characteristic based time dependent maxwell equation solvers on a general curvilinear frame four cell centered finite volume characteristic based procedures for solving time dependent three dimensional maxwell equations on a general curvilinear frame are developed and implemented on a spherical coordinate system these methods generate simulations or an oscillating electric dipole without wave reflection from the truncated computational domain through a comparative study it is established that an upwind biased third order scheme demonstrates less dispersive and dissipative errors than second order schemes

practical aspects of higher order numerical schemes for wave propagation phenomena this paper examines practical issues related to the use of compact difference based fourth and sixth order schemes for wave propagation phenomena with focus on maxwell s equations of electromagnetics an outline of the formulation and scheme optimization is followed by an assessment of the error accruing from application on stretched meshes with two approaches transformed plane method and physical space differencing in the first technique the truncation error expansion for the sixth order compact scheme confirms that the order of accuracy is preserved if a consistent mesh refinement strategy is followed and further that metrics should be evaluated numerically even if analytic expressions are available physical space differencing formulas are derived for the five point stencil by expressing the coefficients in terms of local spacing ratios the order of accuracy of the reconstruction operator is then verified with a numerical experiment on stretched meshes to ensure stability for a broad range of problems fourier analysis is employed to develop a single parameter family of up to tenth order tridiagonal based spatial filters the implementation of these filters is discussed in terms of their effect on the interior scheme as well as in a 1 d cavity where they are employed to suppress a late time instability the paper concludes after demonstrating the application of the scheme to several 3 d canonical problems utilizing cartesian as well as curvilinear meshes published in 1999 by john wiley sons ltd this article is a u s government work and is in the public domain in the united states

the diameter of the commuting graph of a finite group with trivial centre abstract the commuting graph of a finite group with trivial centre is examined it is shown that the connected components of have diameter at most 10

a new alternating bi diagonal compact scheme for non uniform grids a new compact scheme has been developed for any non uniform grid the compact scheme has been developed for spatial discretization and is analyzed here in conjunction with four stage fourth order runge kutta rk4 scheme for time integration while solving the one dimensional convection equation the space time discretization combination is calibrated by subjecting the system to global spectral analysis gsa which was developed by the authors group here the compact scheme has been obtained by using a combination of two bi diagonal schemes the novel aspect of this scheme is its application in the physical plane directly without the necessity of mapping or transformations some typical cases for problems in acoustics as well as fluid mechanics have been studied here and potential use in large eddy simulations les has been demonstrated by solving navier stokes equation for lid driven cavity

regular article on a class of pade finite volume methods a class of pade finite volume methods providing an improved spectral resolution is presented and compared with well known methods the formulation is based on the sliding averages of the variables and allows the computation of derivatives of all orders using the fourier analysis these methods are examined with respect to i order of accuracy ii spectral resolution iii boundary conditions and iv stability

the complexity of general valued csps an instance of the valued constraint satisfaction problem vcsp is given by a finite set of variables a finite domain of labels and a sum of functions each function depending on a subset of the variables each function can take finite values specifying costs of assignments of labels to its variables or the infinite value which indicates an infeasible assignment the goal is to find an assignment of labels to the variables that minimizes the sum we study assuming that p ne np how the complexity of this very general problem depends on the set of functions allowed in the instances the so called constraint language the case when all allowed functions take values in 0 infty corresponds to ordinary csps where one deals only with the feasibility issue and there is no optimization this case is the subject of the algebraic csp dichotomy conjecture predicting for which constraint languages csps are tractable i e solvable in polynomial time and for which they are np hard the case when all

fourth order difference methods for hyperbolic ibvps abstract in this paper we consider fourth order difference approximations of initial boundary value problems for hyperbolic partial differential equations we use the method of lines approach with both explicit and compact implicit difference operators in space the explicit operator satisfies an energy estimate leading to strict stability for the implicit operator we develop boundary conditions and give a complete proof of strong stability using the laplace transform technique we also present numerical experiments for the linear advection equation and burgers equation with discontinuities in the solution or in its derivative the first equation is used for modeling contact discontinuities in fluid dynamics the second one is used for modeling shocks and rarefaction waves the time discretization is done with a third order runge kutta tvd method for solutions with discontinuities in the solution itself we add a filter based on second order viscosity in case of the non linear burgers equation we use a flux splitting technique that results in an energy estimate for certain difference approximations in which case also an entropy condition is fulfilled in particular we shall demonstrate that the unsplit conservative form produces a non physical shock instead of the physically correct rarefaction wave in the numerical experiments we compare our fourth order methods with a standard second order one and with a third order tvd method the results show that the fourth order methods are the only ones that give good results for all the considered test problems

