mixed boundary value problems for elliptic and parabolic differential equations of second order on considere les problemes aux valeurs limites mixtes suivants lu f 1 dans mu f 2 sur u f 3 sur avec l operateur elliptique et pu f 1 dans 0 t mu f 2 sur 0 t u f 3 sur 0 t 0 pour des operateurs p paraboliques pour des operateurs obliques generaux m et pour des domaines ou et se rencontrent a des angles arbitraires on montre l existence de solutions classiques quand les angles sont non nuls et f 3 est continue de holder

unconditionally stable meshless integration of time domain maxwell s curl equations grid based methods coupled with an explicit approach for the evolution in time are traditionally adopted in solving pdes in computational electromagnetics the discretization in space with a grid covering the problem domain and a stability step size restriction must be accepted evidence is given that efforts need for overcoming these heavy constraints the connectivity laws among the points scattered in the problem domain can be avoided by using meshless methods among these the smoothed particle electromagnetics gives an interesting answer to the problem overcoming the limit of the grid generation in the original formulation an explicit integration scheme is used providing spatial and time discretization strictly interleaved and mutually conditioned in this paper a formulation of the alternating direction implicit scheme is proposed into the meshless framework the developed formulation preserves the leapfrog marching on in time of the explicit integration scheme studies on the systems matrices arising at each temporal step are reported referring to the meshless discretization the new method not constrained by a grid in space and unconditionally stable in time is validated by numerical simulations

variational multiscale element free galerkin vmefg and local discontinuous galerkin ldg methods for solving two dimensional brusselator reaction diffusion system with and without cross diffusion abstract the finite element method fem is one of the basic methods for solving deterministic and stochastic partial differential equations this method is proposed in the 19 decade and after years several modifications for this well known technique such as mortal fem discontinuous galerkin fem extended fem least squares fem spectral fem mixed fem immersed fem adaptive fem etc have been proposed also for improving the accuracy and for considering complex domain shape functions of the moving least squares approximation have been replaced with the traditional shape function of the finite element technique the name of this improved method is element free galerkin efg method which is classified in the category of meshless methods the efg method has been applied for solving many problems in engineering in the current paper we select two numerical procedures that are extracted from fem the discontinuous galerkin approach is a useful technique for solving problems that their exact solutions have discontinuity it should be noted that many enriched ideas have been explained for improving accuracy of efg method in the current paper the local discontinuous galerkin and variational multiscale efg methods are applied for obtaining numerical solution of two dimensional brusselator system with and without cross diffusion the brusselator system is a theoretical model for a type of autocatalytic reaction up to best of authors knowledge the accuracy of the obtained numerical solutions using local discontinuous galerkin method is very related to the used time discrete scheme therefore fourth order exponential time differencing method has been employed for discretizing the time variable also to achieve a full discretization scheme the local discontinuous galerkin finite element method is used moreover several test problems are given that show the acceptable accuracy and efficiency of the proposed schemes

redundancy of the context tree weighting method on renewal and markov renewal processes the context tree weighting method ctw is shown to be almost adaptive on the classes of renewal and markov renewal processes up to logarithmic factor ctw achieves the minimax pointwise redundancy described by i csiszaacuter and p shields in ieee trans inf theory vol 42 no 6 pp 2065 2072 nov 1996 this result not only complements previous results on the adaptivity of the context tree weighting method on the relatively small class of all finite context tree sources which encompasses the class of all finite order markov sources it shows that almost minimax redundancy can be achieved on massive classes of sources classes that cannot be smoothly parameterized by subsets of finite dimensional spaces moreover it shows that almost adaptive compression can be achieved in a computationally efficient way on those massive classes while previous adaptivity results for ctw could rely on the fact that any markov source is a finite context tree source this is no longer the case for renewal sources in order to prove almost adaptivity of ctw over renewal sources it is necessary to establish that ctw carefully balances estimation error and approximation error

a moving kriging interpolation based element free galerkin method for structural dynamic analysis in this paper a meshfree method based on the moving kriging interpolation is further developed for free and forced vibration analyses of two dimensional solids the shape function and its derivatives are essentially established through the moving kriging interpolation technique following this technique by possessing the kronecker delta property the method evidently makes it in a simple form and efficient in imposing the essential boundary conditions the governing elastodynamic equations are transformed into a standard weak formulation it is then discretized into a meshfree system of time dependent equations which are solved by the standard implicit newmark time integration scheme numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in details as a consequence it is found that the method is very efficient and accurate for dynamic analysis compared with those of other conventional methods

