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

wavelet analysis on the circle the construction of a wavelet analysis over the circle is presented the spaces of infinitely times differentiable functions tempered distributions and square integrable functions over the circle are analyzed by means of the wavelet transform

localization properties of wavelet transforms estimates are given of the localization of wavelet transforms on the half plane in terms of the localization of the analyzed function in time and frequency then a precise formulation of the wavelet analysis of tempered distributions is given the results in this paper are well known to the wavelet community however they are nowhere explicitly written up though they are quite useful this paper therefore serves as reference for these kinds of results

wavelet coorbit spaces viewed as decomposition spaces abstract in this paper we show that the fourier transform induces an isomorphism between the coorbit spaces defined by feichtinger and grochenig of the mixed weighted lebesgue spaces l v p q with respect to the quasi regular representation of a semi direct product r d h with suitably chosen dilation group h and certain decomposition spaces d q l p l u q essentially as introduced by feichtinger and grobner where the localized parts of a function are measured in the f l p norm this equivalence is useful in several ways it provides access to a fourier analytic understanding of wavelet coorbit spaces and it allows to discuss coorbit spaces associated to different dilation groups in a common framework as an illustration of these points we include a short discussion of dilation invariance properties of coorbit spaces associated to different types of dilation groups

continuous wavelet transform on a special homogeneous space we consider a semidirect product of two locally compact groups s and t with s abelian denoted by s t an action of s t on s is introduced to make s a homogeneous space of s t then we define a unitary representation from s t into the unitary group of l2 s which is our main tool for defining the continuous wavelet transform on l2 s also the main properties of the transform are discussed we prove the plancherel and inversion formulas and reproducing kernel s formula for this transform this is finally specialized to the case of the continuous wavelet transform on l2 rd

banach spaces related to integrable group representations and their atomic decompositions i abstract we present a general theory of banach spaces which are invariant under the action of an integrable group representation and give their atomic decompositions with respect to coherent states i e the atoms arise from a single element under the group action several well known decomposition theories are contained as special examples and are unified under the aspect of group theory

transforms associated to square integrable group representations i general results let g be a locally compact group which need not be unimodular let x u x x g be an irreducible unitary representation of g in a hilbert space h u assume that u is square integrable i e that there exists in h u at least one nonzero vector g such that u x g g 2 dx we give here a reasonably self contained analysis of the correspondence associating to every vector f h u the function u x g f on g discussing its isometry characterization of the range inversion and simplest interpolation properties this correspondence underlies many properties of generalized coherent states

hierarchal vector basis functions of arbitrary order for triangular and tetrahedral finite elements new vector finite elements are proposed for electromagnetics the new elements are triangular or tetrahedral edge elements tangential vector elements of arbitrary polynomial order they are hierarchal so that different orders can be used together in the same mesh and p adaption is possible they provide separate representation of the gradient and rotational parts of the vector field explicit formulas are presented for generating the basis functions to arbitrary order the basis functions can be used directly or after a further stage of partial orthogonalization to improve the matrix conditioning matrix assembly for the frequency domain curl curl equation is conveniently carried out by means of universal matrices application of the new elements to the solution of a parallel plate waveguide problem demonstrates the expected convergence rate of the phase of the reflection coefficient for tetrahedral elements to order 4 in particular the full order elements have only the same asymptotic convergence rate as elements with a reduced gradient space such as the whitney element however further tests reveal that the optimum balance of the gradient and rotational components is problem dependent

wavelets associated with representations of the affine weyl heisenberg group the affine weyl heisenberg group generated by time and frequency translations and time dilations is considered and some associated resolutions of the identity are derived as a result it will be shown that they can all be obtained from those associated with the affine group and the weyl heisenberg group by frequency translations of the analyzed function and the analyzing and reconstructing wavelets

generalized coorbit theory banach frames and the relation to α modulation spaces this paper is concerned with generalizations and specific applications of the coorbit space theory based on group representations modulo quotients that has been developed quite recently we show that the general theory applied to the affine weyl heisenberg group gives rise to families of smoothness spaces that can be identified with modulation spaces

