a preconditioner for the steady state navier stokes equations we present a new method for solving the sparse linear system of equations arising from the discretization of the linearized steady state navier stokes equations also known as the oseen equations the solver is an iterative method of krylov subspace type for which we devise a preconditioner through a heuristic argument based on the fundamental solution tensor for the oseen operator the preconditioner may also be conceived through a weaker heuristic argument involving differential operators computations indicate that convergence for the preconditioned discrete oseen problem is only mildly dependent on the viscosity inverse reynolds number and most importantly that the number of iterations does not grow as the mesh size is reduced indeed since the preconditioner is motivated through analysis of continuous operators the number of iterations decreases for smaller mesh size which accords with better approximation of these operators

numerical methods for a multicomponent two phase interface model with geometric mean influence parameters in this paper we consider an interface model for multicomponent two phase fluids with geometric mean influence parameters which is popularly used to model and predict surface tension in practical applications for this model there are two major challenges in theoretical analysis and numerical simulation the first one is that the influence parameter matrix is not positive definite the second one is the complicated structure of the energy function which requires us to find out a physically consistent treatment to overcome these two challenging problems we reduce the formulation of the energy function by employing a linear transformation and a weighted molar density and furthermore we propose a local minimum grand potential energy condition to establish the relation between the weighted molar density and mixture compositions from this we prove the existence of the solution under proper conditions and prove the maximum principle of the weighted molar density for numerical simulation we propose a

stabilized finite element schemes with lbb stable elements for incompressible flows we study stabilized fe approximations of supg type to the incompressible navier stokes problem revisiting the analysis for the linearized model we show that for conforming lbb stable elements the design of the stabilization parameters for many practical flows differs from that commonly suggested in literature and initially designed for the case of equal order approximation then we analyze a reduced supg scheme often used in practice for lbb stable elements to provide the reduced scheme with appropriate stability estimates we introduce a modified lbb condition which is proved for a family of fe approximations the analysis is given for the linearized equations numerical experiments for some linear and nonlinear benchmark problems support the theoretical results

weak galerkin finite element methods for darcy flow anisotropy and heterogeneity this paper presents a family of weak galerkin finite element methods wgfems for darcy flow computation the wgfems are new numerical methods that rely on the novel concept of discrete weak gradients the wgfems solve for pressure unknowns both in element interiors and on the mesh skeleton the numerical velocity is then obtained from the discrete weak gradient of the numerical pressure the new methods are quite different than many existing numerical methods in that they are locally conservative by design the resulting discrete linear systems are symmetric and positive definite and there is no need for tuning problem dependent penalty factors we test the wgfems on benchmark problems to demonstrate the strong potential of these new methods in handling strong anisotropy and heterogeneity in darcy flow

covolume upwind finite volume approximations for linear elliptic partial differential equations in this paper we study covolume upwind finite volume methods on rectangular meshes for solving linear elliptic partial differential equations with mixed boundary conditions to avoid non physical numerical oscillations for convection dominated problems nonstandard control volumes covolumes are generated based on local peclet s numbers and the upwind principle for finite volume approximations two types of discretization schemes with mass lumping are developed with use of bilinear or biquadratic basis functions as the trial space respectively some stability analyses of the schemes are presented for the model problem with constant coefficients various examples are also carried out to numerically demonstrate stability and optimal convergence of the proposed methods

a feasibility pump for mixed integer nonlinear programs we present an algorithm for finding a feasible solution to a convex mixed integer nonlinear program this algorithm called feasibility pump alternates between solving nonlinear programs and mixed integer linear programs we also discuss how the algorithm can be iterated so as to improve the first solution it finds as well as its integration within an outer approximation scheme we report computational results

optimal pipe sizing problem of tree shaped gas distribution networks abstract this study addresses the optimal pipe sizing problem of a tree shaped gas distribution network with a single supply source an algorithm was developed with the aim of minimizing the investment for constructing a gas distribution network with a tree shaped layout in which demands are fixed the construction cost is known to depend on the pipe diameters used for each arc in the network however under the assumption that pipe diameters are continuous we prove that it is possible to obtain the minimum construction cost directly and analytically by an iterating procedure that converts the original tree into a single equivalent arc in addition we also show that expanding the converted single arc inversely to the original tree computes the optimal continuous pipe diameter for each arc following this we present an additional heuristic to convert optimal continuous pipe diameters into approximate discrete pipe diameters the algorithms were evaluated by applying them to sample networks the numerical results obtained by comparing the approximate discrete diameters with the optimal discrete diameters confirm the efficiency of our algorithms thereby demonstrating their suitability for designing real gas distribution networks

