stabilization of partitioned solution procedure for pore fluid soil interaction analysis on montre que la solution decalee conventionnelle des problemes d interaction fluide sol dans les pores souffre de restrictions sur la stabilite on presente une forme stabilisee de la procedure de solution decalee de ce probleme on recommande cette procedure pour l implementation des problemes d interaction sol fluide

analogies between finite dimensional irreducible representations of so 2n and infinite dimensional irreducible representations of sp 2n r i characters and products the analogy between the finite dimensional spin representation of so 2n and the infinite dimensional representation of sp 2n r is made precise it is then shown that this analogy can be extended so as to provide a precise link between each finite dimensional unitary irreducible representation of so 2n and a corresponding infinite dimensional unitary irreducible representation of sp 2n r the analogy shows itself at the level of the corresponding characters and difference characters and involves the use of schur function methods to express both characters and difference characters of so 2n and sp 2n r in terms of characters of irreducible representations of their common subgroup u n the analogy is extended still further to cover the explicit decomposition of not only tensor products of and with other unitary irreducible representations of so 2n and sp 2n r respectively but also arbitrary tensor powers of and

convergence to equilibria in scalar nonquasimonotone functional differential equations abstract we consider a class of scalar functional differential equations generating a strongly order preserving semiflow with respect to the exponential ordering introduced by smith and thieme it is shown that the boundedness of all solutions and the stability properties of an equilibrium are exactly the same as for the ordinary differential equation which is obtained by ignoring the delays the result on the boundedness of the solutions combined with a convergence theorem due to smith and thieme leads to explicit necessary and sufficient conditions for the convergence of all solutions starting from a dense subset of initial data under stronger conditions guaranteeing that the functional differential equation is asymptotically equivalent to a scalar ordinary differential equation a similar result is proved for the convergence of all solutions

unconditionally stable staggered solution procedure for soil pore fluid interaction problems this paper presents a simple procedure for modifying the dynamic coupled soil pore fluid equations in a manner which allows a stable and efficient staggered solution procedure to be used the solution method is simpler than an alternative suggested by park15 and has a direct physical interpretation this stabilized procedure is efficient in numerical time domain analysis of soil pore fluid occurring in earthquake and consolidation problems numerical examples of one and two dimensional saturated poroelastic media demonstrate the procedure

analogies between finite dimensional irreducible representations of so 2n and infinite dimensional irreducible representations of sp 2n r ii plethysms the basic spin difference character of so 2n is a useful device in dealing with characters of irreducible spinor representations of so 2n it is shown here that its kth fold symmetrized powers or plethysms associated with partitions of k factorize in such a way that r where r is the frobenius rank of the analogy between so 2n and sp 2n r is shown to be such that the plethysms of the basic harmonic or metaplectic character of sp 2n r factorize in the same way to give r moreover the analogy is shown to extend to the explicit decompositions into characters of irreducible representations of so 2n and sp 2n r not only for the plethysms themselves but also for their factors and explicit formulas are derived for each of these decompositions expressed in terms of various group subgroup branching rule multiplicities particularly those defined by the restriction from o k to the symmetric group sk illustrative examples are included as well as a

existence of global solutions to nonlinear mixed type functional differential equations abstract the paper considers systems of nonlinear mixed type functional differential equations it aims to find conditions for the existence of global solutions with graphs staying in a prescribed domain a relevant result is proved by schauder tychonoff fixed point technique with illustrative examples shown a linear variant of the derived result is formulated comparisons with known results are discussed and some open problems are formulated

holomorphic discrete series and harmonic series unitary irreducible representations of non compact lie groups sp 2n r u p q and so 2n generalised characters of the infinite dimensional holomorphic discrete series unitary irreducible representations of the non compact groups u p q sp 2n r and so 2n are explicitly expressed in terms of characters of finite dimensional unitary group representations these formulae are remarkably succinct despite involving certain infinite series of schur functions similar formulae are derived for harmonic series unitary representation of both u p q and sp 2n r consideration of the branching rules from u p q to u q p and from sp 2n r to u n enables holomorphic representations to be identified as a subset of the harmonic representations the branching rules are established in full generality and are then used in the evaluation of tensor products of both holomorphic and harmonic representations in the case of the former a known result is recast in terms of closed formulae involving schur functions and for the latter various generalisations of these formulae are given a conjecture is also made regarding what might be the simplest possible formulae covering all holomorphic and harmonic representations of sp 2n r and u p q illustrative examples are presented

