experimental study of ilu preconditioners for indefinite matrices incomplete lu factorization preconditioners have been surprisingly successful for many cases of general nonsymmetric and indefinite matrices however their failure rate is still too high for them to be useful as black box library software for general matrices besides fatal breakdowns due to zero pivots the major causes of failure are inaccuracy and instability of the triangular solves when there are small pivots both these problems can occur but these problems can also occur without small pivots through examples from actual problems this paper shows how these problems evince themselves how these problems can be detected and how these problems can sometimes be circumvented through pivoting reordering scaling perturbing diagonal elements and preserving symmetric structure the goal of this paper is to gain a better practical understanding of ilu preconditioners and help improve their reliability

on the stability of relaxed incomplete lu factorizations when solving large linear systems of equations arising from the discretization of elliptic boundary value problems a combination of iterative methods and preconditioners based on incomplete lu factorizations is frequently used given a model problem with variable coefficients we investigate a class of incomplete lu factorizations depending on a relaxation parameter we show that the associated preconditioner and the factorization itself both are numerically stable the theoretical results are complemented by numerical experiments

bilum block versions of multielimination and multilevel ilu preconditioner for general sparse linear systems we introduce block versions of the multielimination incomplete lu ilum factorization preconditioning technique for solving general sparse unstructured linear systems these preconditioners have a multilevel structure and for certain types of problems may exhibit properties that are typically enjoyed by multigrid methods several heuristic strategies for forming blocks of independent sets are introduced and their relative merits are discussed the advantages of block ilum over point ilum include increased robustness and efficiency we compare several versions of the block ilum point ilum and the dual threshold based ilut preconditioners in particular tests with some convection diffusion problems show that it may be possible to obtain convergence that is nearly independent of the reynolds number as well as of the grid size

a hybrid discontinuous galerkin method for computing the ground state solution of bose einstein condensates a numerical method for computing the ground state solution of bose einstein condensates modeled by the gross pitaevskii equation is presented in this method the three dimensional computational domain is divided into hexahedral elements in which the solution is approximated by a sum of basis functions both polynomial and plane wave bases are considered for this purpose and lagrange multipliers are introduced to weakly enforce the interelement continuity of the solution the ground state is computed by an iterative procedure for minimizing the energy the performance results obtained for several numerical experiments demonstrate that the proposed method is more computationally efficient than similar solution approaches based on the standard higher order finite element method

the radical trace property or ii e spec r 4 prop 2 41 using this formulation of tp fontana huckaba and papick gave characterizations for noetherian tp domains and a special class of priifer tp domains 4 it is our goal to extend this work by studying rtp radical trace property domains i e domains satisfying the condition that zz

conducive integral domains this article introduces the concept of a conducive domain that is an integral domain each of whose overrings apart from the quotient field has nonzero conductor the principal examples of conducive domains are all d m constructions and all pseudo valuation domains several characterizations are obtained notably that a domain r is conducive if and only if r has a valuation overring with nonzero conductor it is proved that if r is a conducive domain but not a field then spec r is pinched at a prime p such that the set of primes within p is linearly ordered the converse is shown for r a prufer domain in which case p prp consequences include pullback characterizations of the seminormal resp prufer conducive domains special attention is paid to the class of conducive g domains with attendant interplay between conducive and the property of having a maximum overring

regular incomplete factorizations of real positive definite matrices abstract we study the classes of matrices which admit a regular incomplete factorization with respect to any graph set we extend the construction to the class of real positive definite matrices the convergence of the basic iteration associated with the splittings we have is discussed

classical and enriched finite element formulations for bloch periodic boundary conditions summary in this paper classical and enriched flnite element formulations to impose bloch periodic boundary conditions are proposed bloch periodic boundary conditions arise in the description of wave like phenomena in periodic media we consider the quantum mechanical problem in a crystalline solid and derive the weak formulation and matrix equations for the schrodinger and poisson equations in a parallelepiped unit cell under bloch periodic and periodic boundary conditions respectively for such second order problems these conditions consist of value and derivative periodic parts the value periodic part is enforced as an essential boundary condition by construction of a value periodic basis whereas the derivative periodic part is enforced as a natural boundary condition in the weak formulation we show that the resulting matrix equations can be obtained by suitably specifying the connectivity of element matrices in the assembly of the global matrices or by modifying the neumann