modeling of biological population problems using the element free kp ritz method a degenerate parabolic equation arising in the spatial diffusion of biological population is analyzed using the mesh free kp ritz method the mesh free kernel particle estimate is employed to approximate the 2d displacement field a system of discrete equations is obtained through application of the ritz minimization procedure to the energy expressions to validate the accuracy of the results and stability of the present method convergence studies were carried out based on influences of support size and number of nodes effectiveness of the mesh free kp ritz method for biological population model is investigated by numerical examples in this paper the present results were compared with results reported in extant literature and were found to be in good agreement with the literature

remediation of contaminated groundwater by meshless local weak forms in this paper four meshless local weak form methods such as direct meshless local petrovgalerkin method dmlpg meshless local petrovgalerkin method mlpg local weak radial point interpolation method lwrpim and local weak moving kriging method lwmk are applied to find the numerical solution of coupled non linear advectiondiffusionreaction system arising in the prevention of groundwater contamination problem a comparison between these methods is done from the perspective of accuracy and computational efficiency an efficient fourth order exponential time differencing rungekutta method is utilized for the time discretization the computational efficiency is the most significant advantage of the dmlpg method in comparison with the other meshless local weak form methods because dmlpg reduces the computational costs significantly this is due to the fact that dmlpg shifts the numerical integrations over low degree polynomials rather than over complicated shape functions the main aim of this paper is to show that the meshless local weak form methods can be used for solving the system of non linear partial differential equations especially coupled non linear advectiondiffusionreaction system the numerical results confirm the good efficiency of the proposed methods for solving our model

error estimates for the interpolating moving least squares method in this paper the interpolating moving least squares imls method presented by lancaster and salkauskas is discussed in details the advantage of the imls method is that the meshless method which is constructed based on the imls method can apply the essential boundary conditions directly and easily a simpler expression of the approximation function of the imls method is obtained then the error estimate of the approximation function and its first and second order derivatives of the imls method are presented in one dimensional case in this paper the theoretical results show that if the order of the polynomial basis functions is big enough and the original function is sufficiently smooth then the approximation function and its partial derivatives are convergent to the exact values in terms of the maximum radius of the domains of influence of nodes for the purpose of demonstration some selected numerical examples are given to prove the theories in this paper

a meshless numerical procedure for solving fractional reaction subdiffusion model via a new combination of alternating direction implicit adi approach and interpolating element free galerkin efg method a new numerical algorithm has been investigated for solving time fractional reaction subdiffusion equation the fractional derivative of the considered equation is described in the riemann liouville sense firstly we discrete the temporal dimension of the considered model using a finite difference scheme a central difference scheme has been applied to discrete the first time derivative and then for discretizing the fractional integral term a difference scheme has been employed with convergence order o 1 moreover to achieve a full discretization scheme a type of meshless method has been improved that is known as element free galerkin efg method the efg method for integration uses a background mesh this method is based on the galerkin weak form in which the test and trial functions are shape functions of moving least squares mls approximation since the shape functions of traditional mls lack the kronecker property essential boundary conditions of a boundary value problem can not be directly computed and other methods must be employed for this issue to this end a new class of mls shape functions has been applied that is called shape functions of interpolating mls the new shape function has the mentioned property in the efg method calculating the appeared two dimensional integrals is a basic issue in this research work the alternating direction implicit approach is combined with the element free galerkin method then using the new proposed method the two dimensional integrals on rectangular domain will be changed to simple one dimensional integrals we prove that the new numerical algorithm is unconditionally stable and also we obtain an error bound for the new procedure using the energy method numerical examples are reported which demonstrate the theoretical results and the efficiency of proposed scheme

the numerical analysis of piezoelectric ceramics based on the hermite type rpim in this paper the hermite type radial point interpolation method rpim is applied to analyze the property of piezoelectric ceramics in order to overcome the defects of finite element method in this method the inside and boundary of the problem domain are discreted by a distribution of nodes and then the interpolation function of nodes are constructed to solve the displacement of the evaluation nodes compared with the finite element method it is easier and faster for the hermite type rpim to accurately achieve solution of the local regions in contrast with the existing meshless methods this method would not cause singularity in the process of evaluating the shape function furthermore the shape function of the hermite type rpim has a better stability and it can adapt to any distribution of nodes in addition the accuracy and stability of the method are proved by the numerical simulation

numerical solution of transient heat conduction problems using improved meshless local petrov galerkin method an improved meshless local petrov galerkin mlpg method is presented and applied to calculate the two dimensional unsteady state heat conduction problems in this method the moving kriging interpolation is employed instead of the traditional mls approximation to construct the mlpg shape functions which possess kronecker delta function property and thus make it easy to implement essential boundary conditions and then the heaviside step function is used as the test function over a local sub domain since no mesh is needed either for integration of the local weak form or for construction of the shape functions the presently developed mlpg method is a truly meshless method several examples are performed to illustrate the accuracy and efficiency of the present method a good agreement can be found among the proposed analytical and finite element methods

