generalization of the darboux transformation and generalized harmonic oscillators the darbroux transformation is generalized for time dependent hamiltonian systems which include a term linear in momentum and a time dependent mass the formalism for the n fold application of the transformation is also established and these formalisms are applied for a general quadratic system a generalized harmonic oscillator and a quadratic system with an inverse square interaction up to n 2 among the new features found it is shown for the general quadratic system that the shape of potential difference between the original system and the transformed system could oscillate according to a classical solution which is related to the existence of coherent states in the system

darboux transformations and supersymmetry for the generalized schrodinger equations in 1 1 dimensions we study intertwining relations supersymmetry and darboux transformations for generalized schrodinger equations in 1 1 dimensions we obtain intertwiners in an explicit form by means of which we construct arbitrary order darboux transformations for our class of equations we develop a corresponding supersymmetric formulation and prove equivalence of the darboux transformations with the supersymmetry formalism finally we show that our darboux transformations can also be constructed by means of point transformations avoiding the use of intertwiners

a procedure for efficient generation of solution adapted unstructured grids abstract an efficient procedure for generation of solution adapted unstructured grids is presented the grid generation procedure is based upon a delaunay triangulation scheme combined with new adaptive point source techniques with this method high quality solution adapted grids can be generated efficiently techniques are presented for obtaining adaptation sources which automatically detect relevant features in the flow field the overall procedure is coupled with a finite element flow solver computed solutions are presented which successfully demonstrate the overall procedure for a variety of aerospace configurations

the l fuzzy hypermodules in this paper we introduce the concept of l fuzzy hypermodules over an l fuzzy hyperring and investigate some of their properties we provide the notion of l fuzzyr subhypermodules of an l fuzzy r hypermodule and derive a kind of l fuzzy quotient hypermodule by using an l fuzzy r subhypermodule we also study the properties of l fuzzy a regular relation on l fuzzy r hypermodules and investigate l fuzzy hypermodule strong homomorphism

edges stars superedges and chains abstract several possibilities for the reduction of indirect addressing operations within edge based solvers are discussed it is shown that indirect addressing operations may be reduced by a factor in excess of 1 4 if edges are grouped and linked together tests of benchmark loops on two common engineering computer platforms reveal that cpu saving factors ranging from 1 3 to 3 5 may be realized when switching from edge based to superedge or chain based loops

multigrid solution of the two dimensional euler equations on unstructured triangular meshes a multigrid algorithm has been developed to accelerate the convergence of the euler equations to a steady state on unstructured triangular meshes the method operates on a sequence of coarse and fine unstructured meshes and assumes no relation exists between the various meshes a tree search algorithm is used to efficiently identify regions of overlap between coarse and fine grid cells the multigrid method is applied to two different discretizations of the euler equations and results about multi element airfoils are presented for both discretization schemes convergence is accelerated by an order of magnitude resulting in convergence rates comparable to those obtained with structured multigrid algorithms

implicit flux split euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes improved algorithms for the solution of the time dependent euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes the improvements have been developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers the spatial discretization involves a flux split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure the temporal discretization involves an implicit time integration shceme using a gauss seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems for example very large time steps may be used for rapid convergence to steady state and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability steady and unsteady flow results are presented for the naca 0012 airfoil to demonstrate applications of the new euler solvers the unsteady results were obtained for the airfoil pitching harmonically about the quarter chord the resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data the paper presents a description of the euler solvers along with results and comparisons which assess the capability

intertwining relations and darboux transformations for schrodinger equations in n 1 dimensions we evaluate the intertwining relation for schrodinger equations in n 1 dimensions the conditions for the existence of a darboux transformation are analyzed and compared to their 1 1 dimensional counterparts a complete solution of the conditions is given for 2 1 dimensions and a darboux transformation is constructed

a multigrid method with unstructured adaptive grids for steady euler equations the multigrid method based on multi stage jacobi relaxation earlier developed by the authors for structured grid calculations with euler equations is extended to unstructured grid applications the meshes are generated with delaunay triangulation algorithms and are adapted to the flow solution

strand grid solution procedures for sharp corners the strand cartesian grid approach provides many advantages for complex moving body flow simulations including fully automatic volume grid generation highly scalable domain connectivity and high order accuracy in this work the authors evaluate methods of handling sharp corners with strand grids through combinations of strand vector smoothing multiple strands emanating from a single surface node and telescoping cartesian refinement into corner regions of the near body grid a new discretization strategy is introduced to better tolerate mesh skewness induced by strand smoothing these approaches are tested for unsteady laminar and high reynolds number turbulent flows for standard viscous high aspect ratio grids smoothed strands with telescoping cartesian refinement provide the most accurate results with the least complexity mesh discontinuities associated with the use of multiple strands at sharp corners produce more error than with smoothed strands with both strand approaches vector smoothing

parallel processing for the simulation of problems involving scattering of electromagnetic waves abstract the three dimensional simulation of the scattering of electromagnetic waves by obstacles of arbitrary geometrical shape is considered maxwell s curl equations are solved in the time domain on an unstructured mesh of linear tetrahedral elements the discrete equations are formed by a galerkin procedure with a lax wendroff consistent numerical flux function and explicit time stepping parallelisation of the procedure is achieved by mesh decomposition and the use of a single program multiple data model the approach is first validated and is then applied to problems involving the scattering of plane electromagnetic waves by a complete aircraft

