on computational shells with scale effects abstract the paper deals with the computations of so called geometrically exact shells with scale effects these type of computations are relevant to thin walled structures at small scales e g thin films nanotubes etc the shell formulation exhibits higher order gradients and is developed following some author s recent work on generalised continua the framework has been modified as to account for two dimensional surfaces as well the shell formulation reduces to a standard one upon disregarding the higher gradient terms the classical part of the formulation is a well known 7 parameter model previously developed by one of the authors which takes thickness change into account the numerical treatment is based on a meshfree formulation which provides the necessary c 1 continuity as possible applications dynamic buckling of cylindrical and spherical shells is investigated and some results for various states of loading and scale parameters are presented the examples include also nanotubes of different dimensions where scale effects matter the influence of the extra gradients is well demonstrated resulting in different buckling behaviours

generalized multiple scale reproducing kernel particle methods abstract an approach to unify reproducing kernel methods under one large umbrella and an extension to include time and spatial shifting are proposed the study is divided into three major topics the groundwork is set by revisiting the fourier analysis of discrete systems the multiresolution concept and its significance in devising the reproducing kernel methods and its discrete counterpart reproducing kernel particle methods are explained an edge detection technique based on multiresolution analysis is developed this wavelet approach together with particle methods gives rise to a straightforward h adaptivity algorithm by using this framework a hermite reproducing kernel method is also proposed and its relation to wavelet methods is presented it is also shown that the new approach generalizes existing kernel methods and it can easily be degenerated into other widely used methods such as partition of unity moving least square interpolants smooth particle hydrodynamics scaling functions and wavelets and multiple scale analysis furthermore the hermite reproducing kernel particle method a particle based discrete version of the hermite reproducing kernel method is developed finally multiple scale methods based on frequency and wave number shifting techniques are presented a stability analysis is also presented for newmark time integration schemes for the low frequency equation numerical examples are presented throughout the paper to illustrate the flexibility and accuracy of this class of multiple scale methods

optimized schwarz method with complete radiation transmission conditions for the helmholtz equation in waveguides in this paper we present a nonoverlapping optimized schwarz algorithm with a high order transmission condition for the helmholtz equation posed in waveguides we introduce the new high order transmission conditions based on the complete radiation boundary conditions crbcs that have been developed for high order absorbing boundary conditions we obtain the convergence rate of the algorithm in terms of reflection coefficients of crbcs which decrease exponentially with the order of crbcs it will be shown that damping parameters involved in the transmission conditions can be selected in an optimal way for enhancing the convergence of the schwarz algorithm also this algorithm can be employed efficiently for a preconditioner in gmres implementations based on the substructured form as in m j gander f magoules and f nataf siam j sci comput 24 2002 pp 38 60 finally numerical examples confirming the theory will be presented

optimized double sweep schwarz method by complete radiation boundary conditions we present an optimized double sweep nonoverlapping schwarz method for solving the helmholtz equation in semi infinite waveguides the domain is decomposed into nonoverlapped layered subdomains along the axis of the waveguide and local wave propagation problems equipped with complete radiation conditions for high order absorbing boundary conditions are solved forward and backward sequentially for communication between subdomains neumann data of local solutions in one domain are transferred to the neighboring subdomain in the forward direction and dirichlet data are exploited in the backward direction the complete radiation boundary conditions enable us to not only minimize reflection coefficients for most important modes in an optimal way but also find neumann data without introducing errors that would be produced if finite difference formulas were used for computing neumann data the convergence of the double sweep schwarz method is proved and numerical experiments using it as a preconditioner are presented to confirm the convergence theory

a point interpolation method for simulating dissipation process of consolidation abstract a biot s consolidation problem in foundation engineering is numerically investigated using improved point interpolation method pim a weak form of biot s theory is first developed to consider the unbalanced forces at previous time step and thus guarantees the global equilibrium at current step two independent variables in the weak form displacement and excess pore water pressure are approximated using the same shape functions through pim technique the pim technique constructs its interpolation functions through a cluster of scattered points in problem domain and its shape function is of delta properties thus implementation of essential boundary conditions is as easy as in conventional finite element method crank nicholson s integration scheme is used to discretize time domain finally examples are studied and compared with finite element methods to demonstrate its capability

