on some minimal supervarieties of exponential growth abstract in the present paper we investigate minimal supervarieties of given superexponent over fields of characteristic zero we show that any minimal supervariety of finite basic rank is generated by one of the minimal superalgebras introduced by giambruno and zaicev in 2003 furthermore it is proved that any minimal superalgebra whose graded simple components of the semisimple part are simple generates a minimal supervariety finally we state that the same conclusion holds when the semisimple part of a minimal superalgebra has exactly two arbitrary graded simple components

exponential codimension growth of pi algebras an exact estimate abstract letabe an associative pi algebra over a fieldfof characteristic zero by studying the exponential behavior of the sequence of codimensions cn a ofa we prove thatinv a limn c n a always exists and is an integer we also give an explicit way for computing such integer letbbe a finite dimensionalz2 graded algebra whose grassmann envelopeg b satisfies the same identities ofa theninv a inv g b dim c 0 dim c 1 wherec 0 c 1 is a suitablez2 graded semisimple subalgebra ofb

unconditional stability of corrected explicit implicit domain decomposition algorithms for parallel approximation of heat equations a class of corrected explicit implicit domain decomposition ceidd methods is investigated for the parallel approximation of linear heat equations explicit implicit domain decomposition eidd methods are computationally and communicationally efficient for each time step but always suffer from small time step size restrictions by adding an interface correction step to kuznetsov s eidd the one dimensional ceidd procedure achieves unconditional stability without discarding the time stepwise efficiency of the eidd method in order to maintain the virtues of the ceidd method and improve the flexibility in domain partitioning for solving multidimensional problems special zigzag shaped interfaces are suggested in the ceidd method based on noncrossover and crossover types of zigzag interfaces the resulting ceidd zi algorithms are studied for two strategies of subdomain partition by the energy method it shows that the proposed algorithms including their degenerate cases the corrected explicit hopscotch schemes are convergent in the discrete h1 semi norm and l2 norm numerical experiments confirm the results in our analysis

a method of finite element tearing and interconnecting and its parallel solution algorithm a novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented the spatial domain is partitioned into a set of totally disconnected subdomains each assigned to an individual processor lagrange multipliers are introduced to enforce compatibility at the interface nodes in the static case each floating subdomain induces a local singularity that is resolved in two phases first the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution next the contributions of these modes are related to the lagrange multipliers through an orthogonality condition a parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and lagrange multipliers which completes the solution of the problem when implemented on local memory multiprocessors this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring it is also suitable for parallel vector computers with shared memory moreover unlike parallel direct solvers it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations

a unified approach to some recurrence sequences via faa di bruno s formula abstract the well known faa di bruno formula for higher derivatives of a composite function plays an important role in combinatorics in this paper we obtain a unified approach to some recurrence sequences for the complete bell polynomials by using faa di bruno s formula furthermore we obtain an inverse relation of lah numbers of two types and by using this relation we obtain some new and interesting combinatorial identities

minimal superalgebras generating minimal supervarieties it has been shown that in characteristic zero the generators of the minimal supervarieties of finite basic rank belong to the class of minimal superalgebras introduced by giambruno and zaicev trans am math soc 355 5091 5117 2003 in the present paper the complete list of minimal supervarieties generated by minimal superalgebras whose maximal semisimple homogeneous subalgebra is the sum of three graded simple algebras is provided as a consequence we negatively answer the question of whether any minimal superalgebra generates a minimal supervariety

on the polynomial identities of the algebra m11 e abstract verbally prime algebras are important in pi theory they were described by kemer over a field k of characteristic zero 0 and k t the trivial ones m n k m n e m ab e here k t is the free associative algebra of infinite rank with free generators t e denotes the infinite dimensional grassmann algebra over k m n k and m n e are the n n matrices over k and over e respectively the algebras m ab e are subalgebras of m a b e see their definition below the generic also called relatively free algebras of these algebras have been studied extensively procesi described the generic algebra of m n k and lots of its properties models for the generic algebras of m n e and m ab e are also known but their structure remains quite unclear in this paper we study the generic algebra of m 11 e in two generators over a field of characteristic 0 in an earlier paper we proved that its centre is a direct sum of the field and a nilpotent ideal of the generic algebra and we gave a detailed description of this centre those results were obtained assuming the base field infinite and of characteristic different from 2 in this paper we study the polynomial identities satisfied by this generic algebra we exhibit a basis of its polynomial identities it turns out that this algebra is pi equivalent to a 5 dimensional algebra of certain upper triangular matrices the identities of the latter algebra have been studied these were described by gordienko as an application of our results we describe the subvarieties of the variety of unitary algebras generated by the generic algebra in two generators of m 11 e also we describe the polynomial identities in two variables of the algebra m 11 e

