towards polyalgorithmic linear system solvers for nonlinear elliptic problems the authors investigate the performance of several preconditioned conjugate gradient like algorithms and a standard stationary iterative method block line successive overrelaxation sor on linear systems of equations that arise from a nonlinear elliptic flame sheet problem simulation the nonlinearity forces a pseudotransient continuation process that makes the problem parabolic and thus compacts the spectrum of the jacobian matrix so that simple relaxation methods are viable in the initial stages of the solution process however because of the transition from parabolic to elliptic character as the timestep is increased in pursuit of the steady state solution the performance of the candidate linear solvers spreads as the domain of convergence of newton s method is approached in numerical experiments over the course of a full nonlinear solution trajectory short recurrence or optimal krylov algorithms combined with a gauss seidel gs preconditioning yield better execution times with respect to the s

numerical treatment of grid interfaces to viscous flow abstract numerical treatment of grid interfaces is one of the most important considerations for algorithms that employ different grids within the computational domain the issue of numerical treatment of quadrilateral grid interfaces with a representative finite volume navier stokes integration scheme is addressed interfaces are created by local embedding of quadrilateral grids and are the borders between different grids grid embedding is one of the basic functions of adaptive algorithms that have been developed in order to increase both accuracy and efficiency of computations the present work both develops and investigates interface treatment schemes that have certain properties such as accuracy and conservation it is a novel study of interfaces for the case of viscous flow computations various treatments are proposed and evaluated with the emphasis being on a comparison between accurate and conservative treatments two methodologies have been followed in order to study interface treatments the first is analytical and yields orders of possible numerical errors while the second approach employs model test cases which are especially designed to evaluate certain aspects of the described interface treatments also a transonic airfoil flow case is included as an example of accuracy and robustness of a particular interface treatment scheme all numerical treatment schemes that are discussed have been coded and evaluated

error rate for psk and qam modulations for non ideal ofdm systems with noisy channel estimates and receive diversity this paper characterizes the ser for a non ideal ofdm system with either m psk or m qam constellations operating over a frequency selective time varying rayleigh fading channel the imperfections that we consider are inter carrier interference ici and or inter symbol interference isi imperfect time and frequency synchronization and noisy channel estimates we consider an mrc receiver with l diversity branches we present ser characterizations with and without isi and show that the effect of isi especially for higher order modulation schemes e g 8psk and above can be very severe irrespective of the number of diversity branches

a comparison of pilot aided channel estimation methods for ofdm systems this paper deals with the estimation of the channel impulse response cir in orthogonal frequency division multiplexed ofdm systems in particular we focus on two pilot aided schemes the maximum likelihood estimator mle and the bayesian minimum mean square error estimator mmsee the advantage of the former is that it is simpler to implement as it needs no information on the channel statistics on the other hand the mmsee is expected to have better performance as it exploits prior information about the channel theoretical analysis and computer simulations are used in the comparisons at snr values of practical interest the two schemes are found to exhibit nearly equal performance provided that the number of pilot tones is sufficiently greater than the cirs length otherwise the mmsee is superior in any case the mmsee is more complex to implement

application of a primitive variable newton s method for the calculation of an axisymmetric laminar diffusion flame in this paper we present a primitive variable newton based solution method with a block line linear equation solver for the calculation of reacting flows the present approach is compared with the stream function vorticity newton s method and the simpler algorithm on the calculation of a system of fully elliptic equations governing an axisymmetric methane air laminar diffusion flame the chemical reaction is modeled by the flame sheet approximation the numerical solution agrees well with experimental data in the major chemical species the comparison of three sets of numerical results indicates that the stream function vorticity solution using the approximate boundary conditions reported in the previous calculations predicts a longer flame length and a broader flame shape with a new set of modified vorticity boundary conditions we obtain agreement between the primitive variable and stream function vorticity solutions the primitive variable newton s method converges much faster than the other two methods because of much less computer memory required for the block line tridiagonal solver compared to a direct solver the present approach makes it possible to calculate multidimensional flames with detailed reaction mechanisms the simpler algorithm shows a slow convergence rate compared to the other two methods in the present calculation

adaptive gridding for finite difference solutions to heat and mass transfer problems abstract the authors purpose in writing this paper is to review some of their recent work in the calculation of optimal meshes for the solution of parabolic and elliptic partial differential equations pde they first explain our strategies for the adaptive placement of mesh points in addition they make some speculation as to promising avenues for future research in mesh adaptation finally they discuss examples of the application of adaptive gridding to problems of heat and mass transfer they draw these examples from our work in combustion modeling in obtaining numerical solutions of pdes the spatial derivatives are often approximated by discrete representations on a mesh network the accuracy of any numerical solution depends in an important way on the relationship of the location of the mesh points to changes in the dependent variables the authors objective is to investigate finite difference methods in which the mesh networks adapt themselves dynamically to obtain accurate solutions such methods represent an important advance in overcoming a major shortcoming of traditional fixed mesh methods which are often unable to resolve accurately steep fronts or sharp peaks