on the rate of convergence of the preconditioned conjugate gradient method we derive new estimates for the rate of convergence of the conjugate gradient method by utilizing isolated eigenvalues of parts of the spectrum we present a new generalized version of an incomplete factorization method and compare the derived estimates of the number of iterations with the number actually found for some elliptic difference equations and for a similar problem with a model empirical distribution function

robust approximate inverse preconditioning for the conjugate gradient method we present a variant of the ainv factorized sparse approximate inverse algorithm which is applicable to any symmetric positive definite matrix the new preconditioner is breakdown free and when used in conjunction with the conjugate gradient method results in a reliable solver for highly ill conditioned linear systems we also investigate an alternative approach to a stable approximate inverse algorithm based on the idea of diagonally compensated reduction of matrix entries the results of numerical tests on challenging linear systems arising from finite element modeling of elasticity and diffusion problems are presented

solution of time independent schrodinger equation by the imaginary time propagation method numerical solution of eigenvalues and eigenvectors of large matrices originating from discretization of linear and non linear schrodinger equations using the imaginary time propagation itp method is described convergence properties and accuracy of 2nd and 4th order operator splitting methods for the itp method are studied using numerical examples the natural convergence of the method is further accelerated with a new dynamic time step adjustment method the results show that the itp method has better scaling with respect to matrix size as compared to the implicitly restarted lanczos method an efficient parallel implementation of the itp method for shared memory computers is also demonstrated

a domain decomposition method for discontinuous galerkin discretizations of helmholtz problems with plane waves and lagrange multipliers a nonoverlapping domain decomposition dd method is proposed for the iterative solution of systems of equations arising from the discretization of helmholtz problems by the discontinuous enrichment method this discretization method is a discontinuous galerkin finite element method with plane wave basis functions for approximating locally the solution and dual lagrange multipliers for weakly enforcing its continuity over the element interfaces the primal subdomain degrees of freedom are eliminated by local static condensations to obtain an algebraic system of equations formulated in terms of the interface lagrange multipliers only as in the feti h and feti dph dd methods for continuous galerkin discretizations this system of lagrange multipliers is iteratively solved by a krylov method equipped with both a local preconditioner based on subdomain data and a global one using a coarse space numerical experiments performed for two and three dimensional acoustic scattering problems suggest that the proposed dd based iterative solver is scalable with respect to both the size of the global problem and the number of subdomains copyright 2009 john wiley sons ltd

iterative solution methods for certain sparse linear systems with a non symmetric matrix arising from pde problems abstract in this paper methods are described for the solution of certain sparse linear systems with a non symmetric matrix the power of these methods is demonstrated by extensive numerical experiments application of the methods is limited to problems where the matrix has only eigenvalues with positive real part an important class of this type of matrix arises from discretisation of second order partial differential equations with first order derivative terms

trace properties in rings with zero divisors an integral domain d is said to have the radical trace property if i d i is a radical ideal for each noninvertible nonzero ideal i of d for a commutative ring r with nonzero identity the dual of a dense ideal i is the set r i t q r ti r where q r is the complete ring of quotients of r in this article the radical trace property is extended to rings with nonzero zero divisors specifically r has the radical trace property for regular ideals if i r i is a radical ideal for each noninvertible regular ideal i and r has the radical trace property for semiregular ideals if the same conclusion holds for noninvertible semiregular ideals so to those ideals that contain finitely generated dense ideals alternately r is said to be a rtp ring in the regular case and a q0 rtp in the semiregular case if r is an rtp ring and s is an overring of r so between r and the total quotient ring t r that is r flat then s is an rtp ring a similar statement holds for q0 rtp rings in the case s is r flat and between r and the ring of finite fractions q0 r

