spatial prediction of soil salinity using electromagnetic induction techniques 1 statistical prediction models a comparison of multiple linear regression and cokriging we describe a regression based statistical methodology suitable for predicting field scale spatial salinity ec conditions from rapidly acquired electromagnetic induction ec data this technique uses multiple linear regression mlr models to estimate soil salinity from ec survey data the mlr models incorporate multiple ec measurements and trend surface parameters to increase the prediction accuracy and can be fitted from limited amounts of ec calibration data this estimation technique is compared to some commonly recommended cokriging techniques with respect to statistical modeling assumptions calibration sample size requirements and prediction capabilities we show that mlr models are theoretically equivalent to and cost effective relative to cokriging for estimating a spatially distributed random variable when the residuals from the regression model are spatially uncorrelated mlr modeling and prediction techniques are demonstrated with data from three salinity surveys

symbol by symbol map demodulation of cpm and psk signals on rayleigh flat fading channels demodulation using the symbol by symbol maximum a posteriori probability map algorithm is presented the algorithm is derived for the case of continuous phase modulation cpm signals transmitted over rayleigh flat fading channels and a corresponding receiver structure is specified it is shown that the map algorithm requires computing for each trellis branch the sum of the products of the weights of all paths through the trellis which pass through that branch and that this generic computational problem can be solved efficiently by an approach that uses a forward and backward recursion through the trellis simulation results are presented which show both the hard and soft decision performance of the map receiver to be robust even in the presence of fade rates of up to 30 of the symbol rate the application of the receiver concept to phase shift keying psk signals is also discussed and then evaluated via simulation the concept of joint demodulation and decoding using iterative processing techniques is introduced it is shown that the map receiver is well suited for iterative processing applications due to its use of a priori symbol probabilities and its production of optimal soft decisions simulation results for the reception of quaternary psk qpsk show that the bit error rate ber performance of the iterative map receiver can approach that of a receiver operating with perfect knowledge of the fading process

continuous phase modulation part i full response signaling the continuous phase modulation cpm signaling scheme has gained interest in recent years because of its attractive spectral properties data symbol pulse shaping has previously been studied with regard to spectra for binary data and modulation index 0 5 in this paper these results have been extended to the m ary case where the pulse shaping is over a one symbol interval the so called full response systems results are given for modulation indexes of practical interest concerning both performance and spectrum comparisons are made with minimum shift keying msk and systems have been found which are significantly better in e b n 0 for a large signal to noise ratio snr without expanded bandwidth schemes with the same bit error probability as msk but with considerably smaller bandwidth have also been found significant improvement in both power and bandwidth are obtained by increasing the number of levels m from 2 to 4

the orthogonal decomposition theorems for mimetic finite difference methods accurate discrete analogs of differential operators that satisfy the identities and theorems of vector and tensor calculus provide reliable finite difference methods for approximating the solutions to a wide class of partial differential equations these methods mimic many fundamental properties of the underlying physical problem including conservation laws symmetries in the solution and the nondivergence of particular vector fields i e they are divergence free and should satisfy a discrete version of the orthogonal decomposition theorem this theorem plays a fundamental role in the theory of generalized solutions and in the numerical solution of physical models including the navier stokes equations and in electrodynamics we are deriving mimetic finite difference approximations of the divergence gradient and curl that satisfy discrete analogs of the integral identities satisfied by the differential operators we first define the natural discrete divergence gradient and curl operators based on coordinate invariant definitions such as gauss s theorem for the divergence next we use the formal adjoints of these natural operators to derive compatible divergence gradient and curl operators with complementary domains and ranges of values in this paper we prove that these operators satisfy discrete analogs of the orthogonal decomposition theorem and demonstrate how a discrete vector can be decomposed into two orthogonal vectors in a unique way satisfying a discrete analog of the formula vec a ggrad varphi curl vec b we also present a numerical example to illustrate the numerical procedure and calculate the convergence rate of the method for a spiral vector field

the discrete duality finite volume method for stokes equations on three dimensional polyhedral meshes we develop a discrete duality finite volume method for the three dimensional steady stokes problem with a variable viscosity coefficient on polyhedral meshes under very general assumptions on the mesh which may admit nonconforming polyhedrons we prove the stability and well posedness of the scheme we also prove the convergence of the numerical approximation to the velocity velocity gradient and pressure and derive a priori estimates for the corresponding approximation error final numerical experiments confirm the theoretical predictions