two dimensional fully adaptive solutions of solid solid alloying reactions abstract solid solid alloying reactions occur in a variety of pyrotechnical applications they arise when a mixture of powders composed of appropriate oxidizing and reducing agents is heated the large quantity of heat evolved produces a self propagating reaction front that is often very narrow with sharp changes in both the temperature and the concentrations of the reacting species solution of problems of this type with an equispaced or mildly nonuniform grid can be extremely inefficient in this paper we develop a two dimensional fully adaptive method for solving problems of this class the method adaptively adjusts the number of grid points needed to equidistribute a positive weight function over a given mesh interval in each direction at each time level we monitor the solution from one time level to another to ensure that the local error per unit step associated with the time differencing method is below some specified tolerance the method is applied to several examples involving exothermic diffusion controlled self propagating reactions in packed bed reactors

unitary matrix digraphs and minimum semidefinite rank for an undirected simple graph g the minimum rank among all positive semidefinite matrices with graph g is called the minimum semidefinite rank msr of g in this paper we show that the msr of a given graph may be determined from the msr of a related bipartite graph finding the msr of a given bipartite graph is then shown to be equivalent to determining which digraphs encode the zero nonzero pattern of a unitary matrix we provide an algorithm to construct unitary matrices with a certain pattern and use previous results to give a lower bound for the msr of certain bipartite graphs

adaptive zoning for singular problems in two dimensions abstract winslow s method for the automatic generation of computation meshes is extended to adaptively vary the zone sizes and orthogonality of grid lines in the resulting mesh through simple analysis and numerical examples the adaptive mesh is shown to give significant increases in accuracy in the computation of singular problems

adaptive methods for elliptic grid generation on developpe une methode generale pour l application de techniques de grille adaptative precises et efficaces a la generation de grilles elliptiques

an adaptive finite element method with crosswind diffusion for low mach steady laminar combustion we investigate adaptive finite element methods for low mach steady laminar combustion the finite element discretization of the flame equations involves least squares control of streamline derivatives and pressure velocity coupling as well as a new shock capturing term based on nonlinear crosswind diffusion yielding a suitable discrete maximum principle for the discrete solution a posteriori error estimates derived from the dual weighted residual method are used to refine the mesh adaptively numerical results are presented for a bunsen flame with simple chemistry on locally refined as well as fully unstructured delaunay meshes solution quality is evaluated in terms of overall flame characteristics including length lift off and width as well as undershoots in species and temperature profiles

an exact error probability analysis of ofdm systems with frequency offset in this paper we derive exact closed form bit error rate ber or symbol error rate ser expressions for orthogonal frequency division multiplexing ofdm systems with carrier frequency offset cfo we consider the performance of an ofdm system subject to cfo error in additive white gaussian noise awgn frequency flat and frequency selective rayleigh fading channels the ber ser performances of bpsk and qpsk modulation schemes are analyzed for awgn and frequency flat rayleigh fading channels while bpsk is considered for frequency selective rayleigh fading channels our results can easily be reduced to the respective analytical error rate expressions for the ofdm systems without cfo error furthermore the simulation results are provided to verify the accuracy of the new error rate expressions

predictions of fluid flow and heat transfer problems by the vorticity velocity formulation of the navier stokes equations abstract a relatively novel formulation of the navier stokes equations is evaluated for obtaining solutions of 2 dimensional incompressible fluid flow and convective heat transfer problems a vorticity transport equation along with two poisson equations for the velocity components and the energy equation are solved by a finite difference scheme a direct solution procedure is used for solving simultaneously the dependent variables along a grid line using a block tridiagonal matrix algorithm as test problems laminar flow motion and heat transfer in a square cavity and in a horizontal concentric annulus induced by various strength of buoyancy and external shear forces are investigated the formulation is found to be stable for high reynolds and grashof numbers and has features that may be desirable for solving a wide variety of flow and heat transfer problems

probability of error analysis of bpsk ofdm systems with random residual frequency offset in this paper we derive closed form bit error rate ber expressions for orthogonal frequency division multiplexing ofdm systems with residual carrier frequency offset cfo most of the published work treats cfo as a nonrandom parameter but in our study we consider it as a random parameter the ber performance of binary phase shift keying bpsk ofdm system is analyzed in the cases of additive white gaussian noise awgn frequency flat and frequency selective rayleigh fading channels we further discuss how these expressions can be related to systems with practical estimators the simulation results are provided to verify the accuracy of these error rate expressions

