finite volume modeling of poroelastic fluid wave propagation with mapped grids in this work we develop a high resolution mapped grid finite volume method code to model wave propagation in two dimensions in systems of multiple orthotropic poroelastic media and or fluids with curved interfaces between different media we use a unified formulation to simplify modeling of the various interface conditions open pores imperfect hydraulic contact or sealed pores that may exist between such media our numerical code is based on the clawpack framework but in order to obtain correct results at a material interface we use a modified transverse riemann solution scheme and at such interfaces are forced to drop the second order correction term typical of high resolution finite volume methods we verify our code against analytical solutions for reflection and transmission of waves at a material interface and for scattering of an acoustic wave train around an isotropic poroelastic cylinder for reflection and transmission at a flat interface we achieve second order convergence in the 1 no

a hybridizable discontinuous galerkin method for stokes flow abstract in this paper we introduce a hybridizable discontinuous galerkin method for stokes flow the method is devised by using the discontinuous galerkin methodology to discretize a velocity pressure gradient formulation of the stokes system with appropriate choices of the numerical fluxes and by applying a hybridization technique to the resulting discretization one of the main features of this approach is that it reduces the globally coupled unknowns to the numerical trace of the velocity and the mean of the pressure on the element boundaries thereby leading to a significant reduction in the size of the resulting matrix moreover by using an augmented lagrangian method the globally coupled unknowns are further reduced to the numerical trace of the velocity only another important feature is that the approximations of the velocity pressure and gradient converge with the optimal order of k 1 in the l 2 norm when polynomials of degree k 0 are used to represent the approximate variables based on the optimal convergence of the hdg method we apply an element by element postprocessing scheme to obtain a new approximate velocity which converges with order k 2 in the l 2 norm for k 1 the postprocessing performed at the element level is less expensive than the solution procedure numerical results are provided to assess the performance of the method

extended precise integration method for consolidation of transversely isotropic poroelastic layered media a new numerical method for calculating the consolidation behavior of the stratified transversely isotropic and poroelastic material is presented by combining the extended precise integration algorithm with the integral transformation techniques starting with the governing partial differential equations of a saturated medium with transversely isotropic skeleton and compressible fluid constituents an ordinary differential matrix equation is deduced with the aid of a laplace hankel transform an extended precise integration method for internal loading situations is proposed to solve the ordinary differential matrix equation in the transformed domain and the actual solution is recovered by a numerical inverse transformation numerical examples are also provided to prove the feasibility of this method

a generalized multiscale finite element method gmsfem for perforated domain flows with robin boundary conditions abstract in this work we develop a multiscale method for elliptic problems in perforated media with robin boundary conditions perforated media are encountered in many applications e g in material science applications where the material properties are prescribed outside perforation such a perforated structure can significantly affect the solution for the numerical solution of the equation it is necessary to construct a computational grid with elements resolving the perforations the computational grid calculated in this way is fine scale grid and this can lead to a large number of unknowns for the numerical solution of our problem we construct an approximation of the equation on a coarse grid using the generalized multiscale finite element method gmsfem the main idea of the gmsfem is to construct multiscale basis functions on a coarse grid which can reduce the computational cost the multiscale basis function construction requires snapshots and local spectral problems which are developed in the paper in the paper we study robin boundary conditions which arise in many applications previous works chung et al 2016 considered dirichlet and neumann boundary conditions the construction of multiscale basis functions differs from those in chung et al 2016 1 2 and as we need to impose non homogeneous robin boundary conditions we present several numerical examples in these examples perforated domains with many inclusions are considered our numerical results show a good agreement between the coarse and the fine grid simulations

unified hybridization of discontinuous galerkin mixed and continuous galerkin methods for second order elliptic problems we introduce a unifying framework for hybridization of finite element methods for second order elliptic problems the methods fitting in the framework are a general class of mixed dual finite element methods including hybridized mixed continuous galerkin nonconforming and a new wide class of hybridizable discontinuous galerkin methods the distinctive feature of the methods in this framework is that the only globally coupled degrees of freedom are those of an approximation of the solution defined only on the boundaries of the elements since the associated matrix is sparse symmetric and positive definite these methods can be efficiently implemented moreover the framework allows in a single implementation the use of different methods in different elements or subdomains of the computational domain which are then automatically coupled finally the framework brings about a new point of view thanks to which it is possible to see how to devise novel methods displaying very localized and simple mortaring techniques as well as methods permitting an even further reduction of the number of globally coupled degrees of freedom