three dimensional multigrid reynolds averaged navier stokes solver for unstructured meshes turbulence is simulated using a single field equation model computational overheads are minimized through the use of a single edge based data structure an efficient multigrid solution technique and the use of multitasking on shared memory multiprocessors the accuracy and efficiency of the code are evaluated by computing two dimensional flows in three dimensions and comparing with results from a previously validated two dimensional code that employs the same solution algorithm the feasibility of computing three dimensional turbulent flows on grids or several million points in less than 2 h of wall clock time is demonstrated

mesh generation and adaptivity for the solution of compressible viscous high speed flows an implicit explicit procedure for the solution of the compressible navier stokes equations on unstructured triangular and tetrahedral meshes is outlined a procedure for constructing continuous lines made up of edges in the mesh is employed and the implicit equation system is solved via line relaxation the problem of generating and adapting unstructured meshes for viscous flow simulations is addressed a number of examples are included which demonstrate the numerical performance of the proposed procedures

analytic solutions darboux transformation operators and supersymmetry for a generalized one dimensional time dependent schrodinger equation abstract in this paper analytically investigated is a generalized one dimensional time dependent schrodinger equation using darboux transformation operator technique we construct the first order darboux transformation and the real valued condition of transformed potential for the generalized schrodinger equation to prove the equivalence of the supersymmetry formalism and the darboux transformation we investigate the relationship among first order darboux transformation supersymmetry and factorization of the corresponding effective mass hamiltonian furthermore the nth order darboux transformations are constructed by means of different method finally by using darboux transformation some analytical solutions are generated in a recursive manner for some examples of the schrodinger equation

three dimensional unstructured multigrid for the euler equations the three dimensional euler equations are solved on unstructured tetrahedral meshes using a multigrid strategy the driving algorithm consists of an explicit vertex based finite element scheme which employs an edge based data structure to assemble the residuals the multigrid approach employs a sequence of independently generated coarse and fine meshes to accelerate the convergence to steady state of the fine grid solution variables residuals and corrections are passed back and forth between the various grids of the sequence using linear interpolation the addresses and weights for interpolation are determined in a preprocessing stage using an efficient graph traversal algorithm the preprocessing operation is shown to require a negligible fraction of the cpu time required by the overall solution procedure whereas gains in overall solution efficiencies greater than an order of magnitude are demonstrated on meshes containing up to 350 000 vertices solutions using globally regenerated fine meshes as well as adaptively refined meshes are given

fuzzy hyperrings in this paper we introduce and analyze the fuzzy hyperring notion we consider and study the subfuzzy structures of a such notion and homomorphisms between fuzzy hyperrings finally fundamental relations on fuzzy hyperrings are analyzed in all the paper we follow a connection between hyperrings and fuzzy hyperrings

the generalized confluent supersymmetry algorithm representations and integral formulas we extend the confluent version of the higher order supersymmetry susy formalism to general linear differential equations of second order closed form representations of transformation functions their wronskians and of the general solutions to susy transformed equations are derived we use these results to construct formulas for resolving multiple integrals of special functions in terms of wronskians

algebraic turbulence modeling for unstructured and adaptive meshes an algebraic turbulence model based on the baldwin lomax model has been implemented for use on unstructured grids the implementation is based on the use of local background turbulence meshes at each time step flow variables are interpolated from the unstructured mesh onto the background structured meshes the turbulence model is executed on these meshes and the resulting eddy viscosity values are interpolated back to the unstructured mesh modifications to the algebraic model were required to enable the treatment of more compli cated flows such as confluent boundary layers and wakes the model is used in conjunction with an efficient unstructured multigrid finite element navier stokes solver in order to compute compressible turbulent flows on fully unstructured meshes solutions about single and multiple element airfoils are obtained and compared with experimental data he use of unstructured mesh techniques for computa tional fluid dynamics cfd problems has become more widespread in recent years due to the flexibility they afford in discretizing arbitrarily complex geometries and due to the possibility they offer in resolving highly localized flow phenomena through the use of adaptive meshing however research on unstructured mesh techniques for cfd has con centrated almost exclusively on the solution of the euler equa tions in two or three dimensions for viscous flow calculations about nonsimple geometries hybrid meshes have generally been employed 1 3 where a thin structured mesh is placed in the boundary layer and wake regions and an unstructured mesh is constructed in the outer inviscid region of the flowfield besides leading to an increase in coding complexity this type of compromise limits the generality of the unstruc tured mesh approach in dealing with arbitrarily complex geometries such as multiple body geometries with close toler ances where confluent boundary layers or wakes may occur and complicates the task of performing adaptive meshing in the inviscid as well as viscous regions of flow it appears that the difficulties associated with generating highly stretched unstructured meshes which are required for efficiently resolv ing viscous shear layers as well as the efficient implementa tion of a turbulence model on such meshes has generally im peded the use of fully unstructured meshes for viscous flows the use of unstructured meshes throughout the entire flowfield is advocated in the present work previous work by the author has shown how a highly stretched unstructured mesh suitable for high reynolds number viscous flow calcula tions may be constructed4 and has also discussed the develop ment of an efficient unstructured navier stokes solver for laminar flows 5 this paper is thus concerned with the effi cient implementation of a turbulence model for computing high reynolds number turbulent flows using fully unstruc tured meshes

