a continuous framework for feti dp with a mesh independent condition number for the dual problem abstract we present an abstract setting for a variation of the feti dp method applied to second order elliptic problems in this setting the matrix iteration for the dual problem has a mesh independent condition number this work improves the ideas recently introduced by bernardi et al c bernardi t chacon rebollo e chacon vera a feti method with a mesh independent condition number for the iteration matrix comput methods appl mech engrg 197 13 16 2008 1410 1429 the continuity restrictions for the displacement field across interfaces are weakly imposed using the natural trace norm instead of pointwise continuity although a slight coupling between subdomains is introduced still a parallel computation is possible some numerical tests are also performed to illustrate the method

the construction of preconditioners for elliptic problems by substructuring i in earlier parts of this series of papers we constructed preconditioners for the discrete systems of equations arising from the numerical approximation of elliptic boundary value problems the resulting algorithms are well suited for implementation on computers with parallel architecture in this paper we will develop a technique which utilizes these earlier methods to derive even more efficient preconditioners the iterative algorithms using these new preconditioners converge to the solution of the discrete equations with a rate that is independent of the number of unknowns these preconditioners involve an incomplete chebyshev iteration for boundary interface conditions which results in a negligible increase in the amount of computational work theoretical estimates and the results of numerical experiments are given which demonstrate the effectiveness of the methods

extension operators on tensor product structures in two and three dimensions in this paper a uniformly elliptic second order boundary value problem in two dimensions is discretized by the p version of the finite element method an inexact dirichlet dirichlet domain decomposition preconditioner for the system of linear algebraic equations is investigated the ingredients of such a preconditioner are a preconditioner for the schur complement a preconditioner for the subdomains and an extension operator operating from the edges of the elements into their interior using methods of multiresolution analysis we propose a new method to compute the extension efficiently we prove that this type of extension is optimal i e the h 1 omega norm of the extended function is bounded by the h 0 5 partial omega norm of the given function numerical experiments show the optimal performance of the described extension

a fast iterative method for solving stationary heat conduction problems on regions partitioned into rectangles the paper deals with some finite element approximation of stationary heat conduction problems on regions which can be partitioned into rectangular subregions by a special superelement technique employing fast elimination of the inner nodal parameters the original finite element problem is reduced to a smaller problem which is only connected with the nodes on the boundary of the superelements to solve the reduced system of finite element equations an efficient iterative algorithm is proposed this algorithm is based either on the conjugate gradient method or the tshebysheff method using a special matrix by vector multiplication procedure the explicit form of the matrix is not used the presented numerical method is asymptotically optimal with respect to the memory requirement as well as to the operation count

explicit preconditioned domain decomposition schemes for solving nonlinear boundary value problems abstract a new class of inner outer iterative procedures in conjunction with picard newton methods based on explicit preconditioning iterative methods for solving nonlinear systems is presented explicit preconditioned iterative schemes based on the explicit computation of a class of domain decomposition generalized approximate inverse matrix techniques are presented for the efficient solution of nonlinear boundary value problems on multiprocessor systems applications of the new composite scheme on characteristic nonlinear boundary value problems are discussed and numerical results are given

nonlinear simulation of electromagnetic fields with domain decomposition methods on mind parallel computers abstract an efficient domain decomposition dd algorithm for solving nonlinear boundary value problems on multiple instruction multiple data parallel computers is presented the linearization is done by newton s method and the linear system is solved by cg with dd preconditioning further the dd approach allows finite element and galerkin boundary element methods to be combined in a unifled variational problem test computations on a transputer based system were performed for both model problems and a real life electric motor

a finite element capacitance method for elliptic problems on regions partitioned into subregions a method is given for the solution of linear equations arising in the finite element method applied to a general elliptic problem this method reduces the original problem to several subproblems of the same form considered on subregions and an auxiliary problem very efficient iterative methods with the preconditioning operator and using fft are developed for the auxiliary problem

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

inexact feti dp methods inexact feti dp domain decomposition methods are considered preconditioners based on formulations of feti dp as a saddle point problem are used which allow for an inexact solution of the coarse problem a positive definite reformulation of the preconditioned saddle point problem which also allows for approximate solvers is considered as well in the formulation that iterates on the original feti dp saddle point system it is also possible to solve the local neumann subdomain problems inexactly given good approximate solvers for the local and coarse problems convergence bounds of the same quality as for the standard feti dp methods are obtained numerical experiments which compare the convergence of the inexact methods with that of standard feti dp are shown for 2d and 3d elasticity using gmres and cg as krylov space methods based on parallel computations a comparison of one variant of the inexact feti dp algorithms and the standard feti dp method is carried out and similar parallel performance is achieved parallel scalability of the inexact variant is also demonstrated it is shown that for a very large number of subdomains and a very large coarse problem the inexact method can be superior copyright 2006 john wiley sons ltd