the riemann hilbert problem and the generalized neumann kernel on multiply connected regions this paper presents and studies fredholm integral equations associated with the linear riemann hilbert problems on multiply connected regions with smooth boundary curves the kernel of these integral equations is the generalized neumann kernel the approach is similar to that for simply connected regions see r wegmann a h m murid m m s nasser the riemann hilbert problem and the generalized neumann kernel j comput appl math 182 2005 388 415 there are however several characteristic differences which are mainly due to the fact that the complement of a multiply connected region has a quite different topological structure this implies that there is no longer perfect duality between the interior and exterior problems we investigate the existence and uniqueness of solutions of the integral equations in particular we determine the exact number of linearly independent solutions of the integral equations and their adjoints the latter determine the conditions for solvability an analytic example on a circular annulus and several numerically calculated examples illustrate the results

a fully coupled dynamic model for two phase fluid flow in deformable porous media abstract a fully coupled dynamic model is presented for the analysis of water and air flow in deforming porous media in fully or partially saturated conditions the solid displacements and the pressures of fluids are taken as primary unknowns of the model the finite element method is used for the discrete approximation of the partial differential equations governing the problem the mathematical framework and the numerical implementation of the model are given in detail and the adopted approximations are put into evidence first the model is validated with respect to documented experiments on partially saturated soil behaviour in quasi static condition then the results of a full dynamic analysis are shown and discussed in this paper merits and drawbacks of the proposed model are highlighted

boundary integral equation method for linear porous elasticity with applications to soil consolidation for physical phenomena governed by the biot model of porous elasticity a reciprocal relation similar to the betti s recoprocal theorem in elasticity is constructed in laplace transformed space integrating the reciprocal relation enables one to formulate boundary integral equations the fundamental kernels for the integral equations are solved in closed forms for the case of isotropic material numerical implementation of two dimensional problems includes finite element ideas of discretization and polynomial interpolation and numerical inversion of a laplace transform practical applications of the method are found in consolidation problems in soils which contain compressible as well as incompressible pore fluids also as a numerical experiment consolidation of partially saturated soil is simulated and interesting phenomena are observed the currently developed boundary integral equation method biem for porous elasticity may be viewed as an efficient and accurate alternative of existing finite element and finite difference methods for linear consolidation problems application of biem is always preferred to the other numerical methods whenever possible

a topological result on strong stabilization problem this note studies the robustness of nonstrong stabilizability we consider single input single output siso continuous time linear systems under graph topology a key contribution of this note is to show that there are two classes of nonstrongly stabilizable systems one which contains plants that can be rendered strongly stabilizable by an arbitrary small perturbation and the other which contains plants that are inherently nonstrongly stabilizable even if perturbed an easily implemented test referred to as weak parity interlacing property is developed to check in which class a given model lies

efficient solvers for hybridized three field mixed finite element coupled poromechanics abstract we consider a mixed hybrid finite element formulation for coupled poromechanics a stabilization strategy based on a macro element approach is advanced to eliminate the spurious pressure modes appearing in undrained incompressible conditions the efficient solution of the stabilized mixed hybrid block system is addressed by developing a class of block triangular preconditioners based on a schur complement approximation strategy robustness computational efficiency and scalability of the proposed approach are theoretically discussed and tested using challenging benchmark problems on massively parallel architectures

spiral slits map and its inverse of bounded multiply connected regions this paper presents a boundary integral equation method for computing numerical conformal mapping of bounded multiply connected region onto a spiral slits region the method is an extension of the author s method for computing the circular slits map of bounded multiply connected regions see a w k sangawi et al 2012 16 several numerical examples are given to prove the effectiveness of the proposed methods

flow through porous media due to high pressure gradients abstract while darcy s equations are adequate for studying a large class of flows through porous media there are several situations wherein it would be inappropriate to use darcy s equations one such example is a flow wherein the range of pressures involved is very large and high pressures and pressure gradients are at play here after developing an approximation for the flow through a porous solid that is a generalization of an equation developed by brinkman we study a simple boundary value problem that clearly delineates the difference between the solution to these equations and those due to the equations that are referred to as darcy law we find that the solutions for the equations under consideration exhibit markedly different characteristics from the counterpart for the brinkman equations or darcy s equations or the navier stokes equation if one neglects the porosity in that the solutions for the velocity as well as the vorticity lack symmetry and one finds the maximum value of the vorticity occurs at the boundary near which the fluid is less viscous in virtue of the pressure being lower we also find that for a certain range of values for the non dimensional parameters describing the flow boundary layers develop in that the vorticity is confined next to the boundary adjacent to which the viscosity is lower such boundary layers being absent in the other classical cases