fuzzy h v groups in this paper we introduce the concept of fuzzy subhypergroup of a hypergroup as well as the fuzzy hv group we prove some results in this respect we also consider the fundamental relation defined on an hv group h and for a fuzzy subset of h we define the fuzzy subset of h and prove a fundamental theorem concerning the group h

high order flux correction finite difference schemes for strand grids a novel high order method combining unstructured flux correction along body surfaces and high order finite differences normal to surfaces is formulated for unsteady viscous flows on strand grids the flux correction algorithm is applied in each unstructured layer of the strand grid and the layers are then coupled together via a source term containing derivatives in the strand direction strand direction derivatives are approximated to high order via summation by parts operators for first derivatives and second derivatives with variable coefficients we show how this procedure allows for the proper truncation error canceling properties required for the flux correction scheme the resulting scheme possesses third order design accuracy but often exhibits fourth order accuracy when higher order derivatives are employed in the strand direction especially for highly viscous flows we prove discrete conservation for the new scheme and time stability in the absence of the flux correction terms results in two dimensions are presented that demonstrate improvements in accuracy with minimal computational and algorithmic overhead over traditional second order algorithms

fuzzy hyperrings hv rings based on fuzzy universal sets the aim of this paper is to define and study the concept of a fuzzy hyperring which depends on the concept of a fuzzy universal set a correspondence relation between a fuzzy hyperring based on a fuzzy universal set and both ordinary and fuzzy hyperideal in the sense of davvaz is obtained

time integration algorithms for the two dimensional euler equations on unstructured meshes explicit and implicit time integration algorithms for the two dimensional euler equations on unstructured grids are presented both cell centered and cell vertex finite volume upwind schemes utilizing roe s approximate riemann solver are developed for the cell vertex scheme a four stage runge kutta time integration a four stage runge kutta time integration with implicit residual averaging a point jacobi method a symmetric point gauss seidel method and two methods utilizing preconditioned sparse matrix solvers are presented for the cell centered scheme a runge kutta scheme an implicit tridiagonal relaxation scheme modeled after line gaussseidel a fully implicit lower upper lu decomposition and a hybrid scheme utilizing both runge kutta and lu methods are presented

multigrid acceleration of the flux split euler equations multigrid acceleration is applied to a flux split algorithm for solving the euler equations in three dimensions the basic algorithm is an implicit spatially split approximate factorization method the stability and performance of the scheme in comparison to other factorizations are examined results are presented for three dimensional flows that demonstrate substantially unproved convergence with the multigrid algorithm

learning in the framework of fuzzy lattices a basis for rigorous versatile learning is introduced theoretically that is the framework of fuzzy lattices or fl framework for short which proposes a synergetic combination of fuzzy set theory and lattice theory a fuzzy lattice emanates from a conventional mathematical lattice by fuzzifying the inclusion order relation learning in the fl framework can be effected by handling families of intervals where an interval is treated as a single entity block the way explained here illustrations are provided in a lattice defined on the unit hypercube where a lattice interval corresponds to a conventional hyperbox a specific scheme for learning by clustering is presented namely spl sigma fuzzy lattice learning scheme or spl sigma fll scheme for short inspired from adaptive resonance theory art learning by the spl sigma fll is driven by an inclusion measure spl sigma of the corresponding cartesian product to be introduced here we delineate a comparison of the spl sigma fll scheme with various neural fuzzy and other models applications are shown to one medical data set and two benchmark data sets where spl sigma fll s capacity for treating efficiently real numbers as well as lattice ordered symbols separately or jointly is demonstrated due to its efficiency and wide scope of applicability the spl sigma fll scheme emerges as a promising learning scheme

fuzzy join n ary spaces and fuzzy canonical n ary hypergroups we extend here the fuzzy approach of algebraic structures to the context of fuzzy n ary systems we introduce the notions of a fuzzy join n ary space and of a fuzzy canonical n ary hypergroup which are generalizations of join spaces and canonical hypergroups we find some properties of them and a characterization of fuzzy canonical n ary hypergroups using fuzzy join n ary spaces

fuzzy krasner m n hyperrings recently krasner m n hyperrings were introduced and analyzed by mirvakili and davvaz krasner m n hyperrings are a suitable generalization of krasner hyperrings this paper concerns a relationship between fuzzy sets and hyperstructure theory it is a continuation of the ideas presented by davvaz et al 2009 b davvaz p corsini v leoreanu fotea fuzzy n ary subpolygroups computers mathematics with applications 57 2009 141 152 the aim of the paper is to introduce the notion of a fuzzy hyperideal of a krasner m n hyperring and to extend the fuzzy results to krasner m n hyperrings

