growth rates and explosions in sandpiles we study the abelian sandpile growth model where n particles are added at the origin on a stable background configuration in zd any site with at least 2d particles then topples by sending one particle to each neighbor we find that with constant background height h 2d 2 the diameter of the set of sites that topple has order n1 d this was previously known only for h d our proof uses a strong form of the least action principle for sandpiles and a novel method of background modification we can extend this diameter bound to certain backgrounds in which an arbitrarily high fraction of sites have height 2d 1 on the other hand we show that if the background height 2d 2 is augmented by 1 at an arbitrarily small fraction of sites chosen independently at random then adding finitely many particles creates an explosion a sandpile that never stabilizes

development of high order taylor galerkin schemes for les in this paper we describe the implementation and development of a new taylor galerkin finite element scheme within an unstructured hybrid parallel solver the scheme has been specifically conceived for unsteady les it is third order in space and time and has a low dissipative error minimal additional cpu costs are achieved by using a new approximation of the finite element integrals and a simple iterative method for the approximate inversion of the modified mass matrix basic convective tests are carried out in 2 and 3 dimensions for arbitrary elements numerical estimates of the order of convergence are presented on regular and perturbed grids finally test cases that are relevant to les are carried out and these clearly demonstrate the important improvements that our new scheme offers relative to a selection of existing methods

variable mesh cubic spline technique for n wave solution of burgers equation abstract a variable mesh cubic spline technique is developed for the shock like solution of the one dimensional burgers equation so that the necessity of taking very fine mesh all over the computational region could be avoided the scheme is employed by taking a typical initial solution to study the propagation of plane n waves results are presented for various values of the dissipative parameter numerical results are in good agreement with the known exact results

a characteristic finite element algorithm for time dependent 3 d advection dominated transport using unstructured grids abstract an algorithm based on operator splitting has been successfully implemented for solving unsteady advection dominated transport problems in 3 d specifically the general operator integration factor splitting method of maday et al is applied to the unsteady advection diffusion equation with source sink terms the algorithm incorporates a 3 d characteristic galerkin scheme to treat advection and a standard galerkin treatment of the diffusion and source sink terms up to third order operator splitting was implemented and validated against several analytical solutions the algorithm showed the expected error behaviour and good performance in modeling advection dominated transport problems the practical utility and effectiveness of the proposed numerical scheme was further demonstrated by solving the graetz nusselt problem i e high peclet number mass heat transport in a fully developed pipe flow

the golden code a 2 spl times 2 full rate space time code with nonvanishing determinants in this paper the golden code for a 2 spl times 2 multiple input multiple output mimo system is presented this is a full rate 2 spl times 2 linear dispersion algebraic space time code with unprecedented performance based on the golden number 1 spl radic 5 2

a modified reproducing kernel method for solving burgers equation arising from diffusive waves in fluid dynamics abstract as we known reproducing kernel method rkm has been presented for solving differential equations for initial and boundary value problems however the direct application of the rkm presented in the previous works cannot produce good numerical results for burgers equation to solve this problem this paper give a modified reproducing kernel method by piecewise technique the exact solution is given by reproducing kernel functions in a series expansion form the approximation solution is expressed by n term summation of reproducing kernel functions the three numerical experiments results show that the piecewise method is more easily implemented and effective some numerical results are also compared with the results obtained by other methods

generalized petrov galerkin methods for the numerical solution of burgers equation generalized petrov galerkin methods are applied in two different ways for the numerical solution of burgers equation in the first place it is used to produce upwinding in the way described by mitchell and griffiths 9 10 the main objective of this paper is in the second place to use it as a moving finite element method in particular it is shown that the methods of miller and co workers4 6 and herbst et al 7 8 can be incorporated in the more general approach presented in this paper several choices for the test functions are discussed and numerical results are given

numerical approach for solving diffusion problems using cubic b spline collocation method abstract a numerical approach for modeling the removal of homogeneous solutes from the porous structure is presented pore diffusion equations controlling the overall process are expressed in terms of concentration of solute as a function of position in bed and washing period a computational scheme specifying knot vector s and control points de boor points to solve diffusion model using cubic b spline collocation method cscm is given the knot vector provides sufficient resolution and control points yield an accurate approximation of the desired curve convergence of numerical scheme is of o h 2 four problems have been worked out by the proposed scheme results are plotted graphically for fairly wide range of parameters a comparison with the previous techniques demonstrates the superiority of the proposed method on basis of computational time efficiency and accuracy

riemann roch and abel jacobi theory on a finite graph abstract it is well known that a finite graph can be viewed in many respects as a discrete analogue of a riemann surface in this paper we pursue this analogy further in the context of linear equivalence of divisors in particular we formulate and prove a graph theoretic analogue of the classical riemann roch theorem we also prove several results analogous to classical facts about riemann surfaces concerning the abel jacobi map from a graph to its jacobian as an application of our results we characterize the existence or non existence of a winning strategy for a certain chip firing game played on the vertices of a graph