classifying the complexity of constraints using finite algebras many natural combinatorial problems can be expressed as constraint satisfaction problems this class of problems is known to be np complete in general but certain restrictions on the form of the constraints can ensure tractability here we show that any set of relations used to specify the allowed forms of constraints can be associated with a finite universal algebra and we explore how the computational complexity of the corresponding constraint satisfaction problem is connected to the properties of this algebra hence we completely translate the problem of classifying the complexity of restricted constraint satisfaction problems into the language of universal algebra we introduce a notion of tractable algebra and investigate how the tractability of an algebra relates to the tractability of the smaller algebras which may be derived from it including its subalgebras and homomorphic images this allows us to reduce significantly the types of algebras which need to be classified using our results we also show that if the decision problem associated with a given collection of constraint types can be solved efficiently then so can the corresponding search problem we then classify all finite strictly simple surjective algebras with respect to tractability obtaining a dichotomy theorem which generalizes schaefer s dichotomy for the generalized satisfiability problem finally we suggest a possible general algebraic criterion for distinguishing the tractable and intractable cases of the constraint satisfaction problem

characterising tractable constraints abstract finding solutions to a binary constraint satisfaction problem is known to be an np complete problem in general but may be tractable in cases where either the set of allowed constraints or the graph structure is restricted this paper considers restricted sets of constraints which are closed under permutation of the labels we identify a set of constraints which gives rise to a class of tractable problems and give polynomial time algorithms for solving such problems and for finding the equivalent minimal network we also prove that the class of problems generated by any set of constraints not contained in this restricted set is np complete

optimal biweighted binary trees and the complexity of maintaining partial sums let a be an array the partial sum problem concerns the design of a data structure for implementing the following operations the operation update j x has the effect a j leftarrow a j x and the query operation ssum j returns the partial sum sum i 1 j a i our interest centers upon the optimal efficiency with which sequences of such operations can be performed and we derive new upper and lower bounds in the semigroup model of computation our analysis relates the optimal complexity of the partial sum problem to optimal binary trees relative to a type of weighting scheme that defines the notion of biweighted binary tree

tractable constraints on ordered domains abstract finding solutions to a constraint satisfaction problem is known to be an np complete problem in general but may be tractable in cases where either the set of allowed constraints or the graph structure is restricted in this paper we identify a restricted set of contraints which gives rise to a class of tractable problems this class generalizes the notion of a horn formula in propositional logic to larger domain sizes we give a polynomial time algorithm for solving such problems and prove that the class of problems generated by any larger set of constraints is np complete

a dichotomy theorem for constraint satisfaction problems on a 3 element set the constraint satisfaction problem csp provides a common framework for many combinatorial problems the general csp is known to be np complete however certain restrictions on a possible form of constraints may affect the complexity and lead to tractable problem classes there is therefore a fundamental research direction aiming to separate those subclasses of the csp that are tractable and those which remain np complete schaefer gave an exhaustive solution of this problem for the csp on a 2 element domain in this article we generalise this result to a classification of the complexity of the csp on a 3 element domain the main result states that every subproblem of the csp is either tractable or np complete and the criterion separating them is that conjectured in bulatov et al 2005 and bulatov and jeavons 2001b we also characterize those subproblems for which standard constraint propagation techniques provide a decision procedure finally we exhibit a polynomial time algorithm which for a given set of allowed constraints outputs if this set gives rise to a tractable problem class to obtain the main result and the algorithm we extensively use the algebraic technique for the csp developed in jeavons 1998b bulatov et al 2005 and bulatov and jeavons 2001b