a preconditioner for substructuring based on constrained energy minimization a preconditioner for substructuring based on constrained energy minimization concepts is presented the preconditioner is applicable to both structured and unstructured meshes and offers a straightforward approach for the iterative solution of second and fourth order structural mechanics problems the approach involves constraints associated with disjoint sets of nodes on substructure boundaries these constraints provide the means for preconditioning at both the substructure and global levels numerical examples are presented that demonstrate the good performance of the method in terms of iterations compute time and condition numbers of the preconditioned equations

efficient preconditioning for the p version finite element method in two dimensions parallel preconditioners are formulated and analyzed for systems of equations arising from the p version finite element method applied to second order self adjoint elliptic boundary value problems in two dimensions by using new theoretical results for polynomial spaces it is proved that the condition number of the preconditioned system grows as log 2 p where p is the degree of the polynomial space numerical results are presented showing that the condition number indeed grows very slowly with p

a multiscale preconditioner for stochastic mortar mixed finite elements the aim of this paper is to introduce a new approach to efficiently solve sequences of problems that typically arise when modeling flow in stochastic porous media the governing equations are based on darcy s law with a stochastic permeability field starting from a specified covariance relationship the log permeability is decomposed using a truncated karhunen loeve expansion multiscale mortar mixed finite element approximations are used in the spatial domain and a nonintrusive sampling method is used in the stochastic dimensions a multiscale mortar flux basis is computed for a single permeability called a training permeability that captures the main characteristics of the porous media and is used as a preconditioner for each stochastic realization we prove that the condition number of the preconditioned interface operator is independent of the subdomain mesh size and the mortar mesh size computational results confirm that our approach provides an efficient means to quantify the uncertainty for stochastic flow in porous media

efficient solvers for saddle point problems arising from domain decompositions with lagrange multipliers in this paper we are concerned with the domain decomposition method with lagrange multipliers for solving three dimensional elliptic problems with variable coefficients we shall first introduce a weighted saddle point problem resulting from this domain decomposition which can be solved by existing iterative methods then we will construct two simple preconditioners one for the system associated with the displacement variable and the other for the schur complement system associated with the multiplier variable that are applicable to various discretization schemes the new preconditioners possess such local properties that they can be implemented cheaply we will show that the condition number of the global preconditioned system grows only as the logarithm of the dimension of the local problem associated with an individual substructure and is independent of the large variations of the coefficients across the local interfaces

incomplete iterations in multistep backward difference methods for parabolic problems with smooth and nonsmooth data backward difference methods for the discretization of parabolic boundary value problems are considered in this paper in particular we analyze the case when the backward difference equations are only solved approximately by a preconditioned iteration we provide an analysis which shows that these methods remain stable and accurate if a suitable number of iterations often independent of the spatial discretization and time step size are used results are provided for the smooth as well as nonsmooth initial data cases finally the results of numerical experiments illustrating the algorithms performance on model problems are given

image retrieval based on multi texton histogram this paper presents a novel image feature representation method called multi texton histogram mth for image retrieval mth integrates the advantages of co occurrence matrix and histogram by representing the attribute of co occurrence matrix using histogram it can be considered as a generalized visual attribute descriptor but without any image segmentation or model training the proposed mth method is based on julesz s textons theory and it works directly on natural images as a shape descriptor meanwhile it can be used as a color texture descriptor and leads to good performance the proposed mth method is extensively tested on the corel dataset with 15000 natural images the results demonstrate that it is much more efficient than representative image feature descriptors such as the edge orientation auto correlogram and the texton co occurrence matrix it has good discrimination power of color texture and shape features

on the finite element solution of the pure neumann problem this paper considers the finite element approximation and algebraic solution of the pure neumann problem our goal is to present a concise variational framework for the finite element solution of the neumann problem that focuses on the interplay between the algebraic and variational problems while many of the results that stem from our analysis are known by some experts they are seldom derived in a rigorous fashion and remain part of numerical folklore as a result this knowledge is not accessible or appreciated by many practitioners both novices and experts in one source our paper contributes a simple yet insightful link between the continuous and algebraic variational forms that will prove useful

discrete interpolation norms with applications we describe norm representations for interpolation spaces generated by finite dimensional subspaces of hilbert spaces these norms are products of integer and noninteger powers of the grammian matrices associated with the generating pair of spaces for the interpolation space we include a brief description of some of the algorithms which allow the efficient computation of matrix powers we consider in some detail the case of fractional sobolev spaces both for positive and negative indices together with applications arising in preconditioning techniques numerical experiments are included

