on stable numerical differentiation based on a regularized volterra equation two different approaches for numeri cal differentiation are considered the first approach consists of solving a regularized volterra equation while the second approach is based on solving a disretized version of the regularized volterra equation numerical experiments show that these methods are efficient and compete fa vorably with the variational regularization method for stable calculating the derivatives of noisy functions

standard staggered and staggered newton schemes in thermo hydro mechanical problems the aim of the paper is to compare the rates of iteration convergence of two staggered numerical schemes one using successive substitutions and the other the newton method in the case of very weakly coupled problems the newton method is one order faster but there are specific cases when it is slower than the standard staggered algorithm in both cases a convergence condition must be verified the behaviour of the investigated staggered procedures in case of thermo hydro mechanical problems are shown on examples

interface element method iem for a partitioned system with non matching interfaces abstract a novel method for non matching interfaces on the boundaries of finite elements in partitioned domains is presented by introducing interface elements in this paper the interface element method iem satisfies the continuity conditions exactly through interface element domains without recourse to lagrange multiplier technique the interface elements take an interpolation scheme used in meshless methods to join partitioned domains the moving least square mls approximations in the present study are implemented to construct the shape functions of the interface elements the compatibility of displacements on the boundaries of the finite elements and the interface elements is always preserved in this method and the completeness of the shape functions of the interface elements transfers rigid body motions and strain fields correctly moreover alignment of the boundaries of sub domains in the mls approximations and integration domains provides a consistent numerical integration the numerical examples show that the iem is a useful tool for the analysis of a partitioned system and for a global local analysis

interface element method treatment of non matching nodes at the ends of interfaces between partitioned domains abstract a methodology for interface element method iem to combine partitioned domains with non matching nodes at the ends of interfaces is presented the iem is introduced to satisfy the continuity and the compatibility conditions on non matching interfaces between partitioned finite element domains interface elements are defined on the finite elements bordering on the interfaces and the moving least square mls approximations are employed to construct the shape functions of the interface elements by modifying the shape functions of the interface elements at the ends of non matching interfaces partitioned domains are glued such that all properties of the iem are satisfied the modifications are made to sub domains and weight functions in the mls approximations the numerical examples show that the present iem is very effective for the analysis of a partitioned system and for global local analysis

radial solutions and phase separation in a system of two coupled schrodinger equations we consider the nonlinear elliptic system left begin aligned delta u u u 3 beta v 2u 0 quad rm in mathbb b delta v v v 3 beta u 2v 0 quad rm in mathbb b u v 0 quad rm in mathbb b quad u v 0 quad rm on partial mathbb b end aligned right where n leqq 3 and mathbb b subset mathbb r n is the unit ball we show that for every beta leqq 1 and k in mathbb n the above problem admits a radially symmetric solution u v such that u v changes sign precisely k times in the radial variable furthermore as beta to infty after passing to a subsequence u w and v w uniformly in mathbb b where w w w has precisely k nodal domains and is a radially symmetric solution of the scalar equation w w w3 0 in mathbb b w 0 on partial mathbb b within a hartree fock approximation the result provides a theoretical indication of phase separation into many nodal domains for bose einstein double condensates with strong repulsion

taylor expansions for singular kernels in the boundary element method the problem treated is the integration of singular functions which arise in three dimensional isoparametric formulations of boundary integral equations a taylor expansion in the local parametric co ordinates is developed for the singular integrand so allowing singular terms to be integrated in closed form even for curved surface elements the remainder integral obtained by subtracting out the worst singularities is integrated by repeated gaussian quadrature two groups of tests are presented first the accuracy of the integrations has been checked for plane parallelograms for which exact solutions have been developed and for curved elements on a sphere secondly results from complete boundary element calculations based on point collocation have been compared with known analytical solutions to two problems zonal surface harmonics on a sphere and the capacitance of an ellipsoid the agreement obtained with few degrees of freedom suggests that errors which have previously been attributed to point collocation might have arisen in the numerical integration