a charge simulation method for the numerical conformal mapping of interior exterior and doubly connected domains abstract a simple numerical method is described for computing the following three conformal maps a from a domain interior to a closed jordan curve onto the interior of the unit disk b from a domain exterior to a closed jordan curve onto the exterior of the unit disk and c from a doubly connected domain bounded by two closed jordan curves onto a circular annulus the numerical method is based on the charge simulation method or the method of fundamental solutions applied to the dirichlet problem of laplace s equation in which a pair of conjugate harmonic functions are approximated by a linear combination of complex logarithmic potentials without integration typical examples show that numerical results of high accuracy can be obtained by the simple method if the domains have no concave corners

numerical conformal mappings of bounded multiply connected domains by the charge simulation method we present here a simple method of numerical conformal mappings from bounded multiply connected domains onto the bounded canonical slit domains of nehari i e a disk with concentric circular slits and an annulus with concentric circular slits in this method we express the mapping functions in terms of a pair of conjugate harmonic functions and approximate them using the charge simulation method by a linear combination of complex logarithmic functions some numerical examples show the effectiveness of the method

a galerkin least squares finite element formulation for consolidation a galerkin least squares gls finite element formulation for problem of consolidation of fully saturated two phase media is presented the elimination of spurious pressure oscillations appearing at the early stage of consolidation for standard galerkin finite elements with equal interpolation order for both displacements and pressures is the goal of the approach it will be shown that the least squares term based exclusively on the residuum of the fluid flow continuity equation added to the standard galerkin formulation enhances its stability and can fully eliminate pressure oscillations a reasonably simple framework designed for derivation of one dimensional as well as multi dimensional estimates of the stabilization factor is proposed and then verified the formulation is validated on one dimensional and then on two dimensional linear and non linear test problems the effect of the fluid incompressibility as well as compressibility will be taken into account and investigated copyright 2001 john wiley sons ltd

analysis of nonlinear poro elastic and poro visco elastic models we consider the initial and boundary value problem for a system of partial differential equations describing the motion of a fluid solid mixture under the assumption of full saturation the ability of the fluid phase to flow within the solid skeleton is described by the permeability tensor which is assumed here to be a multiple of the identity and to depend nonlinearly on the volumetric solid strain in particular we study the problem of the existence of weak solutions in bounded domains accounting for non zero volumetric and boundary forcing terms we investigate the influence of viscoelasticity on the solution functional setting and on the regularity requirements for the forcing terms the theoretical analysis shows that different time regularity requirements are needed for the volumetric source of linear momentum and the boundary source of traction depending on whether or not viscoelasticity is present the theoretical results are further investigated via numerical simulations based on a novel dual mixed hybridized finite element discretization when the data are sufficiently regular the simulations show that the solutions satisfy the energy estimates predicted by the theoretical analysis interestingly the simulations also show that in the purely elastic case the darcy velocity and the related fluid energy might become unbounded if indeed the data do not enjoy the time regularity required by the theory

minimum overshoot design for siso discrete time systems the problem of designing a controller to minimize the maximum negative error due to a specific bounded input is studied it is found that the solution can be obtained by solving an infinite linear programming problem in the special case of a step input a simple analytical formula for minimum overshoot is derived for a plant with one unstable pole and one nonminimum phase zero the solution technique has potential application to other control problems which seek to minimize quantities not directly representable as a norm

numerical conformal mapping of multiply connected regions onto the fifth category of koebe s canonical slit regions abstract this paper presents a boundary integral method for approximating the conformal mapping from bounded multiply connected regions onto the fifth category of koebe s classical canonical slit regions the method is based on a uniquely solvable boundary integral equation with generalized neumann kernel the results of some test calculations illustrate the performance of the presented method

upscaling method for problems in perforated domains with non homogeneous boundary conditions on perforations using non local multi continuum method nlmc abstract in this paper we present an upscaling method for problems in perforated domains with non homogeneous boundary conditions on perforations our methodology is based on the recently developed non local multicontinuum method nlmc the main ingredient of the method is the construction of suitable local basis functions with the capability of capturing multiscale features and non local effects we will construct multiscale basis functions for the coarse regions and additional multiscale basis functions for perforations with the aim of handling non homogeneous boundary conditions on perforations we start with describing our method for the laplace equation and then extending the framework for the elasticity problem and parabolic equations the resulting upscaled model has minimal size and the solution has physical meaning on the coarse grid we will present numerical results 1 for steady and unsteady problems 2 for laplace and elastic operators and 3 for neumann and robin non homogeneous boundary conditions on perforations numerical results show that the proposed method can provide good accuracy and provide significant reduction on the degrees of freedoms