an additive schwarz preconditioner for the feti method a new additive schwarz preconditioner for the finite element tearing and interconnecting feti method is analyzed in this paper this preconditioner has the unique feature that the coefficient matrix of its coarse grid problem is mesh independent for a model second order heterogeneous elliptic boundary value problem in two dimensions the condition number of the preconditioned system is shown to be bounded by c 1 ln h h 2 where h is the mesh size h is the typical diameter of the subdomains and the constant c is independent of h h the number of subdomains and the coefficients of the boundary value problem

on serre s conjecture for mod l galois representations over totally real fields in 1987 serre conjectured that any mod two dimensional irre ducible odd representation of the absolute galois group of the rationals came from a modular form in a precise way we present a generalisation of this conjecture to 2 dimensional representations of the absolute galois group of a totally real eld where is unramied the hard work is in formulating an analogue of the weight part of serre s conjecture serre furthermore asked whether his conjecture could be rephrased in terms of a mod langlands philosophy using ideas of emerton and vign eras we formulate a mod local global principle for the group d where d is a quaternion algebra over a totally real eld split above and at 0 or 1 innite places and show how it implies the conjecture

error estimates for the three field formulation with bubble stabilization in this paper we prove convergence and error estimates for the so called 3 field formulation using piecewise linear finite elements stabilized with boundary bubbles optimal error bounds are proved in l 2 and in the broken h 1 norm for the internal variable u and in suitable weighted l 2 norms for the other variables a and

the fast adaptive composite grid fac method for elliptic equation the fast adaptive composite grid fag method is a systematic process for solving differential boundary value problems fac uses global and local uniform grids both to define the composite grid problem and to interact for its fast solution it can with little added cost substantially improve accuracy of the coarse grid solution and is very suitable for vector and parallel computation this paper develops both the theoretical and practical aspects of fac as it applies to elliptic problems 1 introduction the need for local resolution in physical models occurs frequently in practice special local features of the forcing function operator coefficients boundary and boundary conditions can demand resolution in restricted regions of the domain that is much finer than the required global resolution it is important that the discretization and solution processes account for this locally that is that the local phenomena do not precipitate a dramatic increase in the overall computation unfortunately this objective of efficiently adapting to local features is often in conflict with the solution process equation solvers can degrade or even fail to apply in the presence of varying discretization scales data structures that account for irregular grids can be cumbersome the computer architecture may not be able to effectively account for grid irregularity e g vectorizability may be inhibited etc in fact even the discretization process itself may find difficulty with this objective for finite differences it is problematic to develop accurate difference formulae for irregular grids for finite elements this objective is reflected in the substantial overhead costs needed to automate the discretization the fast adaptive composite grid method fac 11 is a discretization and solution method designed to achieve efficient local resolution by constructing the

block preconditioning and domain decomposition methods ii abstract domain decomposition methods for the solution of partial differential equations are attractive on parallel processors because each processor can work independently on a large subtask the corresponding stiffness matrix takes a sparse block structure for which preconditioned iterative methods can be used when solving linear systems with the stiffness matrix for domains decomposed in strips we get a blocktridiagonal structure for which a new block lu preconditioner was presented in an earlier report 5 by the authors an alternative method and also the one more commonly used for substructuring methods is based on approximation of the schur complement matrix this approximation is frequently done by various difference methods see 6 11 and 16 in the present paper we examine methods based on algebraic approximation methods this is similar to methods used by chan 9

multilevel preconditioning for the boundary concentrated hp fem abstract the boundary concentrated finite element method is a variant of the hp version of the finite element method that is particularly suited for the numerical treatment of elliptic boundary value problems with smooth coefficients and low regularity boundary conditions for this method we present two multilevel preconditioners that lead to preconditioned stiffness matrices with condition numbers that are bounded uniformly in the problem size n the cost of applying the preconditioners is o n numerical examples illustrate the efficiency of the algorithms

feti and neumann neumann iterative substructuring methods connections and new results the feti and neumann neumann families of algorithms are among the best know and most severely tested domain decomposition methods for elliptic partial differential equations they are iterative substructuring methods and have many algorithmic components in common but there are also differences the purpose of this paper is to further unify the theory for these two families of methods and to introduce a new family of feti algorithms bounds on the rate of convergence which are uniform with respect to the coefficients of a family of elliptic problems with heterogeneous coefficients are established for these new algorithms the theory for a variant of the neumann neumann algorithm is also redeveloped stressing similarities to that for the feti methods