the complexity of quantified constraint satisfaction collapsibility sink algebras and the three element case the constraint satisfaction probem csp is a well acknowledged framework in which many combinatorial search problems can be naturally formulated the csp may be viewed as the problem of deciding the truth of a logical sentence consisting of a conjunction of constraints in front of which all variables are existentially quantified the quantified constraint satisfaction problem qcsp is the generalization of the csp where universal quantification is permitted in addition to existential quantification the general intractability of these problems has motivated research studying the complexity of these problems under a restricted constraint language which is a set of relations that can be used to express constraints this paper introduces collapsibility a technique for deriving positive complexity results on the qcsp in particular this technique allows one to show that for a particular constraint language the qcsp reduces to the csp we show that collapsibility applies to three known tractable cases of the qcsp that were originally studied using disparate proof techniques in different decades quantified 2 sat aspvall plass and tarjan in 1979 quantified horn sat karpinski kleine buning and schmitt in 1987 and quantified affine sat creignou khanna and sudan in 2001 this reconciles and reveals common structure among these cases which are describable by constraint languages over a two element domain in addition to unifying these known tractable cases we study constraint languages over domains of larger size

optimized compact difference based finite volume schemes for linear wave phenomena high order compact difference based finite volume schemes are developed analyzed and implemented for linear wave propagation phenomena with particular emphasis on computational electromagnetics in the time domain the formulation combines the primitive function approach with five point spatially sixth and fourth order methods optimization in the semi discrete case is achieved by minimizing dispersion and isotropy error the fully discrete scheme is examined by adopting the classical fourth order runge kutta technique stability bounds are established and the coefficients for the spatial discretization are readjusted for optimum performance the scheme is then formally extended to multiple dimensions consistent boundary conditions are presented for the reconstruction operator as well as flux specification several calculations in one and three dimensions confirm the properties of the method

the stability of numerical boundary treatments for compact high order finite difference schemes the stability characteristics of various compact fourth and sixth order spatial operators are assessed with the theory of gustafsson kreiss and sundstrom g k s for the semidiscrete initial boundary value problem these results are generalized to the fully discrete case with a recently developed theory of kreiss and wu in all cases favorable comparisons are obtained between g k s theory eigenvalue determination and numerical simulation the conventional definition of stability then is sharpened to include only those spatial discretizations that are asymptotically stable bounded left half plane eigenvalues many of the higher order schemes that are g k s stable are not asymptotically stable a series of compact fourth and sixth order schemes that are both asymptotically and g k s stable for the scalar case are then developed

symmetrized compact scheme for receptivity study of 2d transitional channel flow in many physical problems one must maintain symmetry of numerical schemes the symmetry arising due to geometry and or physical conditions defining the flow the direct simulation of transitional plane poiseuille flow presents one such case that motivated the present study it has been shown here using the method of analyzing non periodic problems in sengupta et al 2003 that compact and other high accuracy schemes display strong directionality of the algorithm and such methods cannot be used for direct simulation of the physical flow this prevalent but unacceptable situation for dns is rectified in the present work and a new scheme is introduced that prevents this asymmetry from contaminating results the simulated transitional flow past 2d channel here using the new scheme are in agreement with experimental results and other recent views of sub critical instabilities

an explicit higher order difference scheme on a compact stencil for elliptic equations on curvilinear geometries abstract a fourth order explicit finite difference scheme on a compact stencil is proposed for a general steady convection diffusion equation on an arbitrary curvilinear coordinate system with computationally generated non uniform grid the method is dependent on the governing differential equation and attains higher order through consistent discretization and accurate evaluation of the transformation metrics extensive comparison of accuracy convergence rate and computation time is made with standard explicit and implicit schemes to highlight the relatively high efficiency of using the proposed scheme applicability of the scheme to irregular flows and geometries is validated by solving for i potential flow past a cambered airfoil at an angle of attack and ii full incompressible navier stokes calculations for flow past a cylinder performing rotary oscillations at low reynolds number

the complexity of constraint satisfaction games and qcsp we study the complexity of two person constraint satisfaction games an instance of such a game is given by a collection of constraints on overlapping sets of variables and the two players alternately make moves assigning values from a finite domain to the variables in a specified order the first player tries to satisfy all constraints while the other tries to break at least one constraint the goal is to decide whether the first player has a winning strategy we show that such games can be conveniently represented by a logical form of quantified constraint satisfaction where an instance is given by a first order sentence in which quantifiers alternate and the quantifier free part is a conjunction of positive atomic formulas the goal is to decide whether the sentence is true while the problem of deciding such a game is pspace complete in general by restricting the set of allowed constraint predicates one can obtain infinite classes of constraint satisfaction games of lower complexity we use the quantified constraint satisfaction framework to study how the complexity of deciding such a game depends on the parameter set of allowed predicates with every predicate one can associate certain predicate preserving operations called polymorphisms we show that the complexity of our games is determined by the surjective polymorphisms of the constraint predicates we illustrate how this result can be used by identifying the complexity of a wide variety of constraint satisfaction games

