physics based gmres preconditioner for compressible and incompressible navier stokes equations abstract this paper presents the implementation of a local physics preconditioning mass matrix 8 for an unified approach of 3d compressible and incompressible navier stokes equations using an supg finite element formulation and gmres implicit solver during the last years a lot of effort has been dedicated to finding a unified approach for compressible and incompressible flow in order to treat fluid dynamic problems with a very wide range of mach and reynolds numbers 10 26 37 on the other hand supg finite element formulation and gmres implicit solver is one of the most robust combinations to solve state of the art cfd problems 1 6 9 22 29 30 31 the selection of a good preconditioner and its performance on parallel architecture is another open problem in cfd community the local feature of the preconditioner presented here means that no communication among processors is needed when working on parallel architectures due to these facts we consider that this research can make some contributions towards the development of a unified fluid dynamic model with high rates of convergence for any combination of mach and reynolds numbers being very suitable for massively parallel computations finally it is important to remark that while this kind of preconditioning produces stabilized results in nearly incompressible regimes the standard version exhibits some numerical drawbacks that lead to solutions without physical meaning

on category o over triangular generalized weyl algebras abstract we analyze the bgg category o over a large class of generalized weyl algebras henceforth termed gwas given such a triangular gwa for which category o decomposes into a direct sum of subcategories we study in detail the homological properties of blocks with finitely many simples as consequences we show that the endomorphism algebra of a projective generator of such a block is quasi hereditary finite dimensional and graded koszul we also classify all tilting modules in the block as well as all submodules of all projective and tilting modules finally we present a novel connection between blocks of triangular gwas and young tableaux which provides a combinatorial interpretation of morphisms and extensions between objects of the block

down up algebras and ambiskew polynomial rings abstract we show that the down up algebras of g benkart 1998 in recent progress in algebra contemporary mathematics vol 224 am math soc providence and g benkart and t roby 1998 j algebra209 305 344 lie in a certain class of iterated skew polynomial rings called ambiskew polynomial rings in two indeterminates x and y over a commutative ring b in such rings commutation of the indeterminates with elements of b involve the same endomorphism of b but from different sides that is yb b y and bx x b and for some scalar p yx pxy b in previous studies of ambiskew polynomial rings was required to be an automorphism but in order to cover all down up algebras this requirement must be dropped the noetherian down up algebras are those where is an automorphism and in this case we apply existing results on ambiskew polynomial rings to determine the finite dimensional simple modules and the prime ideals we adapt the methods underlying these results so as to apply to the non noetherian down up algebras for which they reveal a surprisingly rich structure

a preconditioning mass matrix to accelerate the convergence to the steady euler solutions using explicit schemes when explicit time marching algorithms are used to reach the steady state of problems governed by the euler equations the rate of convergence is strongly impaired both in the zones with low mach number and in the zones with transonic flow e g mach and mach 1 with 0 2 the rate of convergence becomes slower as diminishes we show in this paper with analytical and numerical results how the use of a preconditioning mass matrix accelerates the convergence in the aforementioned ranges of mach numbers the preconditioning mass matrix pmm we advocate in this paper can be applied to any fem fvm that uses an explicit time marching scheme to find the steady state the method s rate of convergence to the steady state is studied and results for the one and two dimiensional cases are presented in sections 1 3 using the one dimensional euler equations we first explain why there exists a slow rate of convergence when the plain lumping of mass is used then the convergence rate to steady solutions is analysed from its two constituents that is convergence by absorption at the boundaries and by damping in the domain next we give the natural solution to this problem and with several examples we show the effectiveness of the proposed mass matrix when compared with the plain scheme in sections 4 8 we give the multidimensional version of the preconditioning mass matrix we make a stability analysis and compare the group velocities and damping with and without the new mass matrix to finish we show the velocity of convergence for a common test problem