detection of a polymorphic mesoamerican symbol using a rule based approach this paper describes a technique to recognize a mesoamerican symbol whose shape is extremely variable we extract symbols from a drawing and we encode them as discrete curves we perform the recognition using a set of rules that define the correct symbol one of the rules is the presence of a single symmetry axis we describe a comparison metric between curves in order to search for symmetries the other rules used for the recognition concern the morphology of the symbol the proposed technique proves to be fast and efficient we present recognition results obtained on various pre hispanic images the rule based approach proposed and implemented here appears suitable to detect polymorphic signs a common feature of mesoamerican symbols to the best of our knowledge this is the first study of pattern recognition into the field of mesoamerican iconography

boundary concentrated finite element methods a method with optimal up to logarithmic terms complexity for solving elliptic problems is proposed the method relies on interior regularity but the solution may have globally low regularity due to rough boundary data or geometries elliptic regularity results high order approximation results and an efficient preconditioner are presented the method is utilized to realize with linear logarithmic complexity an accurate and data sparse approximation to the associated elliptic poincare steklov operators further applications include the treatment of exterior boundary value problems and the solution of problems in the framework of domain decomposition methods

silhouette based isolated object recognition through curvature scale space a complete fast and practical isolated object recognition system has been developed which is very robust with respect to scale position and orientation changes of the objects as well as noise and local deformations of shape due to perspective projection segmentation errors and non rigid material used in some objects the system has been tested on a wide variety of three dimensional objects with different shapes and material and surface properties a light box setup is used to obtain silhouette images which are segmented to obtain the physical boundaries of the objects which are classified as either convex or concave convex curves are recognized using their four high scale curvature extrema points curvature scale space css representations are computed for concave curves the css representation is a multi scale organization of the natural invariant features of a curve curvature zero crossings or extrema and useful for very reliable recognition of the correct model since it places no constraints on the shape of objects a three stage coarse to fine matching algorithm prunes the search space in stage one by applying the css aspect ratio test the maxima of contours in css representations of the surviving models are used for fast css matching in stage two finally stage three verifies the best match and resolves any ambiguities by determining the distance between the image and model curves transformation parameter optimization is then used to find the best fit of the input object to the correct model

adaptive galerkin boundary element methods with panel clustering in this paper we will propose a boundary element method for solving classical boundary integral equations on complicated surfaces which possibly contain a large number of geometric details or even uncertainties in the given data the small size of such details is characterised by a small parameter varepsilon and the regularity of the solution is expected to be low in such zones on the surface which we call the wire basket zones we will propose the construction of an initial discretisation for such type of problems afterwards standard strategies for boundary element discretisations can be applied such as the h p and the adaptive hp version in a straightforward way for the classical boundary integral equations we will prove the optimal approximation results of our so called wire basket boundary element method and discuss the stability aspects then we construct the panel clustering and mathcal h matrix approximations to the corresponding galerkin bem stiffness matrix the method is shown to have an almost linear complexity with respect to the number of degrees of freedom located on the wire basket

unstructured additive schwarz conjugate gradient method for elliptic problems with highly discontinuous coefficients this paper concerns the iterative solution of symmetric elliptic problems with piecewise constant coefficients in two or three space dimensions discretized by linear finite element methods on unstructured triangular or tetrahedral meshes the effect of the discontinuous coefficients is studied by first postulating that there are d fixed regions of the domain where the coefficient takes constant positive values a a1 ad and then considering certain positive coefficient sequences a m in which some of these values approach 0 or infty as m rightarrow infty we consider the performance of additive schwarz domain decomposition preconditioners constructed from local solves on automatically generated subdomains together with a global solve on some coarser grid assuming no relationship between the regions on which the coefficient function is constant and either the subdomains or the coarse grid we show that the preconditioned conjugate gradient method converges in both the energy and the euclidean norms with a number of iterations which grows only logarithmically in the size of the maximum jump cal j m max a k m a l m k l 1 ldots d as m rightarrow infty the result is obtained by a careful analysis of the preconditioned matrix it cannot be obtained by the usual procedure of estimating condition numbers a simple example is given in which the condition number of both the original and the preconditioned stiffness matrices degrade linearly in cal j m recent results of chan smith and zou have shown that by using this preconditioner together with the conjugate gradient method the number of iterations can be bounded independently of the mesh diameter provided the subdomains have overlap commensurate with the size of the coarse mesh our results now show that this method is also highly resilient to discontinuous coefficients even if no attention is paid to the coefficient discontinuity in the construction of the solver

a comparison of deflation and the balancing preconditioner in this paper we compare various preconditioners for the numerical solution of partial differential equations we compare the well known balancing preconditioner used in domain decomposition methods with a so called deflation preconditioner we prove that the effective condition number of the deflated preconditioned system is always i e for all deflation vectors and all restrictions and prolongations below the condition number of the system preconditioned by the balancing preconditioner even more we establish that both preconditioners lead to almost the same spectra the zero eigenvalues of the deflation preconditioned system are replaced by eigenvalues which are one if the balancing preconditioner is used moreover we prove that the a norm of the errors of the iterates built by the deflation preconditioner is always below the a norm of the errors of the iterates built by the balancing preconditioner depending on the implementation of the balancing preconditioner the amount of work of one iteration of the deflation preconditioned system is less than or equal to the amount of work of one iteration of the balancing preconditioned system if the amount of work is equal both preconditioners are sensitive with respect to inexact computations finally we establish that the deflation preconditioner and the balancing preconditioner produce the same iterates if one uses certain starting vectors numerical results for porous media flows emphasize the theoretical results

