geometric conditions of non self intersecting nurbs surfaces nurbs surface is very useful in geometric modeling animation image morphing and deformation constructing non self intersecting injective nurbs surfaces is an important process in surface and solid modeling in this paper the injective conditions of tensor product nurbs surface are studied based on the geometric positions of control points which are equivalent to the surface to be non self intersecting for all positive weights finally some representative examples are provided

a general mass conservative numerical solution for the unsaturated flow equation numerical approximations based on different forms of the governing partial differential equation can lead to significantly different results for unsaturated flow problems numerical solution based on the standard h based form of richards equation generally yields poor results characterized by large mass balance errors and erroneous estimates of infiltration depth conversely numerical solutions based on the mixed form of richards equation can be shown to possess the conservative property so that mass is perfectly conserved this leads to significant improvement in numerical solution performance while requiring no additional computational effort however use of the mass conservative method does not guarantee good solutions accurate solution of the unsaturated flow equation also requires use of a diagonal time or mass matrix only when diagonal time matrices are used can the solution be shown to obey a maximum principle which guarantees smooth nonoscillatory infiltration profiles this highlights the fact that proper treatment of the time derivative is critical in the numerical solution of unsaturated flow

systolic arrays for the discrete hartley transform recently r n bracewell 1983 introduced the discrete hartley transform dht as an alternative to the discrete fourier transform dft two linear systolic array models for the dht are derived one model requires o 2n 1 in the computational phase and o n in the preloading phase the other model requires o 2n 1 in the computational phase and o n in the output phase a square systolic array for two dimensional dht is also constructed by combining the individual advantages of each model the cordic algorithm is proposed as an alternative to conventional multipliers to speed up the systolic array two level pipelining with cordic is also possible

on computing the split radix fft this paper presents an efficient fortran program that computes the duhamel hollmann split radix fft an indexing scheme is used that gives a three loop structure for the split radix fft that is very similar to the conventional cooley tukey fft both a decimation in frequency and a decimation in time program are presented an arithmetic analysis is made to compare the operation count of the cooley tukey fft fo several different radixes to that of the split radix fft the split radix fft seems to require the least total arithmetic of any power of two dft algorithm

monotonicity considerations for saturated unsaturated subsurface flow it is demonstrated that monotonicity is a sufficient condition to ensure that no new nonphysical local maxima and minima can be produced in the discrete nonlinear unsaturated flow equation monotonicity conditions are derived for various types of weighting for the mobility term the basic discretization is of finite element type but the results can be extended to finite volume discretizations central weightings are only conditionally monotone while upstream weightings are unconditionally monotone sample computations are given for highly heterogeneous problems

estimation of finite difference interblock conductivities for simulation of infiltration into initially dry soils simulations of transient unsaturated vertical flow in different initially dry homogeneous soils using richards equation suggest that for a relatively coarse numerical grid there is no universal weighting scheme to estimate interblock conductivities capable of giving an accurate resolution of the resulting steep wetting fronts except for the scheme associated with the kirchhoff transformation kt the principal drawback of kt is that it can hardly be applied to heterogeneous soils a new asymptotic weighting aw scheme based on the asymptotic behavior of the hydraulic conductivity function in the vicinity of residual saturation is proposed numerical tests demonstrate that the aw scheme describes wetting fronts in homogeneous soils nearly as accurately as a scheme based on kt applicability and robustness of the aw scheme for simulating water infiltration into heterogeneous soils having substantial vertical variation of hydraulic properties are also demonstrated extension of the proposed scheme to higher dimensions is straightforward

on monotonicity of difference schemes for computational physics criteria are developed for monotonicity of linear as well as nonlinear difference schemes associated with the numerical analysis of systems of partial differential equations integrodifferential equations etc difference schemes are converted into variational forms that satisfy the boundary maximum principle and also allow the investigation of monotonicity for nonlinear operators using linear patterns sufficient conditions are provided to review the monotonicity of single and coupled difference schemes necessary as well as necessary and sufficient conditions for monotonicity of explicit schemes are also developed the notion of submonotone difference schemes is considered and the associated criteria are developed we discuss the interrelationship between monotonicity submonotonicity and stability some known schemes serve as examples demonstrating the implementation of the developed approaches among these examples we describe the possibility that stable schemes such as total variation diminishing tvd as well as monotonicity preserving can produce spurious oscillations