numerical solution of burgers equation by lattice boltzmann method in this paper a lattice boltzmann model for burgers equation is proposed through selecting equilibrium distribution function properly the model has been verified by three test examples the numerical results are found in good agreement with analytical solutions and numerical solutions reported in previous studies the advantages of the resulting method are algorithmic simplicity parallel computation easy handling of complicated boundary conditions so it is very easy to implement and deal with more complex problems

one step taylor galerkin methods for convection diffusion problems third and fourth order taylor galerkin schemes have shown to be efficient finite element schemes for the numerical simulation of time dependent convective transport problems by contrast the application of higher order taylor galerkin schemes to mixed problems describing transient transport by both convection and diffusion appears to be much more difficult in this paper we develop two new taylor galerkin schemes maintaining the accuracy properties and improving the stability restrictions in convection diffusion we also present an efficient algorithm for solving the resulting system of the finite element method finally we present two numerical simulations that confirm the properties of the methods

applying multiquadric quasi interpolation to solve burgers equation abstract in this paper we develop a kind of univariate multiquadric mq quasi interpolation and use it to solve burgers equation with viscosity at first we construct the mq quasi interpolation which possesses the properties of linear reproducing and preserving monotonicity next we obtain the numerical scheme by using the derivative of the quasi interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable then we verify our method for two examples with distinguishing initial value condition one example is tested for three reynolds number that is r 10 r 100 and r 10 000 from the numerical experiments we see that the presented method in this paper is valid although the accuracy of the technique is not higher than hon and mao s one another example is used to examine the travelling of the shock we can improve the accuracy by selecting an appropriate shape parameter and using a higher accurate mq quasi interpolation the advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement

third order upwind finite element solutions of high reynolds number flows abstract a full upwind finite element scheme based on the petrov galerkin formulation is presented for accurate solutions of high reynolds number flows and then a simplified finite scheme with third order upwinding is developed in order to obtain a practical algorithm for numerical simulation because structures of the full upwind finite element scheme are very complicated numerical dissipation added in the proposed upwind scheme is represented by high order derivatives of flow velocities and pressure computational results for the subcritical and the supercritical reynolds number flows around a circular cylinder and for flows around twin circular cylinders are shown to illustrate the effectiveness and robustness of the simplified upwind finite element scheme

quintic b spline collocation method for fourth order partial integro differential equations with a weakly singular kernel quintic b spline collocation method for the numerical solution of fourth order partial integro differential equations is considered the scheme is based on the second order backward differential formula in the time direction and the quintic b spline method for the spatial derivative some numerical experiments are included to demonstrate the effectiveness of the discrete technique from the numerical experiments we can find that the present scheme possesses high accuracy and efficiency and the numerical results are in good agreement with the exact solutions

a finite element approach for solution of burgers equation in this study for the burgers equation which is used a model problem in turbulence and shock wave theory was given a finite element solution considering the numerical results obtained for different values of viscosity compared with cole s analytical solution it was seen that they were in good agreement

stabilised finite element methods for steady incompressible flow abstract we give a brief overview of frequently used stabilised finite element schemes for steady incompressible flow we derive taylor galerkin schemes for the flow equations and show how supg type and taylor galerkin methods can be interpreted within the same framework

application of cubic b spline finite element technique to the thermistor problem a numerical solution to the thermistor problem is obtained using the cubic b spline finite elements the resulting system of ordinary differential equations is solved by the finite difference method excellent agreement is obtained between the numerical results and the analytic solution for the three phases