field of values convergence analysis of augmented lagrangian preconditioners for the linearized navier stokes problem we study a block triangular preconditioner for finite element approximations of the linearized navier stokes equations the preconditioner is based on the augmented lagrangian formulation of the problem and was introduced by the authors in siam j sci comput 28 2006 pp 2095 2113 in this paper we prove field of values type estimates for the preconditioned system which lead to optimal convergence bounds for the gmres algorithm applied to solve the system two variants of the preconditioner are considered an ideal one based on exact solves for the velocity submatrix and a more practical variant based on block triangular approximations of the velocity submatrix

analysis of preconditioners for saddle point problems mixed finite element formulations give rise to large sparse block linear systems of equations the solution of which is often sought via a preconditioned iterative technique in this work we present a general analysis of block preconditioners based on the stability conditions inherited from the formulation of the finite element method the babuska brezzi or inf sup conditions the analysis is motivated by the notions of norm equivalence and field of values equivalence of matrices in particular we give sufficient conditions for diagonal and triangular block preconditioners to be norm and field of values equivalent to the system matrix

stabilized mixed continuous enriched galerkin formulations for locally mass conservative poromechanics abstract local element wise mass conservation is often highly desired for numerical solutions to coupled poromechanical problems as an efficient numerical method featuring this property mixed continuous galerkin cg enriched galerkin eg finite elements have recently been proposed in which piecewise constant functions are enriched to the pore pressure interpolation functions of the conventional mixed cg cg elements while this enrichment of the pressure space provides local mass conservation it unavoidably alters the stability condition for mixed finite elements because no stabilization method has been available for the new stability condition high order displacement interpolation has been required for mixed cg eg elements if undrained condition is expected to circumvent this requirement here we develop stabilized formulations for the mixed cg eg elements that permit equal order interpolation functions even in the undrained limit we begin by identifying the inf sup condition for mixed cg eg elements by phrasing an enriched poromechanical problem as a twofold saddle point problem we then derive two types of stabilized formulations one based on the polynomial pressure projection ppp method and the other based on the fluid pressure laplacian fpl method a key finding of this work is that both methods lead to stabilization terms that should be augmented only to the cg part of the pore pressure field not to the enrichment part the two stabilized formulations are verified and investigated through numerical examples that involve various conditions spanning 1d to 3d isotropy to anisotropy and homogeneous to heterogeneous domains the methodology presented in this work may also help stabilize other types of mixed finite elements in which the constraint field is enriched by additional functions

a locking free solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of lagrangian elements abstract this paper presents a new finite element solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of the classical bilinear or trilinear lagrangian elements it solves the primal variable displacement in the strain div formulation and can handle both displacement and traction boundary conditions it is a locking free solver based on conforming finite elements the solver has second order accuracy in displacement and first order accuracy in stress and dilation divergence of displacement as validated by theoretical analysis and illustrated by numerical experiments on benchmarks deal ii implementation is also discussed

dual scale galerkin methods for darcy flow abstract the discontinuous galerkin dg method has found widespread application in elliptic problems with rough coefficients of which the darcy flow equations are a prototypical example one of the long standing issues of dg approximations is the overall computational cost and many different strategies have been proposed such as the variational multiscale dg method the hybridizable dg method the multiscale dg method the embedded dg method and the enriched galerkin method in this work we propose a mixed dual scale galerkin method in which the degrees of freedom of a less computationally expensive coarse scale approximation are linked to the degrees of freedom of a base dg approximation we show that the proposed approach has always similar or improved accuracy with respect to the base dg method with a considerable reduction in computational cost for the specific definition of the coarse scale space we consider raviart thomas finite elements for the mass flux and piecewise linear continuous finite elements for the pressure we provide a complete analysis of stability and convergence of the proposed method in addition to a study on its conservation and consistency properties we also present a battery of numerical tests to verify the results of the analysis and evaluate a number of possible variations such as using piecewise linear continuous finite elements for the coarse scale mass fluxes

postprocessing of non conservative flux for compatibility with transport in heterogeneous media a conservative flux postprocessing algorithm is presented for both steady state and dynamic flow models the postprocessed flux is shown to have the same convergence order as the original flux an