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

analysis of preconditioners for domain decomposition domain decomposition is a class of techniques that are designed to solve elliptic problems on irregular domains and on multiprocessor systems typically a domain is decomposed into many smaller regular subdomains and the capacitance system governing the interface unknowns is solved by some version of the preconditioned conjugate gradient method in this paper we show that for a simple model problem poisson s equation on a rectangle decomposed into two smaller rectangles the capacitance system can be inverted exactly by fast fourier transform an exact eigen decomposition of the capacitance matrix also makes it possible to relate and compare the various preconditioners that have been proposed in the literature for example we show that in the limit as the aspect ratio of the two rectangles tend to infinity the preconditioner proposed by golub and mayers becomes exact but the one proposed by dryja does not both preconditioners however are poor when the aspect ratio is small

domain decomposition methods for eigenvalue problems abstract this paper proposes several domain decomposition methods to compute the smallest eigenvalue of linear self adjoint partial differential operators let us be given a partial differential operator on a domain which consists of two nonoverlapping subdomains suppose a fast eigenvalue solver is available for each of these subdomains but not for the union of them the first proposed method is a scheme which determines an appropriate boundary condition at the interface separating the two regions this boundary condition can be derived from the zero of a nonlinear operator which plays the same role for the eigenvalue problem as the steklov poincare operator for the linear equation an iterative method can be used to solve this nonlinear equation yielding the exact boundary condition at the interface this enables the determination of the eigenpair on the whole domain the same concept can be applied to a schwarz alternating method for the eigenvalue problem in case the subdomains overlap a nonoverlapping scheme in the spirit of schur complement will also be discussed these ideas are also applicable to a domain imbedding algorithm

image retrieval based on shape similarity by edge orientation autocorrelogram abstract this paper introduces a new feature vector for shape based image indexing and retrieval this feature classifies image edges based on two factors their orientations and correlation between neighboring edges hence it includes information of continuous edges and lines of images and describes major shape properties of images this scheme is effective and robustly tolerates translation scaling color illumination and viewing position variations experimental results show superiority of proposed scheme over several other indexing methods averages of precision and recall rates of this new indexing scheme for retrieval as compared with traditional color histogram are 1 99 and 1 59 times respectively these ratios are 1 26 and 1 04 compared to edge direction histogram

multilevel preconditioners for elliptic problems by substructuring we consider the construction of preconditioners for reduced schur problems for solving finite element elliptic equations which are obtained by block gaussian elimination of the unknowns corresponding to a number of subregions the preconditioners are based on approximations of the considered elliptic problem on a sequence of meshes and are derived in a purely algebraic manner it is proved that the proposed algebraic multilevel preconditioner is of nearly optimal order that is its relative condition number with respect to the corresponding reduced schur complement is proportional to l 2 where l is the number of discretization levels used this condition number is bounded uniformly with respect to the number of subregions the way the region is partitioned for example into strips or into boxes and the discontinuity of the coefficients of the elliptic operator if they are constants on the elements from the initial triangulation the data transport except on the coarsest level is of local type and is proportional to the number of nodes on the interface boundary

on the conjugate gradient solution of the schur complement system obtained from domain decomposition for a linear system arising from a finite element discretization on a quasi uniform grid of a second order elliptic partial differential equation it is shown that the condition number of the schur

a domain decomposition method with lagrange multipliers and inexact solvers for linear elasticity a new domain decomposition method with lagrange multipliers for elliptic problems is introduced it is based on a reformulation of the well known finite element tearing and interconnecting feti method as a saddle point problem with both primal and dual variables as unknowns the resulting linear system is solved with block structured preconditioners combined with a suitable krylov subspace method this approach allows the use of inexact subdomain solvers for the positive definite subproblems it is shown that the condition number of the preconditioned saddle point problem is bounded independently of the number of subregions and depends only polylogarithmically on the number of degrees of freedom of individual local subproblems numerical results are presented for a plane stress cantilever membrane problem