poincare series for non riemannian locally symmetric spaces abstract we initiate the spectral analysis of pseudo riemannian locally symmetric spaces g h beyond the classical cases where h is compact automorphic forms or is trivial analysis on symmetric spaces for any non riemannian reductive symmetric space x g h on which the discrete spectrum of the laplacian is nonempty and for any discrete group of isometries whose action on x is sufficiently proper we construct l 2 eigenfunctions of the laplacian on x x for an infinite set of eigenvalues these eigenfunctions are obtained as generalized poincare series i e as projections to x of sums over the orbits of eigenfunctions of the laplacian on x we prove that the poincare series we construct still converge and define nonzero l 2 functions after any small deformation of inside g for a large class of groups thus the infinite set of eigenvalues we construct is stable under small deformations this contrasts with the classical setting where the nonzero discrete spectrum varies on the teichmuller space of a compact riemann surface we actually construct joint l 2 eigenfunctions for the whole commutative algebra of invariant differential operators on x

global rigidity of holomorphic riemannian metrics on compact complex 3 manifolds we study compact complex 3 manifolds m admitting a locally homogeneous holomorphic riemannian metric g we prove the following i if the killing lie algebra of g has a non trivial semi simple part then it preserves some holomorphic riemannian metric on m with constant sectional curvature ii if the killing lie algebra of g is solvable then up to a finite unramified cover m is a quotient g where is a lattice in g and g is either the complex heisenberg group or the complex sol group

a class of algebras similar to the enveloping algebra of sl 2 fix f e c x define r c a b h subject to the relations ha ah a hb bh b ab ba f h we study these algebras for different f and in particular show how they are similar to and different from u sl 2 the enveloping algebra of sl 2 c there is a notion of highest weight modules and a category a for such r for each n 0 if f x x 1 n l xn 1 then r has precisely n simple modules in each finite dimension and every finite dimensional r module is semisimple

on closed anti de sitter spacetimes this article deals with the structure of the fundamental group of compact anti de sitter spacetimes i e lorentz manifolds with constant negative curvature algebraically such a manifold is the quotient of the universal cover of the homogeneous space so 2 n so 1 n by a discrete group gamma acting properly and co compactly on it this exists if and only if n is even indeed as this was observed by kulkarni u 1 d is contained in so 2 2d and acts properly transitively on so 2 2d so 1 2d it then suffices to take gamma as a co compact lattice in u 1 d the results of the present article give evidence to the question in dimension 3 are all compact anti de sitter spacetimes constructed in this way

a stabilized finite element method for generalized stationary incompressible flows abstract in this paper we describe a finite element formulation for the numerical solution of the stationary incompressible navier stokes equations including coriolis forces and the permeability of the medium the stabilized method is based on the algebraic version of the sub grid scale approach we first describe this technique for general systems of convection diffusion reaction equations and then we apply it to the linearized flow equations the important point is the design of the matrix of stabilization parameters that the method has this design is based on the identification of the stability problems of the galerkin method and a scaling of variables argument to determine which coefficients must be included in the stabilization matrix this together with the convergence analysis of the linearized problem leads to a simple expression for the stabilization parameters in the general situation considered in the paper the numerical analysis of the linearized problem also shows that the method has optimal convergence properties

autour de la conjecture de l markus sur les varietes affines for any subgroupg of n we introduce some integer discg n called thediscompacity ofg this number measures to what extent the closure ofg is not compact the markus conjecture says that a compact affinely flat unimodular manifold is complete our main result called the discompact theorem is that this conjecture is true under the assumption that the linear holonomy i e the parallel transport has discompacity 1 because discso n 1 1 1 this ensures that a compact flat lorentz manifoldm is geodesically complete hence by a previous result of w goldman and y kamishima gk such am is up to finite covering a solvmanifold this achieves the proof of a bieberbach s theorem for compact lorentz flat manifolds

nonstandard lorentz space forms in their recent paper 8 kulharni and raymond show that a closed 3 manifold which admits a complete lorentz metric of constant curvature 1 henceforth called a complete lorentz structure must be seifert fibered over a hyperbolic base furthermore on every such seifert fibered 3 manifold with nonzero euler class they construct such a lorentz metric moreover the lorentz structure they construct has a rather strong additional property which they call standard a lorentz structure is standard if its causal double cover possesses a timelike killing vector field equivalently it possesses a riemannian metric locally isometric to a left invariant metric on sl 2 r kulkarni and raymond asked if every closed 3 dimensional lorentz structure is standard this paper provides a negative answer to this question theorem 1 and a positive answer to the implicit question raised in 8 7 1 1 theorem 3 theorem 1 let m3 be a closed 3 manifold which admits a homogeneous lorentz structure and satisfies h m r 0 then there exists a nonstandard complete lorentz structure on m in 8 it is shown that the unit tangent bundle of a closed surface admits a homogeneous lorentz structure therefore we obtain corollary 2 there exists a complete lorentz structure on the unit tangent bundle of any closed surface f of genus greater than one which is not standard the homogeneous lorentz structures are all classified in 8 a circle bundle of euler number j over a closed surface f f 0 has a homogeneous structure if and only if j f an analogous statement holds when m has singular fibers i e when f is an orbifold we also show theorem 3 let m3 be a 3 manifold which admits a complete lorentz structure then m3 is not covered by a product f x s fa closed surface theorem 3 implies that the euler class of the seifert fiber structure of m3 is nonzero