a parallelized meshfree method with boundary enrichment for large scale cfd a parallel computational implementation of a meshfree method the reproducing kernel particle method rkpm is used for 3 d implicit cfd analysis a novel procedure for implementing the essential boundary condition using the hierarchical enrichment method is presented using this enrichment along the essential boundaries produces results that more closely match experimental and analytical results for a flow past a cylinder problem than does either the finite element method or other meshfree methods that require matrix inversion for the application of essential boundary conditions this technique also allows the efficient parallelization of the algorithm and leads to higher parallel speedups than do other boundary condition implementations many of which involve inherently serial steps this is important because the expense of meshfree computations makes parallelization crucial for large size problems the performance of the parallelization technique and the accuracy of the implicit cfd algorithm are demonstrated in two example problems

brownian limits local limits and variance asymptotics for convex hulls in the ball schreiber and yukich ann probab 36 2008 363 396 establish an asymptotic representation for random convex polytope geometry in the unit ball bd d 2 in terms of the general theory of stabilizing functionals of poisson point processes as well as in terms of generalized paraboloid growth processes this paper further exploits this connection introducing also a dual object termed the paraboloid hull process via these growth processes we establish local functional limit theorems for the properly scaled radius vector and support functions of convex polytopes generated by high density poisson samples we show that direct methods lead to explicit asymptotic expressions for the fidis of the properly scaled radius vector and support functions generalized paraboloid growth processes coupled with general techniques of stabilization theory yield brownian sheet limits for the defect volume and mean width functionals finally we provide explicit variance asymptotics and central limit theorems for the k face and intrinsic volume functionals

convergence analysis of a hierarchical enrichment of dirichlet boundary conditions in a mesh free method implementation of dirichlet boundary conditions in mesh free methods is problematic in wagner and liu international journal for numerical methods in engineering 2001 50 507 a hierarchical enrichment technique is introduced that allows a simple implementation of the dirichlet boundary conditions in this paper we provide some error analysis for the hierarchical enrichment mesh free technique we derive optimal order error estimates for the hierarchical enrichment mesh free interpolants for one dimensional elliptic boundary value problems we can directly apply the interpolation error estimates to obtain error estimates for the mesh free solutions for higher dimensional problems derivation of error estimates for the mesh free solutions depends on the availability of an inverse inequality numerical examples in 1d and 2d are included showing the convergence behaviour of mesh free interpolants and mesh free solutions when the hierarchical enrichment mesh free technique is employed copyright 2001 john wiley sons ltd

essential boundary condition enforcement in meshless methods boundary flux collocation method element free galerkin efg methods are based on a moving least squares mls approximation which has the property that shape functions do not satisfy the kronecker delta function at nodal locations and for this reason imposition of essential boundary conditions is difficult in this paper the relationship between corrected collocation and lagrange multiplier method is revealed and a new strategy that is accurate and very simple for enforcement of essential boundary conditions is presented the accuracy and implementation of this new technique is illustrated for one dimensional elasticity and two dimensional potential field problems copyright 2001 john wiley sons ltd

optimized schwarz methods without overlap for the helmholtz equation the classical schwarz method is a domain decomposition method to solve elliptic partial differential equations in parallel convergence is achieved through overlap of the subdomains we study in this paper a variant of the schwarz method which converges without overlap for the helmholtz equation we show that the key ingredients for such an algorithm are the transmission conditions we derive optimal transmission conditions which lead to convergence of the algorithm in a finite number of steps these conditions are however nonlocal in nature and we introduce local approximations which we optimize for performance of the schwarz method this leads to an algorithm in the class of optimized schwarz methods we present an asymptotic analysis of the optimized schwarz method for two types of transmission conditions robin conditions and transmission conditions with second order tangential derivatives numerical results illustrate the effectiveness of the optimized schwarz method on a model problem and on a problem from industry