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

transient heat conduction analysis using the mlpg method and modified precise time step integration method the meshless local petrov galerkin mlpg method in conjunction with the modified precise time step integration method in the time domain is proposed for transient heat conduction analysis in this paper the mlpg method is often referred to as a truly meshless method because it requires no elements or background cells for either field interpolation or background integration local weak forms are developed using weighted residual method locally from the partial differential equation of transient heat conduction in order to simplify the treatment of essential boundary conditions the natural neighbour interpolation nni is employed for the construction of trial functions moreover the three node triangular fem shape functions are taken as test functions to reduce the order of integrands involved in domain integrals the semi discrete heat conduction equation is solved numerically with modified precise time step integration method in the time domain the availability and accuracy of the present method for transient heat conduction analysis are tested through numerical examples

a meshless local moving kriging method for two dimensional solids abstract an improved meshless local petrov galerkin method mlpg for stress analysis of two dimensional solids is presented in this paper the mlpg method based on the moving least squares approximation is one of the recent meshless approaches however accurate imposition of essential boundary conditions in the mlpg method often presents difficulties because the mlpg shape functions does not possess the kronecker delta property in order to eliminate this shortcoming this approach uses the moving kriging interpolation instead of the traditional moving least square approximation to construct the mlpg shape functions and then the heaviside step function is used as the test function over a local sub domain in this method the essential boundary conditions can be enforced as the fem no domain integration is needed and only regular boundary integration is involved in addition the sensitivity of several important parameters of the present method is mainly studied and discussed comparing with the original meshless local petrov galerkin method the present method has simpler numerical procedures and lower computation cost the effectiveness of the present method for two dimensional solids problem is investigated by numerical examples in this paper

on optimal reconstruction of constitutive relations abstract in this investigation we develop and validate a computational method for reconstructing constitutive relations based on measurement data applicable to problems arising in nonequilibrium thermodynamics and continuum mechanics this parameter estimation problem is solved as pde constrained optimization using a gradient based technique in the optimize then discretize framework the principal challenge is that the control variable i e the relation characterizing the constitutive property is not a function of the independent variables in the problem but of the state dependent variable the proposed method allows one to reconstruct a smooth constitutive relation defined over a broad range of the dependent variable it relies on three main ingredients a computationally friendly expression for the cost functional gradient sobolev gradients used in lieu of discontinuous l 2 gradients and a systematic technique for shifting the identifiability region the performance of this approach is illustrated by the reconstruction of the temperature dependence of the thermal conductivity in a one dimensional model problem

proper orthogonal decomposition variational multiscale element free galerkin pod vmefg meshless method for solving incompressible navier stokes equation abstract recently because of simplicity of meshless methods they have been employed for solving many partial differential equations one of the meshless methods is element free galerkin technique the element free galerkin is very similar to the finite element method with this difference that the test and trial spaces of efg procedure are shape functions of moving least squares approximation using the mentioned shape functions solving a problem on a complex domain is very simple some researchers proposed several modifications and enriched approaches for improving the element free galerkin method that one of them is variational multiscale element free galerkin procedure up to the best of authors knowledge the element free galerkin method based on the shape functions of moving least squares approximation needs more cpu time than the element free galerkin method based on the shape functions of moving kriging interpolation thus in the current paper we employ the variational multiscale element free galerkin based on the shape functions of moving kriging interpolation also for reducing the cpu time of the presented numerical scheme we use the proper orthogonal decomposition pod approach therefore in the current paper we propose the proper orthogonal decomposition variational multiscale element free galerkin pod vmefg method for solving time dependent incompressible navier stokes equation moreover several test problems are given that show the acceptable accuracy and efficiency of the proposed scheme