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

coorbit spaces and wavelet coefficient decay over general dilation groups we study continuous wavelet transforms associated to matrix dilation groups giving rise to an irreducible square integrable quasi regular representation on l 2 r d it turns out that these representations are integrable as well with respect to a wide variety of weights thus allowing to consistently quantify wavelet coefficient decay via coorbitspace norms we then show that these spaces always admit an atomic decomposition in terms of bandlimited schwartz wavelets we exhibit spaces of schwartz functions contained in all coorbit spaces and dense in most of them we also present an example showing that for a consistent definition of coorbit spaces the irreducibility requirement cannot be easily dispensed with we then address the question how to predict wavelet coefficient decay from vanishing moment assumptions to this end we introduce a new condition on the open dual orbit associated to a dilation group if the orbit is temperately embedded it is possible to derive rather general weighted l p q estimates for the wavelet coefficients from vanishing moment conditions on the wavelet and the analyzed function these estimates have various applications they provide very explicit admissibility conditions for wavelets and integrable vectors as well as sufficient criteria for membership in coorbit spaces as a further consequence one obtains a transparent way of identifying elements of coorbit spaces with certain cosets of tempered distributions we then show that for every dilation group in dimension two the associated dual orbit is temperately embedded in particular the general results derived in this paper apply to the shearlet group and its associated family of coorbit spaces where they complement and generalize the known results

wiener measures for path integrals with affine kinematic variables the results obtained earlier have been generalized to show that the path integral for the affine coherent state matrix element of a unitary evolution operator exp ith can be written as a well defined wiener integral involving wiener measure on the lobachevsky half plane in the limit that the diffusion constant diverges this approach works for a wide class of hamiltonians including e g d2 dx2 v x on l2 r with v sufficiently singular at x 0

continuous wavelet transforms with abelian dilation groups this paper is devoted to the construction of wavelet or coherent state systems arising from the action of certain semidirect products g rk h on l2 rk for this purpose previous results which guarantee the existence of inversion formulas are applied to the special case where h is abelian the questions of systematic construction and conjugacy of such groups are completely resolved by setting up a correspondence to unit groups of commutative associative algebras as an application the numbers of conjugacy classes of possible abelian groups are computed for k 2 3 4 for k 7 there are uncountably many conjugacy classes we then compute the admissibility conditions belonging to abelian groups the final section contains a characterization of abelian matrix groups acting ergodically on some subset of rk this result ensures that the approach via associative algebras yields all possible groups

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

a general theorem on square integrability vector coherent states we derive a generalization of the well known theorem for the square integrability of a unitary irreducible representation of a locally compact group the generalization covers the case of representations admitting vector coherent states the result is illustrated by an example drawn from the isochronous galilei group the construction yields a wide variety of coherent states labeled by phase space points which satisfy a resolution of the identity condition and incorporate spin degrees of freedom

existence and computation of optimally localized coherent states this paper is concerned with localization properties of coherent states instead of classical uncertainty relations we consider generalized localization quantities this is done by introducing measures on the reproducing kernel in this context we may prove the existence of optimally localized states moreover we provide a numerical scheme for deriving them

a novel efficient algorithm for scattering from a complex bor using mixed finite elements and cylindrical pml an efficient finite element method fem is developed to compute scattering from a complex body of revolution bor the bor is composed of a perfect conductor and impedance surfaces and arbitrary inhomogeneous materials the method uses edge based vector basis functions to expand the transverse field components and node based scalar basis functions to expand the angular component the use of vector basis functions eliminates the problem of spurious solutions suffered by other three component fem formulations the fem mesh is truncated with a perfectly matched layer pml in cylindrical coordinates the use of pml in cylindrical coordinates avoids the wasted computation which results from a spherical mesh boundary with an elongated scatterer the fem equations are solved by ordering the unknowns with a reverse cuthill mckee algorithm and applying a banded matrix solution algorithm the method is capable of handling large realistic radar targets and good agreement with measured results is achieved for benchmark targets