the mimetic finite difference method for the 3d magnetostatic field problems on polyhedral meshes we extend the mimetic finite difference mfd method to the numerical treatment of magnetostatic fields problems in mixed div curl form for the divergence free magnetic vector potential to accomplish this task we introduce three sets of degrees of freedom that are attached to the vertices the edges and the faces of the mesh and two discrete operators mimicking the curl and the gradient operator of the differential setting then we present the construction of two suitable quadrature rules for the numerical discretization of the domain integrals of the div curl variational formulation of the magnetostatic equations this construction is based on an algebraic consistency condition that generalizes the usual construction of the inner products of the mfd method we also discuss the linear algebraic form of the resulting mfd scheme its practical implementation and discuss existence and uniqueness of the numerical solution by generalizing the concept of logically rectangular or cubic meshes by hyman and shashkov to the case of unstructured polyhedral meshes the accuracy of the method is illustrated by solving numerically a set of academic problems and a realistic engineering problem

regularization parameter determination for discrete ill posed problems the straightforward solution of discrete ill posed linear systems of equations or least squares problems with error contaminated data does not in general give meaningful results because the propagated error destroys the computed solution the problems have to be modified to reduce their sensitivity to the error in the data the amount of modification is determined by a regularization parameter it can be difficult to determine a suitable value of the regularization parameter when no knowledge of the norm of error in the data is available this paper proposes a new simple technique for determining a value of the regularization parameter that can be applied in this situation it is based on comparing computed solutions determined by tikhonov regularization and truncated singular value decomposition analogous comparisons are proposed for large scale problems the technique for determining the regularization parameter implicity provides an estimate for the norm of the error in the data

linear receivers for correlatively coded msk in this paper we show that many spectrally efficient modified msk schemes termed generalized msk although not representable as oqpsk may nevertheless be suboptimally demodulated using an i q receiver with a proper choice of carrier phase offset correlatively coded msk schemes with i q receivers are studied and it is concluded that duobinary msk and 1 2d d 2 4 msk represent good performance bandwidth tradeoffs among first and second order correlative coding polynomial schemes the optimal design of these receivers are considered subject to the constraint of a finite duration impulse response especially for asymptotic cases of arbitrarily small and large snr filter design based on a zero intersymbol interference constraint for pam based approximations of the signals is also considered the optimized linear i q receivers for 1 d 2 msk and 1 d 2 4 msk are presented these receivers are only 0 28 and 1 24 db poorer than the optimal viterbi receivers at high snr

convergence analysis of the high order mimetic finite difference method we prove second order convergence of the conservative variable and its flux in the high order mfd method the convergence results are proved for unstructured polyhedral meshes and full tensor diffusion coefficients for the case of non constant coefficients we also develop a new family of high order mfd methods theoretical result are confirmed through numerical experiments

superconvergence of the velocity in mimetic finite difference methods on quadrilaterals superconvergence of the velocity is established for mimetic finite difference approximations of second order elliptic problems over h 2 uniform quadrilateral meshes the superconvergence result holds for a full tensor coefficient the analysis exploits the relation between mimetic finite differences and mixed finite element methods via a special quadrature rule for computing the scalar product in the velocity space the theoretical results are confirmed by numerical experiments

approximation of boundary conditions for mimetic finite difference methods abstract the numerical solution of partial differential equations solved with finite difference approximations that mimic the symmetry properties of the continuum differential operators and satisfy discrete versions of the appropriate integral identities are more likely to produce physically faithful results furthermore those properties are often needed when using the energy method to prove convergence and stability of a particular difference approximation unless special care is taken mimetic difference approximations derived for the interior grid points will fail to preserve the symmetries and identities between the gradient curl and divergence operators at the computational boundary in this paper we describe how to incorporate boundary conditions into finite difference methods so the resulting approximations mimic the identities for the differential operators of vector and tensor calculus the approach is valid for a wide class of partial differential equations of mathematical physics and will be described for poisson s equation with dirichlet neumann and robin boundary conditions we prove that the resulting difference approximation is symmetric and positive definite for each of these boundary conditions