block preconditioners based on approximate commutators this paper introduces a strategy for automatically generating a block preconditioner for solving the incompressible navier stokes equations we consider the pressure convection diffusion preconditioners proposed by kay loghin and wathen siam j sci comput 24 2002 pp 237 256 and silvester elman kay and wathen j comput appl math 128 2001 pp 261 279 numerous theoretical and numerical studies have demonstrated mesh independent convergence on several problems and the overall efficacy of this methodology a drawback however is that it requires the construction of a convection diffusion operator denoted f p projected onto the discrete pressure space this means that integration of this idea into a code that models incompressible flow requires a sophisticated understanding of the discretization and other implementation issues something often held only by the developers of the model as an alternative we consider automatic ways of computing f p based on purely algebraic considerations the new methods are closely related to the bfbt preconditioner of elman siam j sci comput 20 1999 pp 1299 1316 we use the fact that the preconditioner is derived from considerations of commutativity between the gradient and convection diffusion operators together with methods for computing sparse approximate inverses to generate the required matrix f p automatically we demonstrate that with this strategy the favorable convergence properties of the preconditioning methodology are retained

field of values analysis of preconditioned linearized rayleigh benard convection problems abstract in this paper we use the notion of field of values fov equivalence of matrices to study a class of block triangular preconditioners for the fixed point linearization of the rayleigh benard convection problem discretized with inf sup stable finite element spaces first sufficient conditions on the nondimensional parameters of the problem are determined in order to establish the fov equivalence between the system matrix and the preconditioners four upper triangular block preconditioners belonging to the general proposed class are then considered numerical experiments show that the generalized minimal residual gmres convergence is robust with respect to the mesh size for these preconditioned systems we also compare the performance of the different preconditioners in terms of computational time

implications of head loss path choice in the optimization of water distribution networks the effects of varying the paths used to ensure adequate pressure throughout a water distribution network when using iterative linear programming gradient search techniques for least cost solution of the network are analyzed the path choice is shown to affect how the initial flows are changed i e increased or decreased by the gradient expressions in the flow modification step the long term implication of the difference in the way the flows are changed is a variation in the relative importance in terms of flows of the various links within the system the amount of flow in a particular link in the final solution appears to be dependent on how often that link is included in the pressure defining constraints

a bilevel programming method for pipe network optimization this paper is concerned with the optimal dimensioning problem in which the layout of a pipe network is given but several available diameters can be selected for each pipe the purpose is to minimize total cost while satisfying certain restrictions a new method is proposed the main features of which are to treat the problem as a bilevel programming problem then to simplify the lower level problem by conjugate duality theory and to handle the upper level problem by its piecewise linear and convex nature some numerical testing results are also presented

preconditioning techniques for a mixed stokes darcy model in porous media applications we study numerical methods for a mixed stokes darcy model in porous media applications the global model is composed of two different submodels in a fluid region and a porous media region coupled through a set of interface conditions the weak formulation of the coupled model is of a saddle point type the mixed finite element discretization applied to the saddle point problem leads to a coupled indefinite and nonsymmetric linear system of algebraic equations we apply the preconditioned gmres method to solve the discrete system and are particularly interested in efficient and effective decoupled preconditioning techniques several decoupled preconditioners are proposed theoretical analysis and numerical experiments show the effectiveness and efficiency of the preconditioners effects of physical parameters on the convergence performance are also investigated

a locally conservative enriched galerkin approximation and efficient solver for elliptic and parabolic problems we present and analyze an enriched galerkin finite element method eg to solve elliptic and parabolic equations with jump coefficients eg is formulated by enriching the conforming continuous galerkin finite element method cg with piecewise constant functions which can be considered as a penalty stabilization the method is shown to be locally and globally conservative while keeping fewer degrees of freedom in comparison with discontinuous galerkin finite element methods dg moreover we present and analyze a fast effective eg solver whose cost is roughly that of cg and which can handle an arbitrary order of approximations a number of numerical tests in two and three dimensions are presented to confirm our theoretical results as well as to demonstrate the advantages of eg when coupled with transport

