reverse inequalities in μ deformed segal bargmann analysis we prove reverse hypercontractivity inequalities as well as reverse log sobolev inequalities in the context of a space of holomorphic functions which is called the deformed segal bargmann space and arises in the works of wigner rosenblum and marron to achieve this we define deformations of energy and entropy our principle results generalize earlier works of carlen and sontz we also show that the semigroup of this theory is lp bounded and we conjecture that it is lp contractive and even more strongly that it is hypercontractive

bases for some reciprocity algebras ii abstract we construct bases for the stable branching algebras for the symmetric pairs gl n o n o n m o n o m and sp 2 n gl n

infinite boundary elements for dynamic problems of 3 d half space in this paper a new procedure for solving 3 d dynamic problems of unbounded foundations in the frequency domain by using bem is studied for simulations of wave propagations due to far field effects a type of infinite boundary element ibem is presented for modelling a 3 d regular or irregular half space the wave type considered could be compressional shear or a combination of the two through the analysis of the asymptotic behaviour of 3 d fundamental solutions for elasto dynamics a rather feasible technique for obtaining singular integral coefficients for dynamic problems has been developed through the analysis of the dynamic response for a 3 d square foundation under a uniform load distribution excellent accuracy has been achieved in agreement with previous numerical solutions another example analysis of the dynamic compliance of a rigid square plate on a half space has also shown very good results the development of this infinite boundary element provides a powerful tool for dealing with 3 d structure foundation interaction or wave propagation problems for irregular foundations such as arch dam canyons

an effective method for solving the hyper singular integral equations in 3 d acoustics the application of the boundary integral methods to the problem of acoustics exterior to a three dimensional surface suffers in general from the nonexistence of nonuniqueness of its solutions at frequencies that are characteristic of the associated interior problem the formulation that is most suitable for numerical implementation still appears to be that proposed by burton and miller proc r soc london ser a 323 201 210 1971 however the hypersingular kernels present in such a formulation render it computationally unattractive previous attempts to regularize such hypersingular kernels involved the use of double surface integrals or implicit use of tangential operators or closed form evaluations of hypersingular integrals the method of double surface integrals is computationally highly inefficient even though it allows higher order interpolation schemes on the surface the other two approaches are more conducive to the assumption of a constant value for each of the variables pressure a

dynamic response of lined tunnels by an isoparametric boundary element method abstract this work investigates the dynamic stress concentration in the lining of a circular cylindrical tunnel excavated in a linear elastic or viscoelastic medium of infinite extent under conditions of plane strain the dynamic load consists of planar waves of a general transient nature the numerical method employed is the boundary element method formulated in the laplace transformed domain a numerical inverse transformation is used to bring the results obtained by the boundary element method back to the time domain isoparametric boundary elements are utilized in the discretization of the surfaces of the problem the results obtained are in very good agreement with known analytic solutions while they compare favorably with other numerical solutions the method is quite general and can be used for cylindrical tunnels of arbitrary cross section

the 3 d elastodynamic boundary element method semi analytical integration for linear isoparametric triangular elements a semi analytical integration scheme is described in this paper which is designed to reduce the errors incurred when integrals with singular integrands are evaluated numerically this new scheme can be applied to linear triangular elements for use in steady state elastodynamic bem problems and is particularly useful for predicting displacement to high accuracy close to surfaces for a spectrum of frequencies the scheme involves the application of taylor expansions to formulate the integrals into two parts one part is regular and is evaluated numerically and the other part is singular but sufficiently simple to enable its transforma tion into a line integral the line integral is solved numerically using gauss legendre quadrature this approach caters for all the integral types that appear in steady state elastodynamic boundary elements but in particular no special treatment is required for the evaluation of the cauchy principal value singular integrals numerical tests are performed on a simple test problem for which a known analytical solution exists the results obtained using the semi analytical approach are shown to be considerably more accurate than those obtained using standard quadrature methods copyright 1999 john wiley sons ltd

a 2 5d coupled fe be methodology for the dynamic interaction between longitudinally invariant structures and a layered halfspace abstract this paper presents a general 2 5d coupled finite element boundary element methodology for the computation of the dynamic interaction between a layered soil and structures with a longitudinally invariant geometry such as railway tracks roads tunnels dams and pipelines the classical 2 5d finite element method is combined with a novel 2 5d boundary element method a regularized 2 5d boundary integral equation is derived that avoids the evaluation of singular traction integrals the 2 5d green s functions of a layered halfspace computed with the direct stiffness method are used in a boundary element method formulation this avoids meshing of the free surface and the layer interfaces with boundary elements and effectively reduces the computational efforts and storage requirements the proposed technique is applied to four examples a road on the surface of a halfspace a tunnel embedded in a layered halfspace a dike on a halfspace and a vibration isolating screen in the soil

entropy and the segal bargmann transform the segal bargmann transform a is a unitary isomorphism of the quantum mechanical configuration space l2 rn onto the segal bargmann or phase space hl2 cn of entire functions square integrable with respect to here and are gaussian measures and for z cn and measurable f rn caf z rn d t f t exp z2 2 z t if the integral converges af is defined for all f lp rn if 1 1 q 2 which implies p q and in this case a p q 1 q 2 p q 2 1 q 2 n 2q where p is the dual of p moreover a calculation with test functions shows that a p q if q 2 or p 1 q 2 cp q is given explicitly as a function of p and q and s