structure optimization and realization of ffsk trellis codes the structure of combinations of l k binary trellis encoders and fast frequency shift keying ffsk modulation is studied a novel method for the optimization of these combinations is proposed it is concluded that regardless of the particular realization the best combinations can always be obtained by using a so called matched convolutional code optimum ffsk codes of rates 1 2 and 2 3 for up to 64 and 32 states respectively are reported it is shown that the best matched encoders for ffsk modulation are also matched and best for any ffsk type scheme where the pulse shape is required to satisfy nyquist s third criterion

nyquist 1 universal filters the nyquist 1928 1 filters nfls with both nonlinear phase response and amplitude response of nonspecified symmetry are investigated it is shown that one of the filter s responses amplitude or phase can be chosen almost arbitrary the second one is then derived from the condition of zero intersymbol interference isi in data transmission synchronous systems as a specific application of the presented theory a simple procedure for calculating nfl s with isi free matched and unmatched filter properties is proposed

virtual element methods for plate bending problems abstract we discuss the application of virtual elements to linear plate bending problems in the kirchhoff love formulation as we shall see in the virtual element environment the treatment of the c 1 continuity condition is much easier than for traditional finite elements the main difference consists in the fact that traditional finite elements for every element k and for every given set of degrees of freedom require the use of a space of polynomials or piecewise polynomials for composite elements for which the given set of degrees of freedom is unisolvent for virtual elements instead we only need unisolvence for a space of smooth functions that contains a subset made of polynomials whose degree determines the accuracy as we shall see the non polynomial part of our local spaces does not need to be known in detail and therefore the construction of the local stiffness matrix is simple and can be done for much more general geometries

the finite volume scheme preserving extremum principle for diffusion equations on polygonal meshes we construct a new nonlinear finite volume scheme for diffusion equation on polygonal meshes and prove that the scheme satisfies the discrete extremum principle our scheme is locally conservative and has only cell centered unknowns numerical results are presented to show how our scheme works for preserving discrete extremum principle and positivity on various distorted meshes

recovering the electrical conductivity of the soil via a linear integral model abstract electromagnetic induction techniques are often used to ascertain the presence of conductive substances in the subsoil the device we are interested in generates an electromagnetic field and measures the secondary field produced by eddy currents induced by the primary field we analyze a linear model which reproduces the device readings consisting of a system of two fredholm linear integral equations of the first kind after studying the continuous problem in various function spaces we describe three collocation methods to transform the integral equations into a system of linear equations which is solved by a regularization technique numerical experiments show the performance of the different discretizations and of a particular approach to deal with the integral truncation error we also verify the influence on the solution of regularization matrices based on the discretization of the first and second derivative

a new interpretation of the average matched filter for msk type receivers the minimum mean square error approximation to a generalized minimum shift keying msk signal using an offset quadrature phase shift keying waveform with an elementary pulse g t is considered it is shown that the optimum shape of g t gamma t coincides with the average pulse of the generalized msk signal therefore gamma t is the impulse response of the corresponding average matched fiber

the mimetic finite difference discretization of diffusion problem on unstructured polyhedral meshes we study the mimetic finite difference discretization of diffusion type problems on unstructured polyhedral meshes we demonstrate high accuracy of the approximate solutions for general diffusion tensors the second order convergence rate for the scalar unknown and the first order convergence rate for the vector unknown on smooth or slightly distorted meshes on non matching meshes and even on meshes with irregular shaped polyhedra with flat faces we show that in general the meshes with non flat faces require more than one flux unknown per mesh face to get optimal convergence rates

exact and approximate construction of digital phase modulations by superposition of amplitude modulated pulses amp minimum shift keying and offset qpsk are two well known modulations which can be interpreted as a set of time phase shifted am pulses we show in this paper that any constant amplitude binary phase modulation can also be expressed as a sum of a finite number of time limited amplitude modulated pulses amp decomposition new methods for computing autocorrelation and power frequency spectrum are derived which give very simple results for half integer index modulations we also show that the signal can be built with good accuracy using only one optimized pulse main pulse this synthesis is particularly satisfactory for modulations that have good spectral characteristics and or low index

convergence of the mimetic finite difference method for diffusion problems on polyhedral meshes the stability and convergence properties of the mimetic finite difference method for diffusion type problems on polyhedral meshes are analyzed the optimal convergence rates for the scalar and vector variables in the mixed formulation of the problem are proved