a mathematical framework for finite strain elastoplastic consolidation part 1 balance laws variational formulation and linearization a mathematical formulation for finite strain elasto plastic consolidation of fully saturated soil media is presented strong and weak forms of the boundary value problem are derived using both the material and spatial descriptions the algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the kirchhoff pore water pressure balance laws are written for the soil water mixture following the motion of the soil matrix alone it is shown that the motion of the fluid phase only affects the jacobian of the solid phase motion and therefore can be characterized completely by the motion of the soil matrix furthermore it is shown from energy balance consideration that the effective or intergranular stress is the appropriate measure of stress for describing the constitutive response of the soil skeleton since it absorbs all the strain energy generated in the saturated soil water mixture finally it is shown that the mathematical model is amenable to consistent linearization and that explicit expressions for the consistent tangent operators can be derived for use in numerical solutions such as those based on the finite element method

a hyperelastic based large strain elasto plastic constitutive formulation with combined isotropic kinematic hardening using the logarithmic stress and strain measures summary this paper addresses the formulation of a set of constitutive equations for finite deformation metal plasticity the combined isotropic kinematic hardening model of the infinitesimal theory of plasticity is extended to the large strain range on the basis of three main assumptions i the formulation is hyperelastic based ii the stress strain law preserves the elastic constants of the infinitesimal theory but is written in terms of the hencky strain tensor and its elastic work conjugate stress tensor and iii the multiplicative decomposition of the deformation gradient is adopted since no stress rates are present the formulation is of course numerically objective in the time integration it is shown that the model gives adequate physical behaviour and comparison is made with an equivalent constitutive model based on the additive decomposition of the strain tensor

an arbitrary lagrangian eulerian finite element formulation for a poroelasticity problem stemming from mixture theory abstract a finite element formulation is developed for a poroelastic medium consisting of an incompressible hyperelastic skeleton saturated by an incompressible fluid the governing equations stem from mixture theory and the application is motivated by the study of interstitial fluid flow in brain tissue the formulation is based on the adoption of an arbitrary lagrangian eulerian ale perspective we focus on a flow regime in which inertia forces are negligible the stability and convergence of the formulation is discussed and numerical results demonstrate agreement with the theory

symmetrised powers of rotation group representations the results given permit the unambiguous evaluation of all possible kronecker products of the irreducible representations tensor and spinor of on and son for n 2 nu and n 2 nu 1 a complete resolution of the second and third powers of the basic spinor representations of so2 nu and so2 nu 1 is given together with a prescription for analysing the fourth power of these representations detailed application is made to the enumeration of properties of so10 relevant to grand unified theories and sufficient information given to resolve the fourth power of any representation of so10

sufficient conditions for the existence of global solutions of delayed differential equations the purpose of this contribution is to give sufficient conditions for the existence of global solutions or left semi global solutions for some classes of delayed functional differential equations the principle of monotone sequences is used as a main tool of investigation inequalities for coordinates of global solutions are derived as a consequence of used method examples illustrate the results

fractional step methods for index 1 differential algebraic equations in the numerical solution of ordinary differential systems the method of fractional steps also known as operator splitting yields high order accurate schemes based on separate computationally convenient treatments of distinct physical effects such schemes are equally desirable but much less accurate for semi explicit index 1 differential algebraic equations daes in the first half of this note it is shown that email protected ve application to daes of standard splitting schemes suffers from order reduction both first and second order schemes are only first order accurate for daes in the second half of this note a new family of higher order splitting schemes for semi explicit index 1 daes is developed the new schemes are based on a deferred correction paradigm in which an error equation is solved numerically and therefore inherit a simple computationally convenient structure higher order convergence of the new schemes is proved and numerical results confirm the expected order of accuracy in addition to establishing efficiency

existence of global solutions of delayed differential equations via retract approach abstract the purpose of this contribution is to give sufficient conditions for the existence of global solutions or left semi global solutions for some classes of delayed functional differential equations the topological approach known as the topological retract principle is used inequalities for coordinates of global solutions are derived as a consequence of used method examples illustrate the results