symmetric galerkin boundary integral formulation for interface and multi zone problems domains containing an internal boundary such as a bi material interface arise in many applications e g composite materials and geophysical simulations this paper presents a symmetric galerkin boundary integral method for this important class of problems in this situation the physical quantities are known to satisfy continuity conditions across the interface but no boundary conditions are specied the algorithm described herein achieves a symmetric matrix of reduced size moreover the symmetry can also be invoked to lessen the numerical work involved in constructing the system of equations and thus the method is computationally very ecient a prototype numerical example with several variations in the boundary conditions and material properties is employed to validate the formulation and corresponding numerical procedure the boundary element results are compared with analytical solutions and with numerical results obtained with the nite element method 1997 by john wiley sons ltd

on complex hypercontractivity abstract we give a new proof of a hypercontractivity theorem for the mehler transform with a complex parameter earlier proved by weissler 1979 j funct anal 32 102 121 and epperson 1989 j funct anal 87 1 30 the proof uses stochastic integrals and ito calculus the method also yields new proofs of some related results

a general regularization of the hypersingular integrals in the symmetric galerkin boundary element method the symmetric galerkin boundary element method is used to solve boundary value problems by keeping the symmetric nature of the matrix obtained after discretization the matrix elements are obtained from a double integral involving the double derivative of green s operator which is highly singular the paper presents a regularization of the hypersingular integrals which depend only on the properties of green s tensor the method is presented in the case of laplace s operator with an example of application the case of elasticity is finally addressed theoretically showing an easy extension to any case of anisotropy

a simple proof of wehrl s conjecture on entropy based on the hypercontractivity of the free harmonic oscillator hamiltonian and the canonical commutation relation we present a simple proof of wehrl s conjecture on the shannon entropy of phase space probability densities in the fock bargmann representation

strong hypercontractivity and strong logarithmic sobolev inequalities for log subharmonic functions on stratified lie groups abstract on a stratified lie group g equipped with hypoelliptic heat kernel measure we study the behavior of the dilation semigroup on l p spaces of log subharmonic functions we consider a notion of strong hypercontractivity and a strong logarithmic sobolev inequality and show that these properties are equivalent for any group g moreover if g satisfies a classical logarithmic sobolev inequality then both properties hold this extends similar results obtained by graczyk kemp and loeb in the euclidean setting

the numerical evaluation of hadamard finite part integrals a quadrature rule is described for the numerical evaluation of hadamard finite part integrals with a double pole singularity within the range of integration the rule is based upon the observation that such an integral is the derivative of a cauchy principal value integral

coupling bem with fem by a direct computation of the boundary stiffness matrix the boundary stiffness matrix characterizing in a discretized form the response of the boundary to given dirichlet boundary conditions allows the coupling between bem and fem the paper presents an approach based on the direct computation of the stiffness matrix from the potential function related to a given dirichlet boundary condition the method produces a symmetric stiffness matrix as for the singular galerkin boundary element method but does not need to compute hypersingular integrals in addition the method uses only the nodal values of the boundary potential but does not need discretized values of the normal gradient at the boundary as for usual boundary element methods which reduces the number of matrices to be constructed the regularization of the integrals is achieved by means used for simply singular integrals introduced for the collocation boundary element method an example of application is produced in the case of the solution of laplace equation within a plane domain

efficient analytical integration of symmetric galerkin boundary integrals over curved elements thermal conduction formulation abstract substantial improvements are reported in the computational efficiency of galerkin boundary element analysis bea employing curved continuous boundary elements a direct analytical treatment of the singular double integrations involved in galerkin bea adapting a limit to the boundary concept used successfully in collocation bea is used to obviate significant computation in the determination of the galerkin coefficient matrices symbolic manipulation has been strategically employed to aid in the analytical evaluation of the singular contributions to these double integrals the analytical regularization procedure separates the potentially singular galerkin integrands into an essentially singular but simple part plus a regular remainder that can be integrated numerically the finite contribution from the simplified singular term is then computed analytically it is shown that the key to containing the explosive growth in the length of the formulae associated with such a hybrid analytical numerical integration scheme is the strategic timing of when to take the limit to the boundary this regularization also isolates the contribution from the curvature of the boundary element thus facilitating enhanced computational efficiency in problems with many straight elements example problems are presented to quantify the performance of this approach it is concluded that with these techniques galerkin symmetric bea can be more efficient than its collocation based counterpart

elastic scatterer interaction via generalized born series and far field approximations methods for solving elastic wave scattering problems in three dimensions 3d with multiple inhomogeneities are discussed a problem of homogeneous isotropic elastic defects in an otherwise homogeneous isotropic elastic full space is formulated as a boundary integral equation this equation is solved by discretizing the surface of each scatterer in a fashion known as the boundary element method the resulting matrix equation may be solved in a fully implicit manner but an implicit iterative method is more efficient with this hybrid method a portion of the nonsingular integral operator is expanded in a neumann series terms in this series correspond physically to nth order born approximations of the scatterers interaction the relative advantage of this hybrid scheme depends on the number of iterations required except for closely situated strong scatterers terms beyond the first few orders are not significant and thus the method can be quite advantageous when the separation is large another appro

non singular boundary integral formulations for plane interior potential problems in this article a non singular formulation of the boundary integral equation is developed to solve smooth and non smooth interior potential problems in two dimensions the subtracting and adding back technique is used toregularize the singularity of green s function and to simplify the calculation of the normal derivative of green s function after that a global numerical integration is directly applied at the boundary and those integration points are also taken as collocation points to simplify the algorithm of computation the result indicates that this simple method gives the convergence speed of order n 3 in the smooth boundary cases for both dirichlet and mix type problems for the non smooth cases the convergence speed drops at o n 1 2 for the dirichlet problems