an extension of pulse shaping filter theory the article presents a simple alternative approach to pulse shaping filters with isi free matched white noise case and unmatched filter properties a nyquist 1928 1 filter in closed form is proved to be isi free with or without matched filtering when its complex transfer function is derived from an initially given nyquist 1 filter the simplicity of the application of this procedure is illustrated by an example

a residual based error estimator for the mimetic finite difference method we present a local error indicator for the mimetic finite difference method for diffusion type problems on polyhedral meshes under essentially the same general hypotheses used in siam j numer anal 43 1872 1896 2005 to show the convergence of the method we prove the global reliability and local efficiency of the proposed estimator

maximum likelihood sequence estimation of cpm signals transmitted over rayleigh flat fading channels a method for the sequential updating of log likelihood functions for maximum likelihood sequence estimation is presented it is shown that in a general case this method can be implemented using kalman filtering techniques for the special case of rayleigh flat fading and continuous phase modulation cpm signaling this approach is shown to lead to an attractive receiver structure this type of receiver called the linear predictive receiver can be implemented in the form of the viterbi algorithm with the trellis updates being computed using a bank of finite pulse response fir filter and square operations simulation results are presented that demonstrate the superiority of the linear predictive receiver over receivers employing differential detection in the presence of fast fading it is shown that the optimal linear predictive receiver does not possess an irreducible error rate for a class of rayleigh fading channels used to model terrestrial mobile channels

error analysis for a mimetic discretization of the steady stokes problem on polyhedral meshes we present the development convergence analysis and numerical tests of the mimetic finite difference method for the stokes problem on two dimensional polygonal and three dimensional polyhedral meshes

an improved monotone finite volume scheme for diffusion equation on polygonal meshes we construct a new nonlinear monotone finite volume scheme for diffusion equation on polygonal meshes the new scheme uses the cell edge unknowns instead of cell vertex unknowns as the auxiliary unknowns in order to improve the accuracy of monotone scheme our scheme is locally conservative and has only cell centered unknowns numerical results are presented to show how our scheme works for preserving positivity on various distorted meshes specially numerical results show that the new scheme is robust and more accurate than the existing monotone scheme on some kinds of meshes

convergence of the mimetic finite difference method for eigenvalue problems in mixed form optimal convergence rates for the mimetic finite difference method applied to eigenvalue problems in mixed form are proved the analysis is based on a new a priori error bound for the source problem and relies on the existence of an appropriate elemental lifting of the mimetic discrete solution compared to the original convergence analysis of the method the new a priori estimate does not require any extra regularity assumption on the right hand side of the source problem numerical results confirming the optimal behavior of the method are presented

high order mimetic finite difference method for diffusion problems on polygonal meshes the mimetic finite difference mfd methods mimic important properties of physical and mathematical models as a result conservation laws solution symmetries and the fundamental identities of the vector and tensor calculus are held for discrete models the mfd methods retain these attractive properties for full tensor coefficients and arbitrary polygonal meshes which may include non convex and degenerate elements the existing mfd methods for solving diffusion type problems are second order accurate for the conservative variable temperature pressure energy etc and only first order accurate for its flux we developed new high order mfd methods which are second order accurate for both scalar and vector variables the second order convergence rates are demonstrated with a few numerical examples on randomly perturbed quadrilateral and polygonal meshes

a higher order formulation of the mimetic finite difference method a new mimetic finite difference method for the diffusion problem is developed by using a linear interpolation for the numerical fluxes this approach provides a higher order accurate approximation to the flux of the exact solution in analogy with the original formulation a family of local scalar products is constructed to satisfy the fundamental properties of local consistency and spectral stability the scalar solution field is approximated by a piecewise constant function a computationally efficient postprocessing technique is also proposed to get a piecewise quadratic polynomial approximation to the exact scalar variable finally optimal convergence rates and accuracy improvement with respect to the lower order formulation are shown by numerical examples