solution of the euler equations for two dimensional transonic flow by a multigrid method the assumption of potential o w implies that the o w is irrotational this is not strictly correct when shock waves are present an exact description of transonic inviscid o w requires the solution of the euler equations the numerical solution of the euler equations for steady transonic o ws is therefore a problem of great interest to the aeronautical community it also presents a testing challenge to applied mathematicians and numerical analysts

edge based finite element techniques for non linear solid mechanics problems edge based data structures are used to improve computational efficiency of inexact newton methods for solving finite element non linear solid mechanics problems on unstructured meshes edge based data structures are employed to store the stiffness matrix coefficients and to compute sparse matrix vector products needed in the inner iterative driver of the inexact newton method numerical experiments on three dimensional plasticity problems have shown that memory and computer time are reduced respectively by factors of 4 and 6 compared with solutions using element by element storage and matrix vector products copyright 2001 john wiley sons ltd

unsteady transonic two dimensional euler solutions using finite elements a finite element solution of the unsteady euler equations is presented and demonstrated for two dimensional airfoil configurations oscillating in transonic flows computations are performed by spatially discretizing the conservation equations using the galerkin weighted residual method and then employing a multistage rungekutta scheme to march forward in time triangular finite elements are employed in an unstructured o mesh computational grid surrounding the airfoil grid points are fixed in space at the far field boundary and are constrained to move with the airfoil surface to form the near field boundary a mesh deformation scheme has been developed to efficiently move interior points in a smooth fashion as the airfoil undergoes rigid body pitch and plunge motion both steady and unsteady results are presented and a comparison is made with solutions obtained using finite volume techniques the effects of using either a lumped or consistent mass matrix were studied and are presented results show the finite element method provides an accurate solution for unsteady transonic flows about isolated airfoils he accurate determination of the unsteady flowfield surrounding an oscillating airfoil or wing in transonic flow is of paramount importance in the prediction of the flutter characteristics of the body transonic flutter remains an active research topic because of the continued interest by both the military and commercial sectors to operate in these flight regimes with vehicles that are ever lighter and as a result more flexible typically analysis of fluid structure interaction in flight vehicles involves describing the vehicle structure using finite elements whereas finite difference methods are used to model the surrounding fluid coupling of the two dissimilar models then presents problems because of the disparity between the two solution techniques additional complexities arise because of phase mismatching between the fluid pressures and the displacements of the structure it seems a natural progression to use finite element methods to describe the behavior of both the fluid and structure thus bringing more commonality into the analysis of the two media early research efforts concentrated on using the transonic small disturbance equation or the nonlinear full potential equation as the model for the gas dynamic behavior in transonic flows unfortunately this idealization leads to errors when strong shocks are present because of their inability to account for the production of entropy and vorticity to properly account for these effects within the framework of the conservation laws the euler equations must be used these equations although they neglect fluid viscosity have become the standard when unsteady transonic solutions are desired the absence of a viscosity representation is an important limitation of the present formulation and must be considered

an implicit finite element method for high speed flows a fast algorithm is presented for constructing continuous lines made up of element sides which pass once through each node of a general unstructured triangular mesh and which are generally aligned in prescribed directions the lines are used as the basis of an adaptive fully implicit unstructured grid procedure for the solution of two dimensional problems of steady compressible inviscid and laminar viscous high speed flows where the equation system is solved by line relaxation using a block tridiagonal equation solver for three dimensional laminar viscous simulations it is proposed to utilize an implicit explicit finite element formulation in the vicinity of solid walls a grid exhibiting structure in the normal direction is employed while away from this region the grid will be totally unstructured in the structured region lines in the normal direction to the wall are readily identified while lines in the surfaces parallel to the solid wall are constructed using the proposed two dimensional procedure the implicit algorithm is then used in the structured region and the equation solution is achieved via line relaxation an explicit form of the solution algorithm is used elsewhere to illustrate the performance of the proposed method solutions are obtained for both transonic inviscid and transonic and hypersonic laminar viscous problems in two dimensions the application of the proposed procedure to the solution of three dimensional hypersonic laminar viscous flow over a double ellipsoid configuration is also described

intergrid boundary definition method for overset unstructured grid approach the use of the overset concept for the unstructured grid method is relatively unexplored however the overset approach can extend the applicability of the unstructured grid method for real engineering problems without much need for code development the multiple moving body problem is one of those applications improvement in local resolution for euler navier stokes computations on unstructured grids is another use of the overset concept an efficient and robust algorithm to localize the intergrid boundaries for the overset unstructured grid method is proposed simplicity and automation in the intergrid boundary definition are realized using the wall distance as a basic parameter the neighbor to neighbor jump search algorithm is efficiently utilized in the method the robustness and efficiency of the search is improved by the use of subsidiary grids that are generated as a byproduct of the delaunay triangulation method the basic procedure of the present method is described for a multielement airfoil problem the effects of the overset method on the solution accuracy and the convergence are tested by onera m6 wing

three dimensional adaptive grid embedding euler technique a new three dimensional adaptive grid euler procedure is presented that automatically detects high gradient regions in the flow and locally subdivides the computational grid in these regions to provide a uniform high level of accuracy over the entire domain a tunable semistructured data system is utilized that provides global topological unstructured grid flexibility along with the efficiency of a local structured grid system in addition this data structure allows for the flow solution algorithm to be executed on a wide variety of parallel vector computing platforms an explicit lime marching control volume procedure is used to integrate the euler equations to steady state

