangular one with 12mn o m processors for the computational of singular vectors

constructing analysis suitable parameterization of computational domain from cad boundary by variational harmonic method in isogeometric analysis parameterization of computational domain has great effects as mesh generation in finite element analysis in this paper based on the concept of harmonic mapping from the computational domain to parametric domain a variational harmonic approach is proposed to construct analysis suitable parameterization of computational domain from cad boundary for 2d and 3d isogeometric applications different from the previous elliptic mesh generation method in finite element analysis the proposed method focuses on isogeometric version and converts the elliptic pde into a nonlinear optimization problem in which a regular term is integrated into the optimization formulation to achieve more uniform and orthogonal iso parametric structure near convex concave parts of the boundary several examples are presented to show the efficiency of the proposed method in 2d and 3d isogeometric analysis

strong multipatch c1 coupling for isogeometric analysis on 2d and 3d domains abstract the solution spaces of isogoemetric analysis iga constructed from p degree basis functions allow up to c p 1 continuity within one patch however for a multi patch domain the continuity is only c 0 at the boundaries between the patches in this study we present the construction of basis functions of degree p 2 which are c 1 continuous across the common boundaries shared by the patches the new basis functions are computed as a linear combination of the c 0 basis functions on the multi patch domains an advantage of the proposed method is that for the new basis functions the continuity within a patch is preserved without additional treatment of the functions in the interior of the patch we apply continuity constraints to the new basis functions to enforce c 1 continuity where the constraints are developed according to the concept of matched g k constructions always yield c k continuous isogeometric elements discussed in groisser and peters 2015 however for certain geometries the over constrained solution space will lead to c 1 locking collin and sangalli 2016 we discuss and show the usage of partial degree elevation to overcome this problem we demonstrate the potential of the c 1 basis functions for iga applications through several examples involving biharmonic equations