a parallel and adaptive hybridized discontinuous galerkin method for anisotropic nonhomogeneous diffusion abstract the diffusion equation in anisotropic and nonhomogeneous media arises in the study of flow through porous media with sharp material interfaces we discuss the solution of this problem by a hybrid discontinuous galerkin hdg method the method can be applied in three steps first we use a condensation technique to derive the scalar variable and the flux inside each element in terms of the numerical trace on the faces of that element then we form a global system of equations to solve for these numerical traces we then solve the equation inside each element for the internal unknowns using the obtained numerical traces in the global solve step similar to other dg variants hdg is a locally conservative method and a noticeable share of calculations are performed independently within each element in a mesh with p th order elements p 0 this method gives p 1 order of accuracy for smooth solutions for both the scalar variable and the flux moreover by using a simple post processing technique one can reach an accuracy of order p 2 for the scalar variable to be able to handle problems with sharp material discontinuities we use an adaptive refinement strategy with octree grid structure hence we avoid a larger global system which would arise from a fine uniform grid in this process we refine those elements with highest gradient of flux at two sides of their faces we have also utilized shared and distributed memory parallelism to enhance the performance of the method the method is implemented using different modules of deal ii bangerth and kanschat 1999 petsc balay et al 2015 p4est burstedde et al 2011 and hypre falgout and yang 2002 to demonstrate the accuracy efficiency scalability and flexibility of the method several two and three dimensional numerical experiments are studied

calculating digital fm spectra by means of autocorrelation in sharp contrast to the task of calculating the power spectrum for a general digital fm scheme the autocorrelation can easily be obtained by considering a class of fm schemes having a time limited autocorrelation function truncation is avoided and applying a fourier transformation power spectral densities are easily obtained a method is applied taking these properties into account thus a powerful tool is available for investigation of different parameters within the considered digital fm modulation format

an extension of the discrete variational method to nonuniform grids the discrete variational method is a method used to derive finite difference schemes that inherit the conservation dissipation property of the original equations although this method has mainly been developed for uniform grids we extend this method to multidimensional nonuniform meshes

the discrete variational derivative method based on discrete differential forms as is well known for pdes that enjoy a conservation or dissipation property numerical schemes that inherit this property are often advantageous in that the schemes are fairly stable and give qualitatively better numerical solutions in practice lately furihata and matsuo have developed the so called discrete variational derivative method that automatically constructs energy preserving or dissipative finite difference schemes although this method was originally developed on uniform meshes the use of non uniform meshes is of importance for multi dimensional problems on the other hand the theories of discrete differential forms have received much attention recently these theories provide a discrete analogue of the vector calculus on general meshes in this paper we show that the discrete variational derivative method and the discrete differential forms by bochev and hyman can be combined applications to the cahn hilliard equation and the klein gordon equation on triangular meshes are provided as demonstrations we also show that the schemes for these equations are h1 stable under some assumptions in particular one for the nonlinear klein gordon equation is obtained by combination of the energy conservation property and the discrete poincare inequality which are the temporal and spacial structures that are preserved by the above methods

a mimetic discretization of the reissner mindlin plate bending problem we present a mimetic approximation of the reissner mindlin plate bending problem which uses deflections and rotations as discrete variables the method applies to very general polygonal meshes even with non matching or non convex elements we prove linear convergence for the method uniformly in the plate thickness

the first nyquist criterion applied to coherent receiver design for generalised msk signals a simple procedure for designing the post detection filter of an msk type receiver for continuous phase modulation with modulation index h 0 5 generalized msk signals is proposed the criterion descends from a useful general representation of this class of signals the frequency response of the baseband receiver filter is analytically optimized in closed form whatever the modulation pulse shaping of the transmitted signal and signal to noise ratio at the receiver the criterion is pointed out through a significant exact representation of generalized msk signals whatever the modulation pulse shaping waveform which is assumed to be included in a time range equal to lt t symbol time the main part of intersymbol interference as appears from the representation of the cpm signal is cancelled by applying the nyquist criterion to the most significant function among those describing the signal structure the numerical results obtained show a performance improvement with respect to the averaged matched filter amf criterion and are very close to the results reported in the literature deriving from more complex design criteria the suitability of the design criterion is also tested in the presence of interferers showing a significant advantage of the proposed filter when considering adjacent channel interference

h text div h div and h mathbf curl h curl conforming virtual element methods in the present paper we construct virtual element spaces that are h mathrm div h div conforming and h mathbf curl h curl conforming on general polygonal and polyhedral elements these spaces can be interpreted as a generalization of well known finite elements we moreover present the basic tools needed to make use of these spaces in the approximation of partial differential equations finally we discuss the construction of exact sequences of vem spaces