an implicit corrected sph formulation for thermal diffusion with linear free surface boundary conditions the smoothed particle hydrodynamics sph method has proven useful for modeling large deformation of fluids including fluids with stress free surfaces because of the lagrangian nature of the method it is well suited to address the thermal evolution of these free surface flows boundary conditions at the interface of the fluid with a solid wall are usually enforced through the use of boundary particles however applying conditions at free surfaces in particular gradient boundary conditions can be problematic with traditional sph formulations due to the degradation of the gradient approximation in these regions compounding this difficulty is that traditional approximations of the laplacian operator suffer a similar degradation near free surfaces a new sph formulation of the laplacian operator is presented which improves the accuracy near free surface boundaries this new form is based on a gradient approximation commonly used in thermal viscous and pressure projection problems but includes higher order terms in the appropriate taylor series comparisons with other approximations of second order derivatives are given the discretization is tested by solving steady state and transient problems of thermal diffusion using the backward euler method with a gmres solver boundary conditions are imposed through an augmented matrix copyright 2008 john wiley sons ltd

variance asymptotics and scaling limits for gaussian polytopes let k n be the convex hull of i i d random variables distributed according to the standard normal distribution on mathbb r d we establish variance asymptotics as n rightarrow infty for the re scaled intrinsic volumes and k face functionals of k n k in 0 1 ldots d 1 resolving an open problem weil and wieacker handbook of convex geometry vol b pp 1391 1438 north holland elsevier amsterdam 1993 variance asymptotics are given in terms of functionals of germ grain models having parabolic grains with apices at a poisson point process on mathbb r d 1 times mathbb r with intensity e h dh dv the scaling limit of the boundary of k n as n rightarrow infty converges to a festoon of parabolic surfaces coinciding with that featuring in the geometric construction of the zero viscosity solution to burgers equation with random input

parallel computation of meshless methods for explicit dynamic analysis a parallel computational implementation of modern meshless methods is presented for explicit dynamic analysis the procedures are demonstrated by application of the reproducing kernel particle method rkpm aspects of a coarse grain parallel paradigm are detailed for a lagrangian formulation using model partitioning integration points are uniquely defined on separate processors and particle definitions are duplicated as necessary so that all support particles for each point are defined locally on the corresponding processor several partitioning schemes are considered and a reduced graph based procedure is presented partitioning issues are discussed and procedures to accommodate essential boundary conditions in parallel are presented explicit mpi message passing statements are used for all communications among partitions on different processors the effectiveness of the procedure is demonstrated by highly deformable inelastic example problems

the method of polarized traces for the 2d helmholtz equation we present a solver for the 2d high frequency helmholtz equation in heterogeneous acoustic media with online parallel complexity that scales optimally as o n l where n is the number of volume unknowns and l is the number of processors as long as l grows at most like a small fractional power of n the solver decomposes the domain into layers and uses transmission conditions in boundary integral form to explicitly define polarized traces i e up and down going waves sampled at interfaces local direct solvers are used in each layer to precompute traces of local green s functions in an embarrassingly parallel way the offline part and incomplete green s formulas are used to propagate interface data in a sweeping fashion as a preconditioner inside a gmres loop the online part adaptive low rank partitioning of the integral kernels is used to speed up their application to interface data the method uses second order finite differences the complexity scalings are empirical but motivated by an analysis of ranks of off diagonal blocks of oscillatory integrals they continue to hold in the context of standard geophysical community models such as bp and marmousi 2 where convergence occurs in 5 to 10 gmres iterations while the parallelism in this paper stems from decomposing the domain we do not explore the alternative of parallelizing the systems solves with distributed linear algebra routines

