implementation of a generalized exponential basis functions method for linear and non linear problems this is the accepted version of the following article mossaiby f ghaderian m rossi r implementation of a generalized exponential basis functions method for linear and non linear problems international journal for numerical methods in engineering on line jul 2015 which has been published in final form at http dx doi org 10 1002 nme 4985

an efficient 3 d infinite element for water wave diffraction problems an efficient and simple infinite element for modelling the far field potential of water wave diffraction problems is presented the shape functions in the radial direction comprise the first two terms of the asymptotic expansions of hankel functions the integrals with infinite limit for calculating the coefficient matrix have been worked out numerical tests on the diffraction by a surface piercing circular cylinder give surprisingly accurate resultant forces even if the infinite elements are placed very near to the cylinder other typical three dimensional examples also show that satisfactory results can be obtained by the use of this simple infinite element a computer program waload has been developed for computing the wave forces on fixed two and three dimensional bodies

double phase problems with variable growth abstract we consider a class of double phase variational integrals driven by nonhomogeneous potentials we study the associated euler equation and we highlight the existence of two different rayleigh quotients one of them is in relationship with the existence of an infinite interval of eigenvalues while the second one is associated with the nonexistence of eigenvalues the notion of eigenvalue is understood in the sense of pairs of nonlinear operators as introduced by fucik necas soucek and soucek the analysis developed in this paper extends the abstract framework corresponding to some standard cases associated to the p x laplace operator the generalized mean curvature operator or the capillarity differential operator with variable exponent the results contained in this paper complement the pioneering contributions of marcellini mingione et al in the field of variational integrals with unbalanced growth

a simplified analysis of plate structures using trefftz functions this paper presents a method for a quick evaluation of stresses and displacements in a plate structure for elastostatic problems first an approximation is built from the mathematical structure of the solutions for starshaped domains which is representative of long wavelength effects second a variational formulation consistent with this approximation is proposed finally two alternative procedures for coupling adjacent domains are demonstrated

a new boundary type finite element for 2 d and 3 d elastic structures in this paper we discuss the theoretical and numerical formulation of 3 d trefitz elements starting from the variational principle with the so called hybrid stress method the trial functions for the stresses have to fulfil the beltrami equations which means also the compatibility equations for the strains the divergence theorem can be applied and one arrives at a pure boundary formulation in the sense of the trefftz method besides the resulting variational formulation different regularizations of the interelement conditions are investigated by numerical tests two examples show the numerical efficiency of the derived elements first a geometric linear 3 d example is presented to show the effects on distorted element meshes the third example shows the geometrically non linear analysis of a shallow cylindrical shell segment under a singe load

automorphisms of compact kahler manifolds with slow dynamics we study the automorphisms of compact k ahler manifolds having slow dynamics by adapting gromov s classical argument we give an upper bound on the polynomial entropy and study its possible values in dimensions 2 and 3 we prove that every automorphism with sublinear derivative growth is an isometry a counter example is given in the c infty context answering negatively a question of artigue carrasco olivera and monteverde on polynomial entropy finally we classify minimal automorphisms in dimension 2 and prove they exist only on tori we conjecture that this is true for any dimension

dual hybrid trefftz element formulation based on independent boundary traction frame reference epfl article 102727view record in web of science record created on 2007 04 23 modified on 2016 08 08

applications of the direct trefftz boundary element method to the free vibration problem of a membrane in this paper the direct trefftz method is applied to solve the free vibration problem of a membrane in the direct trefftz method there exists no spurious eigenvalue however an ill posed nature of numerical instability encountered in the direct trefftz method requires some treatments the tikhonov s regularization method and generalized singular value decomposition method are used to deal with such an ill posed problem numerical results show the validity of the current approach

applications of the generalized singular value decomposition method on the eigenproblem using the incomplete boundary element formulation in this paper four incomplete boundary element formulations including the real part singular boundary element the real part hypersingular boundary element the imaginary part boundary element and the plane wave element methods are used to solve the free vibration problem among these incomplete boundary element formulations the real part singular and the hypersingular boundary elements are of the singular type and the other two are of the regular type when the incomplete formulation is used the spurious eigensolution may be encountered an auxiliary system whose boundary conditions are linearly independent of those of the original system is required in the proposed method in order to eliminate the spurious eigensolution a mathematical proof is given to show that the spurious eigensolution will appear in both the original and auxiliary systems as a result one can eliminate spurious eigensolution by means of the generalized singular value decomposition method in addition to the spurious eigensolution problem the regular boundary element formulation further suffers ill conditioned behaviors in the problem solver it is explained analytically using a circular domain why ill conditioned behaviors exist two main ill conditioned problems are the numerical instability of solution and the nonexistence of solution to solve the numerical instability of solution problem existing in these proposed regular formulations the tikhonov s regularization technique is used to improve the condition number of the leading coefficient matrix further the generalized singular value decomposition method is used to eliminate spurious eigensolutions numerical examples are given to verify the performance of these proposed methods and the results match the analytical values well