positive solutions for a weakly coupled nonlinear schrodinger system abstract existence of a nontrivial solution is established via variational methods for a system of weakly coupled nonlinear schrodinger equations the main goal is to obtain a positive solution of minimal action if possible with all vector components not identically zero generalizations for nonautonomous systems are considered

arbitrary lagrangian eulerian formulation for fluid rigid body interaction a new formulation for two dimensional fluid rigid body interaction problems is developed in particular vortex induced oscillations of a rigid body in viscous incompressible flow are studied the incompressible navier stokes equations are used to describe the motion of the fluid while it is assumed that the rigid body is mounted on a system consisting of a spring and a dashpot an arbitrary lagrangian eulerian formulation ale is used in order to account for large boundary motion a general formulation for the coupled problem is obtained by uncoupling the translation motion of the body from its rotational motion and developing a specific algorithm to efficiently handle the nonlinear dependence of the rotations this general formulation can be easily applied to multi body problems two numerical examples involving either translations and rotations are presented as an illustration of the proposed methodologies for fluid rigid body interaction

analysis of transient response of saturated porous elastic soil under cyclic loading using element free galerkin method a two dimensional numerical procedure is presented to analyse the transient response of saturated porous elastic soil layer under cyclic loading the procedure is based on the element free galerkin method and incorporated into the periodic conditions temporal and spatial periodicity its shape function is constructed by moving least square approximants essential boundary conditions are implemented through lagrange multipliers and the periodic conditions are implemented through a revised variational formulation time domain is discretized through the crank nicolson scheme analytical solutions are developed to assess the effectiveness and accuracy of the current procedure in one and two dimensions for only temporal periodic problems a one dimensional transient problem of finite thickness soil layer is analysed for sinusoidal surface loading for both temporal and spatial periodic problems a typical two dimensional wave induced transient problem with the seabed of finite thickness is analysed finally a moving boundary problem is analysed it is found that the current procedure is simple efficient and accurate in predicting the response of soil layer under cyclic loading 2002 elsevier science ltd all rights reserved

asymptotic estimates for the spatial segregation of competitive systems abstract for a class of population models of competitive type we study the asymptotic behavior of the positive solutions as the competition rate tends to infinity we show that the limiting problem is a remarkable system of differential inequalities which defines the functional class s in 2 by exploiting the regularity theory recently developed in conti et al indiana univ math j to appear for the elements of functional classes of the form s we provide some qualitative and regularity property of the limiting configurations besides for the case of two competing species we obtain a full description of the limiting states and we prove some quantitative estimates for the rate of convergence finally we prove some new liouville type results which allow to have uniform regularity estimates of the solutions

derivation of a new analytical solution for a general two dimensional finite part integral applicable in fracture mechanics an exact expression is derived for the general finite part integral over an inclined ellipticaldomain r denotes the distance of a point in to the singular point is a general function of the cartesian co ordinates x0 y0 the boundary of the region represents the equation z x0 y0 o these integrals appear during the numerical solution of plane crack problems in three dimensional elasticity where they are the dominant part of a hypersingular integral equation the availability of exact expressions for the integrals with arbitrary integers i and j will increase the accuracy of the numerical results and simultaneously lead to quicker numerical results the considered finite part integral can be expressed in closed form as function of complete elliptical integrals or gauss hypergeometric functions respectively formuias for special cases and some i j values and their numerical verification are given in appendices ii and iii

the two level feti method for static and dynamic plate problems part i an optimal iterative solver for biharmonic systems abstract we present a lagrange multiplier based substructuring method for solving iteratively large scale systems of equations arising from the finite element discretization of static and dynamic plate bending problems the proposed method is essentially an extension of the feti domain decomposition algorithm to fourth order problems the main idea is to enforce exactly the continuity of the transverse displacement field at the substructure corners throughout the preconditioned conjugate projected gradient iterations this results in a two level feti substructuring method where the condition number of the preconditioned interface problem does not grow with the number of substructures and grows at most polylogarithmically with the number of elements per substructure these theoretically proven optimal convergence properties of the new feti method are numerically demonstrated for several finite element plate bending static and transient problems the two level iterative solver presented in this paper is applicable to a large family of biharmonic time independent as well as time dependent systems it is also extendible to shell problems