equal order interpolations a unified approach to stabilize the incompressible and advective effects abstract in this paper we present a new supg formulation for compressible and near incompressible navier stokes equations 5 it introduces an extension of the exact solution for one dimensional systems to the multidimensional case in a similar way to that arising in the scalar problem it is important to note that this formulation satisfies both the one dimensional advective diffusive system limit case and the advection dominated multidimensional system case presented by mallet et al another interesting feature of this formulation is that it introduces naturally a stabilizing term for the incompressibility condition in a similar way to that found by other authors 1 4 however in our formulation the stabilization is introduced to the whole system of equations while other authors introduce a term to stabilize the incompressibility condition and another one for the advective term in section 1 we present navier stokes equations for compressible flow and then we pass to detail several topics related to the numerical discretization of such advective diffusive multidimensional systems of pdes in the petrov galerkin context the method is applicable and described for the general re 0 laminar flow but the nature of the stabilizing effect of the artificial diffusion matrix introduced is discussed in depth for the simpler stokes re 0 flow several numerical results are shown in section 5 taking the well known test problem of the square cavity and a variant of this namely a multiply connected square cavity as a validation for this code

a simple proof of geodesical completeness for compact space times of zero curvature any riemannian metric on a compact manifold is geodesically complete by contrast it is widely known that incomplete compact lorentzian manifolds exist in this article it will be proven that a compact manifold with a smooth lorentz metric must be complete if the metric is flat everywhere this question of completeness which has significant implications for the classification of compact lorentzian space forms has remained unresolved until quite recently when it was finally established by carriere as a special case of an even more general result here a simple alternative proof of this special case of carriere s theorem is given the proof requires minimal mathematical machinery but still involves the use of some intriguing connections between the topology and global geometry of a compact flat space time

basic properties of generalized down up algebras abstract we introduce a large class of infinite dimensional associative algebras which generalize down up algebras let k be a field and fix f k x and r s k define l l f r s to be the algebra generated by d u and h with defining relations d h r d 0 h u r u 0 d u s f h 0 included in this family are smith s class of algebras similar to u sl 2 le bruyn s conformal sl 2 enveloping algebras and the algebras studied by rueda the algebras l have gelfand kirillov dimension 3 and are noetherian domains if and only if rs 0 we calculate the global dimension of l and for rs 0 classify the simple weight modules for l including all finite dimensional simple modules simple weight modules need not be classical highest weight modules

completeness of compact lorentzian manifolds with abelian holonomy we address the problem of finding conditions under which a compact lorentzian manifold is geodesically complete a property which always holds for compact riemannian manifolds it is known that a compact lorentzian manifold is geodesically complete if it is homogeneous or has constant curvature or admits a time like conformal vector field we consider certain lorentzian manifolds with abelian holonomy which are locally modelled by the so called pp waves and which in general do not satisfy any of the above conditions we show that compact pp waves are universally covered by a vector space determine the metric on the universal cover and prove that they are geodesically complete using this we show that every ricci flat compact pp wave is a plane wave