a finiteness property of abelian varieties with potentially ordinary good reduction a g dimensional abelian variety a f over a number field f is of gl 2 type if end a f end a f z q contains a field e of degree g we call such a field e an endomorphism field of a we say that an f simple abelian variety a f over a number field f of dimension g is non cm if end a f f q does not contain any semi simple commutative algebra of degree 2g over q cf acm if an abelian variety a f of gl 2 type is f simple d end a f is a division algebra with a positive involution since d has a maximal commutative subfield stable under we may assume that its endomorphism field e is totally real or a cm field the galois action on the tate module of an f simple abelian variety a f of gl 2 type with endomorphism field e produces a two dimensional strictly compatible system of galois representations a gal q f gl2 e indexed by primes of e thus we have its l function l s a two f simple abelian varieties a and b a are twist equivalent if l s b l s a for a finite order character gal q f q note that the dimension is possibly unbounded over a twist equivalent class since tate s conjecture has been proven by faltings for abelian varieties one could formulate this equivalence by insisting that the two abelian varieties share a simple component over an abelian extension of f in this more geometric context q simple abelian varieties have been studied in depth as q simple factors of modular jacobians by ribet for example see r and his papers quoted there however we adopt an analytic definition of twistequivalence using their l function as it can also be applied to rank 2 q motives for which the tate conjecture is still unknown here the identity of two l functions

robust preconditioners for linear elasticity fem analyses summary this paper deals with two forms of preconditioner which can be easily used with a conjugate gradient solver to replace a direct solution subroutine in a traditional engineering nite element package they are tested in such a package final over a range of 2 d and 3 d elasticity problems from geotechnical engineering quadratic basis functions are used a number of modications to the basic incomplete choleski ic 0 factorization preconditioner are considered an algorithm to reduce positive o diagonal entries is shown in numerical experiments to ensure stability but at the expense of slow convergence an alternative algorithm of jennings and malik is more successful and a relaxation parameter is introduced which can make a further signicant improvement in performance while maintaining stability a heuristic for determining a near optimal value of is proposed a second form of preconditioning symmetrically scaled element by element due to bartelt is also shown to perform robustly over a range of problems it does not require assembly of the global stiness matrix and has great potential for parallelization 1997 by john wiley sons ltd

the method for image retrieval based on multi factors correlation utilizing block truncation coding abstract in this paper we proposed multi factors correlation mfc to describe the image structure element correlation sec gradient value correlation gvc and gradient direction correlation gdc at first the rgb color space image is converted to a bitmap image and a mean color component image utilizing the block truncation coding btc then three correlations will be used to extract the image feature the structure elements can effectively represent the bitmap which is generated by btc and sec can effectively denote the bitmap s structure and the correlation of the block in the bitmap gvc and gdc can effectively denote the gradient relation which is computed by a mean color component image formed by sec gvc and gdc the image feature vectors can effectively represent the image in the end the results demonstrate that the method has better performance than other image retrieval methods in the experiment

the neumann dirichlet domain decomposition method with inexact solvers on the subdomains we consider the neumann dirichlet domain decomposition method for the solution of linear elliptic boundary value problems we study the following question suppose that the auxiliary problems on the subdomains are not solved exactly but only with a fixed mesh size independent accuracy does the speed of convergence remain mesh size independently bounded we show that the answer is no in general but that mesh size independent convergence can be obtained if the accuracy requirement on the subsolvers becomes increasingly severe as the mesh size tends to zero

a hierarchical iterative procedure for the analysis of composite laminates a multilevel recursively defined preconditioner for use with the preconditioned conjugate gradient pcg algorithm is developed and applied to solve thin and thick laminated plate problems the preconditioner is constructed from a sequence of hierarchical vector spaces arising from the p version of the finite element fe method numerical studies have been conducted using quadrilateral elements for two dimensional problems up to p 8 and serendipity brick elements for three dimensional problems up to p 5 the efficiency of the iterative procedure is illustrated using bending response of laminated plates the effects of element span ratios convergence tolerance polynomial order material properties and plate span ratios on the number of iterations required for convergence has been investigated results indicate that the preconditioner developed herein can be used to produce an efficient iterative solver for two and three dimensional problems in structural mechanics

a capacitance matrix method for dirichlet problem on polygon region an efficient algorithm for the solution of linear equations arising in a finite element method for the dirichlet problem is given the cost of the algorithm is proportional ton 2log2 n n 1 h where the cost of solving the capacitance matrix equations isnlog2 n on regular grids andn 3 2log2 n on irregular ones

a preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems this paper provides a preconditioned iterative technique for the solution of saddle point problems these problems typically arise in the numerical approximation of partial differential equations by lagrange multiplier techniques and or mixed methods the saddle point problem is reformulated as a symmetric positive definite system which is then solved by conjugate gradient iteration applications to the equations of elasticity and stokes are discussed and the results of numerical experiments are given