the representation space of the nuclear symplectic sp 6 r shell model the problem of obtaining the sp 6 r irreducible representations that arise from the symmetrized products of a copies of the fundamental representation of sp 6 r is considered a simple method is developed that rapidly leads to the determination of the sp 6 r content up to a prescribed cut off in practical calculations a is identified with the nucleon number it is shown that for a given excitation energy cut off n omega and sufficiently large a the number and multiplicities of the sp 6 r irreducible representations is fixed and the content can be expressed in an a independent manner complete results are given for n or 16 there is no difficulty in principle in going to higher excitations and details are given for determining the sp 6 r content for a or 16

unconditionally stable sequential schemes for all way coupled thermoporomechanics undrained adiabatic and extended fixed stress splits abstract we propose two sequential methods for the all way coupled thermoporomechanical problems the undrained adiabatic split that combines together the undrained and adiabatic methods of poromechanics and thermomechanics respectively and the extended fixed stress split we perform nonlinear stability analysis for the two sequential methods introducing a new extended norm that can encompass the all way coupled thermoporomechanical problems we find that the two sequential methods are unconditionally stable if 0 5 where is the parameter of time discretization for the generalized midpoint rule at t n we also perform the spectral analysis in order to further investigate stability and convergence of the two methods the spectral analysis shows unconditional stability of the two sequential methods which yields the magnitudes of the amplification factor less than unity we then show numerical examples which support the a priori stability and convergence estimates

on convergence conditions of partitioned solution procedures for consolidation problems abstract a systematic approach to determine conditions for convergence of partitioned staggered procedures for consolidation problems is presented consistency convergence and stability is investigated for linear and nonlinear problems and a comparison of the partitioned and direct method is made conclusions based also on numerical evidence are drawn the significance of the ratio of the time step length to the square of the finite element mesh length is shown

frameworks for finite strain viscoelastic plasticity based on multiplicative decompositions part ii computational aspects abstract computational aspects of the two formulations of viscoelastic plasticity at finite strains proposed in part i of this work are examined in detail these formulations are based upon distinct kinematic assumptions resulting from different multiplicative decompositions of the deformation gradient however the corresponding sets of local evolution equations consistent with continuum thermodynamics and adopted in this work have globally the same structures and therefore lead to similar algorithmic treatments the key idea in the design of the integration algorithms is the systematic use of the nowadays well known exponential mapping algorithms in conjunction with the notion of operator split methodology these numerical approximations are then applied to the model examples proposed in part i together with their extensions to incorporate rate dependent plasticity the implementation within the framework of the finite element method is described in detail and finally we present a set of representative numerical simulations to illustrate the features of the proposed models

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

elastic plastic multiplicative decomposition with a stressed intermediate configuration abstract this paper presents an extension to the elastic plastic multiplicative decomposition to permit the origin in stress space to reside outside the closure of the elastic domain in this work the classical assumption of a stress free intermediate configuration is abandoned in favor of a new one where the intermediate configuration could be stressed this stress is identified as the maximal unloading point in stress space and denoted the plastic stress to motivate the discussion the infinitesimal plasticity model is considered first a remarkable result is obtained where for the case of linear elastic response the classical infinitesimal model is after some reinterpretation recovered the fully nonlinear model is developed and is shown to reduce to the classical one when the intermediate configuration is stress free the new framework is then applied to the case of j 2 plasticity where it is shown that when coupled with neo hookean elasticity as in the infinitesimal case after some reinterpretation the classical model is recovered i e the total stress is independent of the plastic stress numerical simulations are used to illustrate the importance of properly modeling the hardening behavior even during external loading in cases where load redistribution may take place

monolithic and splitting solution schemes for fully coupled quasi static thermo poroelasticity with nonlinear convective transport abstract this paper concerns monolithic and splitting based iterative procedures for the coupled nonlinear thermo poroelasticity model problem the thermo poroelastic model problem we consider is formulated as a three field system of pde s consisting of an energy balance equation a mass balance equation and a momentum balance equation where the primary variables are temperature fluid pressure and elastic displacement due to the presence of a nonlinear convective transport term in the energy balance equation it is convenient to have access to both the pressure and temperature gradients hence we introduce these as two additional variables and extend the original three field model to a five field model for the numerical solution of this five field formulation we compare six approaches that differ by how we treat the coupling decoupling between the flow and from heat and from the mechanics suitable for varying coupling strength between the three physical processes the approaches have in common a simultaneous application of the so called l scheme which works both to stabilize iterative splitting as well as to linearize nonlinear problems and can be seen as a generalization of the undrained and fixed stress split algorithms more precisely the derived procedures transform a nonlinear and fully coupled problem into a set of simpler subproblems to be solved sequentially in an iterative fashion we provide a convergence proof for the derived algorithms and demonstrate their performance through several numerical examples investigating different strengths of the coupling between the different processes