strong hypercontractivity and relative subharmonicity abstract a hermitian metric g on a complex manifold m together with a smooth probability measure on m determine minimal and maximal dirichlet forms q d and q max given by q f m g grad f z grad f z d z q d is the form closure of q on c c m and q max is the form closure of q on c 1 b m the corresponding operators a d and a max generate semigroups having standard hypercontractivity properties in the scale of l p spaces p 1 when the corresponding form q satisfies a logarithmic sobolev inequality it was shown by the author 1999 acta math 182 159 206 that the semigroup e ta d has even stronger hypercontractivity properties when restricted to certain holomorphic subspaces of l p these results are extended here to a max when m g is not complete it is necessary that the elliptic differential operator a max degenerate on the boundary of m a second proof of these strong hypercontractive inequalities for both a d and a max is given which depends on an extension of the submean value property of subharmonic functions the riemann surface for z 1 n and the weighted bergman spaces in the unit disc are given as examples

a unified boundary element method for the analysis of sound and shell like structure interactions i formulation and verification a unified boundary element method bem is developed in this paper to model both the exterior acoustic field and the elastic shell like structure in a coupled analysis the conventional boundary integral equation bie for three dimensional 3d elastodynamics is applied to thin shell like structures which can have arbitrary shapes and small thicknesses the nearly singular integrals existing in the bie when applied to thin bodies are transformed to nonsingular line integrals and are evaluated accurately and efficiently for the exterior 3d acoustic domain the burton and miller composite bie formulation is employed to overcome the fictitious eigenfrequency difficulty fed and the thin shape breakdown tsb conforming c0 quadratic elements are employed in the discretization of the two sets of bies the developed bie formulations are valid for both radiation and scattering problems and for all wave numbers numerical examples using spherical and cylindrical shells including nonuniform thickness and nond

the contractivity of the free hamiltonian semigroup in the lp space of entire functions abstract a semigroup of operators t t t 0 generated by the number operator in the complex wave representation is given by t t z e t z for any entire function on c n the problem is to find all possible r p 1 such that t t hlr cn dgn cn dgn is contractive or bounded it turns out that t t hlr cn dgn cn dgn is contractive if and only if p 1 re2t and is unbounded if and only if p re2t furthermore all maximizers are identified they are constant functions if p 1 re2t and exponential functions if p re2t t 0

a fast and high order method for the three dimensional elastic wave scattering problem in this paper we present a fast and high order boundary integral equation method for the elastic scattering by three dimensional large penetrable obstacles the algorithm extends the method introduced in 5 for the acoustic surface scattering to the fully elastic case in our algorithm high order accuracy is achieved through the use of the partition of unity and a semi classical treatment of relevant singular integrals the computational efficiency associated with the nonsingular integrals is attained by the method of equivalent source representations on a cartesian grid and fast fourier transform fft the resulting algorithm computes one matrix vector product associated with the discretization of the integral equation with o n 4 3 log n operations and it shows algebraic convergence several numerical experiments are provided to demonstrate the efficiency of the method

dynamic stress concentration studies by boundary integrals and laplace transform the dynamic stress field and its concentrations around holes of arbitrary shape in infinitely extended bodies under plane stress or plane strain conditions are numerically determined the material may be linear elastic or viscoelastic while the dynamic load consists of plane compressional waves of harmonic or general transient nature the method consists of applying the laplace transform with respect to time to the governing equations of motion and formulating and solving the problem numerically in the transfomed domain by the boundary integral equation method the stress field can then be obtaind by a numerical inversion of the trasformed solution the correspondence principle is invoked for the case of viscoelastic material behavious the method is simplified for the case of harmonic waves where no numerical inversion is involved

on the treatment of corners in the boundary element method abstract a new technique for treating surface discontinuities within boundary element calculations is proposed multiple nodes are used to represent the geometry and the necessary additional equations are obtained by differentiating the usual boundary element integral equation in deriving expressions for the resulting singular integrals it is found that constraints must be placed on the functional approximation at the discontinuity an algorithm for incorporating these constraints is developed and numerical tests for an exactly solvable three dimensional laplace equation problem are presented

acoustic scattering by a modified werner method a modified integral werner method is used to calculate pressure scattered by an axisymmetric body immersed in a perfect and compressible fluid subject to a harmonic acoustic field this integral representation is built as the sum of a potential of a simple layer and a potential of volume it is equivalent to the exterior helmholtz problem with neumann boundary condition for all real wave numbers of the incident acoustic field for elastic structure scattering problems the modified werner method is coupled with an elastodynamic integral formulation in order to account for the elastic contribution of the displacement field at the fluid structure interface the resulting system of integral equations is solved by the collocation method with a quadratic interpolation the introduction of a weighting factor in the modified werner method decreases the number of volume elements necessary for a good convergence of results this approach becomes very competitive when it is compared with other integral methods that are valid for all wave numbers a numerical comparison with an experiment on a tungsten carbide end capped cylinder allows a glimpse of the interesting possibilities for using the coupling of the modified werner method and the integral elastodynamic equation used in this research