codimension growth and minimal superalgebras a celebrated theorem of kemer 1978 states that any algebra satisfying a polynomial identity over a field of characteristic zero is pi equivalent to the grassmann envelope g a of a finite dimensional superalgebra a in this paper by exploiting the basic properties of the exponent of a pi algebra proved by giambruno and zaicev 1999 we define and classify the minimal superalgebras of a given exponent over a field of characteristic zero in particular we prove that these algebras can be realized as block triangular matrix algebras over the base field the importance of such algebras is readily proved a is a minimal superalgebra if and only if the ideal of identities of g a is a product of verbally prime t ideals also such superalgebras allow us to classify all minimal varieties of a given exponent i e varieties v such that exp v d 2 and exp u d for all proper subvarieties u of v this proves in the positive a conjecture of drensky 1988 as a corollary we obtain that there is only a finite number of minimal varieties for any given exponent a classification of minimal varieties of finite basic rank was proved by the authors 2003 as an application we give an effective way for computing the exponent of a t ideal given by generators and we discuss the problem of what functions can appear as growth functions of varieties of algebras

domain decomposition methods for large linearly elliptic three dimensional problems abstract the idea of solving large problems using domain decomposition technique appears particularly attractive on present day large scale parallel computers but the performance of such techniques used on a parallel computer depends on both the numerical efficiency of the proposed algorithm and the efficiency of its parallel implementation the approach proposed herein splits the computational domain in unstructured subdomains of arbitrary shape and solves for unknown on the interface using the associated trace operator the steklov poincare operator on the continuous level or the schur complement matrix after a finite element discretization and a preconditioned conjugate gradient method this algorithm involves the solution of dirichlet and of neumann problems defined on each subdomain and which can be solved in parallel this method has been implemented on a cray 2 computer using multitasking and on an intel hypercube it was tested on a large scale industrial ill conditioned three dimensional linear elasticity problem which gives a fair indication of its performance in a real life environment in such situations the proposed method appears operational and competitive on both machines compared to standard techniques it yields faster results with far less memory requirements

bell polynomials and modified bessel functions of half integral order some representation formulas for the modified bessel functions in terms of bell polynomials are derived in particular the cases of the half integral order modified bessel functions of the first and second kind are considered we also consider the case of the half integral order modified bessel functions of the third kind the so called henkel s functions

a stabilized explicit lagrange multiplier based domain decomposition method for parabolic problems a fully explicit stabilized domain decomposition method for solving moderately stiff parabolic partial differential equations pdes is presented writing the semi discretized equations as a differential algebraic equation dae system where the interface continuity constraints between subdomains are enforced by lagrange multipliers the method uses the runge kutta chebyshev projection scheme to integrate the dae explicitly and to enforce the constraints by a projection with mass lumping techniques and node to node matching grids the method is fully explicit without solving any linear system a stability analysis is presented to show the extended stability property of the method the method is straightforward to implement and to parallelize numerical results demonstrate that it has excellent performance

an iterative procedure with interface relaxation for domain decomposition methods a domain decomposition method for second order elliptic problems is considered an iterative procedure that reduces the problem to a sequence of mixed boundary value problems on each subdomain is proposed at each iteration a relaxation is accomplished at the subdomain interfaces in several circumstances a value of the relaxation parameter that yields exact convergence in a finite number of iterations is explicitly found moreover when such a value is not available an appropriate strategy for the automatic selection of the relaxation parameter at each iteration is indicated and analyzed this iterative method is then applied to the spectral collocation approximation of the differential problem the same kind of convergence results are proven many numerical experiments show the effectiveness of the method proposed here