an efficient multigrid solver for a reformulated version of the poroelasticity system in this paper we present a robust and efficient multigrid solver for a transformed version of the system of poroelasticity equations the transformation enables us to treat the system in a decoupled fashion we show that the transformation boils down to a stabilization term in the iterative scheme and that the solution of the original problem is identical to the solution of the transformed problem a highly efficient multigrid method can be developed confirmed by numerical experiments

plethysm for the non compact group and new s function identities methods of computing plethysms of the fundamental unitary irreducible representations of the non compact symplectic group sp 2n r are considered complete results are given for the symmetrized second powers a number of new s function identities are reported the stability properties of the sp 2n r plethysms are noted as well as a remarkable conjugacy relation the application of the plethysms to n particles in an isotropic harmonic oscillator is briefly outlined

unitary representations branching rules and matrix elements for the non compact symplectic groups the complementarity of the symplectic and orthogonal groups is used to infer properties of the infinite dimensional unirreps of the former from the character theory of the latter the complete set of d series metaplectic unirreps of sp n r is identified and branching rules are given for their restrictions to the maximal compact subgroup u n developed in terms of the properties of schur functions a known algorithm for the evaluation of matrix elements of the sp 3 r lie algebra is extended to any sp n r and analytic expressions are given for important classes of unirreps and multiplicity free states

stability and convergence of sequential methods for coupled flow and geomechanics fixed stress and fixed strain splits abstract we analyze stability and convergence of sequential implicit methods for coupled flow and geomechanics in which the flow problem is solved first we employ the von neumann and energy methods for linear and nonlinear problems respectively we consider two sequential methods with the generalized midpoint rule for tn where is the parameter of time discretization namely the fixed strain and fixed stress splits the von neumann method indicates that the fixed strain split is only conditionally stable and that its stability limit is a coupling strength less than unity if 0 5 on the other hand the fixed stress split is unconditionally stable when 0 5 the amplification factors of the fixed stress split are different from those of the undrained split and are identical to the fully coupled method unconditional stability of the fixed stress split is also obtained from the energy method for poroelastoplasticity we show that the fixed stress split is contractive and b stable when 0 5 we also estimate the convergence behaviors for the two sequential methods by the matrix based and spectral analyses for the backward euler method in time from the estimates the fixed strain split may not be convergent with a fixed number of iterations particularly around the stability limit even though it is stable the fixed stress split however is convergent for a fixed number of iterations showing better accuracy than the undrained split even when we cannot obtain the exact local bulk modulus or exact rock compressibility at the flow step a priori due to complex boundary conditions or the nonlinearity of the materials the fixed stress split can still provide stability and convergence by an appropriate estimation of the local bulk modulus such as the dimension based estimation by which the employed local bulk modulus is less stiff than the exact local bulk modulus we provide numerical examples supporting all the estimates of stability and convergence for the fixed strain and fixed stress splits

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

dynamics of porous media at finite strain we present a finite element model for the analysis of a mechanical phenomenon involving dynamic expulsion of fluids from a fully saturated porous solid matrix in the regime of large deformation momentum and mass conservation laws are written in lagrangian form by a pull back from the current configuration to the reference configuration following the solid matrix motion a complete formulation based on the motion of the solid and fluid phases is first presented then approximations are made with respect to the material time derivative of the relative flow velocity vector to arrive at a so called v p formulation which is subsequently implemented in a finite element model we show how the resulting finite element matrix equations can be consistently linearized using a compressible neo hookean hyperelastic material with a kelvin solid viscous enhancement for the solid matrix as a test function for the nonlinear constitutive model numerical examples are presented demonstrating the significance of large deformation effects on the transient dynamic responses of porous structures as well as the strong convergence profile exhibited by the iterative algorithm