reproducing kernel particle methods for large deformation analysis of non linear structures abstract large deformation analysis of non linear elastic and inelastic structures based on reproducing kernel particle methods rkpm is presented the method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis the current formulation considers hyperelastic and elasto plastic materials since they represent path independent and path dependent material behaviors respectively in this paper a material kernel function and an rkpm material shape function are introduced for large deformation analysis the support of the rkpm material shape function covers the same set of particles during material deformation and hence no tension instability is encountered in the large deformation computation the essential boundary conditions are introduced by the use of a transformation method the transformation matrix is formed only once at the initial stage if the rkpm material shape functions are employed the appropriate integration procedures for the moment matrix and its derivative are studied from the standpoint of reproducing conditions in transient problems with an explicit time integration method the lumped mass matrices are constructed at nodal coordinate so that masses are lumped at the particles several hyperelasticity and elasto plasticity problems are studied to demonstrate the effectiveness of the method the numerical results indicated that rkpm handles large material distortion more effectively than finite elements due to its smoother shape functions and consequently provides a higher solution accuracy under large deformation unlike the conventional finite element approach the nodal spacing irregularity in rkpm does not lead to irregular mesh shape that significantly deteriorates solution accuracy no volumetric locking is observed when applying non linear rkpm to nearly incompressible hyperelasticity and perfect plasticity problems further model adaptivity in rkpm can be accomplished simply by adding more points in the highly deformed areas without remeshing

on a path following method for non linear solid mechanics with applications to structural and cardiac mechanics subject to arbitrary loading scenarios abstract in computational solid mechanics path following methods have been proven useful when dealing with non monotonously evolving loading magnitudes as encountered e g in instability or softening behaviour the present work derives from a displacement based method a cavity volume based path following method and considers its application specifically to cardiac mechanics problems both methods are able to account for an arbitrary number of simultaneously acting loading conditions when applied to the newton raphson method the corresponding loading increments are computed by means of volume increments or point wise prescribed displacement increments respectively no additional variables are required and the physics of the problem at hands is not altered both methods are implemented in an in house meshfree modelling software and successfully applied to non linear elastic and inelastic problems in structural mechanics the cavity volume control method in particular is demonstrated to accurately predict the highly non linear elastic and anisotropic material behaviour encountered when modelling the heart albeit the proposed methods can be equally used e g in finite element methods they are very well suited for meshfree methods where the kronecker delta property does not apply

new boundary condition treatments in meshfree computation of contact problems due to the loss of kronecker delta properties in the meshfree shape functions the imposition of essential boundary conditions consumes significant cpu time in meshfree computation in this work two boundary condition treatments are proposed to enhance the computational efficiency of meshfree methods for contact problems the mixed transformation method is modified from the previous full transformation method by introducing a node partitioning and a mixed coordinate so that the matrix inversion and multiplication of coordinate transformation involves operations only on the sub degrees of freedom associated with the boundary group the boundary singular kernel method introduces singularities to the kernel functions of the essential and contact boundary nodes so that the corresponding coefficients of the singular kernel shape functions recover nodal values and consequently kinematic constraints can be imposed directly the effectiveness of the proposed methods is demonstrated in several numerical examples

central limit theorems for random polygons in an arbitrary convex set we study the probability distribution of the area and the number of vertices of random polygons in a convex set kr 2 the novel aspect of our approach is that it yields uniform estimates for all convex sets kr 2 without imposing any regularity conditions on the boundary k our main result is a central limit theorem for both the area and the number of vertices settling a well known conjecture in the field we also obtain asymptotic results relating the growth of the expectation and variance of these two functionals

central limit theorems for random polytopes let k be a smooth convex set the convex hull of independent random points in k is a random polytope central limit theorems for the volume and the number of i dimensional faces of random polytopes are proved as the number of random points tends to infinity one essential step is to determine the precise asymptotic order of the occurring variances

on controllability methods for the helmholtz equation abstract when the helmholtz equation is discretized by standard finite difference or finite element methods the resulting linear system is highly indefinite and thus notoriously difficult to solve in fact increasingly so at higher frequency the exact controllability approach bristeau et al 1994 instead reformulates the problem in the time domain and seeks the time harmonic solution of the corresponding wave equation by iteratively reducing the mismatch between the solution at initial time and after one period the controllability method greatly speeds up the convergence to the time harmonic asymptotic limit moreover each conjugate gradient iteration solely relies on standard numerical algorithms which are inherently parallel and robust against higher frequencies the original energy functional used to penalize the departure from periodicity is strictly convex only for sound soft scattering problems to extend the controllability approach to general boundary value problems governed by the helmholtz equation new penalty functionals are proposed which are numerically efficient numerical experiments for wave scattering from sound soft and sound hard obstacles inclusions but also for wave propagation in closed wave guides illustrate the usefulness of the resulting controllability methods