exponential growth for codimensions of some p i algebras abstract by the giambruno zaicev theorem for associative p i algebras the exponential rate of growth of the codimensions of such a p i algebra is always a positive integer here we calculate that integer for various generic p i algebras which are given by a single identity these include capelli type identities and the various powers of the standard polynomials

an implicit explicit runge kutta chebyshev scheme for diffusion reaction equations an implicit explicit imex extension of the explicit runge kutta chebyshev rkc scheme designed for parabolic pdes is proposed for diffusion reaction problems with severely stiff reaction terms the imex scheme treats these reaction terms implicitly and diffusion terms explicitly within the setting of linear stability theory the new imex scheme is unconditionally stable for reaction terms having a jacobian matrix with a real spectrum for diffusion terms the stability characteristics remain unchanged a numerical comparison for a stiff nonlinear radiation diffusion problem between an rkc solver an imex rkc solver and the popular implicit bdf solver vodpk using the krylov solver gmres illustrates the excellent performance of the new scheme

proper identities lie identities and exponential codimension growth abstract the exponent exp a of a pi algebra a in characteristic zero is an integer and measures the exponential rate of growth of the sequence of codimensions of a a giambruno m zaicev on codimension growth of finitely generated associative algebras adv math 140 1998 145 155 a giambruno m zaicev exponential codimension growth of p i algebras an exact estimate adv math 142 1999 221 243 in this paper we study the exponential rate of growth of the sequences of proper codimensions and lie codimensions of an associative pi algebra we prove that the corresponding proper exponent exists for all pi algebras except for some algebras of exponent two strictly related to the grassmann algebra we also prove that the lie exponent exists for any finitely generated pi algebra the value of both exponents is always equal to exp a or exp a 1

algebras with involution with linear codimension growth we study the varieties of associative algebras with involution over a field of characteristic zero which are generated by a finite dimensional algebra in this setting we give a list of algebras classifying all such varieties whose sequence of codimensions is linearly bounded moreover we exhibit a finite list of algebras to be excluded from the varieties with such property as a consequence we find all possible linearly bounded codimension sequences

finitely generated algebras with involution and multiplicities bounded by a constant abstract let a be an algebra with involution over a field f of characteristic zero and let n a n 1 2 be the sequence of cocharacters of a for every n 1 let l n a denote the nth colength of a which is the sum of the multiplicities in n a in this article we classify in two different ways the finitely generated algebras satisfying an ordinary polynomial identity whose multiplicities of the cocharacters n a are bounded by a constant as a consequence this also yields a characterization of the varieties whose colength l n a n 1 2 is bounded by a constant

algebras with involution and multiplicities bounded by a constant abstract let a be an algebra with involution over a field of characteristic zero in this paper we characterize in two different ways when the multiplicities of the cocharacter of a are bounded by a constant as a consequence we characterize the algebras with involution of bounded colength

stabilized explicit implicit domain decomposition methods for the numerical solution of parabolic equations we report a class of stabilized explicit implicit domain decomposition seidd methods for the numerical solution of parabolic equations explicit implicit domain decomposition eidd methods are globally noniterative nonoverlapping domain decomposition methods which when compared with schwarz algorithm based parabolic solvers are computationally and communicationally efficient for each simulation time step but suffer from small time step size restrictions by adding a stabilization step to eidd the seidd methods retain the time stepwise efficiency in computation and communication of the eidd methods but exhibit much better numerical stability three seidd algorithms are presented in this paper which are experimentally tested to show excellent stability computation and communication efficiencies and high parallel speedup and scalability

explicit implicit conservative domain decomposition procedures for parabolic problems based on block centered finite differences domain decomposition procedures for solving parabolic equations are considered the underlying discretization consists of block centered finite differences in these procedures fluxes at subdomain interfaces are calculated from the solution at the previous time level these fluxes serve as neumann boundary data for implicit block centered discretizations in the subdomains a priori error estimates are presented and numerical results examining the stability accuracy and parallelism of the scheme are presented

