a linear conceptual subsurface storm flow model a zero dimensional lumped linear conceptual model of the subsurface storm flow from hillslopes has been developed by integrating over the length of the hillslope the linearized one dimensional dupuit forchheimer approximation discharge relationship for saturated flow over an inclined plane the derived two term storage function accounts for gravity and gradient driven flow coupled with the storage balance equation for the plane the model allows direct analytical computation of the outflow hydrograph at the foot of the hill in response to an infiltration step input the model is the conceptual counterpart of the linear advection diffusion lad flow equation derived from the extended boussinesq equation through linearization in contrast to the kinematic wave approximation the outflows normalized by their equilibrium values are properly given as functions of the infiltration rate the outflow hydrographs computed by the conceptual lad model approximate nonlinear behavior closely over a wide range of conditions encountered in field applications

linear theory of subsurface storm flow a solution to the subsurface storm flow problem is developed through linearization of the complete one dimensional governing equation water surface profiles and outflow hydrographs obtained from this approximate theory are compared with the exact solution and with the kinematic approximation to this problem for a number of cases characterized by the parameter 4 i cos k sin2 the accuracy and range of applicability of the proposed theory are greater than that of the kinematic theory its results may be considered satisfactory for the cases with 1 however the kinematic theory is a preferable substitute for 0 25

on discontinuous galerkin methods discontinuous galerkin methods have received considerable attention in recent years for problems in which advection and diffusion terms are present several alternatives for treating the diffusion and advective fluxes have been introduced this report summarizes some of the methods that have been proposed several numerical examples are included in the paper these present discontinuous galerkin solutions of one dimensional problems with a scalar variable results are presented for diffusion reaction problems and advection diffusion problems we discuss the performance of various formulations with respect to accuracy as well as stability of the method copyright 2003 john wiley sons ltd

fast bem fem mortar coupling for acoustic structure interaction a coupling algorithm based on lagrange multipliers is proposed for the simulation of structure acoustic field interaction finite plate elements are coupled to a galerkin boundary element formulation of the acoustic domain the interface pressure is interpolated as a lagrange multiplier thus allowing the coupling of non matching grids the resulting saddle point problem is solved by an approximate uzawa type scheme in which the matrix vector products of the boundary element operators are evaluated efficiently by the fast multipole boundary element method the algorithm is demonstrated on the example of a cavity backed elastic panel

a new bem fem coupling strategy for two dimensional fluid solid interaction problems we present a numerical method to solve a fluid solid interaction problem posed in the plane in this scheme we use a finite element method to approximate the solid vibrations and the near wave field the far field effects are taken into account by means of boundary integral equations posed on an artificial interface that contains the obstacle the boundary unknown involved in our formulation is approximated by a spectral method we obtain a fully discrete galerkin procedure whose main advantage is the simplicity of the quadratures used to approximate the weakly singular boundary integrals we provide numerical results that illustrate the accuracy of our method and the stability of the algorithm used to solve the linear systems of equations that arise from this discretization technique

discontinuous galerkin finite element method for the wave equation the symmetric interior penalty discontinuous galerkin finite element method is presented for the numerical discretization of the second order wave equation the resulting stiffness matrix is symmetric positive definite and the mass matrix is essentially diagonal hence the method is inherently parallel and leads to fully explicit time integration when coupled with an explicit time stepping scheme optimal a priori error bounds are derived in the energy norm and the l 2 norm for the semidiscrete formulation in particular the error in the energy norm is shown to converge with the optimal order cal o h min s ell with respect to the mesh size h the polynomial degree ell and the regularity exponent s of the continuous solution under additional regularity assumptions the l 2 error is shown to converge with the optimal order cal o h min s ell numerical results confirm the expected convergence rates and illustrate the versatility of the method