wavelet based integral representation for solutions of the wave equation an integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built the solutions from a wide class can be used as building blocks for the representation considerations are based on mathematical techniques of continuous wavelet analysis the formulae obtained are justified from the point of view of distribution theory a comparison of the results with those by g kaiser is carried out methods of obtaining physical wavelets are discussed

functions analytic on the half plane as quantum mechanical states a transform between the state space of one dimensional quantum mechanical systems and a direct sum of two spaces of square integrable functions analytic on the open upper half plane is constructed it gives a representation of usual quantum mechanics on which the free evolution is trivial and the representation of canonical transformation very simple generalizations to higher dimensions are also discussed

phase space analysis of the identity decompositions the connections between the decompositions of the identity operator on l2 rn and the decompositions of the function 1 on the phase space r2n are considered the phase space properties of various transformations such as the fourier transform gabor transform and wavelet transform etc are investigated

quantization of a classical system on a coadjoint orbit of the poincare group in 1 1 dimensions the connection is investigated between quantization by means of coherent states and geometric quantization when the base manifold is a coadjoint orbit and hence a homogeneous space of the 1 1 dimensional poincare group coherent states of the poincare group stem from a representation that is square integrable modulo closed subgroup and so they depend on a measurable section on the given homogeneous space for each section that leads to a tight frame a geometric prequantization is constructed i e a hermitian line bundle with metric connection conditions are given under which the two forms associated to the connection and to the coadjoint orbit structure of the base manifold coincide

frame transforms star products and quantum mechanics on phase space using the notions of frame transform and of square integrable projective representation of a locally compact group g we introduce a class of isometries tight frame transforms from the space of hilbert schmidt operators in the carrier hilbert space of the representation into the space of square integrable functions on the direct product group g g these transforms have remarkable properties in particular their ranges are reproducing kernel hilbert spaces endowed with a suitable star product which mimics at the level of functions the original product of operators a phase space formulation of quantum mechanics relying on the frame transforms introduced in the present paper and the link of these maps with both the wigner transform and the wavelet transform are discussed

the weyl correspondence and time frequency analysis describes the weyl correspondence and its properties showing how it gives a window independent definition of time frequency concentration for use in models in signal detection the definition of concentration is justified by showing that it gives reasonable answers in certain intuitive cases the weyl correspondence expresses a linear transformation as a weighted superposition of time frequency shifts of the signal and then authors explain why this is not the same as transforming a signal into the time frequency domain multiplying by a weight in the transform domain and taking the inverse the investigation into time frequency concentration and the weyl correspondence is justified by a new result the authors show that convolving the wigner distribution with a general smoothing function is equivalent to evaluating a weighted sum of spectrograms this is a new interpretation of the process of smoothing the wigner distribution to reduce cross terms it relates smoothing of the wigner distribution to the multiple window technique pioneered by thomson 1982

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

necessary and sufficient conditions for constructing orthonormal wavelet bases this paper proves a previous conjecture of the author characterizing sequences h l2 z that yield orthonormal wavelet bases of l2 r in terms of the multiplicity of the eigenvalue 1 of an operator associated to h the proof utilizes a result of cohen characterizing these sequences in terms of the real zeros of their fourier transforms the mapping from sequences to wavelets is shown to define a continuous mapping from a subset of l2 z into l2 r related conjectures are discussed