directional agglomeration multigrid techniques for high reynolds number viscous flows a preconditioned directional implicit agglomeration algorithm is developed for solving two and three dimensional viscous flows on highly anisotropic unstructured meshes of mixed element types the multigrid smoother consists of a pre conditioned point or line implicit solver which operates on lines constructed in the unstructured mesh using a weighted graph algorithm directional coarsening or agglomeration is achieved using a similar weighted graph algorithm a tight coupling of the line construction and directional agglomeration algorithms enables the use of aggressive coarsening ratios in the multigrid algorithm which in turn reduces the cost of a multigrid cycle convergence rates which are independent of the degree of grid stretching are demonstrated in both two and three dimensions further improvement of the three dimensional convergence rates through a gmres technique is also demonstrated

multiscale finite element method for linear elastic geomechanics the demand for accurate and efficient simulation of geomechanical effects is widely increasing in the geoscience community high resolution characterizations of the mechanical properties of subsurface formations are essential for improving modeling predictions such detailed descriptions impose severe computational challenges and motivate the development of multiscale solution strategies we propose a multiscale solution framework for the geomechanical equilibrium problem of heterogeneous porous media based on the finite element method after imposing a coarse scale grid on the given fine scale problem the coarse scale basis functions are obtained by solving local equilibrium problems within coarse elements these basis functions form the restriction and prolongation operators used to obtain the coarse scale system for the displacement vector then a two stage preconditioner that couples the multiscale system with a smoother is derived for the iterative solution of the fine scale linear system various numerical experiments are presented to demonstrate accuracy and robustness of the method

higher order extensions of a discontinuous galerkin method for mid frequency helmholtz problems recently a discontinuous galerkin method with plane wave basis functions and lagrange multiplier degrees of freedom was proposed for the efficient solution of helmholtz problems in the mid frequency regime in this paper this method is extended to higher order elements performance results obtained for various two dimensional problems highlight the advantages of these elements over classical higher order galerkin elements such as q2 and q4 for the discretization of interior and exterior helmholtz problems copyright 2004 john wiley sons ltd

constituent groups of clifford semigroups arising from t closure the t class semigroup of an integral domain r denoted st r is the semigroup of fractional t ideals modulo its subsemigroup of nonzero principal ideals with the operation induced by ideal t multiplication we recently proved that if r is a krull type domain m griffin rings of krull type j reine angew math 229 1968 1 27 then st r is a clifford semigroup s kabbaj a mimouni t class semigroups of integral domains j reine angew math 612 2007 213 229 in this paper we aim to describe the idempotents of st r and the structure of their associated groups we extend and recover well known results on class semigroups of valuation domains and prufer domains of finite character

the effect of ordering on preconditioned gmres algorithm for solving the compressible navier stokes equations we investigate the effect of the ordering of the blocks of unknowns on the rate of convergence of a preconditioned non linear gmres algorithm for solving the navier stokes equations for compressible flows using finite element methods on unstructured grids the gmres algorithm is preconditioned by an incomplete ldu block factorization of the jacobian matrix associated with the non linear problem to solve we examine a wide range of ordering methods including minimum degree reverse cuthill mckee and snake and consider preconditionings without fill in we show empirically that there can be a significant difference in the number of iterations required by the preconditioned non linear gmres method and suggest a criterion for choosing a good ordering algorithm according to the problem to solve we also consider the effect of orderings when an incomplete factorization which allows some fill in is performed we consider the effect of automatically controlling the sparsity of the incomplete factorization through the level of fill in finally following the principal ideas of non linear gmres algorithm we suggest other inexact newton methods

nested grids ilu decomposition ngilu a preconditioning technique is described which shows in many cases grid independent convergence this technique only requires an ordering of the unknowns based on the different levels of multigrid and an incomplete lu decomposition based on a drop tolerance the method is demonstrated on a variety of well known elliptic test problems including strongly varying coefficients advective terms and grid refinement