fuzzy hyperalgebras we introduce and study the notion of fuzzy multialgebras on the basis of a new definition of a fuzzy hyperoperation we introduce the notion of fuzzy regular resp fuzzy strongly regular relations of hyperalgebras and obtain their basic properties finally we prove that with every fuzzy hyperalgebra we can associate a unique hyperalgebra via a regular resp strongly regular relation

time dependent darboux supersymmetric transformations for non hermitian quantum systems we propose time dependent darboux supersymmetric transformations that provide a scheme for the calculation of explicitly time dependent solvable non hermitian partner hamiltonians together with two hermitian hamilitonians the latter form a quadruple of hamiltonians that are related by two time dependent dyson equations and two intertwining relations in form of a commutative diagram our construction is extended to the entire hierarchy of hamiltonians obtained from time dependent darboux crum transformations as an alternative approach we also discuss the intertwining relations for lewis riesenfeld invariants for hermitian as well as non hermitian hamiltonians that reduce the time dependent equations to auxiliary eigenvalue equations the working of our proposals is discussed for a hierarchy of explicitly time dependent rational hyperbolic airy function and nonlocal potentials

three dimensional calculation of transonic viscous flows by an implicit method a new implicit finitevolume method for solving the three dimensional navier stokes equations for compressible fluids is presented and applied to the calculation of flows over swept wings at moderate reynolds numbers the method makes use of an explicit predictor corrector scheme to calculate a provisional value which is then corrected by using an implicit operator the explicit part is a generalization of the centered thornmen scheme while the implicit operator is a combination of the inviscid schemes proposed by lerate and the viscous treatment of beam and warming results are here presented for a swept wing between two parallel walls and for the finite wing onera m6 at mx 0 8 zero incidence and re 1000 the computations are performed with a time step about 5 to 10 times greater than the explicit step

generalized schrodinger equations with quadratical energy dependence in the potential darboux transformations and application to the heun class we construct darboux transformations of arbitrary order for generalized schrodinger type equations the potentials of which are second degree polynomials in the energy our equations are allowed to contain first derivative terms with arbitrary coefficients such as they occur for example in position dependent mass scenarios our darboux transformations are shown to be applicable to equations from the heun class

adaptive quadrilateral and triangular finite element scheme for compressible flows the development of an adaptive mesh refinement procedure for analyzing high speed compressible flows using the finite element method is described this new adaptation procedure which uses both quadrilateral and triangular elements was implemented with two explicit finite element algorithms the two step taylor galerkin and the multistep galerkin runge kutta schemes a von neumann stability analysis and a rotating cosine hill problem demonstrate the instability of the taylor galerkin scheme when coupled with the adaptation procedure for the same adaptive refinement scheme the galerkin runge kutta procedure yields stable solutions within its explicit stability limit the utility of this new adaptation procedure for the prediction of compressible flow features is illustrated for inviscid problems involving strong shock interactions at hypersonic speeds

three dimensional unstructured adaptive multigrid scheme for the euler equations we present a solution adaptive multigrid scheme for the three dimensional euler equations the procedure begins with an initial coarse mesh and enriches this mesh by h refinement in regions of high solution gradient this adaptive procedure is used to generate the multigrid levels required by the solver new boundary nodes are added in a way to reflect the underlying surface representation of the geometry the h refinement procedure is extremely fast and results in a scheme where only a small percentage of the overall cpu time is spent in the meshing and refinement part of the algorithm the multigrid flow solver typically reduces the cpu time by an order of magnitude over the same case without multigrid

fuzzy hypergroups based on fuzzy relations based on fuzzy reasoning in fuzzy logic this paper studies a fuzzy hyperoperation and a fuzzy hypergroupoid associated with a fuzzy relation a sufficient and necessary condition for such a fuzzy hypergroupoid being a fuzzy hypergroup is given and the properties of the fuzzy hypergroups associated with fuzzy relations are investigated furthermore the definition of normal fuzzy hypergroups is put forward and it is shown that the category nfhg of normal fuzzy hypergroups satisfies all the axioms of topos except for the subobject classifier axiom

multigrid approach to overset grid communication the nonaligned multigrid method is introduced as an alternative to boundary point interpolation for communication in overset grid systems the nonaligned multigrid method treats the individual grids as levels in a multigrid solution procedure this technique was able to converge 69 faster than standard boundary point interpolation for mach 2 flow over a 5 deg ramp and 28 faster for a more complex reflected shock case for these test cases the largest increase in convergence rate came from applying the nonaligned multigrid method to the communication between overset grids further coarsening of the global grid was next in effectiveness and coarsening of local grids gave little improvement

green s functions sum rules and matrix elements for susy partners it is now well known that the solutions in the schrodinger equations for two potentials which are supersymmetric partners are linked by intertwining relations involving first order differential operators in this paper we explore the consequence of this linkage for the green s functions corresponding to susy partners and the relation between the sums over the inverses of the eigenvalues for the two potentials we also establish some relations between the matrix elements of certain operators evaluated between the eigenstates of two partner potentials we show that there can be circumstances where some matrix elements vanish as a consequence of the presence of supersymmetry