the new mass conserving s ddm scheme for two dimensional parabolic equations with variable coefficients abstract in the article a new and efficient mass conserving operator splitting domain decomposition method s ddm is proposed and analyzed for solving two dimensional variable coefficient parabolic equations with reaction term the domain is divided into multiple non overlapping block divided subdomains on each block divided subdomain the interface fluxes are first computed explicitly by local multi point weighted schemes and the solutions in the interior of subdomain are computed by the one directional operator splitting implicit schemes at each time step the scheme is proved to satisfy mass conservation over the whole domain of domain decomposition by combining with some auxiliary lemmas and applying the energy method we analyze theoretically the stability of our scheme and prove it to have second order accuracy in space step in the l2 norm numerical experiments are performed to illustrate its accuracy conservation stability efficiency and parallelism our scheme not only keeps the excellent advantages of the non overlapping domain decomposition and the operator splitting technique but also preserves the global mass

standard polynomials are characterized by their degree and exponent abstract by the giambruno zaicev theorem giambruno and zaicev 1999 5 the exponent exp a of a p i algebra a exists and is always an integer in berele and regev 2001 2 it was shown that the exponent exp st n of the standard polynomial st n of degree n is not smaller than the exponent of any polynomial of degree n here it is proved that exp st n is strictly larger than the exponent of any other polynomial of degree n which is not a multiple of st n

multilevel schwarz methods we consider the solution of the algebraic system of equations which result from the discretization of second order elliptic equations a class of multilevel algorithms are studied using the additive schwarz framework we establish that the condition number of the iteration operators are bounded independent of mesh sizes and the number of levels this is an improvement on dryja and widlund s result on a multilevel additive schwarz algorithm as well as bramble pasciak and xu s result on the bpx algorithm some multiplicative variants of the multilevel methods are also considered we establish that the energy norms of the corresponding iteration operators are bounded by a constant less than one which is independent of the number of levels for a proper ordering the iteration operators correspond to the error propagation operators of certain v cycle multigrid methods using gauss seidel and damped jacobi methods as smoothers respectively

graded polynomial identities and codimensions computing the exponential growth abstract let g be a finite abelian group and a a g graded algebra over a field of characteristic zero this paper is devoted to a quantitative study of the graded polynomial identities satisfied by a we study the asymptotic behavior of c n g a n 1 2 the sequence of graded codimensions of a and we prove that if a satisfies an ordinary polynomial identity lim n c n g a n exists and is an integer we give an explicit way of computing such integer by proving that it equals the dimension of a suitable finite dimension semisimple g z 2 graded algebra related to a

lumped mass matrix in explicit finite element method for transient dynamics of elasticity abstract the mass matrix of structural dynamics is discussed for the approximations by linear elements with constant jacobians the a priori error estimate is derived for the explicit finite element method using diagonal mass matrix with smooth solutions it is shown that by using diagonal mass matrix or consistent mass matrix the displacement velocity and the energies have the same convergence rates in fact the difference in numerical errors by these two methods is of order h2 the same conclusion is valid for a certain type of reissner mindlin plate element for transient dynamics

a star variety with almost polynomial growth abstract let f be a field of characteristic zero in this paper we construct a finite dimensional f algebra with involution m and we study its polynomial identities on one hand we determine a generator of the corresponding t ideal of the free algebra with involution and on the other we give a complete description of the multilinear identities through the representation theory of the hyperoctahedral group as an outcome of this study we show that the variety generated by m var m has almost polynomial growth i e the sequence of codimensions of m cannot be bounded by any polynomial function but any proper subvariety of var m has polynomial growth if g 2 is the algebra constructed in giambruno and mishchenko preprint we next prove that m and g 2 are the only two finite dimensional algebras with involution generating varieties with almost polynomial growth

an iterative method for elliptic problems on regions partitioned into substructures some new preconditioners for discretizations of elliptic boundary problems are studied with these preconditioners the domain under consideration is broken into subdomains and preconditioners are defined which only require the solution of matrix problems on the subdomains analytic estimates are given which guarantee that under appropriate hypotheses the preconditioned iterative procedure converges to the solution of the discrete equations with a rate per iteration that is independent of the number of unknowns numerical examples are presented which illustrate the theoretically predicted iterative convergence rates