k version of finite element method in gas dynamics higher order global differentiability numerical solutions in this paper we consider and examine alternate finite element computational strategies for time dependent navier stokes equations describing high speed compressible flows with shocks in a viscous and conducting medium with the ultimate objective of establishing the desired features of a general mathematical and computational framework for such initial value problems ivp in which a the numerically computed solutions are in agreement with the physics of evolution described by the governing differential equations gdes i e the ivp b the solutions are admissible in the non discretized form of the gdes in the pointwise sense i e anywhere and everywhere in the entire space time domain and hence in the integrated sense as well c the numerical approximations progressively approach the same global differentiability in space and time as the theoretical solutions d it is possible to time march the solutions this is essential for efficiency as well as ensuring desired accuracy of the computed solution for the current increment of time i e to minimize the error build up in the time marching process e the computational process is unconditionally stable and non degenerate regardless of the choice of discretization nature of approximations and their global differentiability and the dimensionless parameters influencing the physics of the process f there are no issues of stability cfl number limitations and g the mathematical and computational methodology is independent of the nature of the space time differential operators we consider one dimensional compressible flow in a viscous and conducting medium with shocks as model problems to illustrate various features of the general mathematical and computational framework used here and to demonstrate that the proposed framework is general and is applicable to all ivp the riemann shock tube with a single diaphragm serves as a model problem the specific details presented in the paper discuss 1 choice of the form of the gdes i e strong form or weak form 2 various choices of variables the paper establishes and considers density velocity and temperature as variables of choice 3 details of the space time least squares ls integral forms meritorious over all others in all aspects are presented and choice of approximation spaces are discussed 4 in all numerical studies we consider a viscous and conducting medium with ideal gas law however results are also presented for non conducting medium extension of this work to real gas models will be presented in a separate paper it is worth noting that when the medium is viscous and conducting the solutions of gas dynamics equations are analytic 5 it is also significant to note that upwinding methods based on addition of artificial diffusion such as supg supg dc supg dc ls and their many variations are neither needed nor used in this present work 6 numerical studies are aimed at resolving the localized details of the shock structure i e shock relations shock width shock speed etc as well as the over all global behaviour of the solution in the entire space time domain 7 numerical studies are presented for riemann shock tube for high mach number flows with special emphasis also on time accuracy of the evolution which is ensured by requiring that the approximations for each increment of time satisfy non discretized form of the gdes in the pointwise sense and hence in the integrated sense as well 8 comparisons are made with published results as well as theoretical solutions when possible it is established that space time least squares processes are the only processes that yield variationally consistent space time integral forms and hence unconditionally non degenerate space time computational processes which when considered in higher order scalar product spaces provide the desired mathematical framework in which progressively higher order global differentiability solutions in space and time yield the same characteristics as the theoretical solutions of the ivp in all aspects copyright 2006 john wiley sons ltd

golden space time block coded modulation in this paper block coded modulation is used to design a 2 times 2 multiple input multiple output mimo space time code for slow fading channels the golden code is chosen as the inner code the scheme is based on a set partitioning of the golden code using two sided ideals whose norm is a power of two in this case a lower bound for the minimum determinant is given by the minimum hamming distance the description of the ring structure of the quotients suggests further optimization in order to improve the overall distribution of determinants simulation results show that the proposed schemes achieve a significant gain over the un coded golden code

enumerating linear systems on graphs the divisor theory of graphs views a finite connected graph g as a discrete version of a riemann surface divisors on g are formal integral combinations of the vertices of g and linear equivalence of divisors is determined by the discrete laplacian operator for g as in the case of riemann surfaces we are interested in the complete linear system d of a divisor d the collection of nonnegative divisors linearly equivalent to d unlike the case of riemann surfaces the complete linear system of a divisor on a graph is always finite we compute generating functions encoding the sizes of all complete linear systems on g and interpret our results in terms of polyhedra associated with divisors and in terms of the invariant theory of the dual of the jacobian group of g if g is a cycle graph our results lead to a bijection between complete linear systems and binary necklaces our results also apply to a model in which the laplacian is replaced by an invertible integral m matrix

an efficient numerical scheme for burgers equation this paper applies the multiquadric mq as a spatial approximation scheme for solving the nonlinear burgers equation for comparison purposes a low order explicit finite difference approximation of the time derivative is employed by decreasing the time step of the computation it is shown that the major numerical error is from the time integration instead of the mq spatial approximation the numerical results indicate that this mq offers an excellent approximation for all possible values of reynolds number an adaptive algorithm is also developed to adjust the mq interpolation points to the peak of the shock wave which is shown to provide an improved numerical result numerical comparisons are made with most of the existing numerical schemes for solving the burgers equation

self organized critical state of sandpile automaton models we study a general bak tang wiesenfeld type automaton model of self organized criticality in which the toppling conditions depend on local height but not on its gradient we characterize the critical state and determine its entropy for an arbitrary finite lattice in any dimension the two point correlation function is shown to satisfy a linear equation the spectrum of relaxation times describing the approach to the critical state is also determined exactly

application of perfect space time codes pep bounds and some practical insights the design of perfect space time codes constructed from cyclic division algebra cda on the quasi static mimo channel has received lots of attention in industry over the last few years however the recent standards that use multiple antennas terminals such as ieee 802 11n ieee 802 16e or lte are based on more realistic assumptions involving the use of outer codes and multi taps channels in this paper the question regarding the utility of using a high dimensional modulation schemes such as space time codes in a standard context is addressed for this we evaluate the performance of the perfect space time codes in term of an upper bound on the pairwise error probability and we compare it to the one of simple spatial division multiplexing sdm schemes finally simulation results considered in the context of ieee 802 11n show that the 2 2 mimo perfect code i e the golden code performs relatively similarly as the sdm scheme in the presence of a good outer code