affine manifolds and orbits of algebraic groups this paper is the sequel to the radiance obstruction and parallel forms on a ffne manifolds lyans amer math soc 286 1984 629 649 which introduced a new family of secondary characteristic classes for affine structures on manifolds the present paper utilizes the representation of these classes in lie algebra cohomology and algebraic group cohomology to deduce new results relating the geometric properties of a compact affine manifold mn to the action on rn of the algebraic hull a r of the affine holonomy group r c aff rn a main technical result of the paper is that if m has a nonzero cohomology class represented by a parallel k form then every orbit of a r has dimension k when m is compact then a r acts transitively provided that m is complete or has parallel volume the converse holds when r is nilpotent a 4 dimensional subgroup of aff r3 is exhibited which does not contain the holonomy group of any compact affine 3 manifold when m has solvable holonomy and is complete then m must have parallel volume conversely if m has parallel volume and is of the homotopy type of a solvmanifold then m is complete if m is a compact homogeneous affine manifold or if m possesses a rational riemannian metric then it is shown that the conditions of parallel volume and completeness are equivalent this paper is the sequel to our previous paper 22 in that paper we exploited certain characteristic classes exterior powers of the radiance obstruction to obtain relationships between various properties of affine manifolds our results supported the conjecture first made by l markus 36 that a compact affine manifold is complete if and only if it has parallel volume we shall refer to this as the main conjecture let m be a compact affine manifold with developing map dev m e and affine holonomy representation h 7r h 7r r c aff e here 1r is the group of deck transformations of the universal cover m e is the vector space rn and aff e is the group of affine automorphisms of e the map dev is a locally affine immersion which is equivariant respecting h the linear holonomy homb morphism is the composition a 1r gl e of h with the natural homomorphism l aff e gl e the obstruction to r fixing a point in e is a 1 dimensional cohomology class cm e h1 m ex with coefficients in e twisted by a it comes from a universal class in the group cohomology h1 aff e el which contains the crossed homomorphism u aff e e g g 0 received by the editors december 12 1984 and in revised form may 29 1985 1980 mathematics subject classification 1985 revision primary 57r99 53c05 secondary 53c10 55r25 1 research partially supported by fellowships and grants from the national science foundation a 1986 american mathematical society 0002 9947 86 1 00 25 per page

three dimensional affine crystallographic groups those groups r which act properly discontinuously and aillnely on ii with compact fundamental domain are classified first it is shown that such a group f contains a solvable subgroup of finite index thus establishing a conjecture of auslander in dimension three then unimodular simply transitive altine actions on ir are classified this leads to a classification of attine crystallographic groups acting on ir3 a characterization of which abstract groups admit such an action is given moreover it is proved that every isomorphism between virtually solvable atline crystallographic groups respectively simply transitive afline groups is induced by conjugation by a polynomial automorphism of the affrne space a characterization is given of which closed 3 manifolds can be represented as quotients of ir by groups of afftne transformations a closed 3 manifold m admits a complete atline structure if and only if m has a finite covering homeomorphic or homotopy equivaient to a 2 torus bundle over the circle

driven cavity flows by efficient numerical techniques abstract efficient and reliable numerical techniques of high order accuracy are presented for solving problems of steady viscous incompressible flow in the plane and are used to obtain accurate solutions for the driven cavity a solution is obtained at reynolds number 10 000 on a 180 180 grid the numerical methods combine an efficient linear system solver an adaptive newton like method for nonlinear systems and a continuation procedure for following a branch of solutions over a range of reynolds numbers

down up algebras abstract the algebra generated by the down and up operators on a differential or uniform partially ordered set poset encodes essential enumerative and structural properties of the poset motivated by the algebras generated by the down and up operators on posets we introduce here a family of infinite dimensional associative algebras called down up algebras we show that down up algebras exhibit many of the important features of the universal enveloping algebrau s l2 of the lie algebra s l 2including a poincare birkhoff witt type basis and a well behaved representation theory we investigate the structure and representations of down up algebras and focus especially on verma modules highest weight representations and category o modules for them we calculate the exact expressions for all the weights since that information has proven to be particularly useful in determining structural results about posets

convex affine domains and markus conjecture in this paper we show that any properly convex quasi homogeneous affine domain with irreducible projective automorphism group is projectively equivalent to a homogeneous affine domain then as an application we answer positively the markus conjecture when the manifold m is in a certain class of convex affine manifolds

new properties and examples of incomplete lorentzian tori a new procedure to construct incomplete metrics on a two torus is introduced relations between curvature and completeness are explored and examples showing a wide independence among them are given incompleteness appears as a usual property of the lorentzian tori and the density of the incomplete metrics in the set of all the lorentzian ones is discussed this article can be seen as a partial study of compact space times and the conformal lorentzian moduli space mod t2 as claimed by yurtsever j math phys 31 3064 1990 and as a continuation of the authors previous article j math phys 34 3768 1993