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

hydromechanical modeling of an initial boundary value problem studies of non uniqueness with a second gradient continuum a non uniqueness study for a hydromechanical boundary value problem is performed a fully saturated porous medium is considered using an elasto plastic constitutive equations to describe the mechanical behavior of the skeleton a real hydromechanical experiment which consists in a hollow cylinder test on a boom clay sample is modelled it is shown that the time step discretisation of the numerical problem has an effect on the initialisation of the newton raphson algorithm on a given time step different solutions for the same initial boundary value problem can consequently be found

an algebraic approach to multiresolution analysis the notion of a weak multiresolution analysis is defined over an arbitrary field in terms of cyclic modules for a certain affine group ring in this setting the basic properties of weak multiresolution analyses are established including characterizations of their submodules and quotient modules the existence and uniqueness of reduced scaling equations and the existence of wavelet bases these results yield some sta ndard facts on classical multiresolution analyses over the rea ls as special cases but provide a different perspective by not relying on orthogonality or topology connections with other areas of algebra and possible further directions are mentioned

a new transform for time frequency analysis the psi decomposition of a signal in which the signal is written as a weighted sum of certain elementary synthesizing functions is described the set s of synthesizing functions consists of dilated and translated copies of two parent functions which are concentrated in both the time and the frequency domains the weighting constants in the psi decomposition define a transform called the phi transform the phi transform of a signal captures both the frequency content and the temporal evolution of a nonstationary signal the phi transform is linear continuous and continuously invertible the set s of synthesizing functions used in the psi decomposition is nonorthogonal hence considerable flexibility is permitted in its construction it is shown with the help of two examples that the set s is easy to construct

the wavelet transform on sobolev spaces and its approximation properties we extend the continuous wavelet transform to sobolev spacesh s for arbitrary reals and show that the transformed distribution lies in the fiber spaces l 2 left left mathbb r 0 frac da a 2 right h s left mathbb r right right cong h 0 s left mathbb r 2 frac dadb a 2 right this generalisation of the wavelet transform naturally leads to a unitary operator between these spaces further the asymptotic behaviour of the transforms ofl 2 functions for small scaling parameters is examined in special cases the wevelet transform converges to a generalized derivative of its argument we also discuss the consequences for the discrete wavelet transform arising from this property numerical examples illustrate the main result

square integrability of metaplectic wave packet representations on l2 r abstract this paper presents a systematic study for harmonic analysis of metaplectic wave packets in l 2 r via group representation theory the abstract notions of metaplectic wave packet groups and metaplectic wave packet representations will be presented and as the main result we prove an admissibility condition on closed subgroups of the special linear group sl 2 r which guarantees square integrability of the associated metaplectic wave packet representation on l 2 r finally we present an analytic study of metaplectic wave packet representations over admissible subgroups of sl 2 r

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

finite element analysis of complex antennas and arrays various technical issues are addressed in the frequency and time domain finite element analysis of complex antennas and arrays that may consist of fine structures and composite materials the paper starts with the finite element formulation of a generic antenna problem formulation for the modeling of general electrically and magnetically dispersive lossy and anisotropic materials in the time domain finite element analysis is presented for the first time this is followed by discussion of three typical techniques for truncation of the finite element computational domain via the use of absorbing boundary conditions perfectly matched layers and boundary integral equations it then describes the modeling of antenna feeds using a current probe including an improved model a voltage gap and a waveguide port boundary condition after that numerical approaches to modeling infinite phased arrays large finite arrays and antenna platform interaction are presented including two novel domain decomposition algorithms in both the frequency and time domains numerical examples are given to demonstrate the capability and application of the finite element analysis of a variety of complex antennas and arrays

investigation of nonplanar perfectly matched absorbers for finite element mesh truncation we present a detailed theoretical and numerical investigation of the perfectly matched layer pml concept as applied to the problem of mesh truncation in the finite element method fem we show that it is possible to extend the cartesian pml concepts involving half spaces to cylindrical and spherical geometries appropriate for closed boundaries in two and three dimensions by defining lossy anisotropic layers in the relevant coordinate systems by using the method of separation of variables it is possible to solve the boundary value problems in these geometries the analytical solutions demonstrate that under certain conditions outgoing waves are absorbed with negligible reflection and the transmitted wave is attenuated within the pml to reduce the white space in radiation or scattering problems conformal pmls are constructed via parametric mappings it is also verified that the pml concept which was originally introduced for problems governed by maxwell s equations can be extended to cases governed by the scalar helmholtz equation finally numerical results are presented to demonstrate the use of the pml in fem mesh truncation