pi algebras and their cocharacters abstract all pi algebras r satisfy identities of the form f x y x 1 y 1 x 2 y 2 y n 1 x n theorem a the existence of these identities imply also that cocharacters x n r lie in a hook shaped strip of width depending on the degree of the minimal identity of r theorem c this extends a characterization of rings satisfying a capelli identity theorem b

a characterization of minimal varieties of zp graded pi algebras abstract let f be a field of characteristic zero and p a prime in the present paper it is proved that a variety of z p graded associative pi f algebras of finite basic rank is minimal of fixed z p exponent d if and only if it is generated by an upper block triangular matrix algebra u t z p a 1 a m equipped with a suitable elementary z p grading whose diagonal blocks are isomorphic to z p graded simple algebras a 1 a m satisfying dim f a 1 a m d

some results concerning the multiplicities of cocharacters of superalgebras with graded involution abstract let a be a finitely generated superalgebra with graded involution over a field f of characteristic zero and let n 1 n 4 a n 1 n 4 n be the n 1 n 4 cocharacter of a in this paper we present some results concerning the multiplicities of cocharacters for this kind of algebras

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

on the minimality of algebras with involution abstract in di vincenzo and la scala 2007 1 given a n tuple a 1 a n of finite dimensional simple algebras over a field of characteristic zero a block triangular matrix algebra with involution denoted by r ut a 1 a n was introduced and it was proved that any finite dimensional algebra with involution which is minimal with respect to its exponent is pi equivalent to r for a suitable choice of the algebras a i motivated by a conjecture stated in the same paper here we show that r is minimal when either it is symmetric or n 2

a finite element semi lagrangian explicit runge kutta chebyshev method for convection dominated reaction diffusion problems explicit runge kutta chebyshev methods have proved to be efficient for reaction diffusion problems of moderate stiffness in this paper we extend such an efficiency to convection dominated reaction diffusion problems by giving a formulation of these methods in a semi lagrangian framework using c0 finite elements of degree m 2 as the space discretization method we also study the convergence in the l2 norm of the methods proposed in this paper

stability of computational methods for constrained dynamics systems many methods have been proposed for numerically integrating the differential algebraic systems arising from the euler lagrange equations for constrained motion these are based on various problem formulations and discretizations we offer a critical evaluation of these methods from the standpoint of stability nconsidering a linear model we first give conditions under which the differential algebraic problem is well conditioned this involves the concept of an essential underlying ode we review a variety of reformulations which have been proposed in the literature and show that most of them preserve the well conditioning of the original problem then we consider stiff and nonstiff discretizations of such reformulated models in some cases the same implicit discretization may behave in a very different way when applied to different problem formulations acting as a stiff integrator on some formulations and as a nonstiff integrator on others we present the approach of projected invariants as a method for yielding problem reformulations which are desirable in this sense

minimal varieties and minimal supervarieties of polynomial growth abstract by a variety v we mean a supervariety or a variety generated by an associative algebra over a field f of characteristic zero in this case we consider its sequence of codimensions c n v and say that v is minimal of polynomial growth n k if c n v grows like n k but any proper subvariety grows like n t with t k in this paper we deal with minimal varieties generated by unitary algebras and prove that for k 2 there is only a finite number of them we also explicit a list of finite dimensional algebras generating such minimal varieties for k 3 we show that the number of minimal varieties can be infinity and we classify all minimal varieties of polynomial growth n k by giving a recipe for the construction of their t ideals

polynomial codimension growth of algebras with involutions and superinvolutions abstract let a be an associative algebra over a field f of characteristic zero endowed with a graded involution or a superinvolution and let c n a be its sequence of codimensions in 4 12 it was proved that if a is finite dimensional such sequence is polynomially bounded if and only if a generates a variety not containing a finite number of algebras the group algebra of z 2 and a 4 dimensional subalgebra of the 4 4 upper triangular matrices with suitable graded involutions or superinvolutions in this paper we focus our attention on such algebras since they are the only finite dimensional algebras up to t 2 equivalence generating varieties of almost polynomial growth i e varieties of exponential growth such that any proper subvariety has polynomial growth we classify the subvarieties of such varieties by giving a complete list of generating finite dimensional algebras along the way we classify all minimal varieties of polynomial growth and surprisingly we show that their number is finite for any given growth finally we describe the algebras whose codimensions are bounded by a linear function