a storm of feasibility pumps for nonconvex minlp one of the foremost difficulties in solving mixed integer nonlinear programs either with exact or heuristic methods is to find a feasible point we address this issue with a new feasibility pump algorithm tailored for nonconvex mixed integer nonlinear programs feasibility pumps are algorithms that iterate between solving a continuous relaxation and a mixed integer relaxation of the original problems such approaches currently exist in the literature for mixed integer linear programs and convex mixed integer nonlinear programs both cases exhibit the distinctive property that the continuous relaxation can be solved in polynomial time in nonconvex mixed integer nonlinear programming such a property does not hold and therefore special care has to be exercised in order to allow feasibility pump algorithms to rely only on local optima of the continuous relaxation based on a new high level view of feasibility pump algorithms as a special case of the well known successive projection method we show that many possible different variants of the approach can be developed depending on how several different orthogonal implementation choices are taken a remarkable twist of feasibility pump algorithms is that unlike most previous successive projection methods from the literature projection is naturally taken in two different norms in the two different subproblems to cope with this issue while retaining the local convergence properties of standard successive projection methods we propose the introduction of appropriate norm constraints in the subproblems these actually seem to significantly improve the practical performance of the approach we present extensive computational results on the minlplib showing the effectiveness and efficiency of our algorithm

optimal design of water distribution networks optimal design of a water distribution network is formulated as a two stage decomposition model the master outer problem is nonsmooth and nonconvex while the inner problem is linear a semi infinite linear dual problem is presented and an equivalent finite linear problem is developed the overall design problem is solved globally by a branch and bound algorithm using nonsmooth optimization and duality theory the algorithm stops with a solution and a global bound such that the difference between this bound and the true global optimum is within a prescribed tolerance the algorithm has been programmed and applied to a number of examples from the literature the results demonstrate its superiority over previous methods

fast nonsymmetric iterations and preconditioning for navier stokes equations discretization and linearization of the steady state navier stokes equations gives rise to a nonsymmetric indefinite linear system of equations in this paper we introduce preconditioning techniques for such systems with the property that the eigenvalues of the preconditioned matrices are bounded independently of the mesh size used in the discretization we confirm and supplement these analytic results with a series of numerical experiments indicating that krylov subspace iterative methods for nonsymmetric systems display rates of convergence that are independent of the mesh parameter in addition we show that preconditioning costs can be kept small by using iterative methods for some intermediate steps performed by the preconditioner

block triangular preconditioners for nonsymmetric saddle point problems field of values analysis a preconditioned minimal residual method for nonsymmetric saddle point problems is analyzed the proposed preconditioner is of block triangular form the aim of this article is to show that a rigorous convergence analysis can be performed by using the field of values of the preconditioned linear system as an example a saddle point problem obtained from a mixed finite element discretization of the oseen equations is considered the convergence estimates obtained by using a field of values analysis are independent of the discretization parameter h several computational experiments supplement the theoretical results and illustrate the performance of the method

a two phase decomposition method for optimal design of looped water distribution networks a two phase decomposition method is proposed for the optimal design of new looped water distribution networks as well as for the parallel expansion of existing ones the main feature of the method is that it generates a sequence of improving local optimal solutions the first phase of the method takes a gradient approach with the flow distribution and pumping heads as decision variables and is an extension of the linear programming gradient method proposed by alperovits and shamir 1977 for nonlinear modeling the technique is iterative and produces a local optimal solution in the second phase the link head losses of this local optimal solution are fixed and the resulting concave program is solved for the link flows and pumping heads these then serve to restart the first phase to obtain an improved local optimal solution the whole procedure continues until no further improvement can be achieved some applications and extensions of the method are also discussed

mathematical programming techniques in water network optimization abstract in this article we survey mathematical programming approaches to problems in the field of drinking water distribution network optimization among the predominant topics treated in the literature we focus on two different but related problem classes one can be described by the notion of network design while the other is more aptly termed by network operation the basic underlying model in both cases is a nonlinear network flow model and we give an overview on the more specific modeling aspects in each case the overall mathematical model is a mixed integer nonlinear program having a common structure with respect to how water dynamics in pipes are described finally we survey the algorithmic approaches to solve the proposed problems and we discuss computation on various types of water networks

convergence of the discontinuous finite volume method for elliptic problems with minimal regularity this paper investigates convergence of the discontinuous finite volume method dfvm under minimal regularity assumptions on solutions of second order elliptic boundary value problems conventional analysis requires the solutions to be in sobolev spaces h 1 s s 12 here we assume the solutions are in h 1 s s 0 and employ the techniques developed in gudi 2010 18 20 to derive error estimates in a mesh dependent energy norm and the l 2 norm for dfvm the theoretical estimates are illustrated by numerical results which include problems with corner singularity and intersecting interfaces