perfectly matched layer in three dimensions for the time domain finite element method applied to radiation problems a new perfectly matched layer pml formulation for the time domain finite element method is described and tested for problems in three dimensional space an integral part of this pml algorithm is a novel time integration scheme based on galerkin s method with a piecewise linear temporal expansion of the electric field our time integration procedure is constructed by forming a linear combination of exact and trapezoidal integration applied to the temporal weak form which reduces to the well known newmark scheme in the case where the pml is not present this technique allows for a consistent time discretization of the electric field vector wave equation augmented with the pml which includes terms that involve the electric field itself time derivatives thereof and exponential functions temporally convolved with the electric field the auxiliary variables that are associated with such convolutions are efficiently updated in an explicit manner by matrix vector products the new pml formulation is successfully tested on canonical problems the pml can very efficiently absorb propagating electromagnetic waves which is demonstrated by reflections coefficients as low as 100 db the pml formulation is capable of giving highly accurate results for very broad frequency bands which is confirmed by tests that show an error smaller than 2 over more than six octaves in frequency finally we apply the pml formulation to a bow tie antenna and comparisons with measurements show good agreement

an overview of wavelet based multiresolution analyses in this paper an overview of wavelet based multiresolution analyses is presented first the continuous wavelet transform in its simplest form is discussed then the definition of a multiresolution analysis is given and how wavelets fit into it is shown the authors take a closer look at orthogonal biorthogonal and semiorthogonal wavelets the fast wavelet transform wavelets on an interval multidimensional wavelets and wavelet packets are discussed several examples of wavelet families are introduced and compared finally the essentials of two major applications are outlined data compression and compression of linear operators

a note on irregular discrete wavelet transforms estimates of frame bounds for wavelet frames generated by discrete sets in phase space satisfying only a certain density condition are deduced numerical examples show that these estimates which are the sharpest results of this kind known to the authors are rather poor compared to daubechies estimates see ibid vol 36 no 5 p 961 1005 1990 for the usual discrete wavelet transforms

modular algebras in geometric quantization presented here is a discussion on the connection between geometric quantization and algebraic quantization the former procedure relies on a construction of unitary irreducible representations that starts from co adjoint orbits and uses polarizations while the latter depends on the purely algebraic characterization of unitary irreducible representations which is based on central decompositions of von neumann algebras in involutive duality and their decompositions in terms of maximal abelian subalgebras intermediate stages of these two quantization methods turn out to be complementary leading thus to a new characterization of the so called discrete series representations

more on the analysis of local regularity through wavelets in this paper we want to extend the results of pointwise analysis through wavelet transforms to the class of functions where the local fluctuation is bounded by any submultiplicative function this generalizez the results obtained before in the well known case of holder regularity

functional calculus using wavelet transforms it is shown how the wavelet transform may be used to compute for a function s the symbol s a for any not necessarily self adjoint operator a whose spectrum is contained in the upper half plane for self adjoint operators it is shown that this functional calculus coincides with the usual one in particular it is shown how the exponential eita can be written in terms of the resolvent rz a z 1 of a as follows eita 1 c 0 da an 2 dbg at eitbrb ian a with c 2i 0 d i n 1g e and n n and the integral is understood as the cesaro limit this shows explicitly how the behavior for large t is determined by the behavior of rz at iz 1 t

wavelet frames and admissibility in higher dimensions this paper is concerned with the relations between discrete and continuous wavelet transforms on k dimensional euclidean space we start with the construction of continuous wavelet transforms with the help of square integrable representations of certain semidirect products thereby generalizing results of bernier and taylor we then turn to frames of l2 rk and to the question when the functions occurring in a given frame are admissible for a given continuous wavelet transform for certain frames we give a characterization which generalizes a result of daubechies to higher dimensions