the combinatorial structure of random polytopes abstract choose n random points in r d let p n be their convex hull and denote by f i p n the number of i dimensional faces of p n a general method for computing the expectation of f i p n i 0 d 1 is presented this generalizes classical results of efron in the case i 0 and renyi and sulanke in the case i d 1 to arbitrary i for random points chosen in a smooth convex body a limit law for f i p n is proved as n for random points chosen in a polytope the expectation of f i p n is determined as n this implies an extremal property for random points chosen in a simplex

stable element free galerkin solution procedures for the coupled soil pore fluid problem it is always difficult to solve the coupled soil pore fluid problem when the soil is saturated and impermeable because this situation often results in intensive oscillations of the solutions this topic has been discussed widely in the field of the finite element method but rarely by meshless methods the element free galerkin efg method has outstanding advantages of solving this problem based on the fact that its interpolation function can be constructed flexibly by the nodes in the compact domain in this study an efg numerical model together with a stabilization technique is proposed to obtain stable solutions especially for the saturated and impermeable soil close agreement between computational results and analytical solutions for one and two dimensional examples shows that the proposed numerical model not only provides highly accurate solutions for the saturated soil with relatively high permeability but also eliminates the oscillations of the solutions very effectively for the saturated and impermeable soil furthermore the influences of the hydraulic anisotropy a typical property of two dimensional problems on the proposed stabilization technique are discussed it is suggested that the optimal distribution of the nodes of essential variables can be designed according to the relative importance of the permeability in different directions copyright c 2010 john wiley sons ltd

element free galerkin method for wave propagation and dynamic fracture abstract element free galerkin method efg is extended to dynamic problems efg method which is based on moving least square interpolants mls requires only nodal data no element connectivity is needed this makes the method particularly attractive for moving dynamic crack problems since remeshing can be avoided in contrast to the earlier formulation for static problems by authors the weak form of kinematic boundary conditions for dynamic problems is introduced in the implementation to enforce the kinematic boundary conditions with this formulation the stiffness matrix is symmetric and positive semi definite and hence the consistency conergence and stability analyses of time integration remain the same as those in finite element method numerical examples are presented to illustrate the performance of this method the relationship between the element free galerkin method and the smooth particle hydrodynamics sph method is also discussed in this paper results are presented for some one dimensional problems and two dimensional problems with static and moving cracks

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

recursive sweeping preconditioner for the three dimensional helmholtz equation this paper introduces the recursive sweeping preconditioner for the numerical solution of the helmholtz equation in three dimensions this is based on the earlier work of the sweeping preconditioner with the moving perfectly matched layers the key idea is to apply the sweeping preconditioner recursively to the quasi two dimensional auxiliary problems introduced in the three dimensional 3d sweeping preconditioner compared to the nonrecursive 3d sweeping preconditioner the setup cost of this new approach drops from o n 4 3 to o n the application cost per iteration drops from o n log n to o n and the iteration count increases only mildly when combined with the standard gmres solver several numerical examples are tested and the results are compared with the nonrecursive sweeping preconditioner to demonstrate the efficiency of the new approach

a lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue we present a novel lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue linear solids are represented by the lagrangian formulation of the stress strain relationship that is extended to nonlinear solids by using the lagrangian evolution of the deformation gradient described in a moving framework the present method introduces a level set description along with the particles to capture the body deformations and to enforce the boundary conditions furthermore the accuracy of the method in cases of large deformations is ensured by implementing a particle remeshing procedure the method is validated in several benchmark problems in two and three dimensions and the results compare well with the results of respective finite elements simulations in simulations of large solid deformation under plane strain compression the finite element solver exhibits spurious structures that are not present in the lagrangian particle simulations the particle simulations are compared with experimental results in an aspiration test of liver tissue