rkc time stepping for advection diffusion reaction problems the original explicit runge kutta chebyshev rkc method is a stabilized second order integration method for pure diffusion problems recently it has been extended in an implicit explicit manner to also incorporate highly stiff reaction terms this implicit explicit rkc method thus treats diffusion terms explicitly and the highly stiff reaction terms implicitly the current paper deals with the incorporation of advection terms for the explicit method thus aiming at the implicit explicit rkc integration of advection diffusion reaction equations in a manner that advection and diffusion terms are treated simultaneously and explicitly and the highly stiff reaction terms implicitly

graded polynomial identities on upper block triangular matrix algebras let g be an arbitrary abelian group in the present paper we study the question of whether g graded upper block triangular matrix algebras over a field of characteristic zero are determined up to g graded isomorphism by their g graded polynomial identities we obtain some results for an elementary grading and as a consequence for any grading over an algebraically closed field

general identities on bell polynomials the exponential partial bell polynomials are polynomials in an infinite number of variables x 1 x 2 and it is well known that some special combinatorial sequences e g stirling numbers of both kinds lah numbers and idempotent numbers can be obtained from the bell polynomials in this paper we study these polynomials by making appropriate choices of the variables x 1 x 2 which are related to associated sequences binomial sequences and sheffer sequences as a consequence many general identities on bell polynomials are proposed from these general identities we can obtain series of identities on bell polynomials it can also be found that many results presented before are special cases of the general identities of this paper

a domain decomposition discretization of parabolic problems in recent years domain decomposition methods have attracted much attention due to their successful application to many elliptic and parabolic problems domain decomposition methods treat problems based on a domain substructuring which is attractive for parallel computation due to the independence among the subdomains in principle domain decomposition methods may be applied to the system resulting from a standard discretization of the parabolic problems or directly be carried out through a discretization of parabolic problems in this paper a direct domain decomposition method is introduced to discretize the parabolic problems the stability and convergence of this algorithm are analyzed

additive schwarz algorithms for parabolic convection diffusion equations in this paper we consider the solution of linear systems of algebraic equations that arise from parabolic finite element problems we introduce three additive schwarz type domain decomposition methods for general not necessarily selfadjoint linear second order parabolic partial differential equations and also study the convergence rates of these algorithms the resulting preconditioned linear system of equations is solved by the generalized minimal residual method numerical results are also reported

schwarz alternating and iterative refinement methods for mixed formulations of elliptic problems part i algorithms and numerical results we describe sequential and parallel algorithms based on the schwarz alternating method for the solution of mixed finite element discretizations of elliptic problems using the raviart thomas finite element spaces these lead to symmetric indefinite linear systems and the algorithms have some similarities with the traditional block gauss seidel or block jacobi methods with overlapping blocks the indefiniteness requires special treatment the sub blocks used in the algorithm correspond to problems on a coarse grid and some overlapping subdomains and is based on a similar partition used in an algorithm of dryja and widlund for standard elliptic problems if there is sufficient overlap between the subdomains the algorithm converges with a rate independent of the mesh size the number of subdomains and discontinuities of the coefficients extensions of the above algorithms to the case of local grid refinement is also described convergence theory for these algorithms will be presented in a subsequent paper

multidimensional bell polynomials of higher order we develop some extensions of the classical bell polynomials previously obtained by introducing a further class of these polynomials called multidimensional bell polynomials of higher order they arise considering the derivatives of functions f in several variables f i i 1 2 m where f i are composite functions of different orders i e f i t i 1 i 2 i r i t i 1 2 m we show that these new polynomials are always expressible in terms of the ordinary bell polynomials by means of suitable recurrence relations or formal multinomial expansions moreover we give a recurrence relation for their computation