dual boundary element method simple error estimator and adaptivity this paper is concerned with the effective numerical implementation of the adaptive dual boundary element method dbem for two dimensional potential problems two boundary integral equations which are the potential and the flux equations are applied for collocation along regular and degenerate boundaries leading always to a single region analysis taking advantage on the use of non conforming parametric boundary elements the method introduces a simple error estimator based on the discontinuity of the solution across the boundaries between adjacent elements and implements the p h and mixed versions of the adaptive mesh refinement examples of several geometries which include degenerate boundaries are analyzed with this new formulation to solve regular and singular problems the accuracy and efficiency of the implementation described herein make this a reliable formulation of the adaptive dbem

existence and concentration of semiclassical ground state solutions for the generalized chern simons schrodinger system in h1 r2 abstract this paper is concerned with the following singularly perturbed problem in h 1 r 2 e 2 u v x u a 0 u x u j 1 2 a j 2 u x u f u e 1 a 2 u x 2 a 1 u x 1 2 u 2 1 a 1 u x 2 a 2 u x 0 e a 0 u 1 a 2 u 2 2 a 1 u 2 where e is a small parameter v c r 2 r and f c r r by using some new variational and analytic techniques joined with the manifold of pohozaev nehari type we prove that there exists a constant e 0 0 determined by v and f such that for e 0 e 0 the above problem admits a semiclassical ground state solution v e with exponential decay at infinity we also establish a new concentration behaviour of v e as e 0 in particular our results are available to the nonlinearity f u u s 2 u for s 4 6 which extend the existing results concerning the case f u u s 2 u for s 6

combined effects of singular and sublinear nonlinearities in some elliptic problems abstract we consider a parametric singular dirichlet equation with the singular term u appearing in the left hand side we establish the existence and nonexistence of positive solutions as the parameter 0 and the exponent 0 of the singularity vary in particular we show that for all 0 and all 1 the problem has no positive solution our approach combines truncation arguments with the method of upper and lower solutions

application of the trefftz method in plane elasticity problems direct and indirect approximations using sets of non singular complete trefftz functions i e the complete systems of solutions have been successfully applied to harmonic problems 1 in this paper the procedure is applied to a more complex situation plane elasticity problems the examples show that the present method can avoid the difficulties relating to singular integration and has good accuracy compared with traditional boundary elements

a new particular solution strategy for hyperbolic boundary value problems using hybrid trefftz displacement elements summary a new indirect approach to the problem of approximating the particular solution of non homogeneous hyperbolic boundary value problems is presented unlike the dual reciprocity method which constructs approximate particular solutions using radial basis functions polynomials or trigonometric functions the method reported here uses the homogeneous solutions of the problem obtained by discarding all time derivative terms from the governing equation nevertheless what typifies the present approach from a conceptual standpoint is the option of not using these trial functions exclusively for the approximation of the particular solution but to fully integrate them with the trefftz compliant homogeneous solution basis the particular solution trial basis is capable of significantly improving the trefftz solution even when the original equation is genuinely homogeneous an advantage that is lost if the basis is used exclusively for the recovery of the source terms similarly a sufficiently refined trefftz compliant basis is able to compensate for possible weaknesses of the particular solution approximation the method is implemented using the displacement model of the hybrid trefftz finite element method the functions used in the particular solution basis reduce most terms of the matrix of coefficients to boundary integral expressions and preserve the hermitian sparse and localized structure of the solving system that typifies hybrid trefftz formulations even when domain integrals are present they are generally easy to handle because the integrand presents no singularity copyright 2015 john wiley sons ltd

sur les groupes de transformations birationnelles des surfaces ni agissant par transformations bi rationnelles sur les surfaces complexes compactes kahl eriennes nous mon trons a que le groupe des transformations birationnelles d une surface satisfait l alternative de tits b que les actions birationnelles de groupes de kazhdan sur les surfaces sont toutes birationnellement conjugu eesa des actions homographiques sur le plan projectif et c que si f et g sont deux transformations birationnelles de surfaces qui commutent alors ou bien f pr eserve un pinceau de courbes ou bien l un des it er es g m de g m 0 concide avec un it er e f n de f n 2 z let s be any compact complex kahler surface and bir s the group of birational transformations of s we study the structure of nitely genera ted subgroups of bir s and prove three main results a bir s satises the tits alternative b if a group with kazhdan property t acts on a compact kahler surface by birational transformations then the action is conjugate to an action by linear projective transformations on the projec tive plane and c if f is an element of bir s which does not preserve any pencil of curves and if g commutes with f then a positive iterate of g coincides with an iterate of f the second statement provides a positive answer to zimmer s conjecture for birational actions on surfaces

hybrid trefftz finite element method for reissner plates on an elastic foundation abstract a modified variational principle for analysis of reissner plates on an elastic foundation prevented the foundation may be of winkler type or pasternak type a hybrid trefftz ht finite element fe model has been developed based on the principle and a new set of t complete functions several numerical examples are considered to assess the effectiveness of the proposed method

standing waves of nonlinear schrodinger equations with the gauge field abstract we study standing waves for nonlinear schrodinger equations with the gauge field some existence results of standing waves are established by applying variational methods to the functional which is obtained by representing the gauge field a in terms of complex scalar field we also show that there exists no standing wave for certain range of parameters by establishing a new inequality of sobolev type