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

a composite fourier wavelet transform and square integrable group representations a formula for a composite fourier wavelet transform is suggested from which the noncommutative fourier and wavelet transforms can be obtained as particular examples as well as several other fourier type transforms it is shown how this composite transform can be used to extend certain results originally obtained for square integrable group representations to more general measures arising in quantum probability theory

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

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

the affine uncertainty principle in one and two dimensions abstract in this paper we construct families of wavelets that minimize an uncertainty relation associated with square integrable representations of some canonical groups especially we obtain a new interpretation of the mexican hat function

image analysis and reconstruction using a wavelet transform constructed from a reducible representation of the euclidean motion group inspired by the early visual system of many mammalians we consider the construction of and reconstruction from an orientation score it u f mathbb r 2 times s 1 to mathbb c as a local orientation representation of an image f mathbb r 2 to mathbb r the mapping f mapsto it u f is a wavelet transform mathcal w psi corresponding to a reducible representation of the euclidean motion group onto mathbb l 2 mathbb r 2 and oriented wavelet psi in mathbb l 2 mathbb r 2 this wavelet transform is a special case of a recently developed generalization of the standard wavelet theory and has the practical advantage over the usual wavelet approaches in image analysis constructed by irreducible representations of the similitude group that it allows a stable reconstruction from one single scale orientation score since our wavelet transform is a unitary mapping with stable inverse we directly relate operations on orientation scores to operations on images in a robust manner furthermore by geometrical examination of the euclidean motion group g mathbb r 2 mathbb r times mathbb t which is the domain of our orientation scores we deduce that an operator on orientation scores must be left invariant to ensure that the corresponding operator mathcal w psi 1 phi mathcal w psi on images is euclidean invariant as an example we consider all linear second order left invariant evolutions on orientation scores corresponding to stochastic processes on g as an application we detect elongated structures in medical images and automatically close the gaps between them finally we consider robust orientation estimates by means of channel representations where we combine robust orientation estimation and learning of wavelets resulting in an auto associative processing of orientation features here linear averaging of the channel representation is equivalent to robust orientation estimation and an adaptation of the wavelet to the statistics of the considered image class leads to an auto associative behavior of the system

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

asymptotic wavelet and gabor analysis extraction of instantaneous frequencies the behavior of the continuous wavelet and gabor coefficients in the asymptotic limit using stationary phase approximations are investigated in particular it is shown how under some additional assumptions these coefficients allow the extraction of some characteristics of the analyzed signal such as frequency and amplitude modulation laws applications to spectral line estimations and matched filtering are briefly discussed

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

monomial cubature rules since stroud a compilation a bibliography of references to cubature rules which have appeared since the publication of stroud s book 1971 is presented the standard regions that are treated in this paper are the n cube the n simplex the n sphere and the entire space

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

finite element analysis of complex axisymmetric radiating structures a finite element method fem is developed for the analysis of complex axisymmetric radiating structures the method is based on the electric field formulation with the transverse field expanded in terms of edge based vector basis functions and the azimuth component expanded using nodal based scalar basis functions this mixed representation of the electric field eliminates spurious solutions and permits an easy treatment of boundary conditions on conducting surfaces as well as across material interfaces the fem mesh is truncated using a previously developed cylindrical perfectly matched layer pml the method has been successfully applied to three radiating structures a corrugated horn antenna a spherical luneburg lens and a half maxwell fish eye numerical results are presented to show the validity accuracy and efficiency of the method