preconditioners for nonsymmetric indefinite linear systems abstract in this paper we develop algorithms for solving nonsymmetric indefinite linear systems by considering the augmented linear systems resulting from a weighted linear least squares problem even though the augmented system is more ill conditioned than the original linear system one can construct preconditioned gmres methods for solving these augmented systems capable of obtaining reasonable approximation of the solution in fewer iterations than the classical ilu preconditioned gmres method for solving the original linear system more specifically we present two different preconditioners for these augmented systems examine the spectral properties of these preconditioned augmented systems and report numerical results to illustrate the effectiveness of these preconditioners

computing the ground state solution of bose einstein condensates by a normalized gradient flow in this paper we present a continuous normalized gradient flow cngf and prove its energy diminishing property which provides a mathematical justification of the imaginary time method used in the physics literature to compute the ground state solution of bose einstein condensates bec we also investigate the energy diminishing property for the discretization of the cngf two numerical methods are proposed for such discretizations one is the backward euler centered finite difference befd method the other is an explicit time splitting sine spectral tssp method energy diminishing for befd and tssp for the linear case and monotonicity for befd for both linear and nonlinear cases are proven comparison between the two methods and existing methods e g crank nicolson finite difference cnfd or forward euler finite difference fefd shows that befd and tssp are much better in terms of preserving the energy diminishing property of the cngf numerical results in one two and three dimensions with magnetic trap confinement potential as well as a potential of a stirrer corresponding to a far blue detuned gaussian laser beam are reported to demonstrate the effectiveness of befd and tssp methods furthermore we observe that the cngf and its befd discretization can also be applied directly to compute the first excited state solution in bec when the initial data is chosen as an odd function

class semigroups of integral domains this paper seeks ring theoretic conditions of an integral domain r that reflect in the clifford property or boolean property of its class semigroup s r that is the semigroup of the isomorphy classes of the nonzero integral ideals of r with the operation induced by multiplication precisely in section 3 we characterize integrally closed domains with boolean class semigroup in this case s r identifies with the boolean semigroup formed of all fractional overrings of r in section 4 we investigate noetherian like settings where the clifford and boolean properties of s r coincide with lipman and sally vasconcelos stability conditions a main feature is that the clifford property forces t locally noetherian domains to be one dimensional noetherian domains section 5 studies the transfer of the clifford and boolean properties to various pullback constructions our results lead to new families of integral domains with clifford or boolean class semigroup moving therefore beyond the contexts of integrally closed domains or noetherian domains

three dimensional discontinuous galerkin elements with plane waves and lagrange multipliers for the solution of mid frequency helmholtz problems recently a discontinuous galerkin finite element method with plane wave basis functions and lagrange multiplier degrees of freedom was proposed for the efficient solution in two dimensions of helmholtz problems in the mid frequency regime in this paper this method is extended to three dimensions and several new elements are proposed computational results obtained for several wave guide and acoustic scattering model problems demonstrate one to two orders of magnitude solution time improvement over the higher order galerkin method

parallel jacobian free newton krylov solution of the discrete ordinates method with flux limiters for 3d radiative transfer the present study introduces a parallel jacobian free newton krylov jfnk general minimal residual gmres solution for the discretized radiative transfer equation rte in 3d absorbing emitting and scattering media for the angular and spatial discretization of the rte the discrete ordinates method dom and the finite volume method fvm including flux limiters are employed respectively instead of forming and storing a large jacobian matrix jfnk methods allow for large memory savings as the required jacobian vector products are rather approximated by semiexact and numerical formulations for which convergence and computational times are presented parallelization of the gmres solution is introduced in a combined memory shared memory distributed formulation that takes advantage of the fact that only large vector arrays remain in the jfnk process results are presented for 3d test cases including a simple homogeneous isotropic medium and a more complex non homogeneous non isothermal absorbing emitting and anisotropic scattering medium with collimated intensities additionally convergence and stability of gram schmidt and householder orthogonalizations for the arnoldi process in the parallel gmres algorithms are discussed and analyzed overall the introduction of jfnk methods results in a parallel yet scalable to the tested 2048 processors and memory affordable solution to 3d radiative transfer problems without compromising the accuracy and convergence of a newton like solution