a particular solution trefftz method for non linear poisson problems in heat and mass transfer this paper proposes a computational procedure based on the trefftz method for the solution of non linear poisson problems the problem is solved by finding an approximate particular solution to the poisson equation and using boundary collocation to solve the resulting laplace equation this method results in a global collocation and hence eliminates the need for discretization of the domain in both two and three dimensions the solution procedure proposed earlier in the literature based upon the above method has been reformulated for increased computational efficiency a quasi newton iteration method along with a new heuristic for source point location is used for efficient convergence of the numerical scheme the efficacy of the new formulation has been demonstrated for two classes of problems viz the thermal explosion problem and the diffusion reaction problem in a partially wetted catalyst pellet a brief error analysis of the method as well as future research directions is presented

application of symmetric indirect trefftz method to free vibration problems in 2d a symmetric indirect trefftz method is developed to solve the free vibration problem of a 2d membrane it is proved that in this approach the spurious eigensolution exists and an auxiliary matrix is constructed to help extraction of the spurious solution using the generalized singular value decomposition in addition to the spurious eigensolution this regular formulation suffers from its ill posed nature i e the numerical instability in order to deal with the numerical instability the tikhonov s regularization method in conjunction with the generalized singular value decomposition is suggested the proposed approach has some merits when compared with other regular boundary element formulations reported so far namely the capacity of representing eigenmodes and the ability to deal with a multiply connected domain of genus 1 several numerical examples are demonstrated to show the validity of the current approach copyright 2003 john wiley sons ltd

new bounding techniques for goal oriented error estimation applied to linear problems the paper deals with the accuracy of guaranteed error bounds on outputs of interest computed from approximate methods such as the finite element method a considerable improvement is introduced for linear problems thanks to new bounding techniques based on saint venant s principle the main breakthrough of these optimized bounding techniques is the use of properties of homothetic domains which enables to cleverly derive guaranteed and accurate boundings of contributions to the global error estimate over a local region of the domain performances of these techniques are illustrated through several numerical experiments

a fourth order compact scheme for the helmholtz equation alpha interpolation of fem and fdm stencils we propose a fourth order compact scheme on structured meshes for the helmholtz equation given by r f x 2 0 the scheme consists of taking the alpha interpolation of the galerkin finite element method and the classical central finite difference method in 1d this scheme is identical to the alpha interpolation method j comput appl math 1982 8 1 15 19 and in 2d making the choice 0 5 we recover the generalized fourth order compact pade approximation j comput phys 1995 119 252 270 comput meth appl mech engrg 1998 163 343 358 therein using the parameter 2 we follow siam rev 2000 42 3 451 484 comput meth appl mech engrg 1995 128 325 359 for the analysis of this scheme and its performance on square meshes is compared with that of the quasi stabilized fem comput meth appl mech engrg 1995 128 325 359 in particular we show that the relative phase error of the numerical solution and the local truncation error of this scheme for plane wave solutions diminish at the rate o l 4 where l represent the wavenumber and the mesh size respectively an expression for the parameter is given that minimizes the maximum relative phase error in a sense that will be explained in section 4 5 convergence studies of the error in the l2 norm the h1 semi norm and the l euclidean norm are done and the pollution effect is found to be small copyright 2010 john wiley sons ltd

normalized solutions for schrodinger poisson equations with general nonlinearities abstract in this paper we prove the existence of normalized solutions to the following schrodinger poisson equation u x 1 u 2 u f u u x r 3 r where f c r r satisfies more general conditions which cover the case f u u q 2 u with q 3 10 3 10 3 6 especially some new analytical techniques are presented to overcome the difficulties due to the presence of three terms in the corresponding energy functional which scale differently

the simplified hybrid combined methods for laplace s equation with singularities abstract in li and liang 1983 the simplified hybrid combined method is presented for combining the ritz galerkin method and the finite element method in this paper we will apply this method to solve singularity problems of laplace s equation error bounds and stability analyses will be provided while taking into account the integration approximation along the coupling boundary a significant coupling relation between the ritz galerkin and the finite element method has been found for the laplace equation with singularities an optimal rate of convergence has also been achieved numerical experiments have been carried out for solving the benchmark problem motz s problem to verify the theoretical results

trefftz method for kirchhoff plate bending problems kirchhoff plate bending problems were studied by both the trefftz direct and indirect approximations in which non singular complete trefftz functions are used as the weighting and or trial functions the trefftz direct method involved only the quantities of engineering interest numerical results are given to show the efficiency and the excellent accuracy of the present method

osculatory interpolation in the method of fundamental solution for nonlinear poisson problems abstract the method of fundamental solution also known as the f trefftz method or the singularity method is an efficient numerical method for the solution of laplace equation for both two and three dimensional problems in recent years the method has also been applied for the solution of poisson equations by finding the particular solution to the nonhomogeneous terms in general approximate particular solutions are constructed using the interpolation of the nonhomogeneous terms by the radial basis functions the method has been validated in recent papers this paper presents an improvement of the solution procedure for such problems the improvement is achieved by using radial basis functions called osculatory radial basis functions such functions make use of the normal gradient at boundary to obtain improved interpolation the efficacy of the method is demonstrated for some prototypical nonlinear poisson problems and for multiple poisson equations