scattering of elastic waves from thin shapes in three dimensions using the composite boundary integral equation formulation in this paper the composite boundary integral equation bie formulation is applied to scattering of elastic waves from thin shapes with small but finite thickness open cracks or thin voids thin inclusions thin layer interfaces etc which are modeled with two surfaces this composite bie formulation which is an extension of the burton and miller s formulation for acoustic waves uses a linear combination of the conventional bie and the hypersingular bie for thin shapes the conventional bie as well as the hypersingular bie will degenerate or nearly degenerate if they are applied individually on the two surfaces the composite bie formulation however will not degenerate for such problems as demonstrated in this paper nearly singular and hypersingular integrals which arise in problems involving thin shapes modeled with two surfaces are transformed into sums of weakly singular integrals and nonsingular line integrals thus no finer mesh is needed to compute these nearly singular integrals

corner treatment by assigning dual tractions to every node for elastodynamics in td bem in this study a corner treatment on the boundary for time domain boundary element method td bem by assigning dual tractions to every node is proposed the proposed corner treatment on boundary mimics the real mechanical situation on the physical boundary for elastodynamic problem and the computation accuracy is good taking the rectangular boundary as an example the numerical implementation of the proposed corner treatment on boundary by assigning dual tractions to every node is demonstrated two verification examples one dimensional rod in finite medium and two dimensional circular cavity in infinite medium under dynamic loads are conducted in which the results from the td bem based on the proposed corner treatment on boundary are compared with the results from the analytical solutions good agreement between the analytical results and the td bem results based on the proposed corner treatment on boundary for td bem is achieved for the two verification examples

evaluation of 2 d green s boundary formula and its normal derivative using legendre polynomials with an application to acoustic scattering problems this paper presents the non singular forms in a global sense of two dimensional green s boundary formula and its normal derivative the main advantage of the modified formulations is that they are amenable to solution by directly applying standard quadrature formulas over the entire integration domain that is the proposed element free method requires only nodal data the approach includes expressing the unknown function as a truncated fourier legendre series together with transforming the integration interval a b to 1 1 the series coefficients are thus to be determined the hypersingular integral interpreted in the hadamard finite part sense and some weakly singular integrals can be evaluated analytically the remaining integrals are regular with the limiting values of the integrands defined explicitly when a source point coincides with a field point the effectiveness of the modified formulations is examined by an elliptic cylinder subject to prescribed boundary conditions the regularization is further applied to acoustic scattering problems the well known burton miller method using a linear combination of the surface helmholtz integral equation and its normal derivative is adopted to overcome the non uniqueness problem a general non singular form of the composite equation is derived comparisons with analytical solutions for acoustically soft and hard circular cylinders are made copyright 2001 john wiley sons ltd

some efficient boundary integral strategies for time harmonic wave problems in an elastic halfspace abstract when boundary integral equation boundary element methods bie bems are used for halfspace problems such as occur frequently in elastodynamics the fullspace stokes fundamental solution or halfspace lamb fundamental solution can be used to formulate the bie both stokes and lamb approaches have advantages and disadvantages this paper presents systematic strategies based on the bem for 3d halfspace elastodynamic problems wherein the best features of formulations based on the stokes and the lamb solutions are exploited strategies are illustrated and numerical results are given for point sources and radiation from a spherical void in a halfspace

nystrom method for elastic wave scattering by three dimensional obstacles nystrom method is developed to solve for boundary integral equations bie s for elastic wave scattering by three dimensional obstacles to generate the matrix equation from a bie nystrom method applies a quadrature rule to the integrations of smooth integrands over a discretized element directly and chooses the values of the unknown function at quadrature points as the system s unknowns to be solved this leads to a simple procedure to form the off diagonal entries of matrix by simply evaluating the integrands without numerical integrations for the diagonal or near diagonal entries corresponding to the integrals over a singular or near singular element where the kernels are singular or near singular we develop a systematic singularity treatment technique known as the local correction scheme based on the linear approximation of elements the scheme differs from the singularity regularization or subtraction technique used in the boundary element method bem it applies the series expansion of scalar green s function to the kernels and derives analytical solutions for the strongly singular integrals under the cauchy principal value like cpv like sense since the approach avoids the need for reformulating the bie for singularity removal in bem and solves for the somigliana s equation directly it is easy to implement and efficient in calculation numerical examples are used to demonstrate its robustness

stress analysis of an unbounded elastic solid with orthotropic inclusions and voids using a new integral equation technique a recently developed numerical method based on a volume integral formulation is applied to calculate the elastostatic field in an unbounded isotropic elastic medium containing orthotropic inclusions subject to remote loading a modified form of the method in which the integral equations involve volumes of the inclusions and boundaries of voids or cracks is used to deal with the presence of both types of inhomogeneity a detailed analysis of displacement and stress fields is carried out for orthotropic cylindrical and elliptic cylindrical inclusions as well as voids the accuracy and effectiveness of the new methods are examined through comparison with results obtained from analytical and boundary integral equation methods

a method for direct evaluation of singular integral in direct boundary element method a new method is presented for evaluating the cauchy principal value integral and the free term in the three dimensional elastic boundary element method this method expresses the singular integral as the sum of a weakly singular integral and an integrable cauchy principal value integral the former can be computed by means of the usual standard gaussian quadrature after a transformation suggested by lachat and watson 10 who correctly limited its use only to weakly singular integral the latter can be calculated by direct integration in the cauchy principal value sense this paper also points out some limitations in the use of triangle polar co ordinate suggested by li et al 11 and later extended by zhang and xu 16 the general expression of the free term for a boundary point with arbitrary characteristic surface is also presented simple numerical examples which verify the efficiency and accuracy of the present method are given