higher order mimetic methods for unstructured meshes a higher order mimetic method for the solution of partial differential equations on unstructured meshes is developed and demonstrated on the problem of conductive heat transfer mimetic discretization methods create discrete versions of the partial differential operators such and the gradient and divergence that are exact in some sense and therefore mimic the important mathematical properties of their continuous counterparts the proposed numerical method is an interesting mixture of both finite volume and finite element ideas while the ideas presented can be applied to arbitrarily high order accuracy we focus in this work on the details of creating a third order accurate method the proposed method is shown to be exact for piecewise quadratic solutions and shows third order convergence on arbitrary triangular tetrahedral meshes the numerical accuracy of the method is confirmed on both two dimensional and three dimensional unstructured meshes the computational cost required for a desired accuracy is analyzed against lower order mimetic methods

mimetic finite difference method for the stokes problem on polygonal meshes various approaches to extend finite element methods to non traditional elements general polygons pyramids polyhedra etc have been developed over the last decade the construction of basis functions for such elements is a challenging task and may require extensive geometrical analysis the mimetic finite difference mfd method works on general polygonal meshes and has many similarities with low order finite element methods both schemes try to preserve the fundamental properties of the underlying physical and mathematical models the essential difference between the two schemes is that the mfd method uses only the surface representation of discrete unknowns to build the stiffness and mass matrices since no extension of basis functions inside the mesh elements is required practical implementation of the mfd method is simple for polygonal meshes that may include degenerate and non convex elements in this article we present a new mfd method for the stokes problem on arbitrary polygonal meshes and analyze its stability the method is developed for the general case of tensor coefficients which allows us to apply it to a linear elasticity problem as well numerical experiments show for the velocity variable second order convergence in a discrete l 2 norm and first order convergence in a discrete h 1 norm for the pressure variable first order convergence is shown in the l 2 norm

a two level method for mimetic finite difference discretizations of elliptic problems we propose and analyze a two level method for mimetic finite difference approximations of second order elliptic boundary value problems we prove that the two level algorithm is uniformly convergent i e the number of iterations needed to achieve convergence is uniformly bounded independently of the characteristic size of the underlying partition we also show that the resulting scheme provides a uniform preconditioner with respect to the number of degrees of freedom numerical results that validate the theory are also presented

parametric construction of nyquist i pulses a novel parametric approach for constructing families of intersymbol interference isi free pulses is presented and examined some new pulses so constructed have smaller maximum distortion a more open receiver eye and a smaller probability of error in the presence of symbol timing error than the nyquist raised cosine pulse for the same excess bandwidth the parametric approach gives more degrees of freedom in the design of isi free pulses and subsumes previous isi free pulses as special cases a number of theorems that relate time domain behaviors of a pulse to the pulse s frequency spectrum are proved a previously known result relating pulse tail time decay to discontinuity of the pulse frequency spectrum is corrected and clarified

an a posteriori error estimator for the mimetic finite difference approximation of elliptic problems we present an a posteriori error indicator for the mimetic finite difference approximation of elliptic problems in the mixed form we show that this estimator is reliable and efficient with respect to an energy type error comprising both flux and pressure its performance is investigated by numerically solving the diffusion equation on computational domains with different shapes different permeability tensors and different types of computational meshes copyright 2008 john wiley sons ltd

legendre multi projection methods for solving eigenvalue problems for a compact integral operator in this paper we consider the m galerkin and m collocation methods for solving the eigenvalue problem for a compact integral operator with smooth kernels using legendre polynomial bases we obtain error bounds for the eigenvalues and the gap between the spectral subspaces in both legendre m galerkin and legendre m collocation methods we also obtain superconvergence results for the eigenvalues and iterated eigenvectors in both l 2 and infinity norm we illustrate our results with numerical examples

analysis of the monotonicity conditions in the mimetic finite difference method for elliptic problems the maximum principle is one of the most important properties of solutions of partial differential equations its numerical analog the discrete maximum principle dmp is one of the most difficult properties to achieve in numerical methods especially when the computational mesh is distorted to adapt and conform to the physical domain or the problem coefficients are highly heterogeneous and anisotropic violation of the dmp may lead to numerical instabilities such as oscillations and to unphysical solutions such as heat flow from a cold material to a hot one in this work we investigate sufficient conditions to ensure the monotonicity of the mimetic finite difference mfd method on two and three dimensional meshes these conditions result in a set of general inequalities for the elements of the mass matrix of every mesh element efficient solutions are devised for meshes consisting of simplexes parallelograms and parallelepipeds and orthogonal locally refined elements as those used in the amr methodology on simplicial meshes it turns out that the mfd method coincides with the mixed hybrid finite element methods based on the low order raviart thomas vector space thus in this case we recover the well established conventional angle conditions of such approximations instead in the other cases a suitable design of the mfd method allows us to formulate a monotone discretization for which the existence of a dmp can be theoretically proved moreover on meshes of parallelograms we establish a connection with a similar monotonicity condition proposed for the multi point flux approximation mpfa methods numerical experiments confirm the effectiveness of the considered monotonicity conditions