generalized multiscale finite element methods gmsfem in this paper we propose a general approach called generalized multiscale finite element method gmsfem for performing multiscale simulations for problems without scale separation over a complex input space as in multiscale finite element methods msfems the main idea of the proposed approach is to construct a small dimensional local solution space that can be used to generate an efficient and accurate approximation to the multiscale solution with a potentially high dimensional input parameter space in the proposed approach we present a general procedure to construct the offline space that is used for a systematic enrichment of the coarse solution space in the online stage the enrichment in the online stage is performed based on a spectral decomposition of the offline space in the online stage for any input parameter a multiscale space is constructed to solve the global problem on a coarse grid the online space is constructed via a spectral decomposition of the offline space and by choosing the eigenvectors corresponding to the largest eigenvalues the computational saving is due to the fact that the construction of the online multiscale space for any input parameter is fast and this space can be re used for solving the forward problem with any forcing and boundary condition compared with the other approaches where global snapshots are used the local approach that we present in this paper allows us to eliminate unnecessary degrees of freedom on a coarse grid level we present various examples in the paper and some numerical results to demonstrate the effectiveness of our method

asymptotic behavior of semidiscrete finite element approximations of biot s consolidation problem error estimates for spatially discrete galerkin finite element approximations of biot s model for consolidation of saturated porous media are presented the short and long time behaviors of such approximations based on both stable and unstable combinations of finite element spaces of displacement and pore pressure fields are discussed

object oriented finite element analysis of thermo hydro mechanical thm problems in porous media the design implementation and application of a concept for object oriented in finite element analysis of multi field problems is presented in this paper the basic idea of this concept is that the underlying governing equations of porous media mechanics can be classified into different types of partial differential equations pdes in principle similar types of pdes for diverse physical problems differ only in material coefficients local element matrices and vectors arising from the finite element discretization of the pdes are categorized into several types regardless of which physical problem they belong to i e fluid flow mass and heat transport or deformation processes element ele objects are introduced to carry out the local assembly of the algebraic equations the object orientation includes a strict encapsulation of geometrical geo topological msh process related fem data and methods of element objects geometric entities of an element such as nodes edges faces and neighbours are abstracted into corresponding geometric element objects ele geo the relationships among these geometric entities form the topology of element meshes ele msh finite element objects ele fem are presented for the local element calculations in which each classification type of the matrices and vectors is computed by a unique function these element functions are able to deal with different element types lines triangles quadrilaterals tetrahedra prisms hexahedra by automatically choosing the related element interpolation functions for each process of a multi field problem only a single instance of the finite element object is required the element objects provide a flexible coding environment for multi field problems with different element types here the c implementations of the objects are given and described in detail the efficiency of the new element objects is demonstrated by several test cases dealing with thermo hydro mechanical thm coupled problems for geotechnical applications copyright 2006 john wiley sons ltd

a combined discontinuous galerkin finite element method for miscible displacement problem a new combined method is constructed for solving incompressible miscible displacement in porous media in this procedure a hybrid mixed element method is constructed for the pressure and velocity equation while a symmetric discontinuous galerkin finite element method is proposed for the concentration equation the introduction of these two numerical methods not only makes the coefficient matrixes symmetric positive definite but also conserves the local mass balance the stability and consistency of the method are analyzed and the optimal error estimate in l l 2 for velocity and concentration and the super convergence in l h 1 for pressure are derived finally some numerical results are presented

a least squares mixed finite element method for biot s consolidation problem in porous media a least squares mixed finite element method for the coupled problem of flow and deformation is presented and analyzed in this paper for the analysis we restrict ourselves to fully saturated conditions for the flow process and to a linearly elastic material law for the deformation process this is known in the literature as biot s consolidation problem for simplicity the analysis is presented for the problem in two space dimensions our least squares approach is motivated by the fact that all process variables i e fluid pressure and flux as well as displacement field and stress tensor are approximated directly by suitable finite element spaces ellipticity of the corresponding variational formulation is proven for the stationary case as well as for the subproblems arising at each step of an implicit time discretization in the general time dependent case standard h1 conforming piecewise linear and quadratic finite elements are used for the fluid pressure and for each component of the displacement respectively for the flux and stress components the h div conforming raviart thomas spaces of lowest order are used computational results are presented for some two dimensional test problems