biorthogonal multiwavelets on the interval for numerical solutions of burgers equation to numerically solve the burgers equation in this paper we propose a general method for constructing wavelet bases on the interval 0 1 derived from symmetric biorthogonal multiwavelets on the real line in particular we obtain wavelet bases with simple structures on the interval 0 1 from the hermite cubic splines in comparison with all other known constructed wavelets on the interval 0 1 our constructed wavelet bases on the interval 0 1 from the hermite cubic splines not only have good approximation and symmetry properties with extremely short supports but also employ a minimum number of boundary wavelets with a very simple structure these desirable properties make them to be of particular interest in numerical algorithms our constructed wavelet bases on the interval 0 1 are then used to solve the nonlinear burgers equation our method is based on the finite difference formula combined with the collocation method therefore our proposed numerical scheme in this paper is abbreviated as mfdcm mixed finite difference and collocation method some numerical examples are provided to demonstrate the validity and applicability of our proposed method which can be easily implemented to produce a desired accuracy

an analysis of time discretization in the finite element solution of hyperbolic problems abstract the problem of the time discretization of hyperbolic equations when finite elements are used to represent the spatial dependence is critically examined a modified equation analysis reveals that the classical second order accurate time stepping algorithms i e the lax wendroff leap frog and crank nicolson methods properly combine with piecewise linear finite elements in advection problems only for small values of the time step on the contrary as the courant number increases the numerical phase error does not decrease uniformly at all wavelengths so that the optimal stability limit and the unit cfl property are not achieved these fundamental numerical properties can however be recovered while still remaining in the standard galerkin finite element setting by increasing the order of accuracy of the time discretization this is accomplished by exploiting the taylor series expansion in the time increment up to the third order before performing the galerkin spatial discretization using piecewise linear interpolations as a result it appears that the proper finite element equivalents of second order finite difference schemes are implicit methods of incremental type having third and fourth order global accuracy on uniform meshes taylor galerkin methods numerical results for several linear examples are presented to illustrate the properties of the taylor galerkin schemes in one and two dimensional calculations

high order accurate time stepping schemes for convection diffusion problems the paper discusses the formulation of high order accurate time stepping schemes for transient convection diffusion problems to be combined with finite element methods of the least squares type for a stable discretization of highly convective problems pade approximations of the exponential function are considered for deriving multi stage time integration schemes involving first time derivatives only thus easier to implement in conjunction with c0 finite elements than standard time stepping schemes which incorporate higher order time derivatives after a brief discussion of the stability and accuracy properties of the multi stage pade schemes and having underlined the similarity between pade and runge kutta methods the paper closes with the presentation of illustrative examples which indicate the effectiveness of the proposed methods

fourth order finite difference method for solving burgers equation abstract in this paper we present fourth order finite difference method for solving nonlinear one dimensional burgers equation this method is unconditionally stable the convergence analysis of the present method is studied and an upper bound for the error is derived numerical comparisons are made with most of the existing numerical methods for solving this equation

explicit and implicit fem fct algorithms with flux linearization a new approach to the design of flux corrected transport fct algorithms for continuous linear multilinear finite element approximations of convection dominated transport problems is pursued the algebraic flux correction paradigm is revisited and a family of nonlinear high resolution schemes based on zalesak s fully multidimensional flux limiter is considered in order to reduce the cost of flux correction the raw antidiffusive fluxes are linearized about an auxiliary solution computed by a high or low order scheme by virtue of this linearization the costly computation of solution dependent correction factors is to be performed just once per time step and there is no need for iterative defect correction if the governing equation is linear a predictor corrector algorithm is proposed as an alternative to the hybridization of high and low order fluxes three fem fct schemes based on the runge kutta crank nicolson and backward euler time stepping are introduced a detailed comparative study is performed for linear convection diffusion equations

a novel numerical scheme for solving burgers equation abstract in this paper we propose a novel numerical scheme for solving burgers equation the scheme is based on a cubic spline quasi interpolant and multi node higher order expansion which make the algorithm simple and easy to implement the numerical experiments show that the proposed method produces high accurate results

a space time coupled p version least squares finite element formulation for unsteady two dimensional navier stokes equations this paper presents a p version least squares finite element formulation for two dimensional unsteady fluid flow described by navier stokes equations where the effects of space and time are coupled the dimensionless form of the navier stokes equations are first cast into a set of first order differential equations by introducing auxiliary variables this permits the use of c0 element approximation the element properties are derived by utilizing the p version approximation functions in both space and time and then minimizing the error functional given by the space time integral of the sum of squares of the errors resulting from the set of first order differential equations this results in a true space time coupled least squares minimization procedure the application of least squares minimization to the set of coupled first order partial differential equations results in finding a solution vector which makes gradient of error functional with respect to a null vector this is accomplished by using newton s method with a line search a time marching procedure is developed in which the solution for the current time step provides the initial conditions for the next time step equilibrium iterations are carried out for each time step until the error functional and each component of the gradient of the error functional with respect to nodal degrees of freedom are below a certain prespecified tolerance the space time coupled p version approximation functions provide the ability to control truncation error which in turn permits very large time steps what literally requires hundreds of time steps in uncoupled conventional time marching procedures can be accomplished in a single time step using the present space time coupled approach the generality success and superiority of the present formulation procedure is demonstrated by presenting specific numerical examples for transient couette flow and transient lid driven cavity the results are compared with the analytical solutions and those reported in the literature the formulation presented here is ideally suited for space time adaptive procedures the element error functional values provide a mechanism for adaptive h p or hp refinements