finite difference schemes for long time integration a general method for constructing finite difference schemes for longtime integration problems is presented it is demonstrated for discretizations of first and second space derivatives however the approach is not limited to these cases the schemes are constructed so as to minimize the global truncation error taking into account the initial data the resulting second order compact schemes can be used for integration times fourfold or more longer than previously studied schemes with similar computational complexity a similar approach was used to obtain improved integration schemes

analysis of central and upwind compact schemes central and upwind compact schemes for spatial discretization have been analyzed with respect to accuracy in spectral space numerical stability and dispersion relation preservation a von neumann matrix spectral analysis is developed here to analyze spatial discretization schemes for any explicit and implicit schemes to investigate the full domain simultaneously this allows one to evaluate various boundary closures and their effects on the domain interior the same method can be used for stability analysis performed for the semi discrete initial boundary value problems ibvp this analysis tells one about the stability for every resolved length scale some well known compact schemes that were found to be g k s and time stable are shown here to be unstable for selective length scales by this analysis this is attributed to boundary closure and we suggest special boundary treatment to remove this shortcoming to demonstrate the asymptotic stability of the resultant schemes numerical solution of the wave equation is compared with analytical solution furthermore some of these schemes are used to solve two dimensional navier stokes equation and a computational acoustic problem to check their ability to solve problems for long time it is found that those schemes that were found unstable for the wave equation are unsuitable for solving incompressible navier stokes equation in contrast the proposed compact schemes with improved boundary closure and an explicit higher order upwind scheme produced correct results the numerical solution for the acoustic problem is compared with the exact solution and the quality of the match shows that the used compact scheme has the requisite drp property

compact fourth order finite volume method for numerical solutions of navier stokes equations on staggered grids the development of a compact fourth order finite volume method for solutions of the navier stokes equations on staggered grids is presented a special attention is given to the conservation laws on momentum control volumes a higher order divergence free interpolation for convective velocities is developed which ensures a perfect conservation of mass and momentum on momentum control volumes three forms of the nonlinear correction for staggered grids are proposed and studied the accuracy of each approximation is assessed comparatively in fourier space the importance of higher order approximations of pressure is discussed and numerically demonstrated fourth order accuracy of the complete scheme is illustrated by the doubly periodic shear layer and the instability of plane channel flow the efficiency of the scheme is demonstrated by a grid dependency study of turbulent channel flows by means of direct numerical simulations the proposed scheme is highly accurate and efficient at the same level of accuracy the fourth order scheme can be ten times faster than the second order counterpart this gain in efficiency can be spent on a higher resolution for more accurate solutions at a lower cost

a new compact spectral scheme for turbulence simulations we propose a new kind of compact difference scheme for the computation of the first and second derivatives in the simulation of high reynolds number turbulent flows the scheme combines and truncates the pseudospectral representation of derivative for convergence acceleration comparison of the wave resolution property with available optimized compact schemes minimizing the prescribed wave resolution error reveals our scheme s superiority for the same size of stencils without introducing optimization parameters an accompanying boundary scheme is also proposed with the stability analysis the proposed scheme is tested for the evaluation of derivatives of a function that decays very slowly in the wavenumber space and for the simulation of three dimensional isotropic turbulence

a finite volume formulation of compact central schemes on arbitrary structured grids in the present paper a formulation allowing the use of compact schemes in the finite volume context on arbitrary meshes is presented the proposed formulation is based on the use of an implicit formula to evaluate the fluxes on the cell faces a series of numerical experiments for a 2d model convection equation a flat plate a subsonic vortical problem as well as the les simulation of channel flow has been carried out the results indicate an important improvement in obtained accuracy compared to a standard central finite volume formulation