machine learning and transport simulations for groundwater anomaly detection abstract this paper presents studies on modeling and algorithms for groundwater anomaly detection specifically conductivity along with four other surrogates are used for identifying anomaly in groundwater the one class support vector machine 1 svm technique is utilized for model training and real data from colorado water watch is used for testing the model and algorithms design of code modules in python is briefly discussed since groundwater contamination rarely happens in reality we also use synthetic data from numerical simulations of flow and transport in porous media to test this model for anomaly detection

constraint preconditioning for the coupled stokes darcy system the use of a constraint indefinite preconditioner for the iterative solution of the linear system arising from the finite element discretization of coupled stokes darcy flow is studied spectral and field of values bounds for the preconditioned system which are independent of the underlying mesh size are presented numerical experiments on several two and three dimensional problems illustrate the effectiveness of our approach

a locally conservative finite element method based on piecewise constant enrichment of the continuous galerkin method this paper presents a locally conservative finite element method based on enriching the approximation space of the continuous galerkin method with elementwise constant functions the proposed method has a smaller number of degrees of freedom than the discontinuous galerkin method numerical examples on coupled flow and transport in porous media are provided to illustrate the advantages of this method we also present a theoretical analysis of the method and establish optimal convergence of numerical solutions

the lowest order weak galerkin finite element method for the darcy equation on quadrilateral and hybrid meshes abstract this paper investigates the lowest order weak galerkin finite element method for solving the darcy equation on quadrilateral and hybrid meshes consisting of quadrilaterals and triangles in this approach the pressure is approximated by constants in element interiors and on edges the discrete weak gradients of these constant basis functions are specified in local raviart thomas spaces specifically r t 0 for triangles and unmapped r t 0 for quadrilaterals these discrete weak gradients are used to approximate the classical gradient when solving the darcy equation the method produces continuous normal fluxes and is locally mass conservative regardless of mesh quality and has optimal order convergence in pressure velocity and normal flux when the quadrilaterals are asymptotically parallelograms implementation is straightforward and results in symmetric positive definite discrete linear systems we present numerical experiments and comparisons with other existing methods

optimization of pipe networks the paper treats a piping system where the layout of the network is given but the diameters of the pipes should be chosen among a small number of different values the cost of realizing the system should be minimized while keeping the energy heads at the nodes above some lower limits a new algorithm using successive linear programming is presented the performance of the algorithm is illustrated by optimizing a network with 201 pipes and 172 nodes it is concluded that the new algorithm seems to be very efficient and stable and that it always finds a solution with a cost near the best possible

the feasibility pump in this paper we consider the np hard problem of finding a feasible solution if any exists for a generic mip problem of the form min ctx ax b xj integer j trivially a feasible solution can be defined as a point x p x ax b that is equal to its rounding where the rounded point is defined by x j if j and x j otherwise and represents scalar rounding to the nearest integer replacing equal with as close as possible relative to a suitable distance function x suggests the following feasibility pump fp heuristic for finding a feasible solution of a given mip we start from any x p and define its rounding at each fp iteration we look for a point x p that is as close as possible to the current by solving the problem min x x p assuming x is chosen appropriately this is an easily solvable lp problem if x 0 then x is a feasible mip solution and we are done otherwise we replace by the rounding of x and repeat we report computational results on a set of 83 difficult 0 1 mips using the commercial software ilog cplex 8 1 as a benchmark the outcome is that fp in spite of its simple foundation proves competitive with ilog cplex both in terms of speed and quality of the first solution delivered interestingly ilog cplex could not find any feasible solution at the root node for 19 problems in our test bed whereas fp was unsuccessful in just 3 cases

unconditionally stable methods for simulating multi component two phase interface models with peng robinson equation of state and various boundary conditions in this paper we consider multi component dynamic two phase interface models which are formulated by the cahn hilliard system with peng robinson equation of state and various boundary conditions these models can be derived from the minimum problems of helmholtz free energy or grand potential in the realistic thermodynamic systems the resulted cahn hilliard systems with various boundary conditions are fully coupled and strongly nonlinear a linear transformation is introduced to decouple the relations between different components and as a result the models are simplified from this we further propose a semi implicit unconditionally stable time discretization scheme which allows us to solve the cahn hilliard system by a decoupled way and thus our method can significantly reduce the computational cost and memory requirements the mixed finite element methods are employed for the spatial discretization and the approximate errors are also analyzed for both space and time numerical examples are tested to demonstrate the efficiency of our proposed methods