numerical flow modelling in a locally refined grid summary an algorithm is presented to model two dimensional non isothermal low mach number flows with a local steep density gradient the algorithm uses an adaptive locally refined non staggered grid and has been developed especially for modelling laminar flames the governing equations based on a stream function vorticity formulation are presented and discretized using hybrid finite differences a isothermal tcst problem is presented to compare the accuracy of the results of the solver presented in this paper with the results of algorithms found in the literature however this test problem proves to be not well suited for the application of a locally refined grid since it does not contain a local steep gradient for this reason an additional test problem is constructed that clearly shows the advantages of the locally refined grid as compared to a uniform grid with respect to both the calculation time as well as the number of grid nodes needed furthermore a laminar premixed flame is modelled with simple chemistry to show that the algorithm presented in this paper converges to a stabilized flame when an adaptive grid technique is used

local rectangular refinement with application to nonreacting and reacting fluid flow problems a new solution adaptive gridding method has been developed for the solution of discretized systems of coupled nonlinear elliptic partial differential equations on rectangular domains such a method is required for the numerical solution of realistic combustion problems in which physical quantities may vary by orders of magnitude over one tenth of a millimeter at atmospheric pressure or over micrometers at higher pressures the local rectangular refinement lrr method maintains orthogonality at grid line intersections but lifts the tensor product restriction common to traditional grids producing unstructured grids governing equations are discretized throughout the domain using newly derived forms and newton s method is used to solve the resulting system on a simple test case with a known solution the lrr method and its new discretizations are found to be more accurate than gridding methods representative of those appearing previously in the literature for the more realistic problem of nonreacting driven square cavity flow the lrr solution agrees very well with previously published data when the lrr method is applied to a practical reacting flow a rich axisymmetric laminar bunsen flame with complex chemistry multicomponent transport and an optically thin radiation submodel grid spacing highly influences the inner flame s position which stabilizes only with adequate refinement the vorticity velocity formulation of the governing equations is shown to produce valid results when used in conjunction with the lrr gridding technique furthermore each lrr grid is used to form a nonuniform equivalent tensor product etp grid and also in most cases an equispaced fully refined fr grid these additional grids are supersets of the lrr grids and thus contain refinement in exactly the same regions performance comparisons between the lrr etp and fr grids indicate that the lrr method provides substantial savings in execution time and computer memory requirements without compromising solution accuracy

performance analysis of linear modulation schemes with generalized diversity combining on rayleigh fading channels with noisy channel estimates generalized diversity combining gdc also known as hybrid selection maximal ratio combining or generalized selection combining is a low complexity diversity combining technique by which a fixed subset of a large number of available diversity channels is chosen and then combined using the rules of maximal ratio combining in this paper we analyze the performance of gdc on time correlated rayleigh fading channels with noisy channel estimates we derive expressions for the probability of error for various linear modulation schemes with coherent detection and discuss the conditions under which the analysis can be extended to noncoherent and differentially coherent receiver structures throughout the paper using a fundamental approach to obtain the decision statistic at the combiner output a number of new expressions for the error probabilities are obtained in a rigorous way along with a presentation of their performance with channel estimation errors the final expressions have roughly the same complexity of evaluation as that for the channel with only additive gaussian noise our results correct various inaccuracies in the literature and show that coherent receivers based on imperfectly estimated channel knowledge incur a significant performance loss

three dimensional adaptive mesh refinement for hyperbolic conservation laws a local adaptive mesh refinement algorithm for solving hyperbolic systems of conservation laws in three space dimensions is described the method is based on the use of local grid patches superimpo

channel estimation for ofdm transmission in multipath fading channels based on parametric channel modeling we present an improved channel estimation algorithm for orthogonal frequency division multiplexing mobile communication systems using pilot subcarriers this algorithm is based on a parametric channel model where the channel frequency response is estimated using an l path channel model in the algorithm we employ the esprit estimation of signal parameters by rotational invariance techniques method to do the initial multipath time delays acquisition and propose an interpath interference cancellation delay locked loop to track the channel multipath time delays with the multipath time delays information a minimum mean square error estimator is derived to estimate the channel frequency response it is demonstrated that the use of the parametric channel model can effectively reduce the signal subspace dimension of the channel correlation matrix for the sparse multipath fading channels and consequently improve the channel estimation performance

shepard s interpolation for solution adaptive methods in numerical simulations of fluid dynamics problems solution adaptive methods have proven to be very powerful the implementation of the modified shepard s interpolation to the structured grids used in cfd is suggested and described in this paper which takes advantage of the logical grid structure this technique which is demonstrated to be robust efficient smoother and a more accurate alternative to linear interpolation is used in the remapping step during the solution adaption procedure applications to the solutions of the incompressible navier stokes equations both 2d and 3d are included