numerical study of three dimensional turing patterns using a meshless method based on moving kriging element free galerkin efg approach in this paper a numerical procedure is presented for solving a class of three dimensional turing system first we discrete the spatial direction using element free galerkin efg method based on the shape functions of moving kriging interpolation then to achieve a high order accuracy we use the fourth order exponential time differencing runge kutta etdrk4 method using this discretization for the temporal dimension we obtain an explicit scheme and do not need to solve nonlinear system of equations the efg method uses a weak form of the considered equation that is similar to the finite element method with the difference that in the efg method test and trial functions are moving least squares approximation mls shape functions since the shape functions of moving least squares mls approximation do not have kronecker delta property we cannot implement the essential boundary condition directly also building shape functions of mls approximation is a time consuming procedure because of the mentioned reasons we employ the shape functions of moving kriging interpolation technique which have the mentioned property and less cpu time is required for building them for testing this method on three dimensional pdes we select some equations and system of pdes such as allen cahn gray scott ginzburg landau brusselator models predator prey model with additional food supply to predator several test problems are solved and numerical simulations are reported which confirm the efficiency of the proposed scheme

development of a novel meshless local kriging lokriging method for structural dynamic analysis this paper presents a novel meshless approach to study the dynamic responses of structures it is called local kriging lokriging method where the kriging interpolation is employed to construct the field approximation function and meshless shape functions and the local weak form of partial differential governing equations is derived by the weighted residual technique since the shape functions constructed by this interpolation possess the delta function property even for a set of randomly distributed points the essential boundary condition can be easily imposed in implementation of local weak form the spline function with high continuity is used as the weight function no mesh is required either for integration of the local weak form or for construction of the shape functions thus the present lokriging method is a truly meshless method several numerical examinations for the free forced vibrational analysis of structures and the dynamic performance of microelectromechanical systems mems device are carried out to demonstrate the accuracy and efficiency of the lokriging method the numerical results show that the presently developed method is quite easy to implement very accurate and highly efficient for the problems considered

error analysis of a meshless weak form method based on radial point interpolation technique for sivashinsky equation arising in the alloy solidification problem abstract in this paper meshless weak form techniques are applied to find the numerical solution of nonlinear biharmonic sivashinsky equation arising in the alloy solidification problem stability and convergence analysis of time discrete scheme are proved an error analysis of meshless global weak form method based on radial point interpolation technique is proposed for this nonlinear biharmonic equation in addition a comparison between meshless global and local weak form methods is done from the perspective of accuracy and efficiency the main purpose of this paper is to show that the meshless weak form techniques can be used for solving the nonlinear biharmonic partial differential equations especially sivashinsky equation the numerical results confirm the good efficiency of the proposed methods for solving this nonlinear biharmonic model

a moving kriging interpolation based meshless method for numerical simulation of kirchhoff plate problems this paper mainly proposes an alternative way for numerical implementation of thin plates bending based on a new improvement of meshless method which is combined between the standard element free galerkin method and one different shape functions building technique the moving kriging mk interpolation is applied instead of the traditional moving least square approximation in order to overcome kronecker s delta property where the standard method does not satisfy obviously the deflection of the thin plates is approximated via the mk interpolation to illustrate this approach numerical analysis is examined in both regular and irregular systems three examples with different geometric shapes of thin plates undergoing a simply supported boundary are performed in addition two important parameters of the present method are also analyzed a good agreement can be found among the proposed analytical and finite element methods copyright 2008 john wiley sons ltd

optimal a posteriori parameter choice for tikhonov regularization for solving nonlinear ill posed problems the authors propose an a posteriors strategy for choosing the regularization parameter in tikhonov regularization for solving nonlinear ill posed problems and show that under certain conditions the convergence rate obtained with this strategy is optimal as a by product a new stability estimate for the regularized solutions is given which applies to a class of parameter identification problems the authors compare the parameter choice strategy with morozov s discrepancy principle finally numerical results are presented

the complex variable meshless local petrov galerkin method for elasticity problems of functionally graded materials this paper proposed the complex variable meshless local petrov galerkin cvmlpg method for the static analysis of functionally graded materials fgms in the presented method the complex variable moving least square cvmls approximation which is established based on the moving least square mls approximation by introducing the complex variable theory is adopted for construction of the field approximation function compared with the conventional mls method the number of the unknown coefficients in the trial function of the cvmls method is less than that of the mls approximation thus higher efficiency and accuracy can be achieved under the same node distributions one advantage of the cvmlpg method for the fgms is that the variations of the functionally graded material properties are simulated by using material parameters at gauss points so it totally avoids the issue of the assumption of homogeneous in each element in the finite element method fem for the fgms some of selected benchmark examples are considered to confirm the validity and accuracy of the proposed method