three dimensional simulation of unstable gravity driven infiltration of water into a porous medium infiltration of water in dry porous media is subject to a powerful gravity driven instability although the phenomenon of unstable infiltration is well known its description using continuum mathematical models has posed a significant challenge for several decades the classical model of water flow in the unsaturated flow the richards equation is unable to reproduce the instability here we present a computational study of a model of unsaturated flow in porous media that extends the richards equation and is capable of predicting the instability and captures the key features of gravity fingering quantitatively the extended model is based on a phase field formulation and is fourth order in space the new model poses a set of challenges for numerical discretizations such as resolution of evolving interfaces stiffness in space and time treatment of singularly perturbed equations and discretization of higher order spatial partial differential operators we develop a numerical algorithm based on isogeometric analysis a generalization of the finite element method that permits the use of globally smooth basis functions leading to a simple and efficient discretization of higher order spatial operators in variational form we illustrate the accuracy efficiency and robustness of our method with several examples in two and three dimensions in both homogeneous and strongly heterogeneous media we simulate for the first time unstable gravity driven infiltration in three dimensions and confirm that the new theory reproduces the fundamental features of water infiltration into a porous medium our results are consistent with classical experimental observations that demonstrate a transition from stable to unstable fronts depending on the infiltration flux

the vector split radix algorithm for 2d dht a decimation in frequency vector split radix algorithm is proposed to decompose an n n 2d discrete hartley transform dht into one n 2 n 2 dht and twelve n 4 dhts the proposed algorithm possesses the in place property and needs no matrix transpose its computational structure is very regular and is simpler than those of all existing nonseparable 2d dhts

non standard shocks in the buckley leverett equation abstract it is shown how delta shock waves which consist of dirac delta distributions and classical shocks can be used to construct non monotone solutions of the buckley leverett equation these solutions are interpreted using a recent variational definition of delta shock waves in which the rankine hugoniot deficit is explicitly accounted for 6 the delta shock waves are also limits of approximate solutions constructed using a recent extension of the weak asymptotic method to complex valued approximations 15 finally it is shown how these non standard shocks can be fitted together to construct similarity and traveling wave solutions which are non monotone but still admissible in the sense that characteristics either enter or are parallel to the shock trajectories

injectivity of nurbs curves the injectivity of nurbs curve implies the curve has no self intersection in this paper we propose a geometric condition on the control polygon which guarantees the nurbs curve to be injective for all possible choices of positive weights the proof is based on the degree elevation algorithm and toric degeneration theory of nurbs curve

improved fourier and hartley transform algorithms application to cyclic convolution of real data this paper highlights the possible tradeoffs between arithmetic and structural complexity when computing cyclic convolution of real data in the transform domain both fourier and hartley based schemes are first explained in their usual form and then improved either from the structural point of view or in the number of operations involved namely we first present an algorithm for the in place computation of the discrete fourier transform on real data a decimation in time split radix algorithm more compact than the previously published one second we present a new fast hartley transform algorithm with a reduced number of operations a more regular convolution scheme based on fft s is also proposed finally we show that hartley transforms belong to a larger class of algorithms characterized by their generalized convolution property

implementation of split radix fft algorithms for complex real and real symmetric data a new algorithm is presented for the fast computation of the discrete fourier transform this algorithm belongs to that class of recently proposed 2n fft s which present the same arithmetic complexity the lowest among any previously published one moreover this algorithm has the advantage of being performed in place by repetitive use of a butterfly type structure without any data reordering inside the algorithm furthermore it can easily be applied to real and real symmetric data with reduced arithmetic complexity by removing all redundancy in the algorithm