simple ambiskew polynomial rings abstract we determine simplicity criteria in characteristics 0 and p for a ubiquitous class of iterated skew polynomial rings in two indeterminates over a base ring one obstruction to simplicity is the possible existence of a canonical normal element z in the case where this element exists we give simplicity criteria for the rings obtained by inverting z and the rings obtained by factoring out the ideal generated by z the results are illustrated by numerous examples including higher quantized weyl algebras and generalizations of some low dimensional symplectic reflection algebras

isometry groups of lorentz manifolds soit v une variete de lorentz a n dimensions si v g est compacte analytique reelle simplement convexe alors le groupe d isometrie is v g est compact

on the completeness of geodesics obtained as a limit the process to obtain a geodesic as a limit from a sequence of geodesics in a lorentzian manifold is analyzed in detail it is found that the limit of incomplete geodesics in a compact manifold is not incomplete in general a new class of incomplete compact lorentzian manifolds one of them showing this anomalous behavior is constructed thus a counterexample to the proof given by u yurtsever j math phys 33 1295 1992 to the result originally proven by y carriere invent math 95 615 1989 in a quite different way is given that proof should imply that an incomplete compact lorentzian manifold must be null incomplete it is not known if this assertion is true and hence remains as an open question

virtual bubbles and galerkin least squares type methods ga l s abstract the equivalence between stabilized finite element methods or galerkin least squares tyoe methods ga l s and the standard galerkin method with bubble functions is established in an abstract framework the results are applicable to various finite element spaces including high order elements and applications to the advective diffusive model and to the stokes problem are presented illustrating the potential of the abstract theory introduced here

compact affine manifolds with precompact holonomy are geodesically complete abstract this note proves the geodesic completeness of any compact manifold endowed with a linear connection such that the closure of its holonomy group is compact

on upwind methods for parabolic finite elements in incompressible flows we study the performance of various upwind techniques implemented in parabolic finite element discretizations for incompressible high reynolds number flow the characteristics of an ideal upwind procedure are first discussed then the streamline upwind petrov galerkin method a simplified version thereof the galerkin least squares technique and a high order derivative artificial diffusion method are evaluated on test problems we conclude that none of the methods displays the desired solution characteristics there is still need for the development of a reliable and efficient upwind method with characteristics close to those of the ideal procedure copyright 2000 john wiley sons ltd

the radiance obstruction and parallel forms on affine manifolds a manifold m is affine if it is endowed with a distinguished atlas whose coordinate changes are locally affine when they are locally linear m is called radiant the obstruction to radiance is a one dimensional class cm with coefficients in the flat tangent bundle of m exterior powers of cm give information on the existence of parallel forms on m especially parallel volume forms as applications various kinds of restrictions are found on the holonomy and topology of compact affine manifolds introduction an affine manifold m is a manifold with a distinguished maximal atlas of charts all of whose coordinate changes are locally affine on such a manifold there is an intrinsic notion of a parallel tensor one whose components in any affine chart are constants more generally there is the notion of a polynomial tensor field of given degree in 1962 l markus conjectured in mk that a compact orientable affine n dimensional manifold has parallel volume form if and only if it is complete meaning that its universal covering is affinely isomorphic to euclidean n space rn the problem of constructing a parallel volume form determines an n dimensional twisted real cohomology class originally studied by j smillie sm2 in this paper we express this class as the nth exterior power of a twisted one dimensional real class which we call the radiance obstruction cm by computing cm in various cohomology theories cech singular de rham and others we are able to exploit cm in several ways to yield more information on the structure of affine manifolds some of these results will appear in a subsequent paper gh3 the basic tool used is a formula proved in 2 6 which expresses the cohomology class of a parallel exterior k form in terms of the k th exterior power of the radiance obstruction akcvf min 2 7 the special case of a parallel volume form on a compact n dimensional manifold m is examined the existence of such a form implies that ancm 0 in 2 8 we show that the affine holonomy group f of such an m cannot preserve a proper affine subspace in gh3 this result will be improved by showing that r preserves no proper semialgebraic subset of rn in 2 10 we show that there tend to be plenty of parallel forms on a compact affine manifold with nilpotent affine holonomy received by the editors may 26 1983 1980 mathematics subject classification primary 57r99 53c05 secondary 53c10 55r25 4c1984 amencan mathematical society 0002 9947 84 1 00 25 per page