a new numerically stable sequential algorithm for coupled finite strain elastoplastic geomechanics and flow abstract we propose a new numerically stable sequential implicit method for coupled flow and finite strain multiplicative elastoplastic geomechanics we find from stability analysis that the sequential method that solves the flow problem first by fixing the first piola kirchhoff total stress solving the geomechanics solid deformation problem at the next step is unconditionally stable contractive and b stable in this sense this method named the fixed first piola kirchhoff stress method is an extension of the fixed stress method in coupled flow and infinitesimal geomechanics we also study the fixed second piola kirchhoff stress method comparing it with the fixed first piola kirchhoff stress method because the constitutive relations are formulated by the second piola kirchhoff total stress although fixing the second piola kirchhoff total stress field does not provide theoretical unconditional stability in space discretization we use the finite element method for the geomechanics problem with the total lagrangian approach while employing the finite volume method for the flow problem geometrical nonlinearity from the total lagrangian approach results in full tensor permeability even if the initial permeability is isotropic to consider the full tensor permeability accurately we employ the multipoint flux approximation in solving the flow problem in time discretization the backward euler method is used then we perform numerical experiments of the two fixed stress sequential methods with various scenarios and find superiority of their numerical stability specifically the two fixed stress sequential methods provide almost identical results for elasticity for j 2 plasticity the two sequential methods yield slightly different numerical results although the trends of the results are similar for the drucker prager plasticity we find that the results from the two methods are almost identical for all the test cases the two sequential methods are numerically stable

stability and convergence of sequential methods for coupled flow and geomechanics drained and undrained splits abstract we perform a stability and convergence analysis of sequential methods for coupled flow and geomechanics in which the mechanics sub problem is solved first we consider slow deformations so that inertia is negligible and the mechanical problem is governed by an elliptic equation we use biot s self consistent theory to obtain the classical parabolic type flow problem we use a generalized midpoint rule parameter between 0 and 1 time discretization and consider two classical sequential methods the drained and undrained splits the von neumann method provides sharp stability estimates for the linear poroelasticity problem the drained split with backward euler time discretization 1 is conditionally stable and its stability depends only on the coupling strength and it is independent of time step size the drained split with the midpoint rule 0 5 is unconditionally unstable the mixed time discretization with 1 0 for mechanics and 0 5 for flow has the same stability properties as the backward euler scheme the von neumann method indicates that the undrained split is unconditionally stable when 0 5 we extend the stability analysis to the nonlinear regime poro elastoplasticity via the energy method it is well known that the drained split does not inherit the contractivity property of the continuum problem thereby precluding unconditional stability for the undrained split we show that it is b stable therefore unconditionally stable at the algorithmic level when 0 5 we also analyze convergence of the drained and undrained splits and derive the a priori error estimates from matrix algebra and spectral analysis we show that the drained split with a fixed number of iterations is not convergent even when it is stable the undrained split with a fixed number of iterations is convergent for a compressible system i e finite biot modulus for a nearly incompressible system i e very large biot modulus the undrained split loses first order accuracy and becomes non convergent in time we also study the rate of convergence of both splits when they are used in a fully iterated sequential scheme when the medium permeability is high or the time step size is large which corresponds to a high diffusion of pressure the error amplification of the drained split is lower and therefore converges faster than the undrained split the situation is reversed in the case of low permeability and small time step size we provide numerical experiments supporting all the stability and convergence estimates of the drained and undrained splits in the linear and nonlinear regimes we also show that our spatial discretization finite volumes for flow and finite elements for mechanics removes the well documented spurious instability in consolidation problems at early times

on nonoscillation of mixed advanced delay differential equations with positive and negative coefficients for a mixed advanced delay differential equation with variable delays and coefficients email protected t a t x g t b t x h t 0 t t 0 where a t 0 b t 0 g t t h t t explicit nonoscillation conditions are obtained

symmetrised kronecker products of the fundamental representation of sp n r the role played by s function series in the character theory of the non compact symplectic group sp n r is exploited to derive general formulae for the evaluation of symmetrised kronecker products of the fundamental sp n r representation applications of the results to sp 3 r and their impact on the nuclear symplectic shell model are discussed for simple cases