on the incompatibility of richards equation and finger like infiltration in unsaturated homogeneous porous media 1 it is demonstrated by means of a mathematical proof that richards equation in principle cannot admit finger like solutions for three dimensional homogeneous unsaturated porous media flow subject to monotone boundary conditions this is demonstrated for any reasonable type of homogeneous porous material the result is not dependent on any particular form of the hydraulic conductivity or the retention curve moreover it is explained why hysteresis of the retention curve does not play any role in the proof consequently the proof is true for any type of hysteretic behavior of the retention curve an alternative approach to finger flow modeling is discussed which uses the ideas of cellular automata

development and evaluation of closed form expressions for hysteretic soil hydraulic properties a concise representation of hysteretic soil hydraulic properties is given based on a combination of m t van genuchten s 1980 parametric k h model and p s scott et al s 1983 empirical hysteresis model modified to account for air entrapment the resulting model yields compact closed form expressions for the hysteretic water retention curve h and soil water capacity c h as well as for the hydraulic conductivity function k h depending on the degree of simplification involved the model entails a total of 6 9 parameters which can be calibrated from direct measurements of h and saturated conductivity or by an inverse solution approach from transient flow experiments comparison of model predicted and measured k h relations for eight soils revealed one case in which model predictions were very poor model accuracy was judged to be acceptably good in the other cases mualern s modified y mualem 1984 dependent domain model was found to be more accurate for soils with very narrow pore size distributions use of a simplified version of the proposed model with two parameters eliminated provided overall accuracy very similar to that of the more complex model numerical simulations of flow during transient infiltration and drainage using the proposed model and a variant of y mualem s 1984 modified dependent domain model did not differ greatly and agreed reasonably well with experimental water content distributions even when scanning curves were not described very accurately by contrast simulations without consideration of hysteresis produced highly unacceptable results it is concluded that the proposed model provides a convenient and simple means of incorporating hysteretic effects into numerical flow models to provide significant improvement in prediction accuracy with little additional effort and with minimal data requirements

an improved algorithm for checking the injectivity of 2d toric surface patches abstract injective parametrizations are widely used both in theory and in applications the injectivity of parameteric curves and surfaces means that there are no self intersections toric surface patch is defined by a set of integer lattice points a and corresponding control points and weights which includes rational tensor product and triangle bezier patches as special cases in 2011 sottile and zhu presented a geometric method to check the injectivity of 2d toric surface patches in this paper we present an improved algorithm of their method the complexity of the improved algorithm is reduced from o n 3 to o n 2 where n a some examples are shown to illustrate the effectiveness of our algorithm moreover the algorithm is also applied to check the injectivity of parameterization in isogeometric analysis

on computing the discrete hartley transform the discrete hartley transform dht is a real valued transform closely related to the dft of a real valued sequence bracewell has recently demonstrated a radix 2 decimation in time fast hartley transform fht algorithm in this paper a complete set of fast algorithms for computing the dht is developed including decimation in frequency radix 4 split radix prime factor and winograd transform algorithms the philosophies of all common fft algorithms are shown to be equally applicable to the computation of the dht and the fht algorithms closely resemble their fft counterparts the operation counts for the fht algorithms are determined and compared to the counts for corresponding real valued fft algorithms the fht algorithms are shown to always require the same number of multiplications the same storage and a few more additions than the real valued fft algorithms even though computation of the fht takes more operations in some situations the inherently real valued nature of the discrete hartley transform may justify this extra cost

systolic architectures for the computation of the discrete hartley and the discrete cosine transforms based on prime factor decomposition two dimensional systolic array implementations for computing the discrete hartley transform dht and the discrete cosine transform dct when the transform size n is decomposable into mutually prime factors are proposed the existing two dimensional formulations for dht and dct are modified and the corresponding algorithms are mapped into two dimensional systolic arrays the resulting architecture is fully pipelined with no control units the hardware design is based on bit serial left to right msb most significant bit to lsb least significant bit binary arithmetic