least squares spectral element method for non linear hyperbolic differential equations the least squares spectral element method has been applied to the one dimensional inviscid burgers equation which allows for discontinuous solutions in order to achieve high order accuracy both in space and in time a space time formulation has been applied the burgers equation has been discretized in three different ways a non conservative formulation a conservative system with two variables and two equations one first order linear pde and one linearized algebraic equation and finally a variant on this conservative formulation applied to a direct minimization with a qr decomposition at elemental level for all three formulations an h p convergence study has been performed and the results are discussed in this paper

space time codes from structured lattices we present constructions of space time st codes based on lattice coset coding first we focus on st code constructions for the short block length case i e when the block length is equal to or slightly larger than the number of transmit antennas we present constructions based on dense lattice packings and nested lattice voronoi shaping our codes achieve the optimal diversity multiplexing tradeoff dmt of quasi static multiple input multiple output mimo fading channels for any fading statistics and perform very well also at practical moderate values of signal to noise ratios snr then we extend the construction to the case of large block lengths by using trellis coset coding we provide constructions of trellis coded modulation tcm schemes that are endowed with good packing and shaping properties both short block and trellis constructions allow for a reduced complexity decoding algorithm based on minimum mean squared error generalized decision feedback equalizer mmse gdfe lattice decoding and a combination of this with a viterbi tcm decoder for the tcm case beyond the interesting algebraic structure we exhibit codes whose performance is among the state of the art considering codes with similar encoding decoding complexity

numerical solution of burgers fisher equation by cubic b spline quasi interpolation abstract in this paper numerical solution of the burgers equation is presented based on the cubic b spline quasi interpolation at first the cubic b spline quasi interpolation is introduced moreover the numerical scheme is presented by using the derivative of the quasi interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable the accuracy of the proposed method is demonstrated by some test problems the numerical results are found in good agreement with exact solutions the advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement

numerical solutions of nonlinear burgers equation with modified cubic b splines collocation method abstract in this paper a numerical method is proposed to approximate the solution of the nonlinear burgers equation the method is based on collocation of modified cubic b splines over finite elements so that we have continuity of the dependent variable and its first two derivatives throughout the solution range we apply modified cubic b splines for spatial variable and derivatives which produce a system of first order ordinary differential equations we solve this system by using ssp rk43 or ssp rk54 scheme this method needs less storage space that causes less accumulation of numerical errors the numerical approximate solutions to the burgers equation have been computed without transforming the equation and without using the linearization illustrative eleven examples are included to demonstrate the validity and applicability of the technique easy and economical implementation is the strength of this method

a space time coupled p version least squares finite element formulation for unsteady fluid dynamics problems this paper presents a p version least squares finite element formulation for unsteady fluid dynamics problems where the effects of space and time are coupled the dimensionless form of the differential equations describing the problem are first cast into a set of first order differential equations by introducing auxiliary variables this permits the use of c element approximation the element properties are derived by utilizing p version approximation functions in both space and time and then minimizing the error functional given by the space time integral of the sum of squares of the errors resulting from the set of first order differential equations this results in a true space time coupled least squares minimization procedure a time marching procedure is developed in which the solution for the current time step provides the initial conditions for the next time step the space time coupled p version approximation functions provide the ability to control truncation error which in turn permits very large time steps what literally requires hundreds of time steps in uncoupled conventional time marching procedures can be accomplished in a single time step using the present space time coupled approach for non linear problems the non linear algebraic equations resulting from the least squares process are solved using newton s method with a line search this procedure results in a symmetric hessian matrix equilibrium iterations are carried out for each time step until the error functional and each component of the gradient of the error functional with respect to nodal degrees of freedom are below a certain prespecified tolerance the generality success and superiority of the present formulation procedure is demonstrated by presenting specific formulations and examples for the advection diffusion and burgers equations the results are compared with the analytical solutions and those reported in the literature the formulation presented here is ideally suited for space time adaptive procedures the element error functional values provide a mechanism for adaptive h p or hp refinements the work presented in this paper provides the basis for the extension of the space time coupled least squares minimization concept to two and three dimensional unsteady fluid flow

numerical solution of nonlinear burgers equation using high accuracy multi quadric quasi interpolation in this paper a numerical method is presented to approximate the solution to nonlinear burgers equation which is related to many scientific research topics a numerical scheme by using high accuracy multi quadric quasi interpolation is presented in which a kind of multi quadric quasi interpolant is used to approximate the derivatives of the solution in spatial domain and finite difference is used to approximate the derivatives of the solution in temporal domain the advantage of the scheme is that it is mesh free and in each time step only a multi quadric quasi interpolant is employed so that the algorithm is easy to implement the numerical results of this scheme are also shown and compared with other numerical schemes