computation of thermal stresses in quasistatic non stationary thermoelasticity using boundary elements in this paper we present the boundary integral formulation for the solution of quasi static problems of two dimensional uncoupled thermoelasticity a detailed scheme for the numerical solution of the boundary integral equations and computation of internal stresses by regularized integral representation is developed in time formulation the method is tested in a numerical example

some integral identities and inequalities for entire functions and their application to the coherent state transform let be an entire function on cn and for any h 0 and r 0 define fr z r e 2 z 2h let d h denote h n times lebesgue measure on cn frs2 2 d h n sh frsd h from this and a logarithmic sobolev inequality we easily deduce qnq fr q pnp fr p for all 0 p q t8 where the lp norms are taken with respect to the measure d h above we apply these results to the study of the spaces ap consisting of all entire functions satisfying z pe 2 z 2h d h obtaining sharp bounds for some associated operators and proving denseness of analytic polynomials in ap for 1 p we then apply our results to the coherent state transform extending and simplifying some previously known results

tangential derivative of singular boundary integrals with respect to the position of collocation points this paper investigates the evaluation of the sensitivity with respect to tangential perturbations of the singular point of boundary integrals having either weak or strong singularity both scalar potential and elastic problems are considered a proper definition of the derivative of a strongly singular integral with respect to singular point perturbations should accommodate the concomitant perturbation of the vanishing exclusion neighbourhood involved in the limiting process used in the definition of the integral itself this is done here by esorting to a shape sensitivity approach considering a particular class of infinitesimal domain perturbations that move individual points and especially the singular point but leave the initial domain globally unchanged this somewhat indirect strategy provides a proper mathematical setting for the analysis moreover the resulting sensitivity expressions apply to arbitrary potential type integrals with densities only subjected to some regularity requirements at the singular point and thus are applicable to approximate as well as exact bem solutions quite remarkable is the fact that the analysis is applicable when the singular point is located on an edge and simply continuous elements are used the hypersingular bie residual function is found to be equal to the derivative of the strongly singular bie residual when the same values of the boundary variables are substituted in both sbie and hbie formulations with interesting consequences for some error indicator computation strategies 1998 john wiley sons ltd

three dimensional crack analysis using singular boundary elements a multi domain method of solving three dimensional elastic crack problems in an infinite elastic body using the boundary element method is proposed the displacement and traction behaviours near a crack front are incorporated in special crack elements the elimination of singularities arising from the term combined with kelvin s kernel for displacement in the integrals is discussed in detail stress intensity factors of modes i ii and iii are obtained directly from crack front nodal values without any extrapolation as in some other methods no differentiation of conventional boundary integral equations with kelvin s tensor kernels is necessary in the current approach this method is applicable to cracks of arbitrary shape infinite bodies are modelled precisely as such not approximated as large finite bodies numerical solutions of stress intensity factors are given for several problems involving a penny shaped crack

a galerkin symmetric boundary element method in elasticity formulation and implementation a symmetric boundary element method based on a weighted residual galerkin approach for elastoplastic analysis is revisited and its computer implementation for two dimensional homogeneous problems is described

degenerate principal series representations of gln c and gln r let f be the field c or r for 1 k n 2 let pk be the maximal parabolic subgroup of gln f with its levi factor isomorphic to gln k f glk f in this paper we explicitly calculate the action of the enveloping algebra of gln f on the degenerate principal series representations induced from characters of pk we address composition series k types and unitarity

acoustic scattering by a hard or soft body across a wide frequency range by the helmholtz integral equation method in this paper the acoustic scattering by an obstacle across a wide frequency range of sound waves is investigated on the basis of the helmholtz integral formulation to overcome the nonuniqueness difficulties the methods proposed by burton npl report nac 30 jan 1973 and by burton and miller proc r soc london ser a 323 201 210 1971 are adopted for the dirichlet and neumann problems respectively the aim of this paper is twofold the first is to bring together completely regular formulations of the helmholtz integral equation and its normal derivative the second is to extend these formulations to treat the higher frequency problems the weakly singular integrals are regularized by subtracting out one term and adding it back depending on the problem concerned the additional integral can finally be expressed in an explicit form or results in solving a surface source distribution of the equipotential body the hypersingular kernels are regularized by the method of using some properties of the associated laplace equation originally proposed by chien et al j acoust soc am 88 918 937 1990 the completely regularized integral equations are amenable to computation by direct use of the standard quadrature methods to study the acoustic scattering due to higher frequency waves filon s quadrature method proc r soc edinburgh 49 38 47 1928 is extended to treat the rapidly oscillatory integrands numerical examples consist of acoustic scattering from a hard or soft sphere of radius a across a wide spectrum of wave numbers ka 20 comparisons of the numerical results with the exact solutions demonstrate the validity and efficiency of the implementation

a novel time marching scheme using numerical green s functions a comparative study for the scalar wave equation abstract the present paper presents the formulation of a novel time marching method based on the explicit green s approach exga to solve scalar wave propagation problems by means of the weighted residual method in both time and space the time integral expression concerning the exga is readily established the arising exga time integral expression is spatially discretized in a finite element sense and a recursive scheme that employs time domain numerical green s function matrices is adopted to evaluate the displacement and the velocity vectors these green s matrices are computed by the time discontinuous galerkin finite element method only at the first time step the system of coupled equations originated from the time discontinuous galerkin method is then solved by an iterative predictor multicorrector algorithm once the green s matrices are computed no iterative process is required to obtain the displacement and the velocity vectors at any time level at the end of the paper numerical examples are presented in order to compare the proposed approach with other approaches