ipic domain decomposition algorithm for parabolic problems a domain decomposition algorithm which is based on a semi implicit prediction and then a fully implicit correction at the interface for solving parabolic partial differential equations is presented the numerical results show that the algorithm is unconditionally stable and very efficient in this paper high speed up is analyzed with respect to the spectral radius and operation counts

some nonoverlapping domain decomposition methods the purpose of this paper is to give a unified investigation of a class of nonoverlapping domain decomposition methods for solving second order elliptic problems in two and three dimensions the methods under scrutiny fall into two major categories the substructuring type methods and the neumann neumann type methods the basic framework used for analysis is the parallel subspace correction method or additive schwarz method and other technical tools include local global and global local techniques the analyses for both two and three dimensional cases are carried out simultaneously some internal relationships between various algorithms are observed and several new variants of the algorithms are also derived

explicit synchronous partitioned algorithms for interface problems based on lagrange multipliers abstract traditional explicit partitioned schemes exchange boundary conditions between subdomains and can be related to iterative solution methods for the coupled problem as a result these schemes may require multiple subdomain solves acceleration techniques or optimized transmission conditions to achieve sufficient accuracy and or stability we present a new synchronous partitioned method derived from a well posed mixed finite element formulation of the coupled problem we transform the resulting differential algebraic equation dae to a hessenberg index 1 form in which the algebraic equation defines the lagrange multiplier as an implicit function of the states using this fact we eliminate the multiplier and reduce the dae to a system of explicit odes for the states explicit time integration both discretizes this system in time and decouples its equations as a result the temporal accuracy and stability of our formulation are governed solely by the accuracy and stability of the explicit scheme employed and are not subject to additional stability considerations as in traditional partitioned schemes we establish sufficient conditions for the formulation to be well posed and prove that classical mortar finite elements on the interface are a stable choice for the lagrange multiplier we show that in this case the condition number of the schur complement involved in the elimination of the multiplier is bounded by a constant the paper concludes with numerical examples illustrating the approach for two different interface problems

block triangular matrix algebras and factorable ideals of graded polynomial identities abstract we study the graded polynomial identities of block triangular matrix algebras with respect to the grading defined by an abelian group g in particular we describe conditions for the t g ideal of a such algebra to be factorable as a product of t g ideals corresponding to the algebras defining the diagonal blocks moreover for the factorable t 2 ideal of a superalgebra we give a formula for computing its sequence of graded cocharacters once given the sequences of cocharacters of the t 2 ideals that factorize it we finally apply these results to a specific example of block triangular matrix superalgebra

on finite element method flux corrected transport stabilization for advection diffusion problems in a partial differential algebraic framework an extension of the finite element method flux corrected transport stabilization for hyperbolic problems in the context of partial differential algebraic equations is proposed given a local extremum diminishing property of the spatial discretization the positivity preservation of the one step q scheme when applied to the time integration of the resulting differential algebraic equation is shown under a mild restriction on the time step size as a crucial tool in the analysis the drazin inverse and the corresponding drazin ordinary differential equation are explicitly derived numerical results are presented for non constant and time dependent boundary conditions in one space dimension and for a two dimensional advection problem with a sinusoidal inflow boundary condition and the advection proceeding skew to the mesh

involution codimensions of finite dimensional algebras and exponential growth abstract let f be a field of characteristic zero and let a be a finite dimensional algebra with involution over f we study the asymptotic behavior of the sequence of codimensions c n a of a and we show that exp a lim n c n a exists and is an integer we give an explicit way for computing exp a and as a consequence we obtain the following characterization of simple algebras a is simple if and only if exp a dim f a

runge kutta chebyshev projection method in this paper a fully explicit stabilized projection method called the runge kutta chebyshev rkc projection method is presented for the solution of incompressible navier stokes systems this method preserves the extended stability property of the rkc method for solving odes and it requires only one projection per step an additional projection on the time derivative of the velocity is performed whenever a second order approximation for the pressure is desired we demonstrate both by numerical experiments and by order analysis that the method is second order accurate in time for both the velocity and the pressure being explicit the rkc projection method is easy to implement and to parallelize hence it is an attractive candidate for the solution of large scale moderately stiff diffusion like problems