constant query testability of assignments to constraint satisfaction problems for each finite relational structure a let csp a denote the csp instances whose constraint relations are taken from a the resulting family of problems csp a has been considered heavily

a fourth order accurate finite volume compact method for the incompressible navier stokes solutions abstract this paper presents a finite volume fourth order accurate compact scheme for discretization of the incompressible navier stokes equations in primitive variable formulation the numerical method of integrating the navier stokes equations comprises a compact finite volume formulation of the average convective and diffusive fluxes the pressure velocity coupling is achieved via the coupled solution of the resulting system of equations the solution of the coupled set of equations is performed with an implicit newton krylov matrix free method for stationary problems for simulation of unsteady flows a standard fourth order runge kutta method was used for temporal discretization and the velocity pressure coupling was ensured at each stage also using the matrix free method several incompressible viscous steady and unsteady flow problems have been computed to assess the robustness and accuracy of the proposed method

tractability and learnability arising from algebras with few subpowers a constraint language gamma on a finite set a has been called polynomially expressive if the number of n ary relations expressible by exists wedge atomic formulas over gamma is bounded by exp o n k for some constant k it has recently been discovered that this property is characterized by the existence of a k 1 ary polymorphism satisfying certain identities such polymorphisms are called k edge operations and include mal cev and near unanimity operations as special cases we prove that if gamma is any constraint language which for some k 1 has a k edge operation as a polymorphism then the constraint satisfaction problem for langle gamma rangle the closure of gamma under exists wedge atomic expressibility is globally tractable we also show that the set of relations definable over gamma using quantified generalized formulas is polynomially exactly learnable using improper equivalence queries

optimised boundary compact finite difference schemes for computational aeroacoustics a set of optimised boundary closure schemes is presented for use with compact central finite difference schemes in computational aeroacoustics caa involving non trivial boundaries the boundary schemes are given in a form of non central compact finite differences they maintain fourth order accuracy a pentadiagonal matrix system and seven point stencil which the main interior scheme employs this paper introduces a new strategy to optimise the boundary schemes in the spectral domain and achieve the best resolution characteristics given a strict tolerance for the dispersion and dissipation errors the boundary schemes are derived from sophisticated extrapolation of solutions outside the domain the extrapolation functions are devised by combining polynomials and trigonometric series which contain extra control variables used to optimise the resolution characteristics the differencing coefficients of the boundary schemes are determined in association with the existing coefficients of the interior scheme which is also optimised through an improved procedure in this paper the accuracy of the proposed schemes is demonstrated by their application to caa benchmark problems

closure properties of constraints many combinatorial search problems can be expressed as constraint satisfaction problems and this class of problems is known to be np complete in general in this paper we investigate the subclasses that arise from restricting the possible constraint types we first show that any set of constraints that does not give rise to an np complete class of problems must satisfy a certain type of algebraic closure condition we then investigate all the different possible forms of this algebraic closure property and establish which of these are sufficient to ensure tractability as examples we show that all known classes of tractable constraints over finite domains can be characterized by such an algebraic closure property finally we describe a simple computational procedure that can be used to determine the closure properties of a given set of constraints this procedure involves solving a particular constraint satisfaction problem which we call an indicator problem

analysis of error control strategies for continuous runge kutta methods there has been considerable recent progress in the analysis and development of interpolation schemes that can be associated with discrete runge kutta methods with the availability of these schemes it can now be asked that a numerical method provide a continuous approximation to the solution thispaper rather than view such a continuous method as an interpolant superimposed on a standard discrete method considers how the interpolant and its associated defect can be effectively used in the underlying error and stepsize control mechanism in particular four error control strategies are considered that can be used in methods based on runge kutta formula pairs with interpolants an asymptotic and a nonasymptotic analysis of each strategy are presented it is shown that a strategy based on direct defect control can provide significant advantages over existing strategies with only a modest increase in cost

conservative form of interpolated differential operator scheme for compressible and incompressible fluid dynamics the proposed scheme which is a conservative form of the interpolated differential operator scheme ido cf can provide high accurate solutions for both compressible and incompressible fluid equations spatial discretizations with fourth order accuracy are derived from interpolation functions locally constructed by both cell integrated values and point values these values are coupled and time integrated by solving fluid equations in the flux forms for the cell integrated values and in the derivative forms for the point values the ido cf scheme exactly conserves mass momentum and energy retaining the high resolution more than the non conservative form of the ido scheme a direct numerical simulation of turbulence is carried out with comparable accuracy to that of spectral methods benchmark tests of riemann problems and lid driven cavity flows show that the ido cf scheme is immensely promising in compressible and incompressible fluid dynamics studies