some notes on singular integral techniques in boundary element analysis the paper presented here reviews the numerical techniques used currently to calculate the singular integrals and nearly singular integrals in the boundary element analysis some incorrect algorithms published before are discussed and a new numerical technique to calculate the nearly singular integral is developed the numerical results show a significant improvement in both accuracy and efficiency compared to the traditional adaptive gaussian quadrature and subdivision techniques

gaussian kernels have only gaussian maximizers a gaussian integral kernel g x y on rn x rn is the exponential of a quadratic form in x and y the fourier transform kernel is an example the problem addressed here is to find the sharp bound of g as an operator from l p rp to l q rn and to prove that the l p rn functions that saturate the bound are necessarily gaussians this is accomplished generally for 1 q in some special cases besides greatly extending previous results in this area the proof technique is also essentially different from earlier ones a corollary of these results is a fully multidimensional multilinear generalization of young s inequality

on the singularities of green s formula and its normal derivative with an application to surface wave body interaction problems the paper presents the non singular forms of green s formula and its normal derivative of exterior problems for three dimensional laplace s equation the main advantage of these modified formulations is that they are amenable to solution by directly using quadrature formulas thus the conventional boundary element approximation which locally regularizes the singularities in each element is not required the weak singularities are treated by both the gauss flux theorem and the property of the associated equipotential body the hypersingularities are treated by further using the boundary formula for the associated interior problems the efficacy of the modified formulations is examined by a sphere in an infinite domain subject to neumann and dirichlet conditions respectively the modified integral formulations are further applied to a practical problem i e surface wave body interactions using the conventional boundary integral equation formulation is known to break down at certain discrete frequencies for such a problem removing the irregular frequencies is performed by linearly combining the standard integral equation with its normal derivative computations are presented of the added mass and damping coefficients and wave exciting forces on a floating hemisphere comparing the numerical results with that by other approaches demonstrates the effectiveness of the method copyright 2000 john wiley sons ltd

transient analysis of three dimensional wave propagation using the boundary element method in the past the time domain solution of the wave equation has been limited to simplified problems this was due to the limitations of analytical methods and the capacity of computers to manipulate and store large blocks of spatial information with the advent of super computers the ability to solve such problems has significantly increased this paper outlines a method for transient analysis of wave propagation in arbitrary domains using a boundary element method the technique presented will allow the definition of a domain the input of impedance conditions on the domain s surface the specification of inputs on the surface and the specification of initial conditions within the domain it will produce a complete solution of the wave equation inside the domain the techniques are demonstrated using a program with a boundary element formulation of kirchhoff s equation the elements used are triangular and compatible

a general boundary integral formulation for zoned three dimensional media a new boundary integral formulation is proposed to analyse the heat transfer in zoned three dimensional geometries the proposed formulation couples the boundary formula the gradient of the boundary formula and the exterior formula an advantage of this method over the traditional methods is that any linear condition at the interface between subdomains may be incorporated into the formulation at the outset in addition the new method provides a sparse and well conditioned matrix of coefficients with a minimum number of equations

seismic soil structure interaction analysis by direct boundary element methods abstract upon establishing the mathematical framework necessary for a proper understanding of the analytical theory a regularized form of the conventional direct boundary integral equation formulation for three dimensional elastodynamics is presented for a general anisotropic medium founded on the basis of a full decomposition of the greens functions into regular and singular parts the alternative boundary integral equation format is compact and without demand ingmathematical and numerical complexities such as cauchy principal values extended to deal with general seismic soil structure interaction problems in semi infinite media the formulation is implemented computationally together with a rigorous treatment of singular dynamic multi layered viscoelastic half space greens functions and interfacial boundary tractions arising in typical soil structure foundation configurations a set of new benchmark numerical results are included

a boundary integral method for acoustic radiation and scattering in this article a computational method is proposed for computing the helmholtz integral equation for acoustic radiation and scattering problems with a three dimensional body shape unlike the previous boundary element method the integration of acoustic properties is based on the global body surface instead of local elements the approximation function of body geometry and the weighting function of numerical integration are independently chosen when the singular kernels of helmholtz equation are regularized as bounded discontinuous functions the order of integration polynomials for acoustic properties can be arbitrarily chosen therefore the accuracy and efficiency of computation can be increased

a comparative study on three boundary element method approaches to problems in elastodynamics in this study three boundary element method approaches are compared by solving a typical problem in linear elastodynamics the first approach formulates and solves the problem in the real time domain in conjunction with a time stepping algorithm the other two approaches formulate and solve the problem in the laplace and the fourier transformed domains which necessitates a numerical inversion of the results to the time domain the results obtained compare favourably with available analytic solutions a detailed tabulation of the computer time and memory requirements of each approach is presented

a volume integral equation technique for multiple scattering problems in elastodynamics abstract a volume integral equation method is introduced as a new numerical scheme for the solution of certain elastodynamic problems in unbounded solids containing multiple inclusions the effectiveness of the method is compared with the boundary integral equation method for different problem geometries for the single inclusion problem both methods are found to work equally well for multiple inclusions the volume integral equation method is shown to be much more convenient for numerical formulation and to give very accurate results

on time harmonic elastic wave analysis by the boundary element method for moderate to high frequencies abstract certain inherent difficulties in obtaining accurate boundary element solutions to problems of elastodynamics at moderate to high frequencies are examined some procedures for overcoming or compensating for these difficulties are described in addition results demonstrating the effectiveness of these procedures are presented finally the use of these procedures in solving transient problems via fourier transform inversion is illustrated