computational algorithms for transient analysis the burden of weight and consequences towards formalizing discrete numerically assigned dna algorithmic markers wp family abstract different from the way we have been looking in the past at developments encompassing modal type and a wide class of step by step time stepping approaches for transient and dynamic field problems and significantly different from the way these have been developed and described in standard text books over the years this paper outlines the theoretical ideas and basis towards providing a generalized methodology and formulations leading to integral and a wide class of integration operators for the resulting solution of these transient equation systems it is herein postulated that integral operators and a wide class of integration operators pertain to and emanate from the same family with the burden which is being carried by a virtual field or weighted function field specifically introduced for the time discretization is strictly enacted in a mathematically consistent manner so as to first permit obtaining the adjoint operator of the original semi discretized equation system subsequently the selection or burden carried by the virtual or weighted function fields originally introduced to facilitate the time discretization process determines the formal development and outcome of exact integral operators approximate integral operators and a wide class of integration operators thus the present developments not only serve as a prelude towards the formal developments for exact integral operators but also demonstrate that the resulting approximate integral operators and a wide class of integration operators and known methods are simply subsets of the generalizations of a standardized w p family and emanate from the principles presented herein the burden of weight and the resulting consequences towards subsequently enabling a formal basis for the selection of discrete numerically assigned dna algorimmic markers to particularly identitfy a wide class of algorithms is described for transient field problems and dynamic field problems respectively

adaptive remeshing for three dimensional compressible flow computations an adaptive mesh procedure for computing steady state solutions of the compressible euler equations in three dimensions is presented the method is an extension of previous work in two dimensions the approach requires the coupling of a surface triangulator an automatic tetrahedral mesh generator a finite element flow solver and an error estimation procedure an example involving flow at high mach number is included to demonstrate the numerical performance of the proposed approach the example shows that the use of this form of adaptivity in three dimensions offers the potential of even greater computational savings than those attained in the corresponding two dimensional implementation

numerical solution of one dimesional burgers equation explicit and exact explicit finite difference methods this paper presents finite difference solution and analytical solution of the finite difference approximations based on the standard explicit method to the one dimensional burgers equation which arises frequently in the mathematical modelling used to solve problems in fluid dynamics results obtained by these ways for some modest values of viscosity have been compared with the exact fourier one it is shown that they are in good agreement with each other

space time coding techniques with bit interleaved coded modulations for mimo block fading channels the space time bit interleaved coded modulation st bicm is an efficient technique to obtain high diversity and coding gain on a block fading multiple input multiple output mimo channel its maximum likelihood ml performance is computed under ideal interleaving conditions which enables a global optimization taking into account channel coding thanks to a diversity upper bound derived from the singleton bound an appropriate choice of the time dimension of the space time coding is possible which maximizes diversity while minimizing complexity based on the analysis an optimized interleaver and a set of linear precoders called dispersive nucleo algebraic dna precoders are proposed the proposed precoders have good performance with respect to the state of the art and exist for any number of transmit antennas and any time dimension with turbo codes they exhibit a frame error rate which does not increase with frame length

a space time least square finite element scheme for advection diffusion equations abstract a space time least square finite element scheme is presented for the advection diffusion problems at moderate to high peclet numbers this scheme is designed to eliminate spurious oscillations and can be used to define the steady state solution as the asymptotic transient solution for large time numerical results using linear elements in a 1d space and bilinear elements in a 2d space demonstrate the accuracy and the stability of the new scheme

linear systems on tropical curves a tropical curve gamma is a metric graph with possibly unbounded edges and tropical rational functions are continuous piecewise linear functions with integer slopes we define the complete linear system d of a divisor d on a tropical curve gamma analogously to the classical counterpart we investigate the structure of d as a cell complex and show that linear systems are quotients of tropical modules finitely generated by vertices of the cell complex using a finite set of generators d defines a map from gamma to a tropical projective space and the image can be modified to a tropical curve of degree equal to mathrm deg d the tropical convex hull of the image realizes the linear system d as a polyhedral complex

a geometric realization of the periodic discrete toda lattice and its tropicalization an explicit formula concerning curve intersections equivalent to the time evolution of the periodic discrete toda lattice pdtl is presented first the time evolution is realized as a point addition on a hyperelliptic curve which is the spectral curve of the pdtl then the point addition is translated into curve intersections next it is shown that the curves which appear in the curve intersections are explicitly given by using the conserved quantities of the pdtl finally the formulation is lifted to the framework of tropical geometry and a tropical geometric realization of the periodic box ball system is constructed via tropical curve intersections