resolution of three dimensional stokes fluid flows using a trefftz method a new method to solve three dimensional linear stokes problems is proposed in this paper it is shown that in using extended trefftz polynomials associated with an original weak formulation which is suited to these special functions it is possible to get a high precision at a reasonnable numerical coast three dimensional examples show the accuracy of the proposed approach which is then applied to domain optimization as for the free surface problem

boundary approximation methods for solving elliptic problems on unbounded domains abstract boundary approximation methods with partial solutions are presented for solving a complicated problem on an unbounded domain with both a crack singularity and a corner singularity also an analysis of partial solutions near the singular points is provided these methods are easy to apply have good stability properties and lead to highly accurate solutions hence boundary approximation methods with partial solutions are recommended for the treatment of elliptic problems on unbounded domains provided that piecewise solution expansions in particular asymptotic solutions near the singularities and infinity can be found

the hybrid trefftz finite element model and its application to plate bending this paper presents a new hybrid element approach and applies it to plate bending in contrast to more conventional models the formulation is based on displacement fields which fulfil a priori the non homogeneous lagrange equation trefftz method the interelement continuity is enforced by using a stationary principle together with an independent interelement displacement the final unknowns are the nodal displacements and the elements may be implemented without any difficulty in finite element libraries of standard finite element programs the formulation only calls for integration along the element boundaries which enables arbitrary polygonal or even curve sided elements to be generated where relevant known local solutions in the vicinity of a singularity or stress concentration may be used as an optional expansion basis to obtain for example particular singular corner elements elements presenting circular holes etc thus a high degree of accuracy may be achieved without a troublesome mesh refinement another important advantage of the formulation is the possibility of generating by a single element subroutine a large number of various elements triangles quadrilaterals etc presenting an increasing degree of accuracy the paper summarizes the results of numerical studies and shows the excellent accuracy and efficiency of the new elements the conclusions present some ideas concerning the adaptive version of the new elements extension to nonlinear problems and some other developments

integration free coons macroelements for the solution of 2d poisson problems large isoparametric macroelements with closed form cardinal global shape functions under the label coons patch macroelements cpm have been previously proposed and used in conjunction with the finite element method and the boundary element method this paper continues the research on the performance of cpm in conjunction with the collocation method in contrast to the previous cpm that was based on a galerkin ritz formulation no domain integration is now required a fact that justifies the name integration free coons macroelements therefore in addition to avoiding mesh generation and saving human effort the proposed technique has the additional advantage of further reducing the computer effort the theory is supported by five test cases concerning poisson and laplace problems within 2d smooth quadrilateral domains copyright 2008 john wiley sons ltd

periodic points for area preserving birational maps of surfaces it is a basic problem to count the number of periodic points of a surface mapping since the growth rate of this number as the period tends to infinity is an important dynamical invariant however this problem becomes difficult when the map admits curves of periodic points in this situation we give a precise estimate of the number of isolated periodic points for an area preserving birational map of a projective complex surface

the effective condition number applied to error analysis of certain boundary collocation methods abstract the boundary collocation method bcm is widely used in the engineering community for the numerical solution of linear boundary value problems it is commonly stated that the results computed by this method are affected by large rounding errors this conclusion is based on a simple worst case analysis using the conventional condition number for linear systems in this paper we present a refined error analysis for a class of boundary value problems using the concept of effectively well conditioned systems this analysis leads to much smaller a priori bounds for the rounding error in the computed bcm solution these smaller bounds imply that the numerically computed solution expresses much more accurately than previously supposed properties of the ideal bcm solution computed with infinite precision therefore the intrinsic properties of the bcm can be investigated through numerical computations to a far larger extent than previously supposed thus allowing for a numerical diagnostic investigation of the bcm for example when the bcm is applied to problems with certain geometries it is observed that the approximation does not converge using our new smaller error bounds we conclude that the lack of convergence of the bcm solution for these geometries is due to the bcm itself and not to rounding errors

least squares trefftz type elements for the helmholtz equation trefftz type elements or t elements are finite elements the internal field of which fulfills the governing differential equations of the problem a priori whereas the prescribed boundary conditions and the interelement continuity must be enforced by some suitable method in this paper the relevant matching is achieved by means of a least squares procedure the so called frameless or least squares t elements for helmholtz s equation related to the scattering of waves by offshore structures in 2 d are developed and studied the required accuracy of the solution can be obtained by increasing the number of either the subdomains or t functions which can be regarded as the h or p type approach respectively convergence studies are performed with much attention to the use of special purpose elements for a doubly connected domain with a circular hole and for an angular corner subdomain the most attractive features of the presented formulation are its simplicity and robustness the matrix of the resulting linear system is always hermitian and positive definite 1998 john wiley sons ltd