discontinuous galerkin methods for the helmholtz equation with large wave number this paper develops and analyzes some interior penalty discontinuous galerkin ipdg methods using piecewise linear polynomials for the helmholtz equation with the first order absorbing boundary condition in two and three dimensions it is proved that the proposed discontinuous galerkin methods are stable hence well posed without any mesh constraint for each fixed wave number k optimal order with respect to h error estimate in the broken h 1 norm and suboptimal order estimate in the l 2 norm are derived without any mesh constraint the latter estimate improves to optimal order when the mesh size h is restricted to the preasymptotic regime i e k 2 h gtrsim 1 numerical experiments are also presented to gauge the theoretical result and to numerically examine the pollution effect with respect to k in the error bounds the novelties of the proposed ipdg methods include the following first the methods penalize not only the jumps of the function values across the element edges but also the jumps of the normal and tangential derivatives second the penalty parameters are taken as complex numbers of positive imaginary parts so essentially and practically no constraint is imposed on the penalty parameters since the helmholtz problem is a non hermitian and indefinite linear problem as expected the crucial and the most difficult part of the whole analysis is to establish the stability estimates i e a priori estimates for the numerical solutions to this end the cruxes of our analysis are to establish and to make use of a local version of the rellich identity for the laplacian and to mimic the stability analysis for the pde solutions given in p cummings analysis of finite element based numerical methods for acoustic waves elastic waves and fluid solid interactions in the frequency domain ph d thesis the university of tennessee knoxville tn 2001 p cummings and x feng math models methods appl sci 16 2006 pp 139 160 u hetmaniuk commun math sci 5 2007 pp 665 678

wavenumber explicit convergence analysis for galerkin discretizations of the helmholtz equation we develop a stability and convergence theory for a class of highly indefinite elliptic boundary value problems bvps by considering the helmholtz equation at high wavenumber k as our model problem the key element in this theory is a novel k explicit regularity theory for helmholtz bvps that is based on decomposing the solution into two parts the first part has the sobolev regularity properties expected of second order elliptic pdes but features k independent regularity constants the second part is an analytic function for which k explicit bounds for all derivatives are given this decomposition is worked out in detail for several types of bvps namely the helmholtz equation in bounded smooth domains or convex polygonal domains with robin boundary conditions and in exterior domains with dirichlet boundary conditions we present an error analysis for the classical hp version of the finite element method hp fem where the dependence on the mesh width h the approximation order p and the wavenumber k is given explicitly in particular under the assumption that the solution operator for helmholtz problems is polynomially bounded in k it is shown that quasi optimality is obtained under the conditions that kh p is sufficiently small and the polynomial degree p is at least o log k

a class of discontinuous petrov galerkin methods part iv the optimal test norm and time harmonic wave propagation in 1d the phase error or the pollution effect in the finite element solution of wave propagation problems is a well known phenomenon that must be confronted when solving problems in the high frequency range this paper presents a new method with no phase errors for one dimensional 1d time harmonic wave propagation problems using new ideas that hold promise for the multidimensional case the method is constructed within the framework of the discontinuous petrov galerkin dpg method with optimal test functions we have previously shown that such methods select solutions that are the best possible approximations in an energy norm dual to any selected test space norm in this paper we advance by asking what is the optimal test space norm that achieves error reduction in a given energy norm this is answered in the specific case of the helmholtz equation with l 2 norm as the energy norm we obtain uniform stability with respect to the wave number we illustrate the method with a number of 1d numerical experiments using discontinuous piecewise polynomial hp spaces for the trial space and its corresponding optimal test functions computed approximately and locally a 1d theoretical stability analysis is also developed

three dimensional finite element calculations in acoustic scattering using arbitrarily shaped convex artificial boundaries we report on a generalization of the bayliss gunzburger turkel non reflecting boundary conditions to arbitrarily shaped convex artificial boundaries for elongated scatterers such as submarines we show that this generalization can improve significantly the computational efficiency of finite element methods applied to the solution of three dimensional acoustic scattering problems copyright 2001 john wiley sons ltd

efficient dg like formulation equipped with curved boundary edges for solving elasto acoustic scattering problems summary a discontinuous galerkin dg based approach is proposed for computing the scattered field from an elastic bounded object immersed in an infinite homogeneous fluid medium the proposed method possesses two distinctive features first it employs higher order polynomial shape functions needed to address the high frequency propagation regime second it is equipped with curved boundary edges to provide an accurate representation of the fluid structure interface the most salient benefits resulting from the latter feature as demonstrated by the numerical investigation are the following i an improvement by at least two orders of magnitude on the relative error and ii the disappearance of spurious resonance frequencies in the surrounding fluid medium in addition the reported numerical results reveal that when using cubic polynomials with less than three elements per wavelength the proposed dg method computes the scattered field with a relative error below 1 for an elastic scatterer of about 30 wavelengths this observation highlights the potential of the proposed solution methodology for efficiently solving mid frequency to high frequency elasto acoustic scattering problems copyright 2014 john wiley sons ltd