feti dp a dual primal unified feti method part i a faster alternative to the two level feti method the feti method and its two level extension feti 2 are two numerically scalable domain decomposition methods with lagrange multipliers for the iterative solution of second order solid mechanics and fourth order beam plate and shell structural problems respectively the feti 2 method distinguishes itself from the basic or one level feti method by a second set of lagrange multipliers that are introduced at the subdomain cross points to enforce at each iteration the exact continuity of a subset of the displacement field at these specific locations in this paper we present a dual primal formulation of the feti 2 concept that eliminates the need for that second set of lagrange multipliers and unifies all previously developed one level and two level feti algorithms into a single dual primal feti dp method we show that this new feti dp method is numerically scalable for both second order and fourth order problems we also show that it is more robust and more computationally efficient than existing feti solvers particularly when the number of subdomains and or processors is very large copyright 2001 john wiley sons ltd

a higher order discontinuous enrichment method for the solution of high peclet advection diffusion problems on unstructured meshes a higher order discontinuous enrichment method dem with lagrange multipliers is proposed for the efficient finite element solution on unstructured meshes of the advection diffusion equation in the high peclet number regime following the basic dem methodology the usual galerkin polynomial approximation is enriched with free space solutions of the governing homogeneous partial differential equation pde in this case these are exponential functions that exhibit a steep gradient in a specific flow direction exponential lagrange multipliers are introduced at the element interfaces to weakly enforce the continuity of the solution the construction of several higher order dem elements fitting this paradigm is discussed in detail numerical tests performed for several two dimensional benchmark problems demonstrate their computational superiority over stabilized galerkin counterparts especially for high peclet numbers copyright 2009 john wiley sons ltd

a discontinuous galerkin method with lagrange multipliers for the solution of helmholtz problems in the mid frequency regime we present a discontinuous galerkin method dgm for the solution of the helmholtz equation in the mid frequency regime our approach is based on the discontinuous enrichment method in which the standard polynomial field is enriched within each finite element by a non conforming field that contains free space solutions of the homogeneous partial differential equation to be solved hence for the helmholtz equation the enrichment field is chosen here as the superposition of plane waves we enforce a weak continuity of these plane waves across the element interfaces by suitable lagrange multipliers preliminary results obtained for two dimensional model problems discretized by uniform meshes reveal that the proposed dgm enables the development of elements that are far more competitive than both the standard linear and the standard quadratic galerkin elements for the discretization of helmholtz problems

preconditioning techniques for nonsymmetric and indefinite linear systems abstract the standard preconditioning techniques for conjugate gradient methods often fail for matrices that are indefinite and or strongly nonsymmetric the most common alterative considered for these cases are either to use expensive direct solvers or to resort to one of many techniques based on the normal equations this paper examines several such alternatives and compares them in particular an incomplete lq factorization is proposed and some of its implementation details are described a number of experiments are reported to compare these methods

two level domain decomposition methods with lagrange multipliers for the fast iterative solution of acoustic scattering problems we present two different but related lagrange multiplier based domain decomposition dd methods for solving iteratively large scale systems of equations arising from the finite element discretization of high frequency exterior helmholtz problems the proposed methods are essentially two distinct extensions of the regularized finite element tearing and interconnecting feti method to indefinite or complex problems the first method employs a single lagrange multiplier field to glue the local solutions at the subdomain interface boundaries the second method employs two lagrange multiplier fields for that purpose the key ingredients of both of these feti methods are the regularization of each subdomain matrix by a complex lumped mass matrix defined on the subdomain interface boundary and the preconditioning of the global interface problem by a coarse second level problem constructed with planar waves we show numerically that both methods are scalable with respect to the mesh size the subdomain size and the wavenumber but that the feti method with a single lagrange multiplier field labeled feti h h for helmholtz in this paper delivers superior computational performances we apply the feti h method to the parallel solution on a 24 processor origin 2000 of an acoustic scattering problem with a submarine shaped obstacle and report performance results that highlight the unique efficiency of this dd method for the solution of high frequency acoustic scattering problems