simulation of three dimensional turbulent flows on unstructured meshes a three dimensional navier stokes flow solver is developed on unstructured tetrahedral meshes for a turbulence closure a standard high reynolds number k e model with a wall function boundary condition is used the seven equations of motion are discretized and integrated in a tightly coupled manner the time integration is achieved using an explicit runge kutta time stepping scheme the inviscid flux terms are discretized based on a cell centered finite volume formulation with roe s flux difference splitting the numerical method is applied for flows on a two dimensional backward facing step and a three dimensional turbomachinery geometry the results are compared with analytical and experimental data for validations

three dimensional unstructured adaptive multigrid scheme for the navier stokes equations a solution adaptive multigrid scheme for solving the three dimensional navier stokes equations on unstructured meshes is presented the algorithm solves the equations on a fully unstructured mesh of tetrahedral elements using a multigrid time marching scheme the initial unstructured mesh is successively refined based on gradients in the flow solution with the multigrid levels being determined by the refinement procedure important issues related to solving viscous flows on unstructured meshes are discussed these include calculation of the viscous stress terms in a manner that prevents wiggles calculation of the time steps to include both inviscid and viscous effects numerical smoothing considerations minimization of computer storage requirements and implementation of the k e turbulence model solutions are presented for several examples of industrial importance that illustrate the potential of the method including transonic flow about an aircraft engine nacelle and in both rotating and nonrotating turbomachinery passages

a trace formula for dirac green s functions related by darboux transformations we construct green s functions and a trace formula for pairs of stationary dirac equations under sturm liouville boundary conditions where the equations are related to each other by a darboux transformation our findings generalize former results pozdeeva e 2008 j phys a math theor at press

accelerated convergence of euler solutions using time inclining the use of time inclining for accelerating the convergence to steady state of inviscid flow computations is examined this technique is based upon a local inclination in time of the computational cells for convergence acceleration these inclinations are chosen so as to balance the time step restrictions for upwind and downwind running pressure waves the effectiveness of time inclining is demonstrated in two dimensions with freestream mach numbers ranging from 0 2 to 3 0

the time dependent schrodinger equation of dimension k 1 explicit and rational solutions via gbdt and multinodes a version of the binary darboux transformation is constructed for a non stationary schrodinger equation of dimension k 1 where k 1 is the number of space variables this is an iterated generalized backlund darboux transformation version new families of non singular and rational potentials and solutions are obtained some results are also new for the case that k 1 a certain generalization of a colligation introduced by m s livsic and a generalization of the s node introduced by l a sakhnovich have been successfully used in our construction

implicit methods of second order accuracy for the euler equations this paper presents a study of noniterative implicit finite difference methods for hyperbolic systems new space centered methods involving two time levels are considered an analysis is made of various properties such as solvability stability dissipation dispersion and efficient solution of the algebraic systems the computation of shock waves with a cfl number larger than the unity is discussed unconditional stability results are proved for a case having several space variables accurate solutions of the euler equations are obtained that offer major reductions in computing costs over explicit methods

mpdata an edge based unstructured grid formulation we present an advancement in the evolution of mpdata multidimensional positive definite advection transport algorithm over the last two decades mpdata has proven successful in applications using single block structured cuboidal meshes viz cartesian meshes while employing homeomorphic mappings to accommodate time dependent curvilinear domains motivated by the strengths of the cartesian mesh mpdata we develop a new formulation in an arbitrary finite volume framework with a fully unstructured polyhedral hybrid mesh in mpdata as in any taylor series based integration method for pde the choice of data structure has a pronounced impact on the technical details of the algorithm aiming at a broad range of applications with a large number of control volume cells we select a general compact and computationally efficient edge based data structure this facilitates the use of mpdata for problems involving complex geometries and or inhomogeneous anisotropic flows where mesh adaptivity is advantageous in this paper we describe the theory and implementation of the basic finite volume mpdata and document extensions important for applications a fully monotone scheme diffusion scheme and generalization to complete flow solvers theoretical discussions are illustrated with benchmark results in two and three spatial dimensions

a vertex centred finite volume jameson schmidt turkel jst algorithm for a mixed conservation formulation in solid dynamics a vertex centred finite volume algorithm is presented for the numerical simulation of fast transient dynamics problems involving large deformations a mixed formulation based upon the use of the linear momentum the deformation gradient tensor and the total energy as conservation variables is discretised in space using linear triangles and tetrahedra in two dimensional and three dimensional computations respectively the scheme is implemented using central differences for the evaluation of the interface fluxes in conjunction with the jameson schmidt turkel jst artificial dissipation term the discretisation in time is performed by using a total variational diminishing tvd two stage runge kutta time integrator the jst algorithm is adapted in order to ensure the preservation of linear and angular momenta the framework results in a low order computationally efficient solver for solid dynamics which proves to be very competitive in nearly incompressible scenarios and bending dominated applications