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

non linear analysis of nearly saturated porous media theoretical and numerical formulation a formulation for a porous medium saturated with a compressible fluid undergoing large elastic and plastic deformations is presented a consistent thermodynamic formulation is proposed for the two phase mixture problem thus preserving a straightforward and robust numerical scheme a novel feature is the specification of the fluid compressibility in terms of a volumetric logarithmic strain which is energy conjugated to the fluid pressure in the entropy inequality as a result the entropy inequality is used to separate three different mechanisms representing the response effective stress response according to terzaghi in the solid skeleton fluid pressure response to compressibility of the fluid and dissipative darcy flow representing the interaction between the two phases the paper is concluded with a couple of numerical examples that display the predictive capabilities of the proposed formulation in particular we consider results for the kinematically linear theory as compared to the kinematically non linear theory

joint estimation of real squeezing and displacement we study the problem of joint estimation of real squeezing and amplitude of the radiation field deriving the measurement that maximizes the probability density of detecting the true value of the unknown parameters more generally we provide a solution for the problem of estimating the unknown unitary action of a nonunimodular group in the maximum likelihood approach remarkably in this case the optimal measurements do not coincide with the so called square root measurements in the case of squeezing and displacement we analyse in detail the sensitivity of estimation for coherent states and displaced squeezed states deriving the asymptotic relation between the uncertainties in the joint estimation and the corresponding uncertainties in the optimal separate measurements of squeezing and displacement a two mode set up is also analysed showing how entanglement between optical modes can be used to approximate perfect estimation

a calculation with a biorthogonal wavelet transformation the use of a biorthogonal basis for continuous wavelet transformations is explored thus relaxing the so called admissibility condition on the analyzing wavelet as an application the eigenvalues and corresponding radial eigenfunctions of the hamiltonian of relativistic hydrogen like atoms are determined

time frequency localization operators a geometric phase space approach the author defines a set of operators which localize in both time and frequency these operators are similar to but different from the low pass time limiting operator the singular functions of which are the prolate spheroidal wave functions the author s construction differs from the usual approach in that she treats the time frequency plane as one geometric whole phase space rather than as two separate spaces for disk shaped or ellipse shaped domains in time frequency plane the associated localization operators are remarkably simple their eigenfunctions are hermite functions and the corresponding eigenvalues are given by simple explicit formulas involving the incomplete gamma functions

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

perfectly matched layer for the time domain finite element method a new perfectly matched layer pml formulation for the time domain finite element method is described and tested for maxwell s equations in particular we focus on the time integration scheme which is based on galerkin s method with a temporally piecewise linear expansion of the electric field the time stepping scheme is constructed by forming a linear combination of exact and trapezoidal integration applied to the temporal weak form which reduces to the well known newmark scheme in the case without pml extensive numerical tests on scattering from infinitely long metal cylinders in two dimensions show good accuracy and no signs of instabilities for a circular cylinder the proposed scheme indicates the expected second order convergence toward the analytic solution and gives less than 2 root mean square error in the bistatic radar cross section rcs for resolutions with more than 10 points per wavelength an ogival cylinder which has sharp corners supporting field singularities shows similar accuracy in the monostatic rcs

numerical analysis of a pml model for time dependent maxwell s equations in this paper we study a perfectly matched layer model for the three dimensional time dependent maxwell s equations we develop both semi and fully discrete finite element methods for solving the truncated pml problem by nedelec edge elements optimal convergence rates are proved for both semi and fully discrete schemes to our knowledge this is the first error analysis obtained for time domain finite element method for pml models

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

evaluation of a spherical pml for vector fem applications the implementation and evaluation of a spherical perfectly matched layer pml within a cartesian finite element method context using standard curl conforming elements is presented in this paper results are compared to the long standing 1st order absorbing boundary condition abc and a new rigorous implementation of a 2nd order abc for curl conforming elements the 4 and 8 layer spherical pmls are shown to offer very attractive levels of absorption with reflections on the order of 60 to 70db demonstrated numerical tests show that the guidelines for cartesian pml absorbers in terms of maximum conductivity also carry over to the spherical pml the 2nd order abc is also shown to offer very good performance finally coding issues for both the spherical pml and the analytical abcs are briefly addressed