postbuckling analysis of thin plates by a hybrid trefftz finite element method abstract a hybrid trefftz finite element ht fe model for postbuckling analysis of thin plates is presented based on a modified variational principle with the aid of incremental form of equilibrium equations all non linear terms may be viewed as pseudo loads and then the in plane and out of plane equations can be uncoupled as a consequence the solution procedure for the postbuckling plate becomes very simple two numerical examples are considered to illustrate the correctness and accuracy of the proposed formulation

an asymmetric indirect trefftz method for solving free vibration problems in this paper a new asymmetric indirect trefftz method aitm has been developed to solve free vibration problems the proposed method is categorized into a regular type of boundary element methods bems such that no singular or hypersingular integration is necessary however like other regular bems the proposed approach encounters the numerical instability as the number of elements increases to deal with such an ill posed behavior tikhonov s regularization method in conjunction with the generalized singular value decomposition gsvd is adopted it is proved that the degeneracy of the proposed indirect trefftz method has the same mathematical structure as the direct trefftz method thus no special effort should be paid in programming besides such an equivalency indicates that the current method does not have spurious eigensolutions furthermore the proposed approach can easily treat a multiply connected domain of genus 1 as shown in fig 1 due to its indirect nature the present approach can also represent the mode shapes within its own mathematical formulations several numerical examples are given to show the validity of the proposed approach

an application of trefftz method to the sensitivity analysis of two dimensional potential problem this paper presents a new formulation for the sensitivity analysis with the help of the trefftz boundary type solution procedure direct differentiation of the expressions of the field variables leads to the expressions of the sensitivities since the field variables are approximated by linear combination of regular t complete functions the analytical expressions of the sensitivities are also regular sensitivity analysis schemes with respect to variations of dimensions of the object and boundary conditions are explained in detail two dimensional potential problems in the bounded region are considered as a numerical example in order to confirm its validity

trefftz method fitting boundary conditions the paper presents various ways of fitting the boundary conditions in the t complete functions method the authors point out the distinct advantages of the orthogonal collocation in comparison to the equidistant collocation and the integral fit the convergence of the collatz error measures and the conditioning of the solution matrices are investigated in detail

a trefftz approach to computational mechanics this paper presents a trefftz method for solving structural elasticity problems and flow problems of incompressible viscous fluids the problem of unilateral contact is also dealt with for each type of problem trefftz polynomials and associated variational formulations are given complex structures are studied by a sub structuring technique this method requires the resolution of a non symmetrical linear system it is shown that it is possible to take advantage of this trefftz approximation in two ways i the approach presented can be considered as a simplified method which enables a solution to be evaluated quickly ii this approach also makes it possible to obtain a good quality solution associated with high degree polynomial bases this method is adapted to optimization processes because the discretization of the structure requires only very few sub domains to build a good approximation and offers a great flexibility in use copyright 2003 john wiley sons ltd

on solving boundary value problems of modified helmholtz equations by plane wave functions plane wave functions e x w in r2 where 0 x x y w cos sin and x w x cos y sin are used as basis functions to solve boundary value problems of modified helmholtz equations u x 2u x 0 x u x h x x where is the laplace operator and a bounded and simply connected domain in r2 approximations of the exact solution of the above problem by plane wave functions are explicitly constructed for the case that is a disc and the order of approximations is derived a computational algorithm by collocation methods based on a simple singular decomposition of circular matrices is proposed and numerical examples are shown to demonstrate the efficiency of the methods

on the equivalence of the trefftz method and method of fundamental solutions for laplace and biharmonic equations in this paper it is proved that the two approaches known in the literature as the method of fundamental solutions mfs and the trefftz method are mathematically equivalent in spite of their essentially minor and apparent differences in formulation in deriving the equivalence of the trefftz method and the mfs for the laplace and biharmonic problems it is interesting to find that the complete set in the trefftz method for the laplace and biharmonic problems are embedded in the degenerate kernels of the mfs the degenerate scale appears using the mfs when the geometrical matrix is singular the occurring mechanism of the degenerate scale in the mfs is also studied by using circulant the comparison of accuracy and efficiency of the two methods was addressed

post critical set and non existence of preserved meromorphic 2 forms we present a family of birational transformations in cp2 depending on two or three parameters which do not generically preserve meromorphic 2 forms with the introduction of the orbit of the critical set vanishing condition of the jacobian also called the post critical set we get some new structures some non analytic 2 form which reduce to meromorphic 2 forms for particular subvarieties in the parameter space on these subvarieties the iterates of the critical set have a polynomial growth in the degrees of the parameters while one has an exponential growth out of these subspaces the analysis of our birational transformation in cp2 is first carried out using the diller favre criterion in order to find the complexity reduction of the mapping the integrable cases are found the identification between the complexity growth and the topological entropy is once again verified we perform plots of the post critical set as well as calculations of lyapunov exponents for many orbits confirming that generically no meromorphic 2 form can be preserved for this mapping these birational transformations in cp2 which generically do not preserve any meromorphic 2 form are extremely similar to other birational transformations we previously studied which do preserve meromorphic 2 forms we note that these two sets of birational transformations exhibit totally similar results as far as topological complexity is concerned but drastically different results as far as a more probabilistic approach of dynamical systems is concerned lyapunov exponents with these examples we see that the existence of a preserved meromorphic 2 form explains most of the numerical discrepancies between the topological and probabilistic approaches of dynamical systems