a galerkin finite element approach to burgers equation a galerkin finite element method is presented for the numerical solution of burgers equation a linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is found via a crank nicolson approach involving a product approximation it is shown that this method is capable of solving burgers equation accurately for a wide range of viscosity values the results show that the new method performs better than the most of the methods available in the literature

an adaptive characteristic petrov galerkin finite element method for convection dominated linear and nonlinear parabolic problems in one space variable a new adaptive finite element method for convection dominated problems is presented a special feature of the method is that it is based on a petrov galerkin scheme for spatial approximation at a typical time step which employs test functions chosen so that the approximate solution coincides with the exact solution at the nodes of finite element grid this procedure makes possible the derivation of truly local a posteriori error estimates and a very effective solver numerical examples are discussed which illustrate the efficiency and effectively of the method

achieving full frequency and space diversity in wireless systems via bicm ofdm stbc and viterbi decoding orthogonal frequency division multiplexing ofdm is known as an efficient technique to combat frequency selective channels in this paper we show that the combination of bit interleaved coded modulation bicm and ofdm achieves the full frequency diversity offered by a frequency selective channel with any kind of power delay profile pdp conditioned on the minimum hamming distance dfree of the convolutional code this system has a simple viterbi decoder with a modified metric we then show that by combining such a system with space time block coding stbc one can achieve the full space and frequency diversity of a frequency selective channel with n transmit and m receive antennas bicm stbc ofdm achieves the maximum diversity order of nml over l tap frequency selective channels regardless of the pdp of the channel this latter system also has a simple viterbi decoder with a properly modified metric we verify our analytical results via simulations including channels employed in the ieee 802 11 standards

a numerical solution of the burgers equation using cubic b splines in the present paper numerical solutions of the one dimensional burgers equation are obtained by a method based on collocation of cubic b splines over finite elements the accuracy of the proposed method is demonstrated by three test problems the numerical results are found in good agreement with exact solutions time space integration of the burgers equation yields a system of difference equation which is shown to be unconditionally stable

local rbf method for multi dimensional partial differential equations abstract in this paper a local meshless differential quadrature collocation method is utilized to solve multi dimensional reaction convection diffusion pdes numerically in some cases global version of the meshless method is considered as well the meshless methods approximate solution on scattered and uniform nodes in both local and global sense in the case of convection dominated pdes the local meshless method is coupled with an upwind technique to avoid spurious oscillations for this purpose a physically motivated local domain is utilized in the flow direction both regular and irregular geometries are taken into consideration numerical experiments are performed to demonstrate effective applications and accuracy of the meshless method on regular and irregular domains

a tropical proof of the brill noether theorem we produce brill noether general graphs in every genus confirming a conjecture of baker and giving a new proof of the brill noether theorem due to griffiths and harris over any algebraically closed field

time accurate solution of advection diffusion problems by finite elements abstract the taylor galerkin method recently proposed for the spatial and temporal discretization of hyperbolic equations is employed to derive accurate and efficient numerical schemes for the solution of time dependent advection diffusion problems two distinct numerical strategies are discussed the first is suitable for evolutionary problems while the second is appropriate for situations in which a steady state is eventually reached for purely evolutionary problems the taylor galerkin method is applied to the complete advection diffusion equation and through modifications of the standard mass matrix is shown to generate an incremental form of the crank nicolson time stepping method such an incremental form also lends itself to the derivation of computationally simple but accurate explicit algorithms to deal with transient situations which evolve towards a highly convective steady state the global taylor galerkin method is found to be ineffective since it reduces to the standard galerkin formulation as the temporal term vanishes for such cases we suggest the use of a splitting up method in which advection and diffusion are treated separately by appropriate taylor galerkin methods the proposed methods are illustrated first for linear constant coefficient equations they are successively extended to deal with nonlinear and multi dimensional problems numerical applications indicate their effectiveness

perfect space time block codes in this paper we introduce the notion of perfect space time block codes stbcs these codes have full rate full diversity nonvanishing constant minimum determinant for increasing spectral efficiency uniform average transmitted energy per antenna and good shaping we present algebraic constructions of perfect stbcs for 2 3 4 and 6 antennas

jacobi iteration in implicit difference schemes for the wave equation it is shown how a jacobi iteration can be used to approximate the linear algebra required by a class of implicit finite difference element schemes for a linear hyperbolic pde while preserving the important properties of the implicit scheme in particular it is shown that order of accuracy stability energy conservation and isotropy of the implicit scheme are all carried over into the new scheme in general the new scheme is much more efficient than the implicit scheme it is derived from for problems in more than one space variable and can be vectorized and or parallelized quite easily furthermore it is shown that a modification of the technique can be used to improve some properties of the underlying implicit scheme at little or no extra cost

tropical theta functions and riemann roch inequality for tropical abelian surfaces we show that the space of theta functions on tropical tori is identified with a convex polyhedron we also show a riemann roch inequality for tropical abelian surfaces by calculating the self intersection numbers of divisors