variance asymptotics for random polytopes in smooth convex bodies let k subset mathbb r d be a smooth convex set and let mathcal p lambda be a poisson point process on mathbb r d of intensity lambda the convex hull of mathcal p lambda cap k is a random convex polytope k lambda as lambda rightarrow infty we show that the variance of the number of k dimensional faces of k lambda when properly scaled converges to a scalar multiple of the affine surface area of k similar asymptotics hold for the variance of the number of k dimensional faces for the convex hull of a binomial process in k

hierarchical enrichment for bridging scales and mesh free boundary conditions the finite element method when used with a basis made up of piecewise polynomials often requires the generation of a very fine computational mesh in order to capture localized solution phenomena such as boundary layers or near singularities enrichment of the basis with additional functions obtained through analytical or experimental means can allow for a coarser mesh and more accurate solution we introduce an enrichment scheme in which an interaction or bridging scale term is used to separate the basis formed by the enrichment functions from the original set of basis functions in effect making the enrichment hierarchical this separation of scales allows the simple application of essential boundary conditions it also allows a quantification of the effects of the enrichment leading to strategies for error estimation and control of the stiffness matrix condition number we also find that this formulation allows for the simple application of essential boundary conditions for mesh free shape functions which are notoriously problematic we find that for multiple dimensions care must be taken to derive a weak form which is truly consistent with the strong form on the essential boundary copyright 2001 john wiley sons ltd

a shell theory with scale effects and higher order gradients abstract this works follows a generalised continuum framework developed by sansour 1998 to derive a strain gradient formulation suitable to address scale effects of structures where one dimension is very small e g thin films nano tubes etc whereas a previous strain gradient approach by sansour et al 2009 considered the fully three dimensional setting the approach here proposes a shell theory which aims to run computations of thin structures more efficiently and to include scale effects the theory features a generalised deformation description new strain and stress measures as consequence of these new quantities a corresponding generalised variational principle is formulated the approach is completed by dirichlet boundary conditions for the displacement field and its derivatives a numerical example is presented based on a meshfree formulation which provides the necessary c 1 continuity

on convergence conditions of partitioned solution procedures for consolidation problems abstract a systematic approach to determine conditions for convergence of partitioned staggered procedures for consolidation problems is presented consistency convergence and stability is investigated for linear and nonlinear problems and a comparison of the partitioned and direct method is made conclusions based also on numerical evidence are drawn the significance of the ratio of the time step length to the square of the finite element mesh length is shown

a point interpolation method for two dimensional solids a point interpolation method pim is presented for stress analysis for two dimensional solids in the pim the problem domain is represented by properly scattered points a technique is proposed to construct polynomial interpolants with delta function property based only on a group of arbitrarily distributed points the pim equations are then derived using variational principles in the pim the essential boundary conditions can be implemented with ease as in the conventional finite element methods the present pim has been coded in fortran the validity and efficiency of the present pim formulation are demonstrated through example problems it is found that the present pim is very easy to implement and very flexible for obtained displacements and stresses of desired accuracy in solids as the elements are not used for meshing the problem domain the present pim opens new avenues to develop adaptive analysis codes for stress analysis in solids and structures copyright 2001 john wiley sons ltd

imposing essential boundary conditions in mesh free methods imposing essential boundary conditions is a key issue in mesh free methods the mesh free interpolation does not verify the kronecker delta property and therefore the imposition of prescribed values is not as straightforward as for the finite element method the aim of this paper is to present a general overview on the existing techniques to enforce essential boundary conditions in galerkin based mesh free methods special attention is paid to the mesh free coupling with finite elements for the imposition of prescribed values and to methods based on a modification of the galerkin weak form particular examples are used to analyze and compare their performance in different situations