variational multiscale analysis the fine scale green s function projection optimization localization and stabilized methods we derive an explicit formula for the fine scale green s function arising in variational multiscale analysis the formula is expressed in terms of the classical green s function and a projector which defines the decomposition of the solution into coarse and fine scales the theory is presented in an abstract operator format and subsequently specialized for the advection diffusion equation it is shown that different projectors lead to fine scale green s functions with very different properties for example in the advection dominated case the projector induced by the h 1 0 seminorm produces a fine scale green s function which is highly attenuated and localized these are very desirable properties in a multiscale method and ones that are not shared by the l 2 projector by design the coarse scale solution attains optimality in the norm associated with the projector this property combined with a localized fine scale green s function indicates the possibility of effective methods with local character for dominantly hyperbolic problems the constructs lead to a new class of stabilized methods and the relationship between h 1 0 optimality and the streamline upwind petrov galerkin supg method is described

numerical conformal mapping and its inverse of unbounded multiply connected regions onto logarithmic spiral slit regions and straight slit regions this paper presents a boundary integral equation method with the adjoint generalized neumann kernel for computing conformal mapping of unbounded multiply connected regions and its inverse onto several classes of canonical regions for each canonical region two integral equations are solved before one can approximate the boundary values of the mapping function cauchy s type integrals are used for computing the mapping function and its inverse for interior points this method also works for regions with piecewise smooth boundaries three examples are given to illustrate the effectiveness of the proposed method

a generalized multiscale finite element method for poroelasticity problems i in this paper we consider the numerical solution of poroelasticity problems that are of biot type and develop a general algorithm for solving coupled systems we discuss the challenges associated with mechanics and flow problems in heterogeneous media the two primary issues being the multiscale nature of the media and the solutions of the fluid and mechanics variables traditionally developed with separate grids and methods for the numerical solution we develop and implement a generalized multiscale finite element method gmsfem that solves problem on a coarse grid by constructing local multiscale basis functions the procedure begins with construction of multiscale bases for both displacement and pressure in each coarse block using a snapshot space and local spectral problems we construct a basis of reduced dimension finally after multiplying by a multiscale partitions of unity the multiscale basis is constructed in the offline phase and the coarse grid problem then can be solved for arbitrary forcing and boundary conditions we implement this algorithm on two heterogeneous media and compute error between the multiscale solution with the fine scale solutions randomized oversampling and forcing strategies are also tested

an immersed interface method for a 1d poroelasticity problem with discontinuous coefficients we introduce an immersed interface method iim based on a staggered grid for the 1d biot s poroelasticity model when the coefficients have discontinuities along material interfaces the iim uses a standard finite difference method away from the interfaces and modifies the numerical schemes near or on the interfaces to treat the irregularities using the method of undetermined coefficients a second order accuracy in the infinity norm has been derived for both pressure and displacement regardless of the position of the interfaces we present some numerical results to confirm the theoretical error estimates

splitting schemes for poroelasticity and thermoelasticity problems abstract in this work we consider the coupled systems of linear unsteady partial differential equations which arise in the modelling of poroelasticity processes stability estimates of weighted difference schemes for the coupled system of equations are presented approximation in space is based on the finite element method we construct splitting schemes and give some numerical comparisons for typical poroelasticity problems the results of numerical simulation of a 3d problem are presented special attention is given to using high performance computing systems

numerical stabilization of biot s consolidation model by a perturbation on the flow equation in this paper a stabilized finite element scheme for the poroelasticity equations is proposed this method based on the perturbation of the flow equation allows us to use continuous piecewise linear approximation spaces for both displacements and pressure obtaining solutions without oscillations independently of the chosen discretization parameters the perturbation term depends on a parameter which is established in terms of the mesh size and the properties of the material in the one dimensional case this parameter is shown to be optimal some numerical experiments are presented indicating the efficiency of the proposed stabilization technique copyright 2008 john wiley sons ltd

a coupling of hybrid mixed and continuous galerkin finite element methods for poroelasticity abstract a coupling finite element method for biot s model in poroelasticity is considered the method is based on a coupling of a hybrid mixed finite element method for the pressure and velocity of the fluid phase with a continuous galerkin finite element method for the displacement of the solid phase the subproblem for pressure and darcy velocity are solved at element level and these variables are eliminated in favor of the lagrange multiplier identified as pressure trace at the element interfaces the method is consistent and locally mass conservative by introducing the energy norm we can obtain the stability of this system the optimal error estimates are derived for both semi discrete and fully discrete schemes finally numerical results illustrate the accuracy of the method

consolidation of multilayered half space with anisotropic permeability and compressible constituents abstract this paper presents analytical solutions of consolidation for poroelastic and multilayered half space and anisotropy of the permeability and the compressibility of the pore fluid are considered state vector method together with laplace hankel transform techniques are used to solve the basic governing equations and obtain the transfer matrix in a clearly arranged way forward and backward transfer matrix techniques are utilized in the analytical formulation of solutions for the multilayered half space a numerical inversion scheme of crump s method is adopted to obtain time domain solution numerical results are presented for a single homogeneous soil layer and a multilayered half space and they illustrate the influences of the anisotropy of permeability and the compressibility of the pore fluid on the consolidation of the soils