a nonconforming combination for solving elliptic problems with interfaces abstract nonconforming combinations are provided for solving interface problems of elliptic equations in these approaches the ritz galerkin method with particular solutions is used for the part of a solution domain where there are interface singular points and the conventional finite element method is used for the rest of the solution domain in addition admissible functions chosen are constrained to be continuous only at the element nodes on the common boundary of the subdomains error bounds are derived in the sobolev norms and numerical experiments are given for solving a model interface problem of the equation u u 0 moreover a significant coupling relation l 1 o ln h is found for interface problems by using the nonconforming combinations where l 1 is the total number of particular solutions used in the ritz galerkin method and h is the maximal boundary length of triangular elements in the finite element method

a combined method for solving elliptic problems on unbounded domains abstract a noncomforming combined method of the ritz galerkin and finite element methods is applied in solving unbounded domain problems of the equation u u 0 the ritz galerkin method is used in an exterior subdomain and the traditional finite element method is used in a bounded subdomain errors of numerical solutions have been derived in the sobolev norms and a significant coupling relation n 1 o ln h as h 0 is found where n 1 is the total number of asymptotic particula ritz galerkin method and h is the maximal boundary length of triangular elements used in the finite element method numerical experiments have been carried out for a model problem on unbounded domains by using the nonconforming combination and the coupling strategy 1 showing that only two or three terms i e n 1 2 or 3 of particular solutions near the infinity are in general cases required for good approximate solutions in engineering application

nodal standing waves for a gauged nonlinear schrodinger equation in r2 abstract this paper investigates the existence and asymptotic behavior of nodal solutions to the following gauged nonlinear schrodinger equation u u h 2 x x 2 x h s s u 2 s d s u u p 2 u x r 2 u x u x h 1 r 2 where 0 p 6 and h s 1 2 0 s r u 2 r d r is the so called chern simons term we prove that for any positive integer k the problem has a sign changing solution u k which changes sign exactly k times moreover the energy of u k is strictly increasing in k and for any sequence n n there exists a subsequence n s such that n s 1 p 2 u k n s converges in h 1 r 2 to w k as s where w k also changes sign exactly k times and solves the following equation u u u p 2 u u h 1 r 2

trefftz indirect methods for plane piezoelectricity in this paper a unified theory for the general solutions of three dimensional elasticity is employed to transform the governing equations of plane piezoelectricity into three generalized laplace equations the latter equations are uncoupled and can be pursued separately by introducing three generalized complex variables the complete solution sets for plane piezoelectricity are constructed by adopting the constituents in the solution sets as the trial functions the trefftz collocation and the trefftz galerkin methods are formulated both methods fall into the category of trefftz indirect methods as the coefficients of their trial functions are non physical numerical examples are presented to illustrate the efficacy of the formulations copyright 2005 john wiley sons ltd

a regularized xfem model for the transition from continuous to discontinuous displacements this work focuses on the modelling through the extended finite element method of structural problems characterized by discontinuous displacement as a model problem an elastic isotropic domain characterized by a displacement discontinuity across a surface is studied a regularization of the displacement field is introduced depending on a scalar parameter the regularized solution is defined in a layer the emerging strain and stress fields are independently modelled using specific constitutive assumptions in particular it is shown that the mechanical work spent within the regularization layer can be interpreted as an interface work provided that a spring like constitutive law is adopted the accuracy of the integration procedures adopted for the stiffness matrix is assessed as highly non linear terms appear standard gauss quadrature is compared with adaptive quadrature and with a new technique based on an equivalent polynomial approach one and two dimensional results are reported for varying discretization size regularization parameter and constitutive parameters copyright 2007 john wiley sons ltd

a systematic construction of b bar functions for linear and non linear mixed enhanced finite elements for plane elasticity problems in a previous paper a modified hu washizu variational formulation has been used to derive an accurate four node plane strain stress finite element denoted qe2 for the mixed element qe2 two enhanced strain terms are used and the assumed stresses satisfy the equilibrium equations a priori for the linear elastic case in this paper an alternative approach is discussed the new formulation leads to the same accuracy for linear elastic problems as the qe2 element however it turns out to be more efficient in numerical simulations especially for large deformation problems using orthogonal stress and strain functions we derive b functions which avoid numerical inversion of matrices the b strain matrix is sparse and has the same structure as the strain matrix b obtained from a compatible displacement field the implementation of the derived mixed element is basically the same as the one for a compatible displacement element the only difference is that we have to compute a b strain matrix instead of the standard b matrix accordingly existing subroutines for a compatible displacement element can be easily changed to obtain the mixed enhanced finite element which yields a higher accuracy than the q4 and qm6 elements copyright 1999 john wiley sons ltd

generalized finite element analysis with t complete boundary solution functions the use of a complete and nonsingular set of trefftz functions in the solution of quasi harmonic equations is demonstrated and shown to be often superior to the more conventional singularity distribution in boundary type approximation procedures for coupling separate domains of such solution and indeed of deriving equivalent finite elements are demonstrated