domain decomposition and parallel processing of a finite element model of the shallow water equations abstract we present nonoverlapping domain decomposition techniques applied to a two stage numerov galerkin finite element model of the shallow water equations over a limited area domain the schur complement matrix formulation is employed and a modified interface matrix approach is proposed to handle the coupling between subdomains the resulting nonsymmetric schur complement matrices modified interface matrices as well as the subdomain coefficient matrices are solved using preconditioned conjugate gradient squared pcgs non symmetric iterative solvers various stages of the finite element solution are parallelized and the code is implemented ona four processor cray y mp supercomputer applying multitasking techniques in a dedicated environment

analysis of iterative methods for saddle point problems a unified approach in this paper two classes of iterative methods for saddle point problems are considered inexact uzawa algorithms and a class of methods with symmetric preconditioners in both cases the iteration matrix can be transformed to a symmetric matrix by block diagonal matrices a simple but essential observation which allows one to estimate the convergence rate of both classes by studying associated eigenvalue problems the obtained estimates apply for a wider range of situations and are partially sharper than the known estimates in literature a few numerical tests are given which confirm the sharpness of the estimates

solution techniques for the p version of the adaptive finite element method this paper investigates the performance of a class of methods based on the preconditioned conjugate gradient pcg method for the solution of large and sparse systems of linear equations which arise from the p version of the adaptive finite element method the hierarchical type of preconditioning used in the past is extended to the ssor and incomplete factorization type preconditioning and applied with a global handling of the stiffness matrix the paper also presents some new ideas on domain decomposition dd matrix handling techniques whereby the explicit formulation of the resulting schur complement is avoided by utilizing the pcg method with efficient preconditioners and by processing separately on the coarse and the fine mesh the suitability of the methods to the p version of the adaptive finite element method is demonstrated through extensive numerical tests in two dimensions

a gradient method approach to optimization based multidisciplinary simulations and nonoverlapping domain decomposition algorithms it has been shown recently that optimization based nonoverlapping domain decomposition algorithms are connected to many well known algorithms using a gradient type iterative strategy for the optimization problem we present further discussion on how to develop various algorithms that can integrate subdomain solvers into a solver for the problem in the whole domain in particular the algorithms we discuss can be used to develop efficient solvers of multidisciplinary problems which are constructed using existing subdomain solvers without the need for making changes in the latter

a numerical study on neumann neumann and feti methods for hp approximations on geometrically refined boundary layer meshes in two dimensions abstract we present extensive numerical tests showing the performance and robustness of certain balancing neumann neumann and one level feti methods for the solution of algebraic linear systems arising from hp finite element approximations of scalar elliptic problems on geometrically refined boundary layer meshes in two dimensions the numerical results confirm the theoretical results derived in a toselli x vasseur technical report 02 15 seminar fur angewandte mathematik eth zurich september 2002 the condition numbers are independent of the aspect ratio of the mesh and of potentially large jumps of the coefficients in addition they only grow polylogarithmically with the polynomial degree as in the case of p approximations on shape regular meshes

on the construction of preconditioners by subspace decomposition abstract a preconditioner for the iterative solution of symmetric linear systems which arise in galerkin s method is obtained by decomposition of the space into orthogonal subspaces the preconditioner corresponds to a particular bilinear form and is actually a 2 level multigrid method applications are presented to the numerical solution of elliptic problems by the finite element method and to the numerical solution of first kind fredholm integral equations by tikhonov regularization

primal and dual interface concentrated iterative substructuring methods this paper is devoted to the fast solution of interface concentrated finite element equations the interface concentrated finite element schemes are constructed on the basis of a nonoverlapping domain decomposition where a conforming boundary concentrated finite element approximation is used in every subdomain similar to boundary element domain decomposition methods the total number of unknowns per subdomain behaves like o h h d 1 where h h and d denote the usual scaling parameter of the subdomains the average discretization parameter of the subdomain boundaries and the spatial dimension respectively we propose and analyze primal and dual substructuring iterative methods which asymptotically exhibit the same or at least almost the same complexity as the number of unknowns in particular the so called all floating finite element tearing and interconnecting solvers are highly parallel and very robust with respect to large coefficient jumps

inexact data sparse boundary element tearing and interconnecting methods the boundary element tearing and interconnecting beti methods have recently been introduced as boundary element counterparts of the well established finite element tearing and interconnecting feti methods in this paper we present inexact data sparse versions of the beti methods which avoid the elimination of the primal unknowns and dense matrices however instead of symmetric and positive definite systems we finally have to solve twofold saddle point problems the proposed iterative solvers and preconditioners result in almost optimal solvers whose complexity is proportional to the number of unknowns on the skeleton up to some polylogarithmical factor moreover the solvers are robust with respect to large coefficient jumps