a source transfer domain decomposition method for helmholtz equations in unbounded domain we propose and study a domain decomposition method for solving the truncated perfectly matched layer pml approximation in bounded domain of helmholtz scattering problems the method is based on the decomposition of the domain into nonoverlapping layers and the idea of source transfer which transfers the sources equivalently layer by layer so that the solution in the final layer can be solved using a pml method defined locally outside the last two layers the convergence of the method is proved for the case of constant wave number based on the analysis of the fundamental solution of the pml equation the method can be used as an efficient preconditioner in the preconditioned gmres method for solving discrete helmholtz equations with constant and heterogeneous wave numbers numerical examples are included

moving particle finite element method with superconvergence nodal integration formulation and applications abstract a new approach of moving particle finite element method has been developed which is capable to gain a global superconvergence through solving particle kernel function to satisfy high order consistencies the nodal based moving particle finite element method inconjunction with the proposed superconvergence approach provides an optimized combination in numerical accuracy and computation efficiency the three dimensional engineering scale simulations demonstrate that this scheme is robust and capable to handle high speed penetration and dynamic crack propagation with intersonic and supersonic speeds

imposing nonlocal boundary conditions in galerkin type methods based on non interpolatory functions abstract the imposition of inhomogeneous dirichlet essential boundary conditions is a fundamental challenge in the application of galerkin type methods based on non interpolatory functions i e functions which do not possess the kronecker delta property such functions typically are used in various meshfree methods as well as methods based on the isogeometric paradigm the present paper analyses a model problem consisting of the poisson equation subject to non standard boundary conditions namely instead of classical boundary conditions the model problem involves dirichlet and neumann type nonlocal boundary conditions variational formulations with strongly and weakly imposed inhomogeneous dirichlet type nonlocal conditions are derived and compared within an extensive numerical study in the isogeometric framework based on non uniform rational b splines nurbs the attention in the numerical study is paid mainly to the influence of the nonlocal boundary conditions on the properties of the considered discretisation methods

gpu acceleration of stiffness matrix calculation and efficient initialization of efg meshless methods abstract meshless methods have a number of virtues in problems concerning crack growth and propagation large displacements strain localization and complex geometries among other despite the fact that they do not rely on a mesh meshless methods require a preliminary step for the identification of the correlation between nodes and gauss points before building the stiffness matrix this is implicitly performed with the mesh generation in fem but must be explicitly done in efg methods and can be time consuming furthermore the resulting matrices are more densely populated and the computational cost for the formulation and solution of the problem is much higher than the conventional fem this is mainly attributed to the vast increase in interactions between nodes and integration points due to their extended domains of influence for these reasons computing the stiffness matrix in efg meshless methods is a very computationally demanding task which needs special attention in order to be affordable in real world applications in this paper we address the pre processing phase dealing with the problem of defining the necessary correlations between nodes and gauss points and between interacting nodes as well as the computation of the stiffness matrix a novel approach is proposed for the formulation of the stiffness matrix which exhibits several computational merits one of which is its amenability to parallelization which allows the utilization of graphics processing units gpus to accelerate computations

reproducing kernel element method part i theoretical formulation in this paper and its sequels we introduce and analyze a new class of methods collectively called the reproducing kernel element method rkem the central idea in the development of the new method is to combine the strengths of both finite element methods fem and meshfree methods two distinguished features of rkem are the arbitrarily high order smoothness and the interpolation property of the shape functions these properties are desirable especially in solving galerkin weak forms of higher order partial differential equations and in treating dirichlet boundary conditions so unlike the fem there is no need for special treatment with the rkem in solving high order equations compared to meshfree methods dirichlet boundary conditions do not present any difficulty in using the rkem a rigorous error analysis and convergence study of the method are presented the performance of the method is illustrated and assessed through some numerical examples

elasto plastic analysis of reinforced soils using mesh free method in this paper the application of the mesh free method mfm for the elasto plastic analysis of reinforced soils is studied for the first time the applied mesh free method is called the radial point interpolation method rpim in mfm unlike the finite element method fem there is no need of mesh in the traditional sense and the shape functions are based on nodes in the present study the reinforced soil is divided into three separate parts of soil reinforcements and interface layers the displacement field in each part is constructed by rpim the final system of equations is derived by the substitution of the displacement field into the weak form of the governing equation the elasto plastic behaviors of soil reinforcements and interface layers are considered there is also the ability of slippage modeling between the soil and reinforcement based on the derived equations a computer code has been developed and its validity investigated by solving some examples at the end of the paper