new green s function for stress field and a note of its application in quantum wire structures abstract the elastic field caused by the lattice mismatch between the quantum wires and the host matrix can be modeled by a corresponding two dimensional hydrostatic inclusion subjected to plane strain conditions the stresses in such a hydrostatic inclusion can be effectively calculated by employing the green s functions developed by downes and faux which tend to be more efficient than the conventional method based on the green s function for the displacement field in this study downes and faux s paper is extended to plane inclusions subjected to arbitrarily distributed eigenstrains an explicit green s function solution which evaluates the stress field due to the excitation of a point eigenstrain source in an infinite plane directly is obtained in a closed form here it is demonstrated that both the interior and exterior stress fields to an inclusion of any shape and with arbitrarily distributed eigenstrains are represented in a unified area integral form by employing the derived green s functions in the case of uniform eigenstrain the formulae may be simplified to contour integrals by green s theorem however special care is required when green s theorem is applied for the interior field the proposed green s function is particularly advantageous in dealing numerically or analytically with the exterior stress field and the non uniform eigenstrain two examples concerning circular inclusions are investigated a linearly distributed eigenstrain is attempted in the first example resulting in a linear interior stress field the second example solves a circular thermal inclusion where both the interior and exterior stress fields are obtained simultaneously

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

a point interpolation meshless method based on radial basis functions a point interpolation meshless method is proposed based on combining radial and polynomial basis functions involvement of radial basis functions overcomes possible singularity associated with the meshless methods based on only the polynomial basis this non singularity is useful in constructing well performed shape functions furthermore the interpolation function obtained passes through all scattered points in an influence domain and thus shape functions are of delta function property this makes the implementation of essential boundary conditions much easier than the meshless methods based on the moving least squares approximation in addition the partial derivatives of shape functions are easily obtained thus improving computational efficiency examples on curve surface fittings and solid mechanics problems show that the accuracy and convergence rate of the present method is high copyright 2002 john wiley sons ltd

the numerical evaluation of a 2 d cauchy principal value integral arising in boundary integral equation methods in this paper we consider the problem of computing 2 d cauchy principal value integrals of the form

numerical analysis of biot s consolidation process by radial point interpolation method an algorithm is proposed to solve biot s consolidation problem using meshless method called a radial point interpolation method radial pim the radial pim is advantageous over the meshless methods based on moving least square mls method in implementation of essential boundary condition and over the original pim with polynomial basis in avoiding singularity when shape functions are constructed two variables in biot s consolidation theory displacement and excess pore water pressure are spatially approximated by the same shape functions through the radial pim technique fully implicit integration scheme is proposed in time domain to avoid spurious ripple effect some examples with structured and unstructured nodes are studied and compared with closed form solution or finite element method solutions

the zero set of a solution of a parabolic equation on etudie l ensemble nul d une solution u t x de l equation u t a x t u xx b x t u x c x t u sous des hypotheses tres generales sur les coefficients a b et c

a weak coupling algorithm for seabed wave interaction analysis this paper proposes a weak coupling algorithm for the seabed wave interaction analysis this algorithm is based on the error integration over a time interval and space along fluid seabed interfaces with this weak coupling algorithm seabed wave interaction analysis can be easily carried out with a fluid solver in fluid domain and a meshless solver in seabed domain independently the fluid solver is based on a two step projection method for navier stokes equation the free surface of seawaters during wave propagation is traced through the volume of fluid vof the meshless solver is based on the biot s consolidation theory of saturated poroelasticity which considers the interaction of soil deformation and pore water pressure in seabed data exchange at the interface between fluid and porous medium domains is carried out through a point interpolation method interface condition is approximately satisfied in a variational sense through an iteration scheme between two solvers this algorithm does allow not only non matching mesh along the interface but also non matching time step in different subdomains numerical examples show that this weak coupling algorithm is able to capture the deformation of interface and improve the computation accuracy and efficiency 2004 elsevier b v all rights reserved