preconditioning of the p version of the finite element method the p version finite element method for linear second order elliptic equations in an arbitrary sufficiently smooth incl polygonal bounded domain is studied in the framework of the domain decomposition dd method two types of square reference elements are used with coordinate functions given by the products of the integrated legendre polynomials estimates for the condition numbers and some useful inequalities are given we consider preconditioning of the problems arising on subdomains and of the schur complement as well as the derivation and analysis of the dd preconditioner for the entire system this is done for a class of curvilinear finite elements we obtain several dd preconditioners for which the generalized condition numbers vary from o log p 3 to o 1 this paper is based on 19 21 27 we have omitted most of the proofs in order to shorten it and have described instead what could be done as well as outlined some additional ideas the full proofs omitted can in most cases be found in 19 20 27

image categorization graph edit distance edge direction histogram this paper presents a novel algorithm for computing graph edit distance ged in image categorization this algorithm is purely structural i e it needs only connectivity structure of the graph and does not draw on node or edge attributes there are two major contributions 1 introducing edge direction histogram edh to characterize shape features of images it is shown that ged can be employed as distance of edhs this algorithm is completely independent on cost function which is difficult to be defined exactly 2 computing distance of edhs with earth mover distance emd which takes neighborhood bins into account so as to compute distance of edhs correctly a set of experiments demonstrate that the newly presented algorithm is available for classifying and clustering images and is immune to the planar rotation of images compared with ged from spectral seriation our algorithm can capture the structure change of graphs better and consume 12 79 time used by the former one the average classification rate is 5 and average clustering rate is 25 higher than the spectral seriation method

automatic spectral coarse spaces for robust finite element tearing and interconnecting and balanced domain decomposition algorithms we introduce spectral coarse spaces for the balanced domain decomposition and the finite element tearing and interconnecting methods these coarse spaces are specifically designed for the two level methods to be scalable and robust with respect to the coefficients in the equation and the choice of the decomposition we achieve this by solving generalized eigenvalue problems on the interfaces between subdomains to identify the modes that slow down convergence theoretical bounds for the condition numbers of the preconditioned operators which depend only on a chosen threshold and the maximal number of neighbors of a subdomain are presented and proved for the finite element tearing and interconnecting method there are two versions of the two level method one based on the full dirichlet preconditioner and the other on the cheaper lumped preconditioner some numerical tests confirm these results copyright 2013 john wiley sons ltd

domain decomposition technique for the continuity equations of semiconductor device models abstract in this paper we use the pcg method to solve the linear systems obtained from the continuity equations of semiconductor models a new kind of preconditioner which is based on the domain decomposition technique is used this kind of preconditioner is suitable for parallel computing and efficient for the linear system with rapidly varied solutions since the class of the linear system we considered is a special kind of an unsymmetric matrix we modify the pcg to this case as well with our modified pcg method we compare the preconditioner which is constructed by using incomplete cholesky decomposition without fill in preconditioner to our preconditioners which are based on the domain decomposition technique we find that the latter is much more efficient than the former for our semiconductor model problem

convergence rate estimate for a domain decomposition method we provide a convergence rate analysis for a variant of the domain decomposition method introduced by gropp and keyes for solving the algebraic equations that arise from finite element discretization of nonsymmetric and indefinite elliptic problems with dirichlet boundary conditions in 2 we show that the convergence rate of the preconditioned gmres method is nearly optimal in the sense that the rate of convergence depends only logarithmically on the mesh size and the number of substructures if the global coarse mesh is fine enough

the iwasawa mu invariant of p adic hecke l functions for an odd prime p we compute the invariant of the anticyclotomic katz p adic l function of a p ordinary cm field if the conductor of the branch character is a product of primes split over the maximal real subfield except for rare cases where the root number of the p adic functional equation is congruent to 1 modulo p the invariant vanishes

spectral analysis of the anisotropic steklov poincare matrix abstract in this work we analyse the steklov poincare or interface schur complement matrix arising in a domain decomposition method in the presence of anisotropy our problem is formulated such that three types of anisotropy are being considered refinements with high aspect ratios uniform refinements of a domain with high aspect ratio and anisotropic diffusion problems discretized on uniform meshes our analysis indicates a condition number of the interface schur complement with an order ranging from o 1 to o h 2 by relating this behaviour to an underlying scale of fractional sobolev spaces we propose optimal preconditioners which are spectrally equivalent to fractional matrix powers of a discrete interface laplacian numerical experiments to validate the analysis are included extensions to general domains and non uniform meshes are also considered