a discontinuous enrichment method for three dimensional multiscale harmonic wave propagation problems in multi fluid and fluid solid media an evanescent wave occurs when a propagating incident wave impinges on an interface between two fluid solid or fluid solid media at a subcritical angle mathematical properties of such a wave make it difficult to capture with standard finite element discretization schemes for this reason the discontinuous enrichment method dem developed in comput methods appl mech eng 2001 190 6455 6479 comput methods appl mech eng 2003 192 1389 1419 comput methods appl mech eng 2003 192 3195 3210 int j numer meth engng 2004 61 1938 1956 wave motion 2004 39 4 307 317 int j numer meth engng 2006 66 2086 2114 int j numer meth engng 2006 66 796 815 is extended here to the solution of a class of three dimensional evanescent wave problems in the frequency domain to this effect new dem elements for three dimensional elastodynamic problems are first proposed then these and other dem elements previously developed for the efficient solution of the helmholtz problem are further enriched with free space solutions of model evanescent wave problems in order to achieve high accuracy at practical mesh resolution for fluid fluid and fluid solid applications the performance of the extended dem elements is reported to be better than that of its basic helmholtz and navier counterparts and superior to that achieved by the classical high order polynomial finite element method copyright 2008 john wiley sons ltd

a least squares method for the helmholtz equation abstract we investigate the use of least squares methods to approximate the helmholtz equation the basis used in the discrete method consists of solutions of the helmholtz equation either consisting of plane waves or bessel functions on each element of a finite element grid unlike previous methods of this type we do not use polynomial based finite elements the use of small elements and relatively few basis functions per element allows us to prove convergence theorems for the method and to some extent control the conditioning of the resulting linear sy stem numerical results show the efficiency of the new method and suggest that it may be possible to obtain accurate results with a coarser grid than is usual for standard finite element methods

a discontinuous finite element formulation for helmholtz equation abstract a discontinuous finite element formulation for helmholtz problems is presented with c 0 continuity across inter element boundaries enforced in a weak sense depending on two parameters and whose choice is crucial for the performance of the proposed method these parameters are chosen through one dimension numerical experiments aiming at minimizing the pollution error optimal values of these parameters are then adopted in more general situations the accuracy and stability of the proposed formulation for linear and bilinear shape functions are demonstrated in several numerical examples in one and two dimensions

an ultra weak method for acoustic fluid solid interaction we introduce the ultra weak variational formulation uwvf for fluid solid vibration problems in particular we consider the scattering of time harmonic acoustic pressure waves from solid elastic objects the problem is modeled using a coupled system of the helmholtz and navier equations the transmission conditions on the fluid solid interface are represented in an impedance type form after which we can employ the well known ultra weak formulations for the helmholtz and navier equations the uwvf approximation for both equations is computed using a superposition of propagating plane waves a condition number based criterion is used to define the plane wave basis dimension for each element as a model problem we investigate the scattering of sound from an infinite elastic cylinder immersed in a fluid a comparison of the uwvf approximation with the analytical solution shows that the method provides a means for solving wave problems on relatively coarse meshes however particular care is needed when the method is used for problems at frequencies near the resonance frequencies of the fluid solid system

absolutely stable local discontinuous galerkin methods for the helmholtz equation with large wave number two local discontinuous galerkin ldg methods using some non standard numerical uxes are developed for the helmholtz equation with the rst order absorbing boundary condition in the high frequency regime it is shown that the proposed ldg methods are absolutely stable hence well posed with respect to both the wave number and the mesh size optimal order with respect to the mesh size error estimates are proved for all wave numbers in the preasymptotic regime to analyze the proposed ldg methods they are recasted and treated as non conforming mixed nite element methods the crux of the analysis is to establish a generalized inf sup condition which holds without any mesh constraint for each ldg method the generalized inf sup conditions then easily infer the desired absolute stability of the proposed ldg methods in return the stability results not only guarantee the well posedness of the ldg methods but also play a crucial role in the derivation of the error estimates numerical experiments which conrm the theoretical results and compare the proposed two ldg methods are also presented in the paper

generalized 3 d constellation design for spatial modulation spatial modulation sm conveys information bits by utilizing both the antenna index and complex symbols to form a 3 d constellation similar to 2 d modulation the structure of 3 d constellation could greatly affect the transmission reliability in this paper a generalized 3 d constellation design is proposed to optimize the constellation diagram used for each antenna i e to optimize the complex symbols and their total number for each antenna and finally to enhance the transmission reliability the optimal design method with exhaustive search algorithm may cause prohibitive computational complexity especially when the cardinality of 3 d constellation is large to overcome this issue a recursive design algorithm is proposed with a computational complexity increasing polynomially with the cardinality of 3 d constellation extensions of the proposed methods to the sm constellation design for massive multiple input multiple output transmission generalized spatial modulation gsm constellation design and the sm constellation design with transmit antenna correlation are also discussed simulations are done to validate those theoretical analysis and results show that the proposed 3 d constellation design is a generalized design scheme and can be adopted in any sm gsm systems without constraints on the number of transceiver antennas it is also shown that the proposed approach offers better symbol error rate performance than other solutions