elastic and piezoelectric fields due to polyhedral inclusions abstract we derive explicit closed form expressions describing elastic and piezoelectric deformations due to polyhedral inclusions in uniform half space and bi materials our analysis is based on the linear elasticity theory and green s function method the method involves evaluation of volume and surface integrals of harmonic and bi harmonic potentials in case of polyhedra such integrals are expressed through algebraic functions our results generalize numerous studies on this subject and they allow to obtain fully analytical solutions for a number of physical and engineering problems in the limiting case of an infinite space our relations have an essentially more compact form than relations obtained by other authors we present solutions to classical mindlin and cherruti problems we describe the elastic relaxation of a misfitting polygonal quantum dot in bi materials assuming isotropic and vertically isotropic properties it is explained how to analyze non hydrostatic and non uniform inclusions we also study piezoelectric fields induced by inclusions in materials with cubic and hexagonal lattices among other results we have found that a cubic inclusion in an isotropic material reproduces fields of quantum dots in gaas 0 0 1 and gaas 1 1 1 depending on the orientation of the cube this suggests that one can qualitatively model crystals with different lattices by choosing an appropriate inclusion shape

ground state of n coupled nonlinear schrodinger equations in mathbb r n n leq 3 we establish some general theorems for the existence and nonexistence of ground state solutions of steady state n coupled nonlinear schrodinger equations the sign of coupling constants ij s is crucial for the existence of ground state solutions when all ij s are positive and the matrix is positively definite there exists a ground state solution which is radially symmetric however if all ij s are negative or one of ij s is negative and the matrix is positively definite there is no ground state solution furthermore we find a bound state solution which is non radially symmetric when n 3

the influence of strain on confined electronic states in semiconductor quantum structures a continuum finite element technique is adopted to study electronic properties of submicron electronic devices where function hinges on quantum mechanical eaects of particular interest is the influence of mechanical strain on confined electronic states the steady state schrequation which governs the electronic behavior of such devices is modified to include the potential induced by a strain field which is present as a consequence of the fabrication the governing equation is cast in a variational form and it is discretized on a standard finite element mesh which is more refined in regions where large quantum mechanical wave function gradients are expected multiple energy bands and three dimensional structures can be considered and eaects including strain enhanced charge confinement and strain induced energy band mixing are studied as examples a ge 5 0 1 faceted island or quantum dot on a si substrate and a ge v groove quantum wire on a si substrate are considered the technique is used to determine size ranges in which these devices are expected to be most useful the nonuniform mismatch strain field in the structures is found to aaect the energies of experimentally accessible confined states and in some cases to enhance quantum mechanical confine ment 2001 elsevier science ltd all rights reserved

radial solutions of superlinear equations on ℝn part i global variational approach we present a global variational approach to the search for multiple nodal solutions u h 1 n to a class of elliptic equations of type u x f x u x x n where n 2 f is superlinear and subcritical and f x 0

on the optimal shape parameters of radial basis functions used for 2 d meshless methods abstract a radial point interpolation meshless or radial pim method was proposed by authors to overcome the possible singularity associated with only polynomial basis the radial pim used multiquadric mq or gaussian as basis functions these two radial basis functions all included shape parameters although choice of shape parameters has been a hot topic in approximation theory and some empirical formulae were proposed how these shape parameters affect the accuracy of the radial pim has not been studied yet this paper studied the effect of shape parameters on the numerical accuracy of radial pim a range of suitable shape parameters is obtained from the analysis of the condition number of the system matrix error of energy and irregularity of node distribution it is observed that the widely used shape parameters for mq and reciprocal mq basis are not even close to their optimums the optimal shape parameters are found in this paper to be simply q 1 03 and r 1 42 for mq basis and c 0 003 0 03 for gaussian basis