two boundary integral equation methods for linear elastodynamics problems on unbounded domains abstract we consider transient 3d elastic wave propagation problems in unbounded isotropic homogeneous media which can be reduced to corresponding 2d ones for their solution we propose and compare two boundary integral equation approaches both based on the coupling of a discrete time convolution quadrature with a classical space collocation discretization in the first approach the pde problem is preliminarily replaced by the equivalent well known vector space time boundary integral equation formulation while in the second the same pde is replaced by a system of two coupled wave equations each one of which is then represented by the associated boundary integral equation the construction of these two approaches is described and discussed some numerical testing are also presented

a reverse log sobolev inequality in the segal bargmann space this article is based on recent results of the author on the properties of the reproducing kernel of the segal bargmann space those results are used here to demonstrate a family of energy entropy inequalities in the segal bargmann space in some cases this is a log sobolev inequality while in other cases this is actually a reverse log sobolev inequality which means that the energy term is bounded above by the entropy term plus a norm term this implies that in the segal bargmann space the entropy is finite if and only if the energy is finite applications of this result to the segal bargmann transform are given as well as a discussion of its possible relation with reverse hypercontractivity it should be noted that all of the results of this article are proved without using hypercontractivity estimates

singular operators on boson fields as forms on spaces of entire functions on hilbert space abstract invariant scales of entire analytic functions on hilbert space are introduced and applied singular operators represented by sesquilinear forms on spaces of regular vectors are given explicit integral representations via kernels that are entire functions on the direct sum of the hilbert space with its dual the weyl or exponentiated boson field operators act smoothly and irreducibly on corresponding spaces of entire functions arbitrary symplectic operators on a single particle hilbert space are shown to be implementable on the corresponding boson field by appropriate generalized operators

on certain rings of highest weight vectors abstract let r m n be the ring of highest weight vectors of the action of o m gl n on the polynomial algebra of m n matrices we determine r m 2 and find generators for r m 3 in particular the results about r m 2 give branching rules and information about the structure of holomorphic representations of sp 4

hypersingular boundary integral equations for radiation and scattering of elastic waves in three dimensions abstract a weakly singular form of the hypersingular boundary integral equation bie traction equation for 3 d elastic wave problems is developed in this paper all integrals involved are at most weakly singular and except for a stronger smoothness requirement on boundary elements regular quadrature and collocation procedures used for conventional bies are sufficient for the discretization of the original hypersingular bie this weakly singular form of the hypersingular bie is applied to the composite bie formulation which uses a linear combination of the conventional bie and the hypersingular bie to remove the fictitious eigenfrequencies existing in the conventional bie formulation for elastic wave problems numerical examples employing different types of boundary elements clearly demonstrate the effectiveness and efficiency of the developed formulation

coupled finite element hierarchical boundary element methods for dynamic soil structure interaction in the frequency domain summary this paper discusses the coupling of finite element and fast boundary element methods for the solution of dynamic soil structure interaction problems in the frequency domain the application of hierarchical matrices in the boundary element formulation allows considering much larger problems compared to classical methods three coupling methodologies are presented and their computational performance is assessed through numerical examples it is demonstrated that the use of hierarchical matrices renders a direct coupling approach the least efficient as it requires the assembly of a dynamic soil stiffness matrix iterative solution procedures are presented as well and it is shown that the application of such schemes to dynamic soil structure interaction problems in the frequency domain is not trivial as convergence can hardly be achieved if no relaxation procedure is incorporated aitken s 2 method is therefore employed in sequential iterative schemes for the calculation of an optimized interface relaxation parameter while a novel relaxation technique is proposed for parallel iterative algorithms it is demonstrated that the efficiency of these algorithms strongly depends on the boundary conditions applied to each subdomain the fastest convergence is observed if neumann boundary conditions are imposed on the stiffest subdomain the use of a dedicated solver for each subdomain hence results in a reduced computational effort a monolithic coupling strategy often used for the solution of fluid structure interaction problems is also introduced the governing equations are simultaneously solved in this approach while the assembly of a dynamic soil stiffness matrix is avoided copyright 2013 john wiley sons ltd

efficient analytical integration of symmetric galerkin boundary integrals over curved elements elasticity formulation abstract substantial improvements are reported in the computational efficiency of galerkin boundary element analysis bea 1employing curved continuous boundary elements for elasticity problems a direct analytical treatment of the singular and hypersingular double integrations employing a limit to the boundary definition is adapted to gain computational economy symbolic manipulation has been employed to derive the analytical expressions for the singular contributions to these double integrals the analytical regularization procedure separates the potentially singular galerkin integrands into an essentially singular but simple part plus a regular remainder that can be integrated numerically the exact finite contributions from the simplified singular terms are then computed analytically it is shown that the key to containing the explosive growth in the length of the formulae associated with such a hybrid analytical numerical integration scheme is the strategic timing of when to take the limit to the boundary this regularization also isolates the contribution from the curvature of the boundary element thus facilitating enhanced computational efficiency in problems with many straight elements although the evaluation of the integrals of the kelvin fundamental solution essentially follows the procedures described earlier for the scalar laplace equation the analytical treatment is now more involved in terms of the complexity and number of terms present in each of these second rank tensor kernel functions the complete analytical formulation is explicitly provided in a series of tables example problems indicate that with these techniques galerkin symmetric bea can be more efficient than collocation for moderate or large scale problems

a boundary integral equation method for radiation and scattering of elastic waves in three dimensions etude du rayonnement et de la diffusion d ondes elastiques par des obstacles de forme arbitraire