symplectic reflection algebras calogero moser space and deformed harish chandra homomorphism to any finite group sp v of automorphisms of a symplectic vector space v we associate a new multi parameter deformation h of the algebra v smash product of with the polynomial algebra on v the parameter runs over points of r where r number of conjugacy classes of symplectic reflections in the algebra h called a symplectic reflection algebra is related to the coordinate ring of a poisson deformation of the quotient singularity v this leads to a symplectic analogue of mckay correspondence which is most complete in case of wreath products if is the weyl group of a root system in a vector space and v then the algebras h are certain rational degenerations of the double affine hecke algebra introduced earlier by cherednik

finite element methods for first order hyperbolic systems with particular emphasis on the compressible euler equations a petrov galerkin finite element formulation is presented for first order hyperbolic systems of conservation laws with particular emphasis on the compressible euler equations applications of the methodology are made to one and two dimensional steady and unsteady flows with shocks results obtained suggest the potential of the type of methods developed

prime ideals in skew polynomial rings and quantized weyl algebras the concern of this paper is to investigate the structure of skew polynomial rings ore extensions of the form t r where and are both nontrivial and in particular to analyze the prime ideals of t the main focus is on the case that r is commutative noetherian in this case the prime ideals of t are classified polynomial identities and artin rees separation in prime factor rings are investigated and cliques of prime ideals are studied the second layer condition is proved as well as boundedness of uniform ranks for the prime factor rings corresponding to any clique futher q skew derivations on noncommutative coefficient rings are introduced and some preliminary results on contractions of prime ideals of t are obtained in this setting finally prime ideals in quantized weyl algebras over fields are analyzed

the fundamental group of a compact flat lorentz space form is virtually polycyclic a flat lorentz space form is a geodesically complete lorentzian manifold of zero curvature it is well known see auslander markus 3 that such a space m may be represented as a quotient r where r is an dimensional minkowski space n equals the dimension of m and is a group of lorentz isometries acting properly discontinuously and freely on r in particular the universal covering of m is isometric to r and the fundamental group m is isomorphic to theorem let m be a compact flat lorentz space form then m is virtually poly cyclic recall that a group is virtually polycyclic if it can be built by iterated extensions from finitely many finite groups and cyclic groups this result affirms a conjecture of milnor 13 in a special case for discussion of this conjecture as well as another special case we refer to fried goldman 8 the importance of this result is that it reduces the classification of compact flat lorentz space forms to fairly elementary problems concerning lie algebras and lattices in solvable lie groups we hope to pursue this classification in a future publication for a description of this reduction and the classification in dimension 3 see fried goldman 8 in dimension 4 the classification is worked out in fried 7 one immediate consequence of the structure theory developed in fried goldman 8 1 and kamishima 12 is the following corollary let m be the compact flat lorentz space form then m has a finite covering which is diffeomorphic to a solvmanifold the outline of this paper is as follows in the first section we collect some basic facts about the group e n 1 1 of isometries of dimensional minkowski space in the second section we prove the theorem in the special

incompressibility without tears how to avoid restrictions of mixed formulation the severe restrictions of the babuska brezzi stability criteria permit only a limited number of interpolations for velocities displacements and pressure to be used for incompressible behaviour these restrictions preclude the use of many useful elements we show in this paper how such difficulties can be side stepped by seeking the steady state solution through the use of various time marching schemes this permits a simple iterative approach to incompressible or nearly incompressible problems of fluid mechanics or solid mechanics and provides a stimulus for the use of such procedures in metal forming flow etc

object oriented finite elements iv symbolic derivations and automatic programming of nonlinear formulations reference epfl article 102770view record in web of science record created on 2007 04 23 modified on 2016 08 08

affine transformations and parallel lightlike vector fields on compact lorentzian 3 manifolds we describe the compact lorentzian 3 manifolds admitting a parallel lightlike vector field the classification of compact lorentzian 3 manifolds admitting non isometric affine diffeomorphisms follows together with the complete description of these morphisms such a lorentzian manifold is in some sense an equivariant deformation of a flat one