the complexity of temporal constraint satisfaction problems a temporal constraint language is a set of relations that has a first order definition in q an extended abstract of this article appeared in the proceedings of stoc 08

a proof of the csp dichotomy conjecture many natural combinatorial problems can be expressed as constraint satisfaction problems this class of problems is known to be np complete in general but certain restrictions on the form of the constraints can ensure tractability the standard way to parameterize interesting subclasses of the constraint satisfaction problem is via finite constraint languages the main problem is to classify those subclasses that are solvable in polynomial time and those that are np complete it was conjectured that if a constraint language has a weak near unanimity polymorphism then the corresponding constraint satisfaction problem is tractable otherwise it is np complete in the article we present an algorithm that solves constraint satisfaction problem in polynomial time for constraint languages having a weak near unanimity polymorphism which proves the remaining part of the conjecture 1

fast parallel constraint satisfaction a constraint satisfaction problem csp involves searching for an assignment of values to a given set of variables so that the values assigned satisfy a given set of constraints the general csp is np complete to confront the intractability of the general csp relaxation procedures have been devised instead of searching for a globally consistent assignment of values to the variables try to restrict the domain of values of each variable in a way that ensures local consistency only the relaxation procedures are efficient but have been proved to be inherently sequential in this paper we define a class of csps for which a global solution can be found by a fast parallel algorithm no relaxation preprocessing is needed for the parallel algorithm to work the result is motivated from the problem of labelling a 2 d line drawing of a 3 d object by the clowes huffman malik labelling scheme an important application of csp in computer vision for such a labelling csp the constraint graph can be general but the constraint relations are usually of the type we call implicational it is shown here that a csp with this type of constraint relations and no restrictions on its graph can be solved by an efficient i e with polynomial time complexity sequential algorithm also it is shown that it can be solved by a fast parallel algorithm that executes in time o log3n with o m n3 log n processors on a exlusive read exclusive write parallel random access machine n is the number of variables and m is the number of constrain relations the constraint relations may have arity more than two

non abelian sylow subgroups of finite groups of even order we have been able to prove that every nonabelian sylow subgroup of a finite group of even order contains a nontrivial element which commutes with an involution the proof depends upon the consequences of the classification of finite simple groups the purpose of this note is to announce 4 main theorem every nonabelian sylow subgroup of a finite group of even order contains a nontrivial element which commutes with an involution let g be a finite group and g the prime graph of g g is the graph such that the vertex set is the set of prime divisors of g and two distinct vertices p and r are joined by an edge if and only if there exists an element of order pr in g let n g be the number of connected components of g and dg p r the distance between two vertices p and r of g it has been proved that n g 6 in 12 10 11 9 theorem 1 let g be a finite group of even order and p a prime divisor of g if dg 2 p 2 then a sylow p subgroup of g is abelian theorem 1 is a restatement of the main theorem in terms of the prime graph g corollary 1 let g be a finite group of even order and p a prime divisor of g if is a connected component of g p not containing 2 then a sylow r subgroup of g is abelian for any r there is a certain relation between a subgraph g p of g and brauer characters of p modular representations of g see 3 theorem 2 let g be a finite nonabelian simple group and p an odd prime divisor of g then dg 2 p 1 or 2 provided dg 2 p the significance of the prime graphs of finite groups can be found in 1 3 5 6 7 8 14 15 we apply the classification of finite simple groups see 1 2 4 7 10 13 it has been proved that a minimal counterexample to theorem 1 received by the editors october 20 1997 1991 mathematics subject classification primary 20d05 20d06 20d20

on the algebraic structure of combinatorial problems abstract we describe a general algebraic formulation for a wide range of combinatorial problems including satisfiability graph colorability and graph isomorphism in this formulation each problem instance is represented by a pair of relational structures and the solutions to a given instance are homomorphisms between these relational structures the corresponding decision problem consists of deciding whether or not any such homomorphisms exist we then demonstrate that the complexity of solving this decision problem is determined in many cases by simple algebraic properties of the relational structures involved this result is used to identify tractable subproblems of satisfiability and to provide a simple test to establish whether a given set of boolean relations gives rise to one of these tractable subproblems