symetries birationnelles des surfaces feuilletees we provide a classification of complex projective surfaces with a holomorphic foliation whose group of birational symetries is infinite

trefftz solutions for piezoelectricity by lekhnitskii s formalism and boundary collocation method in this paper a solution procedure for plane piezoelectricity is developed by trefftz boundary collocation method starting with the general plane piezoelectricity solution derived by lekhnitskii s formalism the basic sets of trefftz functions which satisfy the homogeneous governing equations are derived moreover special sets of trefftz functions are derived for impermeable elliptical voids impermeable sharp cracks and permeable sharp cracks with arbitrary orientations with respect to the material poling direction the functions in the special sets satisfy not only the homogeneous governing equations but also the boundary conditions at the peripheries of the pertinent defects by adopting trefftz functions as the trial functions multi domain trefftz boundary collocation method is formulated numerical examples are presented to illustrate the efficacy of the formulation copyright 2005 john wiley sons ltd

foliations invariant by rational maps we give a classification of pairs mathcal f phi where mathcal f is a holomorphic foliation on a projective surface and phi is a non invertible dominant rational map preserving mathcal f

comments on vibration analysis of arbitrary shaped membranes using non dimensional dynamic influence function in reference 1 the authors presented the so called non dimensional dynamic in uence function method for membrane vibration a regular formulation and singularity free method were obtained also a symmetry and meshless formulation can be achieved the auxiliary system is a complementary solution instead of fundamental function it is source free in the in uence function many successful examples of the dirichlet types were demonstrated it seems that this method is very attractive however this method can be treated as one kind of the tre tz method 2 4 based on the dual formulation developed by chen and hong 5 6 the in uence function is nothing but the imaginary part of the fundamental solution s x ih 1 0 kr 7 the method by kang et al 1 can be treated as a special case of the imaginary part dual bem also the real part dual bem was developed and many references can be referred 8 9 mrm formulation can also be viewed as a real part formulation and its occurrence of spurious eigenvalues have been found in references 10 15 it is well known that the real part imaginary part formulations and multiple reciprocity method all result in spurious eigensolutions particularly the imaginary part formulation also results in an ill posed problem since the condition number for the in uence matrix is very large many approaches have been employed to lter out the spurious solutions and extract the true solution for example residue method 11 12 singular value decomposition svd technique 9 13 15 generalized singular value decomposition gsvd technique 16 and domain partition technique 17 it is expected that the kang s method has the problems of spurious solutions and ill conditioned behavior since it is an imaginary part formulation however no such information was addressed some points will be discussed as follows 1 spurious eigensolution it is interesting to nd that all the examples in reference 1 are of the dirichlet type according to the theoretical derivation the neumann problem has the problems of spurious solutions using the imaginary part formulation we will prove that in the following as mentioned earlier spurious eigenvalues occur in the real part of mrm formulation 9 11 12 also the imaginary part bem results in spurious solutions 7 here we will derive the true and spurious solutions in the discrete system analytically for a circular domain by using the non dimensional in uence function method 1 and the imaginary part dual bem 7 in a uni ed way the degenerate kernels and circulants are employed to study the discrete system in an exact form the relation between the non dimensional in uence function method and the imaginary part dual bem is also addressed and is summarized in table 1 the symbols in table 1 follow the dual model of chen and hong 6

nonlinear analysis of thick plates on an elastic foundation by ht fe with p extension capabilities the paper is concerned with the development of hybrid trefftz ht p element for nonlinear analysis of reissner mindlin plates resting on an elastic foundation the foundation may be of winkler type or pasternak type exact solutions of the lame navier equations are used for the in plane intraelement displacement field and an incremental form of the basic equations is adopted with the aid of incremental form of these equations all nonlinear terms may be taken as pseudo loads moreover some modifications have been made on the nonlinear boundary equations to simplify the ensuing derivation as a result the in plane and out of plane equations are uncoupled and then the derivation for the ht finite element fe formulation becomes very simple the practical efficiency of the new element model has been assessed through several examples

hybrid trefftz plane elasticity elements with p method capabilities a family of p method plane elasticity elements is derived based on the hybrid trefftz formulation 1 exact solutions of the lame navier equations are used for the intra element displacement field together with an independent displacement frame function field along the element boundary the final unknowns are the parameters of the frame function field consisting of the usual degrees of freedom at corner nodes and an optional number of hierarchic degrees of freedom associated with the mid side nodes since the element matrices do not involve integration over the element area the elements have a polygonal contour with an optional number of curved sides the quadrilateral element has the same external appearance as the conventional p method plane elasticity element 2 3 but unlike in the conventional p method approach suitable special purpose trefftz functions are generally used to handle the singularity and or stress concentration problems rather than a local mesh refinement the practical efficiency of the new elements is assessed through a series of examples

how to detect the integrability of discrete systems several integrability tests for discrete equations will be reviewed all tests considered can be applied directly to a given discrete equation and do not rely on the a priori knowledge of the existence of related structures such as lax pairs specifically singularity confinement algebraic entropy nevanlinna theory diophantine integrability and discrete systems over finite fields will be described