minimizing a convex combination of the overshoot and undershoot abstract we study the problem of minimizing a parameterized convex combination of the overshoot and undershoot of siso continuous time system in response to a known input from a dual formulation we develop a condition for solution existence and specify the structure of optimal solution in addition an interrelation between the overshoot and undershoot in controller synthesis is analytically explained in our framework

advances on the domain decomposition solution of large scale porous media problems abstract in this paper a family of state of the art parallel domain decomposition methods that combine the advantages of both direct and iterative solvers are investigated for the monolithic solution of the u p formulation of the porous media problem moreover a new family of parallel domain decomposition methods specifically tailored for the above problem formulation is presented which outperforms the current state of the art parallel domain decomposition solvers the power of this family of solvers is demonstrated in two large scale porous media problems

a generalized multiscale finite element method for poroelasticity problems ii nonlinear coupling in this paper we consider the numerical solution of some nonlinear poroelasticity problems that are of biot type and develop a general algorithm for solving nonlinear coupled systems we discuss the difficulties associated with flow and mechanics in heterogenous media with nonlinear coupling the central issue being how to handle the nonlinearities and the multiscale scale nature of the media to compute an efficient numerical solution we develop and implement a generalized multiscale finite element method gmsfem that solves nonlinear problems on a coarse grid by constructing local multiscale basis functions and treating part of the nonlinearity locally as a parametric value after linearization with a picard iteration the procedure begins with construction of multiscale bases for both displacement and pressure in each coarse block by treating the staggered nonlinearity as a parametric value using a snapshot space and local spectral problems we construct an offline basis of reduced dimension from here an online parametric dependent space is constructed finally after multiplying by a multiscale partitions of unity the multiscale basis is constructed and the coarse grid problem then can be solved for arbitrary forcing and boundary conditions we implement this algorithm on a geometry with a linear and nonlinear pressure dependent permeability field and compute error between the multiscale solution with the fine scale solutions

boundary integral equations with the generalized neumann kernel for laplace s equation in multiply connected regions this paper presents a new boundary integral method for the solution of laplace s equation on both bounded and unbounded multiply connected regions with either the dirichlet boundary condition or the neumann boundary condition the method is based on two uniquely solvable fredholm integral equations of the second kind with the generalized neumann kernel numerical results are presented to illustrate the efficiency of the proposed method

numerical conformal mapping via the szego kernel abstract a new method to compute the riemann mapping function is numerically implemented and tested on examples the method expresses the szego kernel as the solution of a second kind integral equation the equation has its origin in an earlier non numerical work of stein and one of the authors 8 the experimental results show the algorithm to be effective and stable

localization of elliptic multiscale problems this paper constructs a local generalized finite element basis for elliptic problems with heterogeneous and highly varying coefficients the basis functions are solutions of local problems on vertex patches the error of the corresponding generalized finite element method decays exponentially with respect to the number of layers of elements in the patches hence on a uniform mesh of size h patches of diameter h log 1 h are sufficient to preserve a linear rate of convergence in h without pre asymptotic or resonance effects the analysis does not rely on regularity of the solution or scale separation in the coefficient this result motivates new and justifies old classes of variational multiscale methods see more at http www ams org journals mcom 2014 83 290 s0025 5718 2014 02868 8 sthash z2ccfxig dpuf

parallel slits map of bounded multiply connected regions abstract in this paper we present a boundary integral equation method for the numerical conformal mapping of bounded multiply connected region onto a parallel slit region the method is based on some uniquely solvable boundary integral equations with adjoint classical adjoint generalized and modified neumann kernels these boundary integral equations are constructed from a boundary relationship satisfied by a function analytic on a multiply connected region some numerical examples are presented to illustrate the efficiency of the presented method

l optimal control of siso continuous time systems abstract in this paper we study the problem of designing a controller that minimizes the weighted amplitude of the time response due to a given fixed input signal for siso continuous time systems the main result of the paper shows that this problem admits a minimizing solution in l and that the optimal closed loop system has a special structure a sum of delayed step functions all having the same amplitude thus the optimal controller has a non rational transfer function although in the general case finding this controller entails solving an infinite dimensional linear programming problem we show that in some special cases the optimal solutions have closed form expressions and can be found by solving a set of algebraic equations finally we address the issue of selecting time and frequency domain weighting functions this paper together with our paper rational l suboptimal controller for siso continuous time systems ieee trans autom control ac 41 1358 1363 1996 which deals with the design of rational l suboptimal controllers for general systems give a complete solution of the l control problem