numerical investigations of two phase flow with dynamic capillary pressure in porous media via a moving mesh method abstract motivated by observations of saturation overshoot this paper investigates numerical modeling of two phase flow in porous media incorporating dynamic capillary pressure the effects of the dynamic capillary coefficient the infiltrating flux rate and the initial and boundary values are systematically studied using a traveling wave ansatz and efficient numerical methods the traveling wave solutions may exhibit monotonic non monotonic or plateau shaped behavior special attention is paid to the non monotonic profiles the traveling wave results are confirmed by numerically solving the partial differential equation using an accurate adaptive moving mesh solver comparisons between the computed solutions using the brooks corey model and the laboratory measurements of saturation overshoot verify the effectiveness of our approach

fingered flow in two dimensions 2 predicting finger moisture profile an exact integral solution for the moisture profile in growing fingers in sandy soil is derived from richards equation the solution provides moisture content along a finger as a function of position and time and provides applicable results including the calculation of the asymptotic mattic potential of a growing finger and a method of obtaining the unsaturated conductivity in a single experiment the solution is verified experimentally through comparison with measurements of matric potential and moisture content using high speed tensiometers

comment on on the continuum scale modeling of gravity driven fingers in unsaturated porous media the inadequacy of the richards equation with standard monotonic constitutive relations and hysteretic equations of state authors reply citation deinert m j y parlange k b cady t s steenhuis and j s selker comment on on the continuum scale modeling of gravity driven fingers in unsaturated porous media the inadequacy of the richards equation with standard monotonic constitutive relations and hysteretic equations of state by mehdi eliassi and robert j glass water resour res 39 9 1263 doi 10 1029 2002wr001785 2003

on the continuum scale modeling of gravity driven fingers in unsaturated porous media the inadequacy of the richards equation with standard monotonic constitutive relations and hysteretic equations of state we consider the ability of the continuum scale richards equation re with standard monotonic constitutive relations and hysteretic equations of state to model gravity driven fingers in unsaturated porous media and in particular the underlying nonmonotonicity observed along the vertical extent of fingers as published in a number of recent papers finger like solutions with nonmonotonic profiles can be simulated numerically using a downwind averaging method however we find these fingers to be artifacts generated by the combined effects of a truncation error induced oscillation or oversaturation at the wetting front and capillary hysteresis as the oscillation is removed either through grid refinement or the use of inherently monotone schemes the numerically generated fingers disappear and the solution becomes monotonic thus the re along with standard monotonic hydraulic properties does not contain the critical physics required to model gravity driven fingers and must be considered inadequate for unsaturated flow in initially dry highly nonlinear and hysteretic media where these fingers occur

an efficient design for one dimensional discrete hartley transform using parallel additions this paper presents a new efficient design for the one dimensional 1 d any length discrete hartley transform dht using a similar idea to the chirp z transform an algorithm that can formulate the 1 d any length dht as cyclic convolutions is developed this algorithm has higher flexibility in the transform length as compared with the existing approaches for prime length dht or power of two dht designs moreover the proposed design exploits the cyclic convolution and uses parallel adders instead of multipliers in the hardware realization the presented design not only possesses low hardware cost but also has low input output i o cost high computing speeds and flexibility in transform length

adaptive rational spectral methods for the linear stability analysis of nonlinear fourth order problems this paper presents the application of adaptive rational spectral methods to the linear stability analysis of nonlinear fourth order problems our model equation is a phase field model of infiltration but the proposed discretization can be directly extended to similar equations arising in thin film flows the sharpness and structure of the wetting front preclude the use of the standard chebyshev pseudo spectral method due to its slow convergence in problems where the solution has steep internal layers we discuss the effectiveness and conditioning of the proposed discretization and show that it allows the computation of accurate traveling waves and eigenvalues for small values of the initial water saturation film precursor several orders of magnitude smaller than the values considered previously in analogous stability analyses of thin film flows using just a few hundred grid points