green s functions and trace formulas for generalized sturm liouville problems related by darboux transformations we study green s functions of the generalized sturm liouville problems that are related to each other by darboux equivalently supersymmetrical transformations we establish an explicit relation between the corresponding green s functions and derive a simple formula for their trace the class of equations considered here includes the conventional schrodinger equation and generalizations such as for position dependent mass and with linearly energy dependent potential as well as the stationary fokker planck equation

an nth order darboux transformation for the one dimensional time dependent schrodinger equation solutions for two one dimensional schr dinger equations are linked together using an nth order darboux transformation the resulting coefficients for these darboux transformations give rise to a system of n nonlinear partial differential equations this system is shown to be equivalent to a matrix burgers equation which is linearized using a generalized hopf cole transformation solving this linear system provides the link between solutions of the two schr dinger equations and shows how to factor an nth order darboux transformation into n first order darboux transformations

finite element euler computations in three dimensions an explicit finite element solution procedure for the three dimensional euler equations is presented the solution domain is automatically meshed using a tetrahedral mesh generator which is an extension of our previous two dimensional work several examples are included to illustrate the performance of the generator and solver an adaptive mesh regeneration procedure is used for the first time in three dimensions

multicloud multigrid convergence with a meshless operator the primary objective of this work is to develop and test a new convergence acceleration technique we call multicloud multicloud is well founded in the mathematical basis of multigrid but relies on a meshless operator on coarse levels the meshless operator enables extremely simple and automatic coarsening procedures for arbitrary meshes using arbitrary fine level discretization schemes the performance of multicloud is compared with established multigrid techniques for structured and unstructured meshes for the euler equations on two dimensional test cases results indicate comparable convergence rates per unit work for multicloud and multigrid however because of its mesh and scheme transparency multicloud may be applied to a wide array of problems with no modification of fine level schemes as is often required with agglomeration techniques the implication is that multicloud can be implemented in a completely modular fashion allowing researchers to develop fine level algorithms independent of the convergence accelerator for complex three dimensional problems

finite volume solution of the two dimensional euler equations on a regular triangular mesh the two dimensional euler equations have been solved on a triangular grid by a multigrid scheme using the finite volume approach by careful construction of the dissipative terms the scheme is designed to be secondorder accurate in space provided the grid is smooth except in the vicinity of shocks where it behaves as firstorder accurate in its present form the accuracy and convergence rate of the triangle code are comparable to that of the quadrilateral mesh code of jameson

adaptive mesh generation for viscous flows using delaunay triangulation abstract a method for generating an unstructured triangular mesh in two dimensions suitable for computing high reynolds number flows over arbitrary configurations is presented the method is based on a delaunay triangulation which is perfored in a locally stretched space in order to obtain very high aspect ratio tiangles in the boundary layer and wake regions it is shown how the method can be coupled with an unstructured navier stokes solver to produce a solution adaptive mesh generation procedure for viscous flows

explicit darboux transformations of arbitrary order for generalized time dependent schrodinger equations we construct darboux transformations of arbitrary order for a generalized linear time dependent schrodinger equation special cases of which correspond to time dependent hamiltonians coupled to a magnetic field with position dependent mass and with weighted energy our darboux transformation reduces correctly to these known cases and also to new generalized schrodinger equations furthermore fundamental properties of the conventional darboux transformation are maintained such as factorization of the nth order transformation into first order transformations and existence of a reality condition for the transformed potentials

agglomeration multigrid for the three dimensional euler equations a multigrid procedure that makes use of coarse grids generated by the agglomeration of control volumes is advocated as a practical approach for solving the three dimensional euler equations on unstructured grids about complex configurations it is shown that the agglomeration procedure can be tailored to achieve certain coarse grid properties such as the sizes of the coarse grids and aspect ratios of the coarse grid cells the agglomeration is done as a preprocessing step and runs in linear time the implications for multigrid of using arbitrary polyhedral coarse grids are discussed the agglomeration multigrid technique compares very favorably with existing multigrid procedures both in terms of convergence rates and elapsed times the main advantage of the present approach is the ease with which coarse grids of any desired degree of coarseness may be generated in three dimensions without being constrained by considerations of geometry inviscid flows over a variety of complex configurations are computed using the agglomeration multigrid strategy

operator based preconditioning of stiff hyperbolic systems we introduce an operator based scheme for preconditioning stiff components encountered in implicit methods for hyperbolic systems of pdes posed on regular grids the method is based on a directional splitting of the implicit operator followed by a characteristic decomposition of the resulting directional parts this approach allows for the solution of any number of characteristic components from the entire system to only the fastest stiffness inducing waves we apply the preconditioning method to stiff hyperbolic systems arising in magnetohydrodynamics and gas dynamics we then present numerical results showing that this preconditioning scheme works well on problems where the underlying stiffness results from the interaction of fast transient waves with slowly evolving dynamics scales well to large problem sizes and numbers of processors and allows for additional customization based on the specific problems under study