parameter determination for tikhonov regularization problems in general form abstract tikhonov regularization is one of the most popular methods for computing an approximate solution of linear discrete ill posed problems with error contaminated data a regularization parameter 0 balances the influence of a fidelity term which measures how well the data are approximated and of a regularization term which dampens the propagation of the data error into the computed approximate solution the value of the regularization parameter is important for the quality of the computed solution a too large value of 0 gives an over smoothed solution that lacks details that the desired solution may have while a too small value yields a computed solution that is unnecessarily and possibly severely contaminated by propagated error when a fairly accurate estimate of the norm of the error in the data is known a suitable value of often can be determined with the aid of the discrepancy principle this paper is concerned with the situation when the discrepancy principle cannot be applied it then can be quite difficult to determine a suitable value of we consider the situation when the tikhonov regularization problem is in general form i e when the regularization term is determined by a regularization matrix different from the identity and describe an extension of the cose method for determining the regularization parameter in this situation this method has previously been discussed for tikhonov regularization in standard form i e for the situation when the regularization matrix is the identity it is well known that tikhonov regularization in general form with a suitably chosen regularization matrix can give a computed solution of higher quality than tikhonov regularization in standard form

nyquist 3 pulse shaping in continuous phase modulation continuous phase modulation cpm schemes using nyquist 3 pulse shaping and correlative codes are popular candidates for mobile radio applications this paper presents a detailed study of the effects of nyquist 3 pulse shaping on the spectral characteristics of cpm schemes with a modulation index of 1 2 the influence of pulse parameters such as its shape bandwidth coding polynomial and truncation length on spectral characteristics such as main lobe fractional power bandwidths and out of band power levels is thoroughly investigated error performance is also briefly analyzed among uncoded schemes a new scheme using a pulse satisfying both nyquist 3 and nyquist 2 criteria is pointed out as a promising candidate and as a good compromise between spectral and power efficiencies

a cell centred finite volume method for the poisson problem on non graded quadtrees with second order accurate gradients this paper introduces a two dimensional cell centred finite volume discretization of the poisson problem on adaptive cartesian quadtree grids which exhibits second order accuracy in both the solution and its gradients and requires no grading condition between adjacent cells at t junction configurations which occur wherever resolution differs between neighboring cells use of the standard centred difference gradient stencil requires that ghost values be constructed by interpolation to properly recover second order accuracy in the resulting numerical gradients prior work addressing block structured grids and graded trees has shown that quadratic rather than linear interpolation is required the gradients otherwise exhibit only first order convergence which limits potential applications such as fluid flow however previous schemes fail or lose accuracy in the presence of the more complex t junction geometries arising in the case of general non graded quadtrees which place no restrictions on the resolution of neighboring cells we therefore propose novel quadratic interpolant constructions for this case that enable second order convergence by relying on stencils oriented diagonally and applied recursively as needed the method handles complex tree topologies and large resolution jumps between neighboring cells even along the domain boundary and both dirichlet and neumann boundary conditions are supported numerical experiments confirm the overall second order accuracy of the method in the l norm

equivalent projectors for virtual element methods in the original virtual element space with degree of accuracy k projector operators in the h 1 seminorm onto polynomials of degree k can be easily computed on the other hand projections in the l 2 norm are available only on polynomials of degree k 2 directly from the degrees of freedom here we present a variant of the virtual element method that allows the exact computations of the l 2 projections on all polynomials of degree k the interest of this construction is illustrated with some simple examples including the construction of three dimensional virtual elements the treatment of lower order terms the treatment of the right hand side and the l 2 error estimates

flux reconstruction and solution post processing in mimetic finite difference methods abstract we present a post processing technique for the mimetic finite difference solution of diffusion problems in mixed form our post processing method yields a piecewise linear approximation of the scalar variable that is second order accurate in the l2 norm on quite general polyhedral meshes including non convex and non matching elements the post processing is based on the reconstruction of vector fields projected onto the mimetic space of vector variables this technique is exact on constant vector fields and is shown to be independent of the mimetic scalar product choice if a local consistency condition is satisfied the post processing method is computationally inexpensive optimal performance is confirmed by numerical experiments