fast dht algorithms for length n q 2 sup m this article presents an improved split radix algorithm that can flexibly compute the discrete hartley transforms dht of length q 2 sup m where q is an odd integer comparisons with previously reported algorithms show that savings on the number of arithmetic operations can be made furthermore a wider range of choices on different dht lengths is naturally provided

on the porous continuum modeling of gravity driven fingers in unsaturated materials extension of standard theory with a hold back pile up effect 1 the traditional richards equation re in combination with standard monotonic properties constitutive relations and hysteretic equations of state has been shown to lack critical physics required to model gravity driven fingering gdf we extend the re with an experimentally observed hold back pile up hbpu effect not captured in the standard porous continuum re formulation we postulate the hbpu effect is tied to wetting front sharpness and can be mathematically formulated in a variety of ways to include hypodiffusive hyperbolic and mixed spatial temporal forms involving respectively a laplacian a second order derivative in time and a laplacian of a first order derivative in time of the state variables for each we can infer an extended flux relation comprised of the darcy buckingham flux plus an additional component due to the hbpu effect extended flux relations that are mathematically similar to each can be found in the single phase and multiphase flow literature however all with very different underlying conceptualizations of the possible physics

some new procedures for numerical solution of variably saturated flow problems persistent difficulties that arise in forming numerical solutions of variably saturated flow problems include controlling the stability of the nonlinear equation solvers and devising a reliable yet efficient method for determining the positions of seepage surfaces new techniques for addressing these problems are applied to a subdomain finite element discretization of the governing flow equations a series of test problems demonstrates that the techniques are reliable and efficient for a wide variety of problems

comments on fast computation of the discrete cosine transform and the discrete hartley transform by h s malvar the commenter shows that the algorithm presented in the above paper ibid vol assp 35 no 10 p 1484 5 oct 1987 requires exactly the same number of multiplications as but more additions than prevalent methods for the computation of the dht discrete hartley transform by existing methods contrary to the author s claim

prime length real valued polynomial residue division algorithms one class of efficient algorithms for computing a discrete fourier transform dft is based on a recursive polynomial factorization of the polynomial 1 z sup n the bruun algorithm is a typical example of such algorithms previously the bruun algorithm which is applicable only when system lengths are powers of two in its original form is generalized and modified to be applicable to the case when the length is other than a power of two this generalized algorithm consists of transforms t sub d f with prime d and real f in the range 0 spl les f 0 5 t sub d 0 computes residues x z mod 1 z sup 2 and x z mod 1 2 cos spl pi k d z sup 1 z sup 2 k 1 2 d 1 and t sub d f f spl ne 0 computes residues x z mod 1 2cos 2 spl pi f k d z sup 1 z sup 2 k 0 1 d 1 for a given real signal x z of length 2d the purpose of this paper is to find efficient algorithms for t sub d f first polynomial factorization algorithms are derived for t sub d 0 and t sub d 1 4 when f is neither 0 nor 1 4 it is not feasible to derive a polynomial factorization algorithm two different implementations of t sub d f for such f are derived one implementation realizes t sub d f via a d point dft for which a variety of fast algorithms exist the other implementation realizes t sub d f via t sub d 1 4 for which the polynomial factorization algorithm exists comparisons show that for d spl ges 5 these implementations achieve better performance than computing each output of t sub d f separately

fast hartley transforms for image processing the fast hartley transform fht is used to transform two dimensional image data because the hartley transform is real valued it does not require complex operations both spectra and autocorrelations of two dimensional ultrasound images of normal and abnormal livers were computed

discrete fourier transform algorithms for real valued sequences it is well known that the discrete fourier transformation dft of a real valued sequence contains some redundancies more precisely approximately half of the dft coefficients suffice to completely determine the dft in this paper it is shown that the choice of the set of nonredundant dft coefficients to be calculated affects the efficiency of the resulting algorithm one especially interesting choice is discussed in detail for the case of mixed radix 2 3 dft algorithms algorithms for the dft calculation of both one and more dimensional real valued arrays are discussed