an iterative substructuring method for coupled fluid solid acoustic problems a fast parallel iterative method is proposed for the solution of linear equations arising from finite element discretization of the time harmonic coupled fluid solid systems in fluid pressure and solid displacement formulation the fluid and the solid domains are decomposed into nonoverlapping subdomains continuity of the solution is enforced by lagrange multipliers the system is augmented by duplicating the degrees of freedom on the wet interface the original degrees of freedom are then eliminated and the resulting system is solved by iterations preconditioned by a coarse space correction in each iteration the method requires the solution of one independent local acoustic problem per subdomain and the solution of a global problem with several degrees of freedom per subdomain computational results show that the method is scalable with the problem size frequency and the number of subdomains the method generalizes the feti h method for the helmholtz equation to coupled fluid elastic scattering the number of iterations is about same as for the feti h method for the related helmholtz problem with neumann boundary condition instead of an elastic scatterer if enough coarse space functions are used convergence behavior is explained from the spectrum of the iteration operator and from numerical near decoupling of the equations in the fluid and in the solid regions

application of an ultra weak variational formulation of elliptic pdes to the two dimensional helmholtz problem a new technique to solve elliptic linear pdes called ultra weak variational formulation uwvf in this paper is introduced in b despres c r acad sci paris 318 1994 pp 939 944 this paper is devoted to an evaluation of the potentialities of this technique it is applied to a model wave problem the two dimensional helmholtz problem the new method is presented in three parts following the same style of presentation as the classical one of the finite elements method even though they are definitely conceptually different methods the first part is committed to the variational formulation and to the continuous problem the second part defines the discretization process using a galerkin procedure the third part actually studies the efficiency of the technique from the order of convergence point of view this is achieved using theoretical proofs and a series of numerical experiments in particular it is proven and shown the order of convergence is lower bounded by a linear function of the number of degrees of freedom an application to scattering problems is presented in a fourth part

fluid solid interaction acoustic scattering by a smooth elastic obstacle a bounded three dimensional elastic obstacle is surrounded by an unbounded inviscid compressible fluid acoustic waves are scattered by the obstacle the problem is to find the scattered waves and the response of the obstacle this problem is formulated mathematically existence and uniqueness theorems are proved various systems of boundary integral equations over the interface between the fluid and the solid are derived and analysed these systems include a system obtained by a straightforward direct method and a smaller system for a single vector field

numerical modelling of elastic wave scattering in frequency domain by the partition of unity finite element method in this paper we investigate a numerical approach based on the partition of unity finite element method for the time harmonic elastic wave equations the aim of the proposed work is to accurately model two dimensional elastic wave problems with fewer elements capable of containing many wavelengths per nodal spacing and without refining the mesh at each frequency the approximation of the displacement field is performed via the standard finite element shape functions enriched by superimposing pressure and shear plane wave basis which incorporate knowledge of the wave propagation a variational framework able to handle mixed boundary conditions is described numerical examples dealing with the radiation and the scattering of elastic waves by a circular body are presented the results show the performance of the proposed method in both accuracy and efficiency copyright 2008 john wiley sons ltd

hybrid finite analytic solution of lateral subsurface flow a hybrid finite analytic method a numerical technique was used to solve lateral subsurface storm flow described by the extended dupuit forchheimer equation in subregions the local linearized one dimensional dupuit forchheimer equation was solved analytically in space and discretized in time by a simple difference formula this is called a hybrid finite analytic approach the system of algebraic equations obtained by the hybrid finite analytic approach can approximately preserve the overall nonlinear effect because the term h x 2 and the coefficient of diffusion are treated as constants only in the local regions a four point numerical formula can provide results that are stable and acceptably accurate without complex calculation and without small time steps the comparison between steady state profiles of the water table provided by this study with profiles provided by previous investigations shows that the method performs very well in the analysis of lateral subsurface storm flow

the discontinuous enrichment method for multiscale analysis computation naturally separates scales of a problem according to the mesh size a variety of improved numerical methods are described by multiscale considerations differing in the treatment of the unresolved fine scales the discontinuous enrichment method provides a unique multiscale approach to computation by employing fine scales that contain solutions of the homogeneous partial differential equation in a discontinuous framework the method thus combines relative ease of implementation with improved numerical performance these properties are demonstrated for both multiscale wave and transport problems pointing to the potential of considerable savings in computational resources