wigner based formulation of the chirplet transform using the wigner distribution we derive and analyze a matrix formulation for the chirplet transform a signal analysis tool that generalizes the wavelet and short time fourier transforms the formulation expresses the translations scalings and shears of the chirplet transform in terms of affine matrix transformations on the time frequency plane our approach leads naturally to several new signal transforms which we derive analyze and extend

an analysis of strong discontinuities in a saturated poro plastic solid we present in this paper an analysis of strong discontinuities in fully saturated porous media in the infinitesimal range in particular we describe the incorporation of the local effects of surfaces of discontinuity in the displacement field and thus the singular distributions of the associated strains from a local constitutive level to the large scale problem characterizing the quasi static equilibrium of the solid the characterization of the flow of the fluid through the porous space is accomplished in this context by means of a localized singular distribution of the fluid content that is involving a regular fluid mass distribution per unit volume and a fluid mass per unit area of the discontinuity surfaces in the small scale of the material this framework is shown to be consistent with a local continuum model of coupled poro plasticity with the localized fluid content arising from the dilatancy associated with the strong discontinuities more generally complete stress displacement fluid content relations are obtained along the discontinuities thus identifying the localized dissipative mechanisms characteristic of localized failures of porous materials the proposed framework also involves the coupled equation of conservation of fluid mass and seepage through the porous solid via darcy s law and considers a continuous pressure field with discontinuous gradients thus leading to discontinuous fluid flow vectors across the strong discontinuities all these developments are then examined in detail for the model problem of a saturated shear layer of a dilatant material enhanced finite element methods are developed in this framework for this particular problem the finite elements accommodate the different localized fields described above at the element level several representative numerical simulations are presented illustrating the performance of the proposed numerical methods copyright 1999 john wiley sons ltd

complete signal processing bases and the jacobi group the continuous windowed fourier and wavelet transforms are created from the actions of the heisenberg and affine groups respectively both wavelet and windowed fourier bases are known to be complete that is the only signal which is orthogonal to every element of each basis is the zero signal the jacobi group is a group which contains both the heisenberg and affine groups and it can also be used to produce bases for signal processing this paper investigates completeness for bases of one and two real variables which are produced by the jacobi group

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

remarks on resolutions of hilbert schmidt operators a generalization due to ali antoine and gazeau of the notion of square integrability of representations is used to construct operators as integrals over compact homogeneous spaces x g h it is shown that such operators are hilbert schmidt and a formula for the hilbert schmidt norm is given finally two examples are given demonstrating the dependence of the hilbert schmidt norm on the section x g used to construct it one example involving the three dimensional euclidean group makes interesting use of bessel coefficients

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

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

square integrable imprimitivity systems we give a definition of square integrability for imprimitivity systems and we prove that the square integrable ones share most of the properties of square integrable representations of groups

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

tight frames of compactly supported affine wavelets this paper extends the class of orthonormal bases of compactly supported wavelets recently constructed by daubechies commun pure appl math 41 909 1988 for each integer n 1 a family of wavelet functions having support 0 2n 1 is constructed such that jk x 2j 2 2jx k kj k z is a tight frame of l2 r i e for every f l2 r f c jk jk f jk for some c 0 this family is parametrized by an algebraic subset vn of r4n furthermore for n 2 a proper algebraic subset wn of vn is specified such that all points in vn outside of wn yield orthonormal bases the relationship between these tight frames and the theory of group representations and coherent states is discussed

on informational completeness of covariant localization observables and wigner coefficients an orthogonality theorem is obtained for square integrable representations on homogeneous spaces of a locally compact group from this a series of lemmas is derived showing the informational completeness of natural covariant localization operators as well as of the generalized wigner distributions matrix elements of the group some of these results give explicit reconstruction formulas for the quantum state from its expectation values against these families of operators the results are applied to special phase space representations of the heisenberg affine and galilei groups