explicit space time codes achieving the diversity multiplexing gain tradeoff a recent result of zheng and tse states that over a quasi static channel there exists a fundamental tradeoff referred to as the diversity multiplexing gain d mg tradeoff between the spatial multiplexing gain and the diversity gain that can be simultaneously achieved by a space time st code this tradeoff is precisely known in the case of independent and identically distributed i i d rayleigh fading for tgesnt nr 1 where t is the number of time slots over which coding takes place and nt nr are the number of transmit and receive antennas respectively for t nt case we present two general techniques for building d mg optimal rectangular st codes from their square counterparts a byproduct of our results establishes that the d mg tradeoff for all tgesnt is the same as that previously known to hold for tgesnt n r 1

b spline galerkin methods for numerical solutions of the burgers equation the first order splitting method is applied to the burgers equation and two numerical algorithms are set up for this time splitted burgers equation using both quadratic and cubic b spline galerkin finite element techniques the unknowns in the equation is resolved with the b splines in space and standart crank nicolson differencing schemes is used to advance solution in time results of three numerical test problems are used to compare each schemes with available some results

an algorithm based on exponential modified cubic b spline differential quadrature method for nonlinear burgers equation in this paper the authors developed a new differential quadrature method exponential modified cubic b spline differential quadrature method expo mcb dqm by using exponential modified cubic b spline functions as test functions in the traditional differential quadrature method 32 the new method is tested on one and two dimensional nonlinear burgers equations to check the efficiency and accuracy of the proposed method five numerical problems have been considered the numerical results of the method are compared with some existing methods and found that the proposed numerical method produces more accurate results than existing methods stability analysis of the algorithm is also done by using matrix stability analysis method

unsteady flow simulation using unstructured meshes transient flows involving moving boundaries are more difficult to simulate as the geometry of the computational domain changes with time regardless of the changes occurring in the solution the mesh must be modified during the computation in order to accommodate the changes in the geometry although the literature on this subject describes a number of different approaches for handling this type of problem the approach followed in this paper is to use unstructured mesh methods we consider initially the simulation of inviscid two dimensional transient flows involving moving bodies employing an extension of adaptivity procedures which have been successfully used for steady state problems with the error estimation procedure coupled to an automatic triangular mesh generator this approach is extended to produce a three dimensional capability using tetrahedral meshes a number of examples are included to illustrate the numerical performance of these methods

an efficient characteristic galerkin scheme for the advection equation in 3 d conventional galerkin based finite element algorithms perform poorly when modeling advective transport here we develop and test a characteristic galerkin scheme to solve the unsteady three dimensional advective transport equation the algorithm uses tracking of the gaussian quadrature points to project the information from the eulerian background grid to the lagrangian grid numerical experiments were carried out to investigate the performance of this scheme despite speculations to the contrary in the literature this scheme does not suffer from instability problems further it is conservative and shows good phase characteristics with slight numerical diffusion we conclude that the characteristic galerkin method is a viable and efficient scheme for solving advection problems in three dimensions

a riemann roch theorem in tropical geometry recently baker and norine have proven a riemann roch theorem for finite graphs we extend their results to metric graphs and thus establish a riemann roch theorem for divisors on abstract tropical curves

golden space time trellis coded modulation in this paper we present a multidimensional trellis coded modulation scheme for a high rate 2times2 multiple input multiple output mimo system over slow fading channels set partitioning of the golden code is designed specifically to increase the minimum determinant the branches of the outer trellis code are labeled with these partitions and viterbi algorithm is applied for trellis decoding in order to compute the branch metrics a sphere decoder is used the general framework for code design and optimization is given performance of the proposed scheme is evaluated by simulation and it is shown that it achieves significant performance gains over the uncoded golden code

numerical solution of burgers equation by cubic hermite collocation method abstract in this paper numerical solution of the non linear burgers equation are obtained by using cubic hermite collocation method chcm the advantage of the method is continuity of the dependent variable and its derivative throughout the solution range a linear stability analysis shows that the numerical scheme based on crank nicolson approximation in time is unconditionally stable this method is applied on some test problems with different choice of collocation points to validate the accuracy of the method the obtained numerical results show that the method is efficient robust and reliable even for high reynolds numbers for which the exact solution fails moreover the method can be applied to a wide class of nonlinear partial differential equations

solving partial differential equation by using multiquadric quasi interpolation abstract in this paper we use a kind of univariate multiquadric mq quasi interpolation to solve partial differential equation pde we obtain the numerical scheme by using the derivative of the quasi interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the temporal derivative of the dependent variable the advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement our numerical experiment includes two examples one is solving viscid burgers equation for initial trapezoidal conditions another is simulating the interaction of two waves travelling in opposite direction from the numerical experiment we can see that the present scheme is valid