hybrid trefftz displacement element for spectral analysis of bounded and unbounded media the hybrid trefftz displacement element is applied to the elastodynamic analysis of bounded and unbounded media in the frequency domain the displacements are approximated in the domain of the element using local solutions of the wave equation the neumann conditions are enforced directly and the surface forces are approximated on the dirichlet and inter element boundaries of the finite element mesh two alternative elements are developed to model unbounded media namely a finite element with absorbing boundaries and an unbounded element that satisfies explicitly the sommerfeld condition the finite element equations are derived from the fundamental relations of elastodynamics written in the frequency domain the numerical implementation of these equations is discussed and numerical tests are presented to assess the performance of the formulation

rational surfaces with a large group of automorphisms we classify rational surfaces for which the image of the automorphisms group in the group of linear transformations of the picard group is the largest possible this answers a question raised by arthur coble in 1928 and can be rephrased in terms of periodic orbits of a birational action of an infinite coxeter group on ordered point sets in the projective plane modulo projective equivalence we also outline the classification of non rational surfaces with large automorphism groups

the discontinuous enrichment method we propose a finite element based discretization method in which the standard polynomial field is enriched within each element by a nonconforming field that is added to it the enrichment contains free space solutions of the homogeneous differential equation that are not represented by the underlying polynomial field continuity of the enrichment across element interfaces is enforced weakly by lagrange multipliers in this manner we expect to attain high coarse mesh accuracy without significant degradation of conditioning assuring good performance of the computation at any mesh resolution examples of application to acoustics and advection diffusion are presented

standing waves of the schrodinger equation coupled with the chern simons gauge field we prove the existence of infinitely many radially symmetric standing wave solutions of the chern simons schrodinger system our result is established by applying the mountain pass theorem to the functional which is obtained by representing gauge fields a in terms of a scalar field

nonlinear elliptic equations with variable exponent old and new abstract in this survey paper by using variational methods we are concerned with the qualitative analysis of solutions to nonlinear elliptic problems of the type div a x u u q x 2 u in u 0 on where is a bounded or an exterior domain of r n and q is a continuous positive function the results presented in this paper extend several contributions concerning the lane emden equation and we focus on new phenomena which are due to the presence of variable exponents

superconvergence of coupling techniques in combined methods for elliptic equations with singularities abstract several coupling techniques such as the nonconforming constraints penalty and hybrid integrals of the ritz galerkin and finite difference methods are presented for solving elliptic boundary value problems with singularities based on suitable norms involving discrete solutions at specific points superconvergence rates on solution derivatives are exploited by using five combinations e g the nonconforming combination the penalty combination combinations i and ii and symmetric combination for quasi uniform rectangular grids the superconvergence rates o h 2 of solution derivatives by all five combinations can be achieved where h is the maximal mesh length of difference grids used in the finite difference method and 0 is an arbitrarily small number superconvergence analysis in this paper lies in estimates on error bounds caused by the coupling techniques and their incorporation with finite difference methods therefore a similar analysis and conclusions may be extended to linear finite element methods using triangulation by referring to existing references moreover the five combinations having o h 2 of solution derivatives are well suited to solving engineering problems with multiple singularities and multiple interfaces

a family of quadrilateral hybrid trefftz p elements for thick plate analysis abstract this paper presents a family of quadrilateral hybrid trefftz ht p elements based on reissner mindlin theory of moderately thick plates as compared with existing higher order ht thick plate elements j petrolito which make use of an incomplete set of polynomial homogeneous solutions for the internal displacement and rotation fields and of an auxiliary conforming frame field involving independently interpolated boundary distributions of displacements and rotations the new elements differ essentially with respect to the following two points 1 a t complete set of homogeneous solutions including polynomial and nonpolynomial functions has been derived and used to represent the intraelement displacement and rotations fields 2 the displacement component of the auxiliary frame field has been linked with the tangential component of the rotation so as to satisfy a particular constraint derived from equilibrium considerations the practical efficiency of these modifications has been assessed through a series of numerical examples which have shown that the new p elements are robust more accurate in terms of the number of unknowns and of the computational effort and that they do not lock in the thin limit

infinitesimal deformations of rational surface automorphisms if x is a rational surface without nonzero holomorphic vector field and f is an automorphism of x we study in several examples the zariski tangent space of the local deformation space of the pair x f

boundary methods c complete systems for stokes problems a boundary method for solving stokes problem is presented this is based on the use of systems of solutions of the homogeneous equations which are complete a convenient criterion for the completeness of such systems is the notion of c completeness an apparently new representation of solutions of stokes equations is derived and is used to develop a procedure for constructing a c complete system examples of such systems are constructed

solution of helmholtz equation by trefftz method the application of the trefftz method for calculating wave forces on offshore structures is presented indirect and direct formulations using complete and non singular systems of trefftz functions for the helmholtz equation are posed in this paper an effective technique using different interpolation functions for the velocity potential and wave force are suggested to improve the computational accuracy of the wave force the numerical examples show that the present method is highly efficient and accurate