some extensions of faa di bruno s formula with divided differences the well known formula of faa di bruno s for higher derivatives of a composite function has played an important role in combinatorics in this paper we generalize the divided difference form of faa di bruno s formula and give an explicit formula for the n th divided difference of a multicomposite function more generally we establish the relationships of the bell polynomials with respect to multicomposite functions applying these to multicomposite functions we obtain some extensions of faa di bruno s formula

on codimension growth of finitely generated associative algebras abstract letabe a pi algebra over a fieldf we study the asymptotic behavior of the sequence of codimensionscn a ofa we show that ifais finitely generated overftheninv a limn c n a always exists and is an integer we also obtain the following characterization of simple algebras ais finite dimensional central simple overfif and only ifinv a dim a

noncommutative invariant theory of symplectic and orthogonal groups abstract we present a method for computing the hilbert series of the algebra of invariants of the complex symplectic and orthogonal groups acting on graded noncommutative algebras with homogeneous components which are polynomial modules of the general linear group we apply our method to compute the hilbert series for different actions of the symplectic and orthogonal groups on the relatively free algebras of the varieties of associative algebras generated respectively by the grassmann algebra and the algebra of 2 2 upper triangular matrices these two varieties are remarkable with the property that they are the only minimal varieties of exponent 2

multiplicative schwarz methods for parabolic problems the class of multiplicative schwarz methods originated from the classical schwarz alternating method it has been shown to be one of the most powerful methods for solving finite element or finite d

an extension of the bell polynomials abstract after recalling the most important properties and applications of the bell polynomials we introduce an extension of this special class of functions more precisely we consider the case of multicomposite functions and we show connections with the ordinary bell polynomials

minimal algebras with respect to their exponent abstract given an m tuple a 1 a m of finite dimensional simple algebras we introduce a block triangular matrix algebra with involution denoted as ut a 1 a m where each a i can be embedded as algebra we describe the t ideal of r ut a 1 a m in terms of the ideals t a i and prove that any algebra with involution which is minimal with respect to its exponent is pi equivalent to r for a suitable choice of a 1 a m moreover we show that if m 1 or a i f for all i then r itself is a minimal algebra the assumption for the base field f is characteristic zero

a finite difference domain decomposition algorithm for numerical solution of the heat equation a domain decomposition algorithm for numerically solving the heat equation in one and two space dimensions is presented in this procedure interface values between subdomains are found by an explicit finite difference formula once these values are calculated interior values are determined by backward differencing in time a natural extension of this method allows for the use of different time steps in different subdomains maximum norm error estimates for these procedures are derived which demonstrate that the error incurred at the interfaces is higher order in the discretization parameters

rkc an explicit solver for parabolic pdes the fortran program rkc is intended for the time integration of parabolic partial differential equations discretized by the method of lines it is based on a family of runge kutta chebyshev formulas with a stability bound that is quadratic in the number of stages remarkable properties of the family make it possible for the program to select at each step the most efficient stable formula as well as the most efficient step size moreover they make it possible to evaluate the explicit formulas in just a few vectors of storage these characteristics of the program make it especially attractive for problems in several spatial variables rkc is compared to the bdf solver vodpk on two test problems in three spatial variables

on the factorability of polynomial identities of upper block triangular matrix algebras graded by cyclic groups abstract let f be an algebraically closed field of characteristic zero and g be an arbitrary finite cyclic group in this paper given an m tuple a 1 a m of finite dimensional g simple algebras we focus on the study of the factorability of the t g ideals id g u t a 1 a m of the g graded upper block triangular matrix algebras u t a 1 a m endowed with elementary g gradings induced by some maps when g is a cyclic p group we prove that the factorability of the ideal id g u t a 1 a m is equivalent to the g regularity of all except for at most one the g simple components a 1 a m as well to the existence of a unique isomorphism class of admissible elementary g gradings for u t a 1 a m moreover we present some necessary and sufficient conditions to the factorability of id g u t a 1 a 2 even in case g is not a p group with some stronger assumptions on the gradings of the algebras a 1 and a 2