penalty factor free discontinuous galerkin methods for 2 dim stokes problems this paper presents two new finite element methods for two dimensional stokes problems these methods are developed by relaxing the constraints of the crouzeix raviart nonconforming p 1 finite elements penalty terms are introduced to compensate for lack of continuity or the divergence free property however there is no need for choosing penalty factors and the formulations are symmetric these new methods are easy to implement and avoid solving saddle point linear systems numerical experiments are presented to illustrate the proved optimal error estimates

adaptive enriched galerkin methods for miscible displacement problems with entropy residual stabilization we present a novel approach to the simulation of miscible displacement by employing adaptive enriched galerkin finite element methods eg coupled with entropy residual stabilization for transport in particular numerical simulations of viscous fingering instabilities in heterogeneous porous media and hele shaw cells are illustrated eg is formulated by enriching the conforming continuous galerkin finite element method cg with piecewise constant functions the method provides locally and globally conservative fluxes which are crucial for coupled flow and transport problems moreover eg has fewer degrees of freedom in comparison with discontinuous galerkin dg and an efficient flow solver has been derived which allows for higher order schemes dynamic adaptive mesh refinement is applied in order to reduce computational costs for large scale three dimensional applications in addition entropy residual based stabilization for high order eg transport systems prevents spurious oscillations numerical tests are presented to show the capabilities of eg applied to flow and transport enriched galerkin approximations for coupled flow and transport system entropy residual stabilization for enriched galerkin to stabilize higher order transport scheme dynamic mesh adaptivity for viscous fingering in two and three dimensions

application of a conservative generalized multiscale finite element method to flow models in this paper we propose a method for the construction of locally conservative flux fields from generalized multiscale finite element method gmsfem pressure solutions the flux values are obtained from an element based postprocessing procedure in which an independent set of 4x4 linear systems need to be solved to test the performance of the method we consider two heterogeneous permeability coefficients and couple the resulting fluxes to a two phase flow model the increase in accuracy associated with the computation of the gmsfem pressure solutions is inherited by the postprocessed flux fields and saturation solutions and is closely correlated to the size of the reduced order systems in particular the addition of more basis functions to the enriched coarse space yields solutions that more accurately capture the behavior of the fine scale model a number of numerical examples are offered to validate the performance of the method

a comparative study on the weak galerkin discontinuous galerkin and mixed finite element methods this paper presents a comparative study on the newly introduced weak galerkin finite element methods wgfems with the widely accepted discontinuous galerkin finite element methods dgfems and the classical mixed finite element methods mfems for solving second order elliptic boundary value problems we examine the differences similarities and connection among these methods in scheme formulations implementation strategies accuracy and computational cost the comparison and numerical experiments demonstrate that wgfems are viable alternatives to mfems and hold some advantages over dgfems due to their properties of local conservation normal flux continuity no need for penalty factor and definiteness of discrete linear systems

enriched galerkin methods for two phase flow in porous media with capillary pressure abstract in this paper we propose an enriched galerkin eg approximation for a two phase pressure saturation system with capillary pressure in heterogeneous porous media the eg methods are locally conservative have fewer degrees of freedom compared to discontinuous galerkin dg and have an efficient pressure solver to avoid non physical oscillations an entropy viscosity stabilization method is employed for high order saturation approximations entropy residuals are applied for dynamic mesh adaptivity to reduce the computational cost for larger computational domains the iterative and sequential implicit pressure and explicit saturation impes algorithms are treated in time numerical examples with different relative permeabilities and capillary pressures are included to verify and to demonstrate the capabilities of eg

enriched galerkin finite element approximation for elastic wave propagation in fractured media abstract finite element methods fem are becoming increasingly popular in modeling seismic wave propagation these methods provide higher order accuracy geometrical flexibility and adaptive gridding capabilities that are not easy to incorporate in traditional finite difference methods employed for generation of synthetic seismograms moreover several studies have shown that discontinuous galerkin fem dgm is a promising approach for modeling wave propagation in fractured media here we propose an enriched galerkin fem egm for elastic wave propagation egm uses the same bilinear form as dgm and the continuous galerkin finite element spaces enriched by discontinuous piecewise constants or bilinear functions egm satisfies local equilibrium while reducing the degrees of freedom in dgm formulations in this paper we consider elastic wave propagation and derive optimal a priori error estimates for dgm and egm we present numerical examples in two spatial dimensions that confirm these theoretical results in addition we provide numerical comparisons with the spectral element method in previous work dgm has been shown to be effective in modeling elastic wave propagation in fractured media using the linear slip model we now extend these results to egm with reduced computational costs over dgm