the complex variable meshless local petrov galerkin method for elastodynamic problems the complex variable meshless local petrov galerkin cvmlpg method is further developed for structural dynamic analyses of two dimensional 2d solids the complex variable moving least square cvmls approximation is used to construct the shape function and the heaviside step function is chosen for representing the test function in the construction of the well performed shape function the trial function of 2d problem is formed with a one dimensional 1d basis function thus improving computational efficiency the governing elastodynamic equations are transformed into a standard local weak formulation and then it is discretized into a meshfree system of time dependent equations which are solved by the standard implicit newmark time integration scheme numerical results obtained from the proposed cvmlpg method are compared with the exact solutions and those of the conventional mlpg method and excellent agreement is achieved

a meshless local kriging method for large deformation analyses in this paper a well developed meshless numerical technique local kriging lokriging method is used to develop the lokriging formulation for the large deformation problems which are geometrically nonlinear this is the first work for the geometrically nonlinear analyses by this meshless local weak form method in the lokriging method the kriging interpolation is employed to construct the meshless shape functions the spline function with high continuity is used as the weight function the discrete equations of the large deformation analysis for two dimensional solids are obtained using the local weak forms and based on the total lagrangian tl approach the presently developed lokriging method is a truly meshless method as it does not require the mesh either for the construction of the shape functions or for the integration of the local weak form several numerical examples of the two dimensional geometrically nonlinear analysis are presented to illustrate the performance of the present lokriging method the present nonlinear lokriging formulation is also used for the large deformation analysis of the microelectromechanical systems mems device the numerical results are compared with the experimental results very good results are obtained all these applications have demonstrated that the present lokriging method is very effective for the large deformation analyses because it avoids all mesh distortion issues

moving kriging interpolation and element free galerkin method a new formulation of the element free galerkin efg method is presented in this paper efg has been extensively popularized in the literature in recent years due to its flexibility and high convergence rate in solving boundary value problems however accurate imposition of essential boundary conditions in the efg method often presents difficulties because the kronecker delta property which is satisfied by finite element shape functions does not necessarily hold for the efg shape function the proposed new formulation of efg eliminates this shortcoming through the moving kriging mk interpolation two major properties of the mk interpolation the kronecker delta property i s j i j and the consistency property n i i x i and n i i x x l i x i are proved some preliminary numerical results arc given

the complex variable meshless local petrovgalerkin method for elastodynamic analysis of functionally graded materials as an improvement of the meshless local petrovgalerkin mlpg the complex variable meshless local petrovgalerkin cvmlpg method is extended here to dynamic analysis of functionally graded materials fgms in this method the complex variable moving least squares cvmls approximation is used instead of the traditional moving least squares mls to construct the shape functions the main advantage of the cvmls approximation over mls approximation is that the number of the unknown coefficients in the trial function of the cvmls approximation is less than that of the mls approximation thus higher efficiency and accuracy can be achieved under the same node distributions in implementation of the present method the variations of the fgms properties are computed by using material parameters at gauss points so it totally avoids the issue of the assumption of homogeneous in each element in the finite element method fem for the fgms several numerical examinations for dynamic analysis of fgms are carried out to demonstrate the accuracy and efficiency of the cvmlpg

global uniqueness for a two dimensional inverse boundary value problem we show that the coefficient y x of the elliptic equation vie qyvu 0 in a two dimensional domain is uniquely determined by the corresponding dirichlet to neumann map on the boundary and give a reconstruction pro

identification of a temperature dependent heat conductivity from single boundary measurements considering the identification of a temperature dependent conductivity in a quasilinear elliptic heat equation from single boundary measurements we proof uniqueness in dimensions n ge 2 taking noisy data into account we apply tikhonov regularization in order to overcome the instabilities by using a problem adapted adjoint we give convergence rates under substantially weaker and more realistic conditions than required by the general theory our theory is supported by numerical tests

meshless local b spline fd method and its application for 2d heat conduction problems with spatially varying thermal conductivity abstract in this paper a new class of meshless methods based on local collocation and b spline basis functions is presented for solving elliptic problems the proposed approach is called as meshless local b spline basis functions based finite difference local b fd method the method was straightforward to develop and program as it was truly meshless only scattered nodal distribution was required hence avoiding at all mesh connectivity for field variable approximation and integration in the method any governing equations were discretized by b spline approximation in the spirit of fd technique using local b spline collocation i e any derivative at a point or node was stated as neighboring nodal values based on the b spline interpolants in addition as b spline basis functions pose favorable properties such as i easy to construct to any arbitrary order degree ii have partition of unity property and iii can be easily designed to pose the kronecker delta property the shape function construction as well as the imposition of boundary conditions can be incorporated efficiently in the present method the applicability and capability of the present local b fd method were demonstrated through several heat conduction problems with heat generation and spatially varying conductivity