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

a hybridized discontinuous petrov galerkin scheme for scalar conservation laws summary we present a hybridized discontinuous petrov galerkin hdpg method for the numerical solution of steady and time dependent scalar conservation laws the method combines a hybridization technique with a local petrov galerkin approach in which the test functions are computed to maximize the inf sup condition since the petrov galerkin approach does not guarantee a conservative solution we propose to enforce this explicitly by introducing a constraint into the local petrov galerkin problem when the resulting nonlinear system is solved using the newton raphson procedure the solution inside each element can be locally condensed to yield a global linear system involving only the degrees of freedom of the numerical trace this results in a significant reduction in memory storage and computation time for the solution of the matrix system albeit at the cost of solving the local petrov galerkin problems however these local problems are independent of each other and thus perfectly scalable we present several numerical examples to assess the performance of the proposed method the results show that the hdpg method outperforms the hybridizable discontinuous galerkin method for problems involving discontinuities moreover for the test case proposed by peterson the hdpg method provides optimal convergence of order k 1 copyright 2012 john wiley sons ltd

overview of the discontinuous enrichment method the ultra weak variational formulation and the partition of unity method for acoustic scattering in the medium frequency regime and performance comparisons

a trefftz based numerical modelling framework for helmholtz problems with complex multiple scatterer configurations the aim of the work presented in this paper is the numerical solution of low and mid frequency time harmonic acoustic multiple scattering problem a novel so called multi level modelling approach is proposed which is applicable to the study of a configuration of well separated obstacles of arbitrary shape on which any type of acoustic boundary condition can be applied the generic character of the method is obtained by embedding the superposition principle for the multiple scattering influence in a state of the art acoustic modelling technique the so called wave based method the resulting approach successfully alleviates the geometrical limitations of the underlying trefftz based method and preserves the method s computational efficiency resulting in a generic multiple scattering modelling framework with a superior computational efficiency in the low as well as the mid frequency range several numerical validation examples show that the proposed approach is as accurate as the classical single scattering wave based method and illustrate the computational efficiency as compared to boundary element methods

plane wave discontinuous galerkin methods for the 2d helmholtz equation analysis of the p version plane wave discontinuous galerkin pwdg methods are a class of trefftz type methods for the spatial discretization of boundary value problems for the helmholtz operator delta omega 2 omega 0 they include the so called ultra weak variational formulation from o cessenat and b despres siam j numer anal 35 1998 pp 255 299 this paper is concerned with the a priori convergence analysis of pwdg in the case of p refinement that is the study of the asymptotic behavior of relevant error norms as the number of plane wave directions in the local trial spaces is increased for convex domains in two space dimensions we derive convergence rates employing mesh skeleton based norms duality techniques from p monk and d wang comput methods appl mech engrg 175 1999 pp 121 136 and plane wave approximation theory

on the existence and the uniqueness of the solution of a fluid structure interaction scattering problem the existence and uniqueness of the solution of a fluid structure interaction problem is investigated the proposed analysis distinguishes itself from previous studies by employing a weighted sobolev space framework the dtn operator properties and the fredholm theory the proposed approach allows to extend the range of validity of the standard existence and uniqueness results to the case where the elastic scatterer is assumed to be only lipschitz continuous which is of more practical interest

a discontinuous finite element method at element level for helmholtz equation abstract a discontinuous finite element formulation is presented for helmholtz equation continuity is relaxed locally in the interior of the element instead of across the element edges the interior shape functions can be viewed as discontinuous bubbles and the corresponding degrees of freedom can be eliminated at element level by static condensation yielding a global matrix topologically equivalent to those of classical c0 finite element approximations the discontinuous bubbles are introduced to consistently add stability to the formulation preserving the optimal rates of convergence and improving accuracy a crucial point of the discontinuous formulation relies on the choice of the stabilization parameters related to the weak enforcement of continuity inside each element explicit values of these stabilization parameters minimizing the pollution effect are presented for uniform meshes the accuracy and stability of the proposed formulation for bilinear shape functions are demonstrated in several numerical examples