the discontinuous enrichment method for elastic wave propagation in the medium frequency regime the discontinuous enrichment method dem is specified and developed for the solution of two dimensional elastic wave propagation problems in the frequency domain the classical finite element polynomial approximation of the displacement field is enriched by the superposition of discontinuous pressure and shear wave functions the continuity of the solution across the element interfaces is weakly enforced by suitable lagrange multipliers higher order rectangular dem elements are constructed and benchmarked against the standard higher order polynomial galerkin elements for two dimensional problems in the medium frequency regime in general it is found that for such applications dem can achieve the same accuracy as the p finite element method using a similar computational complexity but with about 10 times fewer degrees of freedom this highlights the potential of this hybrid method for problems where the scale of vibrations is very small compared to the characteristic dimension of the physical medium copyright 2006 john wiley sons ltd

domains satisfying the trace property e h om m r when no confusion will result we will suppress the r and write y m in section 2 we prove that if r is a valuation domain and m a unital r module then y m either equals r or a prime ideal of r it is this result that motivates our work and gives rise to the following definition a domain r is said to satisfy the

a discontinuous enrichment method for variable coefficient advection diffusion at high peclet number a discontinuous galerkin method with lagrange multipliers is presented for the solution of variable coefficient advection diffusion problems at high peclet number in this method the standard finite element polynomial approximation is enriched within each element with free space solutions of a local constant coefficient homogeneous counterpart of the governing partial differential equation hence in the two dimensional case the enrichment functions are exponentials each exhibiting a sharp gradient in a carefully chosen flow direction the continuity of the enriched approximation across the element interfaces is enforced weakly by the aforementioned lagrange multipliers numerical results obtained for two benchmark problems demonstrate that elements based on the proposed discretization method are far more competitive for variable coefficient advection diffusion analysis in the high peclet number regime than their standard galerkin and stabilized finite element comparables copyright 2010 john wiley sons ltd

the perfectly matched layer for the ultra weak variational formulation of the 3d helmholtz equation we investigate the feasibility of using the perfectly matched layer pml as an absorbing boundary condition for the ultra weak variational formulation uwvf of the 3d helmholtz equation the pml is derived using complex stretching of the spatial variables this leads to a modified helmholtz equation for which the uwvf can be derived in the standard discrete uwvf the approximating subspace is constructed from local solutions of the helmholtz equation in previous studies plane wave basis functions have been advocated because they simplify the building of the uwvf matrices for the pml domain we propose a special set of plane wave basis functions which allow fast computations and efficiently reduce spurious numerical reflections the method is validated by numerical experiments in comparison to a low order absorbing boundary condition the pml shows superior performance copyright 2004 john wiley sons ltd

on the eigenvalue distribution of a class of preconditioning methods a class of preconditioning methods depending on a relaxation parameter is presented for the solution of large linear systems of equationax b wherea is a symmetric positive definite matrix the methods are based on an incomplete factorization of the matrixa and include both pointwise and blockwise factorization we study the dependence of the rate of convergence of the preconditioned conjugate gradient method on the distribution of eigenvalues ofc 1a wherec is the preconditioning matrix we also show graphic representations of the eigenvalues and present numerical tests of the methods

fast unsteady flow computations with a jacobian free newton krylov algorithm despite the advances in computer power and numerical algorithms over the last decades solutions to unsteady flow problems remain computing time intensive especially for large reynolds number flows nonlinear multigrid which is commonly used to solve the nonlinear systems of equations converges slowly the stiffness induced by the large aspect ratio cells and turbulence is not tackled well by this solution method in previous work we showed that a jacobian free newton krylov jfnk algorithm preconditioned with an approximate factorization of the jacobian that approximately matches the target residual operator enables a speed up of a factor of 10 compared to standard nonlinear multigrid for two dimensional large reynolds number unsteady flow computations the goal of this paper is to demonstrate that the jfnk algorithm is also suited to tackle the stiffness induced by the maximum aspect ratio the grid density the physical time step and the reynolds number compared to standard nonlinear multigrid speed ups up to a factor of 25 are achieved