unsteady euler algorithm with unstructured dynamic mesh for complex aircraft aerodynamic analysis an euler solution algorithm is presented for unsteady aerodynamic analysis of complex aircr aft configurations the flow solver involves a multistage runge kutta time stepping scheme that uses a finite volume spatial discretization on an unstructured grid made up of tetrahedra a significant contribution of the research is the development and implementation of a moving mesh algorithm that is employed for problems involving static or dynamic deformation of the aircraft the mesh algorithm is a general procedure that can treat realistic motions and deformations of complex aircraft configurations steady and unsteady results are presented for a supersonic fighter configuration to demonstrate applications of the euler solver and dynamic mesh algorithm the unsteady flow results were obtained for the aircraft oscillating harmonically in a complete vehicle bending mode effects of angle of attack and reduced frequency on instantaneous pressures and force responses were investigated the paper presents descriptions of the euler solver and dynamic mesh algorithm along with results that assess the capability

fuzzy hyperlattices in this paper we introduce the notion of fuzzy hyperlattices and establish connections between fuzzy hyperlattices and hyperlattices then we discuss the relations between the weak homomorphism of fuzzy hyperlattices and the weak homomorphism of corresponding hyperlattices moreover we define and analyze the hypercongruence on hyperlattices and the fuzzy strong hypercongruence on fuzzy hyperlattices and we study the interrelation between the fuzzy hypercongruence on fuzzy hyperlattices and the homomorphism of fuzzy hyperlattices also a relation between the fuzzy hypercongruence on fuzzy hyperlattices and the hypercongruence on corresponding hyperlattices is obtained finally we apply the hypercongruence and the fuzzy strong hypercongruence to construct quotient structures of hyperlattices and fuzzy hyperlattices respectively

fuzzy hv submodules abstract in this paper we define the concept of fuzzy h v submodule of an h v module and study a few results in this respect we also consider the fundamental relation e defined on an h v module m and prove a fundamental theorem concerning the module m e

comment on generalization of the darboux transformation and generalized harmonic oscillators the authors song and klauder 2003 j phys a math gen 36 8673 84 present a generalized darboux transformation applicable to hamiltonians with linear terms in the momentum we show here that this generalized darboux transformation is just the standard darboux transformation in different coordinates

susy transformation of the green function and a trace formula an integral relation is established between the green functions corresponding to two hamiltonians which are supersymmetric susy partners and in general may possess both discrete and continuous spectra it is shown that when the continuous spectrum is present the trace of the difference of the green functions for susy partners is a finite quantity which may or may not be equal to zero despite the divergence of the traces of each green function our findings are illustrated by using the free particle example considered both on the whole real line and on a half line

a new type of fuzzy n ary hyperstructures the aim of this paper is to consider and study a new kind of fuzzy n ary hyperstructures such as fuzzy n ary hypergroups and fuzzy m n ary hyperrings

a new fast hybrid adaptive grid generation technique for arbitrary two dimensional domains this paper describes a new fast hybrid adaptive grid generation technique for arbitrary two dimensional domains this technique is based on a cartesian background grid with square elements and quadtree decomposition a new algorithm is introduced for the distribution of boundary points based on the curvature of the domain boundaries the quadtree decomposition is governed either by the distribution of the boundary points or by a size function when a solution based adaptive grid is desired the resulting grid is quaddominant and ready for the application of finite element multi grid or line relaxation methods all the internal angles in the final grid have a lower bound of 45 and an upper bound of 135 although our main interest is in grid generation for unsteady flow simulations the technique presented in this paper can be employed in many other fields several application examples are provided to illustrate the main features of this new approach copyright 2010 john wiley sons ltd

adaptive refinement coarsening scheme for three dimensional unstructured meshes the paper describes the development and application of an adaptive algorithm for tetrahedral grids an initial unstructured grid is adapted by employing local division as well as deletion of the tetrahedral cells the process is dynamic and the adapted grid changes follow evolution of the solution adaptation of the cells consists of normal division of a tetrahedron into eight subcells as well as directional division into two or four subcells a major issue of such adaptive grid algorithms is elimination of hanging nodes that appear on the edges in the interface between the embedded and unembedded zones a novel technique has been developed for treatment of such interface cells that can be applied to eliminate any possible hanging node configuration in a simple way a special data structure based on octrees has been developed which is flexible to handle all different types of cell division deletion application cases include a moving source as well as transonic flow around the onera m6 wing

geometric multigrid with applications to computational fluid dynamics an overview is given of the development of the geometric multigrid method with emphasis on applications in computational fluid dynamics over the last ten years both compressible and incompressible flow problems and their corresponding multigrid solution methods are discussed the state of the art is described with respect to methods employed in industry as well as the multigrid efficiency obtained in academic applications

on fuzzy isomorphism theorems of γ hyperrings in this paper we first derive three isomorphism theorems and a jordan holder theorem of c hyperrings by fuzzy c hyperideals we establish three fuzzy isomorphism theorems of c hyperrings

adaptive remeshing for compressible flow computations an adaptive mesh procedure for improving the quality of steady state solutions of the euler equations in two dimensions is described the procedure is implemented in conjunction with a finite element solution algorithm using linear triangular elements and an explicit time stepping scheme the mesh adaptation is accomplished by regeneration using information provided by the computed solution on the current mesh the meshes produced are characterised by the appearance of stretched elements in the vicinity of one dimensional flow features and can exhibit a large variation in element size this allows solutions of enhanced quality to be produced in a computationally efficient manner