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

new s function series and non compact lie groups a number of new infinite series of s functions are described in terms of their generating functions and s function content applications to the character theory of non compact lie groups are noted

a finite element implementation of the nonlocal granular rheology summary inhomogeneous flows involving dense particulate media display clear size effects in which the particle length scale has an important effect on flow fields hence nonlocal constitutive relations must be used in order to predict these flows recently a class of nonlocal fluidity models has been developed for emulsions and subsequently adapted to granular materials these models have successfully provided a quantitative description of experimental flows in many different flow configurations in this work we present a finite element based numerical approach for solving the nonlocal constitutive equations for granular materials which involve an additional non standard nodal degree of freedom the granular fluidity which is a scalar state parameter describing the susceptibility of a granular element to flow our implementation is applied to three canonical inhomogeneous flow configurations 1 linear shear with gravity 2 annular shear flow without gravity and 3 annular shear flow with gravity we verify our implementation demonstrate convergence and show that our results are mesh independent copyright 2016 john wiley sons ltd

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

kronecker products for compact semisimple lie groups a review is given of the application of s function techniques to the evaluation of kronecker products of irreducible representations of compact semisimple lie groups explicit formulae are derived for all irreducible representations of all such groups recent developments involving composite young diagrams are brought to fruition and the vexed problem of so2k is dealt with completely new branching rules for the classical groups are given in an appendix these are exploited in the evaluation of kronecker products by means of a technique which is applied to both classical and exceptional groups a discussion is made of various modification rules which are needed to express the final results in standard form

products and symmetrized powers of irreducible representations of and their associates the calculation of kronecker products and plethysms of the infinite dimensional harmonic series unitary irreducible representations of the non compact group is considered the complementarity of and o k is used to define associate irreducible representations of this leads to simple relationships between kronecker products and plethysms of irreducible representations of and those of their corresponding associate irreducible representations in the process of proving the validity of these previously conjectured relationships several new identities are found for plethysms involving infinite series of schur functions in addition a general formula for plethysms of arbitrary irreducible representations of is derived and its implementation is illustrated with a detailed example a remarkable analogy is then observed between plethysms of the basic harmonic irreducible representations of and those of the basic spin irreducible representations of so 2n

plethysms of schur functions and the shell model we present a method for evaluating plethysms of schur functions that is conceptually simpler than existing methods moreover the algorithm can be easily implemented with an algebraic computer language plethysms of sums differences and products of s functions are dealt with in exactly the same manner as plethysms of simple s functions sums and differences of s functions are of importance for the description of multi shell configurations in the shell model the number of variables in which the s functions are expressed can be specified in advance significantly simplifying the calculations in typical applications to many body problems the method relies on an algorithm that we have developed for the product of monomial symmetric functions we present a new way of calculating the kostka numbers using gel fand patterns and give as well a new formula for the littlewood richardson coefficients

numerical approximation of poroelasticity with random coefficients using polynomial chaos and hybrid high order methods abstract in this work we consider the biot problem with uncertain poroelastic coefficients the uncertainty is modeled using a finite set of parameters with prescribed probability distribution we present the variational formulation of the stochastic partial differential system and establish its well posedness we then discuss the approximation of the parameter dependent problem by non intrusive techniques based on polynomial chaos decompositions we specifically focus on sparse spectral projection methods which essentially amount to performing an ensemble of deterministic model simulations to estimate the expansion coefficients the deterministic solver is based on a hybrid high order discretization supporting general polyhedral meshes and arbitrary approximation orders we numerically investigate the convergence of the probability error of the polynomial chaos approximation with respect to the level of the sparse grid finally we assess the propagation of the input uncertainty onto the solution considering an injection extraction problem

nonoscillation for functional differential equations of mixed type abstract an example is given to show that the linear autonomous functional differential equation of mixed type t 1 1 d s x t s 0 may have a nonoscillatory solution in spite of the nonexistence of real roots of its characteristic equation under a regularity condition on at 1 exponential boundedness and asymptotic expansions are obtained for the nonoscillatory solutions

computational issues in large strain elasto plasticity an algorithm for mixed hardening and plastic spin in this paper an algorithm for large strain elasto plasticity with isotropic hyperelasticity based on the multiplicative decomposition is formulated the algorithm includes a possible constitutive equation for the plastic spin and mixed hardening in which the principal stress and principal backstress directions are not necessarily preserved it is shown that if the principal trial stress directions are preserved during the plastic flow as assumed in some algorithms a plastic spin is inadvertently introduced for the kinematic mixed hardening case if the formulation is performed in the principal stress space a rotation of the backstress is inadvertently introduced as well the consistent linearization of the algorithm is also addressed in detail copyright 2005 john wiley sons ltd