guidelines for the usage of incomplete decompositions in solving sets of linear equations as they occur in practical problems abstract this paper presents incomplete decompositions for various types of matrices as they occur in the implicit discretisation of practical problems a review is given of methods for the usual five point discretisation of a self adjoint elliptic second order partial differential equation in two dimensions on a square the matrices which occur in this type of problem are symmetric m matrices of very regular structure the convergence behaviour of the different decompositions for this case is demonstrated by numerical experiments the paper also gives decompositions for the following type of matrices i symmetric m matrices of a different structure ii symmetric positive definite matrices iii non symmetric matrices

a finite element method with mesh adaptivity for computing vortex states in fast rotating bose einstein condensates numerical computations of stationary states of fast rotating bose einstein condensates require high spatial resolution due to the presence of a large number of quantized vortices in this paper we propose a low order finite element method with mesh adaptivity by metric control as an alternative approach to the commonly used high order finite difference or spectral approximation methods the mesh adaptivity is used with two different numerical algorithms to compute stationary vortex states an imaginary time propagation method and a sobolev gradient descent method we first address the basic issue of the choice of the variable used to compute new metrics for the mesh adaptivity and show that refinement using simultaneously the real and imaginary part of the solution is successful mesh refinement using only the modulus of the solution as adaptivity variable fails for complicated test cases then we suggest an optimized algorithm for adapting the mesh during the evolution of the solution towards the equilibrium state considerable computational time saving is obtained compared to uniform mesh computations the new method is applied to compute difficult cases relevant for physical experiments large nonlinear interaction constant and high rotation rates

the discontinuous enrichment method we propose a finite element based discretization method in which the standard polynomial field is enriched within each element by a nonconforming field that is added to it the enrichment contains free space solutions of the homogeneous differential equation that are not represented by the underlying polynomial field continuity of the enrichment across element interfaces is enforced weakly by lagrange multipliers in this manner we expect to attain high coarse mesh accuracy without significant degradation of conditioning assuring good performance of the computation at any mesh resolution examples of application to acoustics and advection diffusion are presented

a stability analysis of incomplete lu factorizations abstract the combination of iterative methods with preconditionings based on incomplete lu factorizations constitutes an effective class of methods for solving the sparse linear systems arising from the discretization of elliptic partial differential equations in this paper we show that there are some settings in which the incomplete lu preconditioners are not effective and we demonstrate that their poor performance is due to numerical instability our analysis consists of an analytic and numerical study of a sample two dimensional non self adjoint elliptic problem discretized by several finite difference schemes author

a two phase preconditioning strategy of sparse approximate inverse for indefinite matrices a two phase preconditioning strategy based on a factored sparse approximate inverse is proposed for solving sparse indefinite matrices in each phase the strategy first makes the original matrix diagonally dominant to enhance the stability by a shifting method and constructs an inverse approximation of the shifted matrix by utilizing a factored sparse approximate inverse preconditioner the two inverse approximation matrices produced from each phase are then combined to be used as a preconditioner experimental results show that the presented strategy improves the accuracy and the stability of the preconditioner on solving indefinite sparse matrices furthermore the strategy ensures that convergence rate of the preconditioned iterations of the two phase preconditioning strategy is much better than that of the standard sparse approximate inverse ones for solving indefinite matrices

a minimisation approach for computing the ground state of gross pitaevskii systems in this paper we present a minimisation method for computing the ground state of systems of coupled gross pitaevskii equations our approach relies on a spectral decomposition of the solution into hermite basis functions inserting the spectral representation into the energy functional yields a constrained nonlinear minimisation problem for the coefficients for its numerical solution we employ a newton like method with an approximate line search strategy we analyse this method and prove global convergence appropriate starting values for the minimisation process are determined by a standard continuation strategy numerical examples with two and three component two dimensional condensates are included these experiments demonstrate the reliability of our method and nicely illustrate the effect of phase segregation