design and analysis of feedforward symbol timing estimators based on the conditional maximum likelihood principle this paper presents a general feedforward symbol timing estimation framework based on the conditional maximum likelihood principle the proposed timing estimator presents reduced implementation complexity and is obtained by performing an approximation on the fourier series expansion of the conditional maximum likelihood function the proposed algorithm is applied to linear modulations and two commonly used continuous phase modulations minimum shift keying msk and gaussian msk gmsk for the linear modulations it is shown both analytically and via simulations that the performance of the proposed estimator is very close to the conditional crb and modified crb for signal to noise ratios snrs in the range snr spl les 30 db furthermore the proposed estimator is shown to be asymptotically equivalent to the classic square law nonlinearity estimator under certain conditions in the case of msk and gmsk modulations although the proposed algorithm reaches the conditional crb at certain snrs however the conditional crb is quite far away from the modified crb and there exists an alternative algorithm whose performance comes closer to the modified crb therefore the proposed estimator is more suitable for linear modulations than for msk and gmsk modulations

mimetic finite difference methods for diffusion equations on non orthogonal non conformal meshes mimetic discretizations based on the support operators methodology are derived for non orthogonal locally refined quadrilateral meshes the second order convergence rate on non smooth meshes is verified with numerical examples

virtual elements for linear elasticity problems we discuss the application of virtual elements to linear elasticity problems for both the compressible and the nearly incompressible case virtual elements are very close to mimetic finite differences see for linear elasticity l beirao da veiga m2an math model numer anal 44 2010 pp 231 250 and in particular to higher order mimetic finite differences as such they share the good features of being able to represent in an exact way certain physical properties conservation incompressibility etc and of being applicable in very general geometries the advantage of virtual elements is the ductility that easily allows high order accuracy and high order continuity

reduced complexity detection and phase synchronization of cpm signals based on an extension of laurent 1986 decomposition of continuous phase modulation cpm signals into a sum of linearly modulated components we derive a class of reduced complexity maximum likelihood ml coherent detection and closed loop phase synchronization schemes the complexity of the resulting detection schemes expressed in terms of the number of matched filters and states of a viterbi algorithm is significantly reduced with respect to that of optimal coherent receivers with negligible performance loss this result extends a known one valid for the binary case to multilevel cpm the proposed synchronization schemes do not require an increased number of matched filters and are perfectly suitable to be used in conjunction with these receivers based on the phase locked loop pll equivalent linear model a method for optimizing the parameters of digital second order pll s is presented numerical examples based on theoretical analysis and computer simulation are provided for two specific formats in the cpm class tamed frequency modulation tfm and a quaternary raised cosine rc modulation

a collocated method for the incompressible navier stokes equations inspired by the box scheme we present a new finite difference numerical method to solve the incompressible navier stokes equations using a collocated discretization in space on a logically cartesian grid the method shares some common aspects with and it was inspired by the box scheme it uses centered second order accurate finite difference approximations for the spatial derivatives combined with semi implicit time integration the proposed method is constructed to ensure discrete conservation of mass and momentum by discretizing the primitive velocity pressure form of the equations the continuity equation is enforced exactly to machine accuracy at the collocated locations whereas the momentum equations are evaluated in a staggered manner this formulation preempts the appearance of spurious pressure modes in the embedded elliptic problem associated with the pressure the method shows uniform order of accuracy both in space and time for velocity and pressure in addition the skew symmetric form of the non linear advection term of the navier stokes equations improves discrete conservation of kinetic energy in the inviscid limit to within the order of the truncation error of the time integrator the method has been formulated to accommodate different types of boundary conditions fully periodic periodic channel inflow outflow and lid driven cavity always ensuring global mass conservation a novel aspect of this finite difference formulation is the derivation of the discretization near boundaries using the weak form of the equations as in the finite element method the method of manufactured solutions is utilized to perform accuracy analysis and verification of the solver to assess the applicability of the new method presented in this paper four realistic flow problems have been simulated and results are compared with those in the literature these cases include a lid driven cavity backward facing step kovasznay flow and fully developed turbulent channel