optimized prefactored compact schemes the numerical simulation of aeroacoustic phenomena requires high order accurate numerical schemes with low dispersion and dissipation errors in this paper we describe a strategy for developing high order accurate prefactored compact schemes requiring very small stencil support these schemes require fewer boundary stencils and offer simpler boundary condition implementation than existing compact schemes the prefactorization strategy splits the central implicit schemes into forward and backward biased operators using fourier analysis we show it is possible to select the coefficients of the biased operators such that their dispersion characteristics match those of the original central compact scheme and their numerical wavenumbers have equal and opposite imaginary components this ensures that when the forward and backward stencils are added the original central compact scheme is recovered to extend the resolution characteristic of the schemes an optimization strategy is employed in which formal order of accuracy is sacrificed in preference to enhanced resolution characteristics across the range of wavenumbers realizable on a given mesh the resulting optimized schemes yield improved dispersion characteristics compared to the standard sixth and eighth order compact schemes making them more suitable for high resolution numerical simulations in gas dynamics and computational aeroacoustics the efficiency accuracy and convergence characteristics of the new optimized prefactored compact schemes are demonstrated by their application to several test problems

the csp dichotomy holds for digraphs with no sources and no sinks a positive answer to a conjecture of bang jensen and hell bang jensen and hell conjectured in 1990 using the language of graph homomorphisms a constraint satisfaction problem csp dichotomy for digraphs with no sources or sinks the conjecture states that the csp for such a digraph is tractable if each component of its core is a cycle and is np complete otherwise in this paper we prove this conjecture and as a consequence a conjecture of bang jensen hell and macgillivray from 1995 classifying hereditarily hard digraphs further we show that the csp dichotomy for digraphs with no sources or sinks agrees with the algebraic characterization conjectured by bulatov jeavons and krokhin in 2005

a proof that the discrete singular convolution dsc lagrange distributed approximating function ldaf method is inferior to high order finite differences finite differences approximate the mth derivative of a function u x by a series j n nd j m u x j where the x j are the grid points the closely related discrete singular convolution dsc and lagrange distributed approximating function ldaf methods treated here as a single algorithm approximate derivatives in the same way as finite differences but with different numerical weights that depend upon a free parameter a by means of fourier analysis and error theorems we show that the dsc is worse than the standard finite differences in differentiating exp ikx for all k when a a f d where a f d 1 n 1 with n as the stencil width is the value of the dsc parameter that makes its weights most closely resemble those of finite differences for a

prime graph components of the simple groups of lie type over the field of even characteristic abstract we classify the connected components of the prime graphs of the simple groups of lie type over the field of even characteristic

derivation of high order compact finite difference schemes for non uniform grid using polynomial interpolation in this paper simple polynomial interpolation is used to derive arbitrarily high order compact schemes for the first derivative and tridiagonal compact schemes for the second derivative consisting of three second derivative nodes in the interior and two on the boundary on non uniform grids boundary and near boundary schemes of the same order as the interior are also developed using polynomial interpolation and for a general compact scheme on a non uniform grid it is shown that polynomial interpolation is more efficient than the conventional method of undetermined coefficients for finding coefficients of the scheme the high order non uniform schemes along with boundary closure of up to 14th order thus obtained are shown to be stable on a non uniform grid with appropriate stretching so that more grid points are clustered near the boundary the stability and resolution properties of the high order non uniform grid schemes are studied and the results of three numerical tests on stability and accuracy properties are also presented