implicit dynamic three dimensional finite element analysis of an inelastic biphasic mixture at finite strain part 1 application to a simple geomaterial abstract based on the mixture theory formulation for a fluid saturated inelastic pressure sensitive porous solid subjected to dynamic large strain deformation a 3d finite element implementation with implicit time integration is presented a recently published 2d implementation li et al 2004 cmame v193 p3837 70 is extended to 3d porosity dependent permeability and pressure sensitive inelastic solid skeleton response at finite strain the clausius duhem inequality provides the form of the constitutive equations for the solid and fluid phases as well as the dissipation function a non associative drucker prager cap plasticity model at finite strain is formulated based on a multiplicative decomposition of the deformation gradient and numerically integrated semi implicitly in the intermediate configuration to avoid questions of incremental objectivity the elastic implementation is verified with available 1d analytical and 2d benchmark problems new numerical solutions for 3d large strain dynamic behavior of saturated inelastic porous media are presented the computational efficiency of the implemented formulation in achieving quadratic convergence is illustrated

finite element analysis of poro elastic consolidation in porous media standard and mixed approaches abstract in this paper two different numerical approaches for consolidation in porous media are developed and thoroughly compared galerkin finite element method gfem and least squares mixed finite element methods ls mfem the primary variables of the gfem are fluid pressure and solid displacement fluid fluxes and stresses are derived quantities in the ls mfem method all four unknown functions are primary variables which results in more accurate approximations of fluid fluxes and stresses results of both numerical methods are compared for two examples the first example for which an analytical solution is known is used in order to verify the implementation of the numerical schemes in the second example for a footing problem which was proposed by murad et al m murad v thomee a loula asymptotic behavior of semidiscrete finite element approximations of biot s consolidation problem siam j numer anal 33 1996 1065 1083 a detailed numerical analysis and comparison of both schemes are presented

a coupling of weak galerkin and mixed finite element methods for poroelasticity abstract in this paper we present a coupling of a weak galerkin method for the displacement of the solid phase with a standard mixed finite method for the pressure and velocity of the fluid phase in poroelasticity equation because our method provides a stable element combination for the mixed linear elasticity problem it can avoid the poroelasticity locking mathematically indeed uniform in time error estimates of all the unknowns are obtained for both semidiscrete scheme and fully discrete scheme without assuming that the constrained specific storage coefficient is uniformly positive compared with the method proposed by jeonghun j lee our method can get the arbitrary convergence order by changing degree of the polynomial as for the computational cost we can use the modified weak galerkin method to eliminate the boundary term and reduce the number of unknowns in addition we do not use gronwall inequality in the error analysis finally the numerical experiments verify the theoretical analysis and show the effectiveness to overcome spurious pressure oscillations

exact stiffness method for quasi statics of a multi layered poroelastic medium abstract a method is presented to study the three dimensional quasi static response of a multi layered poroelastic half space with compressible constituents the system under consideration consists of n layers of different thickness and material properties overlying a homogeneous half space fourier expansion laplace transforms and hankel transforms with respect to the circumferential time and radial coordinates respectively are used in the formulation laplace hankel transforms of displacements and pore pressure at layer interfaces are considered as the basic unknowns exact stiffness matrices describing the relationship between generalized displacement and force vectors of a finite layer and a half space are derived explicitly in the transform space the global stiffness matrix of a layered system is assembled by considering the continuity of tractions and fluid flow at layer interfaces the time histories of displacements stresses and pore pressure are obtained by solving the stiffness equation system for discrete values of laplace and hankel transform parameters and using numerical quadrature schemes for laplace and hankel transform inversions selected numerical results for different layered systems are presented to portray the influence of layering and poroelastic material properties the advantage of the present method is that for an n layered system it yields a numerically stable symmetric stiffness matrix of order 4 n 4 n when compared to the unsymmetric and numerically unstable coefficient matrix of order 8 n 8 n associated with the conventional method based on the determination of layer arbitrary coefficients

a fast method for solving certain integral equations of the first kind with application to conforma mapping abstract we describe a fast iterative method for solving fredholm integral equations of the first kind whose kernels have a logarithmic principal part the method is a fourier galerkin method and due to the singularity of the kernel the linear system of simultaneous equations is block diagonally dominant and can be solved rapidly by an iterative method we present examples of the computation of conformal mappings of simply and multiply connected domains