field of values analysis of preconditioned iterative methods for nonsymmetric elliptic problems the convergence rate of krylov subspace methods for the solution of nonsymmetric systems of linear equations such as gmres or fom is studied bounds on the convergence rate are presented which are based on the smallest real part of the field of values of the coefficient matrix and of its inverse estimates for these quantities are available during the iteration from the underlying arnoldi process it is shown how these bounds can be used to study the convergence properties in particular the dependence on the mesh size and on the size of the skew symmetric part for preconditioners for finite element discretizations of nonsymmetric elliptic boundary value problems this is illustrated for the hierarchical basis and multilevel preconditioners which constitute popular preconditioning strategies for such problems

efficient numerical methods for simulating surface tension of multi component mixtures with the gradient theory of fluid interfaces abstract surface tension significantly impacts subsurface flow and transport and it is the main cause of capillary effect a major immiscible two phase flow mechanism for systems with a strong wettability preference in this paper we consider the numerical simulation of the surface tension of multi component mixtures with the gradient theory of fluid interfaces major numerical challenges include that the system of the euler lagrange equations is solved on the infinite interval and the coefficient matrix is not positive definite we construct a linear transformation to reduce the euler lagrange equations and naturally introduce a path function which is proven to be a monotonic function of the spatial coordinate variable by using the linear transformation and the path function we overcome the above difficulties and develop the efficient methods for calculating the interface and its interior compositions moreover the computation of the surface tension is also simplified the proposed methods do not need to solve the differential equation system and they are easy to be implemented in practical applications numerical examples are tested to verify the efficiency of the proposed methods

global optimization of nonlinear network design a novel approach for obtaining globally optimal solutions to design of networks with nonlinear resistances and potential driven flows is proposed the approach is applicable to networks where the potential loss on an edge in the network is governed by a convex and strictly monotonically increasing function of flow rate we introduce a relaxation of the potential loss constraint and formulate the design problem as a mixed integer nonlinear program a linearization based approach with tailored cuts is proposed that improves the computational efficiency over a standard implementation we have also implemented a simple heuristic approach for finding feasible solutions at the root node and during the search process the algorithm has been implemented with ibm ilog cplex and is shown to be computationally effective on a number of examples from the literature

analytical and variational numerical methods for unstable miscible displacement flows in porous media the miscible displacement of one fluid by another in a porous medium has received considerable attention in sub surface environmental and petroleum engineering applications when a fluid of higher mobility displaces another of lower mobility unstable patterns referred to as viscous fingering may arise their physical and mathematical study has been the object of numerous investigations over the past century the objective of this paper is to present a review of these contributions with particular emphasis on variational methods these algorithms are tailored to real field applications thanks to their advanced features handling of general complex geometries robustness in the presence of rough tensor coefficients low sensitivity to mesh orientation in advection dominated scenarios and provable convergence with fully unstructured grids this paper is dedicated to the memory of dr jim douglas jr for his seminal contributions to miscible displacement and variational numerical methods

fields of values and iterative methods abstract the performance of an iterative scheme to solve x t x c t c n n c c n is often judged by spectral properties of t if t is not normal it is however well known that only conclusions about the assymptotic behavior of an iterative method can be drawn from spectral information to anticipate the progress of the iteration after a finite number of steps the knowledge of the eigenvalues alone is often useless in addition the spectrum of t may be highly sensitive to perturbations if t is not normal an iterative method which on the basis of some spectral information is predicted to converge rapidly for t may well diverge if t is slightly perturbed in practice the convergence of the iteration x m t x m 1 c is therefore frequently measured by some norm verbar t verbar rather than by the spectral radius t but apart from the fact that norms lead to error estimates which are often too pessimistic they cannot be used to analyze more general schemes such as e g the chebyshev iterative methods here we discuss another tool to analyze the behavior of an iterative method namely the field of values w t the collection of all rayleigh quotients of t w t contains the eigenvalues of t and the numerical radius t max z w t z defines a norm on c n n the field of values represents therefore an intermediate concept to judge an iterative scheme by it is related to the spectral approach but has also certain norm properties