a new flux vector splitting compact finite volume scheme a new high resolution finite volume method is proposed here that uses flux vector splitting as the building block to represent the physical processes the high accuracy projection in space is obtained here inter alia by using some compact schemes of sengupta et al 1 and lele 2 that have extremely high accuracy in spectral plane this produces a new class of finite volume fv scheme for spatial discretization that has been analyzed for spectral accuracy numerical stability and dispersion relation preservation drp property following the full domain analysis method of 1 using two different time integration strategies these combination of spatial and temporal methods have been tested for two linear wave problems reported in 1 3 and the solution of burgers equation is compared with the analytical results presented in adams and shariff 4 the shock capturing method is based on the proposed technique in 5 that does not require the usage of any nonlinear differencing techniques or limiters to show that the proposed method can also handle irregular grids the burgers equation is solved using non uniform grids also to demonstrate the utility of the proposed scheme to solve practical problems the benchmark problem of nonlinear wave propagation in a one dimensional shock tube has been solved with the initial data as given in 23 by solving the euler equation the analysis and comparison of this flux vector splitting scheme with other well known methods clearly demonstrate the superior scale resolution of the proposed method at the same time providing a neutrally stable scheme when used with four stage runge kutta scheme also the same scheme displays extended ranges of wave numbers and circular frequencies over which drp property is valid the computed results of three test cases and their comparison with analytical results clearly reveal that the presented method can be used for practical problems

higher order solution procedure for three dimensional nonideal magnetogasdynamics a high resolution scheme developed for use in multidisciplinary applications is applied to solve the equations governingthethree dimensionale owofanonidealcompressibleconductinge uidinamagnetice eld both4th order and 6th order spatially implicit schemes are considered in conjunction with up to 10th order e lters the fourthorderclassicalrunge kuttaschemeisemployedfortimeintegration theaccuracyandversatility ofthealgorithm and the accompanying code are explored by solving a wide variety of problems discretized with uniform as well as curvilinear grids with particular emphasis on the unique physical phenomena arising in conducting e uids these

curvilinear finite volume schemes using high order compact interpolation during the last years the need of high fidelity simulations on complex geometries for aeroacoustics predictions has grown most of high fidelity numerical schemes in terms of low dissipative and low dispersive effects lie on finite difference fd approach but for industrial applications fd schemes are less robust compared to finite volume fv ones thus the present study focuses on the development of a new compact fv scheme for two and three dimensional applications the proposed schemes are formulated in the physical space and not in the computational space as it is the case in most of the known works therefore they are more appropriate for general grids they are based on compact interpolation to approximate interface averaged field values using known cell averaged values for each interface the interpolation coefficients are determined by matching taylor series expansions around the interface center two types of schemes can be distinguished the first one uses only the curvilinear abscissa along a mesh line to derive a sixth order compact interpolation formulae while the second more general uses coordinates in a spatial three dimensional frame well chosen this latter is formally sixth order accurate in a preferred direction almost orthogonal to the interface and at most fourth order accurate in transversal directions for non linear problems different approaches can be used to keep the high order scheme however in the present paper a muscl like formulation was sufficient to address the presented test cases all schemes have been modified to treat multiblock and periodic interfaces in such a way that high order accuracy stability good spectral resolution conservativeness and low computational costs are guaranteed this is a first step to insure good scalability of the schemes although parallel performances issues are not addressed as high frequency waves badly resolved could be amplified and then destabilize the scheme compact filtering operators have been used numerous test cases as the linear convection of a gaussian wave the convection of a lamb oseen vortex and the diffraction of an acoustic wave on a plane have been realized to validate the schemes the most efficient schemes are shown to be at least fifth order accurate on linear and non linear convection problems they are also less dissipative and less dispersive on non uniform curvilinear grids than schemes using implicit interpolation with constant coefficients of the same order on uniform cartesian grids

a 2d compact fourth order projection decomposition method a 2d fourth order compact direct scheme projection decomposition method for solving incompressible viscous flows in multi connected rectangular domains is devised in each subdomain the governing navier stokes equations are discretized by using fourth order compact schemes in space and second order scheme in time the coupling between subdomains is based on a direct non overlapping multidomain method it allows to solve each helmholtz poisson problem resulting of a projection method in complex geometries the major difficulty of the poisson neumann problem solvability is addressed and correctly treated the present numerical method is checked through some classical numerical experiments first the second order accuracy in time and the fourth order accuracy in space are shown by matching with the analytical solution of the taylor problem the method is also tested by simulating the flow in a 2d lid driven cavity the utility of the compact scheme projection decomposition method approach is further illustrated by two other benchmark problems viz the flow over a backward facing step and the laminar flow past a square prism the present results are in good agreement with the experimental data and other numerical solutions available in the literature