the hypercontractive approach to exactly bounding an operator with complex gaussian kernel abstract we study operators g l q r n l p r n given by a nondegenerate complex gaussian kernel in many cases such an operator attains its bound at a maximizing gaussian function g l q r n to show this we prove a complexified version of edward nelson s hypercontractive theorem

an elastodynami c hybrid boundary element study for elastic guided wave interactions with a surface breaking defect elastic guided wave interactions with various defects are explored for investigating defect characterization possibilities by using a hybrid boundary element method bem in combination with an elastodynamic boundary integral equation and the lamb wave normal mode expansion technique the bem code accuracy is verified based on energy conservation and available bench marking data for guided wave scattering problems through two dimensional 2 d parametric studies for an arbitrarily shaped defect from a surface breaking crack model to a round surface defect a waveguide cross section including a defect is locally selected as a model for a given incident mode frequency and a specific set of material properties mode reflection and transmission factors are numerically calculated to evaluate mode sensitivities and to obtain the potentially good classification features it turns out that the guided wave scattering profiles show quite different behaviors as functions of incident mode frequency defect shape and size in providing us with enough rich feature extraction information for defect classification and sizing analysis the theoretical analysis can be used to establish efficient guidelines for both data acquisition and feature selection in a pattern recognition analysis program of study sample results are presented

a boundary integral formulation for complex three dimensional geometries a new boundary integral formulation is proposed to analyse the heat transfer in complex three dimensional geometries one example of such geometry is the die sets in the injection moulding process networks of cooling conduits within the mould and the closely spaced die surfaces require special attention both in formulation and numerical treatment of the integral equations the proposed formulation couples the boundary formula the gradient of the boundary formula and the exterior formula the derivation of the integral equations is presented here along with an efficient method for integration of some of the kernels in these equations and a semi analytical procedure for the integration of the highly singular integrands which result from differentiating the boundary formula although the techniques introduced here are applied to a particular problem in heat transfer their potential application is much broader

a first order k space model for elastic wave propagation in heterogeneous media a pseudospectral model of linear elastic wave propagation is described based on the first order stress velocity equations of elastodynamics k space adjustments to the spectral gradient calculations are derived from the dyadic green s function solution to the second order elastic wave equation and used to a ensure the solution is exact for homogeneous wave propagation for timesteps of arbitrarily large size and b also allows larger time steps without loss of accuracy in heterogeneous media the formulation in k space allows the wavefield to be split easily into compressional and shear parts a perfectly matched layer pml absorbing boundary condition was developed to effectively impose a radiation condition on the wavefield the staggered grid which is essential for accurate simulations is described along with other practical details of the implementation the model is verified through comparison with exact solutions for canonical examples and further examples are given to show the efficiency of the method for practical problems the efficiency of the model is by virtue of the reduced point per wavelength requirement the use of the fast fourier transform fft to calculate the gradients in k space and larger time steps made possible by the k space adjustments

multilevel fast multipole algorithm for elastic wave scattering by large three dimensional objects multilevel fast multipole algorithm mlfma is developed for solving elastic wave scattering by large three dimensional 3d objects since the governing set of boundary integral equations bie for the problem includes both compressional and shear waves with different wave numbers in one medium the double tree structure for each medium is used in the mlfma implementation when both the object and surrounding media are elastic four wave numbers in total and thus four fma trees are involved we employ nystrom method to discretize the bie and generate the corresponding matrix equation the mlfma is used to accelerate the solution process by reducing the complexity of matrix vector product from o n 2 to o nlogn in iterative solvers the multiple tree structure differs from the single tree frame in electromagnetics em and acoustics and greatly complicates the mlfma implementation due to the different definitions for well separated groups in different fma trees our nystrom method has made use of the cancellation of leading terms in the series expansion of integral kernels to handle hyper singularities in near terms this feature is kept in the mlfma by seeking the common near patches in different fma trees and treating the involved near terms synergistically due to the high cost of the multiple tree structure our numerical examples show that we can only solve the elastic wave scattering problems with 0 3 0 4 millions of unknowns on our dell precision 690 workstation using one core

hypercontractivity for log subharmonic functions abstract we prove strong hypercontractivity shc inequalities for logarithmically subharmonic functions on r n and different classes of measures gaussian measures on r n symmetric bernoulli and symmetric uniform probability measures on r as well as their convolutions surprisingly a slightly weaker strong hypercontractivity property holds for any symmetric measure on r a log sobolev inequality lsi is deduced from the shc for compactly supported measures on r n still for log subharmonic functions an analogous lsi is proved for gaussian measures on r n and for other measures for which we know the shc holds our log sobolev inequality holds in the log subharmonic category with a constant smaller than the one for gaussian measure in the classical context

hybrid modelling of semi infinite media abstract an accurate and efficient hybrid formulation based on lagrange s equations of motion is presented to solve geometrically axisymmetric problems associated with layered semi infinite media under arbitrary loading a near field region containing all inhomogeneities is modelled using conventional finite elements the contribution of the exterior semi infinite domain to the equations of motion is represented by a surface integral defined over the finite element boundary the integrand of this integral involves a matrix relationship between harmonics of nodal displacements and tractions at the finite element boundary a boundary traction displacement relationship for the exterior domain is established in terms of traction and displacement green s functions for a uniform undisturbed half space the present formulation guarantees a symmetric stiffness matrix for the entire system therefore both direct and indirect versions of the boundary integral equation method can be used the accuracy of the hybrid modelling algorithm is confirmed by solving a few elastostatic and elastodynamic boundary value problems for which analytical solutions can be derived