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

a new unconditionally stable fractional step method for non linear coupled thermomechanical problems a new class of time stepping algorithms for strongly coupled thermomechanical problems is presented which retains the computational convenience of traditional staggered algorithms without upsetting the unconditional stability property characteristic of fully implicit monolithic schemes 11 the proposed schemes are fractional step methods associated with a two phase operator split of the full non linear system of thermoelasticity into an adiabatic elastodynamics phase followed by a heat conduction phase at fixed configuration this operator split is shown to inherit the contractivity property of the full problem of evolution thus leading to unconditionally b stable product formula algorithms in sharp contrast with this stability result traditional staggered algorithms based on an isothermal mechanical phase followed by a heat conduction phase with an effective heat source are shown to lead at best to conditionally stable schemes it is further shown that the actual implementation of these two classes of schemes is essentially identical the numerical simulations presented include both dynamic and quasi static problems and are shown to closely replicate the stability estimates and non linear stability results derived for these two classes of staggered schemes

symmetrized squares and cubes of the fundamental unirreps of we establish the complete decompositions of the symmetrized kronecker squares of the basic harmonic representations of conjectured by grudzinski and wybourne grudzinski k and wybourne b g 1996 j phys a math gen 29 6631 41 and give analogous complete results for the symmetrized cubes equivalence relationships are shown to exist between certain pairs of plethysms

products and symmetrized powers of irreducible representations of the calculation of branching rules tensor products and plethysms of the infinite dimensional harmonic series unitary irreducible representations of the non compact group is considered and the duality between and sp 2k exploited the branching rule for the restriction of an arbitrary harmonic series irreducible representation of to u n is derived and the decomposition is given explicitly for each of the infinite number of fundamental harmonic series irreducible representations of whose direct sum constitutes the metaplectic representation h of a concise expression for the decomposition of tensor products is derived and a complete analysis of the terms in both and is given a general formula for plethysms of arbitrary irreducible representations of is derived and its implementation illustrated both by means of a detailed generic example and by a complete determination of the symmetric and antisymmetric terms of finally relationships that arise from the embedding of the product groups and in the metaplectic group mp 4nk are discussed

partitioned coupling of advection diffusion reaction systems and brinkman flows we present a partitioned algorithm aimed at extending the capabilities of existing solvers for the simulation of coupled advection diffusion reaction systems and incompressible viscous flow the space discretisation of the governing equations is based on mixed finite element methods defined on unstructured meshes whereas the time integration hinges on an operator splitting strategy that exploits the differences in scales between the reaction advection and diffusion processes considering the global system as a number of sequentially linked sets of partial differential and algebraic equations the flow solver presents the advantage that all unknowns in the system here vorticity velocity and pressure can be fully decoupled and thus turn the overall scheme very attractive from the computational perspective the robustness of the proposed method is illustrated with a series of numerical tests in 2d and 3d relevant in the modelling of bacterial bioconvection and boussinesq systems

formulation and finite element implementation of a multiplicative model of coupled poro plasticity at finite strains under fully saturated conditions in this paper we present the formulation and numerical analysis of a finite deformation model of coupled poro plasticity fully saturated conditions are assumed the model is based on a multiplicative decomposition of the deformation gradient in elastic and plastic parts together with an additive elastoplastic decomposition of the fluid content the final relations describing the evolution of the different fields are then obtained in the thermodynamic framework furnished by the principle of maximum plastic dissipation the particular case of an associated drucker prager model in effective stresses is considered as a model example a complete characterization of the dissipative structure of the problem of evolution is described through the derivation of an a priori stability estimate we describe in detail the finite element implementation of the model in the context of staggered algorithms for the solution of the physically coupled problem finally we present representative numerical simulations to illustrate the features of the proposed models in particular the case of strain localization in globally undrained conditions is studied in the proposed framework