fractional derivative modeling for axisymmetric consolidation of multilayered cross anisotropic viscoelastic porous media abstract this paper presents a fractional derivative modeling for axisymmetric consolidation of multilayered cross anisotropic viscoelastic porous media the elastic solution for multilayered porous media is acquired by the extended precise integration method the flexibility coefficient of the fractional merchant viscoelastic model is deduced in the laplace transformed domain and the viscoelastic solution of the problem is further obtained by the elastic viscoelastic correspondence principle the numerical results are compared with those of published literatures to verify the proposed method and the influences of fractional derivative order viscoelasticity of solid skeleton and layering of materials on the axisymmetric consolidation of multilayered viscoelastic porous media are investigated by several examples

generalized multiscale finite element method for the poroelasticity problem in multicontinuum media abstract in this paper we consider a poroelasticity problem in heterogeneous multicontinuum media that is widely used in simulations of the unconventional hydrocarbon reservoirs and geothermal fields mathematical model contains a coupled system of equations for pressures in each continuum and effective equation for displacement with volume force sources that are proportional to the sum of the pressure gradients for each continuum to illustrate the idea of our approach we consider a dual continuum background model with discrete fracture networks that can be generalized to a multicontinuum model for poroelasticity problem in complex heterogeneous media we present a fine grid approximation based on the finite element method and discrete fracture model dfm approach for two and three dimensional formulations the coarse grid approximation is constructed using the generalized multiscale finite element method gmsfem where we solve local spectral problems for construction of the multiscale basis functions for displacement and pressures in multicontinuum media we present numerical results for the two and three dimensional model problems in heterogeneous fractured porous media we investigate relative errors between reference fine grid solution and presented coarse grid approximation using gmsfem with different numbers of multiscale basis functions our results indicate that the proposed method is able to give accurate solutions with few degrees of freedoms

on stability and convergence of finite element approximations of biot s consolidation problem stability and convergence analysis of finite element approximations of biot s equations governing quasistatic consolidation of saturated porous media are discussed a family of decay functions parametrized by the number of time steps is derived for the fully discrete backward euler galerkin formulation showing that the pore pressure oscillations arising from an unstable approximation of the incompressibility constraint on the initial condition decay in time error estimates holding over the unbounded time domain for both semidiscrete and fully discrete formulations are presented and a post processing technique is employed to improve the pore pressure accuracy

a nonconforming finite element method for the biot s consolidation model in poroelasticity a stable finite element scheme that avoids pressure oscillations for a three field biot s model in poroelasticity is considered the involved variables are the displacements fluid flux darcy velocity and the pore pressure and they are discretized by using the lowest possible approximation order crouzeix raviart finite elements for the displacements lowest order raviart thomas nedelec elements for the darcy velocity and piecewise constant approximation for the pressure mass lumping technique is introduced for the raviart thomas nedelec elements in order to eliminate the darcy velocity and therefore reduce the computational cost we show convergence of the discrete scheme which is implicit in time and use these types of elements in space with and without mass lumping finally numerical experiments illustrate the convergence of the method and show its effectiveness to avoid spurious pressure oscillations when mass lumping for the raviart thomas nedelec elements is used

numerical conformal mapping via a boundary integral equation with the generalized neumann kernel we present a unified boundary integral method for approximating the conformal mappings from any bounded or unbounded multiply connected region g onto the five classical canonical slit domains the method is based on a uniquely solvable boundary integral equation with the generalized neumann kernel using the proposed method the approximate mapping functions onto the five canonical slit domains can be computed in a unified way by solving linear systems with a common coefficient matrix the method can be also used for calculating the conformal mappings of simply and doubly connected regions the performance of the method is illustrated by several examples for regions with smooth boundaries and with piecewise smooth boundaries

linear integral equations for conformal mapping of bounded multiply connected regions onto a disk with circular slits abstract in this paper we present a boundary integral equation method for the numerical conformal mapping of bounded multiply connected region onto a disk with circular slits the method is based on some uniquely solvable boundary integral equations with classical adjoint and generalized neumann kernels these boundary integral equations are constructed from a boundary relationship satisfied by a function analytic on a multiply connected region some numerical examples are presented to illustrate the efficiency of the presented method

l 1 optimal compensators for continuous time systems previous work has been concerned with minimizing the l 1 norm of an error pulse response for discrete time siso 1 and mimo 2 systems in this paper we study the problem of minimizing the l1 norm of the error impulse response for siso continuous time systems this problem is quite different from the discrete time problem in that irrational solutions are obtained even when the problem data are rational two methods are suggested for the solution of the continuous time problem an exact method which leads to a finite dimensional nonlinear programming problem and an approximate method which leads to a linear programming problem