a stabilized iterative scheme for coupled hydro mechanical systems using reproducing kernel particle method summary in this paper a novel iterative coupling scheme is developed for solving coupled hydro mechanical problems using reproducing kernel particle method the numerical scheme calls the fluid and the solid solvers sequentially and iteratively until convergent solutions are obtained to overcome the numerical instability problem a simple stabilization technique is developed and proved to be unconditionally stable through stability analysis the accuracy and convergence of the proposed numerical scheme are demonstrated through extensive parametric studies of one dimensional and two dimensional consolidation simulations using fully saturated elastic medium as well as biaxial test using a fully nonlinear soil model copyright 2014 john wiley sons ltd

a collocated c0 finite element method reduced quadrature perspective cost comparison with standard finite elements and explicit structural dynamics summary we demonstrate the potential of collocation methods for efficient higher order analysis on standard nodal finite element meshes we focus on a collocation method that is variationally consistent and geometrically flexible converges optimally embraces concepts of reduced quadrature and leads to symmetric stiffness and diagonal consistent mass matrices at the same time it minimizes the evaluation cost per quadrature point thus reducing formation and assembly effort significantly with respect to standard galerkin finite element methods we provide a detailed review of all components of the technology in the context of elastodynamics that is weighted residual formulation nodal basis functions on gauss lobatto quadrature points and symmetrization by averaging with the ultra weak formulation we quantify potential gains by comparing the computational efficiency of collocated and standard finite elements in terms of basic operation counts and timings our results show that collocation is significantly less expensive for problems dominated by the formation and assembly effort such as higher order elastostatic analysis furthermore we illustrate the potential of collocation for efficient higher order explicit dynamics throughout this work we advocate a straightforward implementation based on simple modifications of standard finite element codes we also point out the close connection to spectral element methods where many of the key ideas are already established copyright 2014 john wiley sons ltd

consistent element free galerkin method an element free galerkin efg method with linear quadratic and cubic approximations which can exactly in a numerical sense pass the corresponding patch tests is proposed and is named as consistent efg cefg method the development of this method is based on the hu washizu three field variational principle numerical integration schemes with corrected nodal derivatives at quadrature points are proposed according to the satisfaction of the orthogonality condition between stress and strain difference thus the method is variationally consistent the consistency of the corrected nodal derivatives and the satisfaction of patch test conditions are theoretically proved and also numerically validated numerical results show that the proposed cefg method greatly improves the numerical performance of the efg method in terms of accuracy convergence efficiency and stability especially the proposed cubic cefg method which shows exceptional accuracy and convergence copyright 2014 john wiley sons ltd

variance asymptotics and central limit theorems for generalized growth processes with applications to convex hulls and maximal points we show that the random point measures induced by vertices in the convex hull of a poisson sample on the unit ball when properly scaled and centered converge to those of a mean zero gaussian field we establish limiting variance and covariance asymptotics in terms of the density of the poisson sample similar results hold for the point measures induced by the maximal points in a poisson sample the approach involves introducing a generalized spatial birth growth process allowing for cell overlap

explicit form and efficient computation of mls shape functions and their derivatives this work presents a general and efficient way of computing both diffuse and full derivatives of shape functions for meshless methods based on moving least squares approximation mls and interpolation it is an extension of the recently introduced consistency approach based on lagrange multipliers which provides a general framework for constrained mls along with robust algorithms for the computation of shape functions and their diffuse derivatives the particularity of the proposed algorithms is that they do not involve matrix inversion or linear system solving the previous approach is limited to diffuse derivatives of the shape functions and not their full derivatives which are usually much more expensive to obtain in the present paper we propose to efficiently compute the full derivatives by a new algorithm based on the formal differentiation of the previous one in this way we obtain a unified low cost consistent methodology for evaluating the shape functions and both their diffuse and full derivatives in the second part of the paper we introduce explicit forms of mls shape functions in 1d 2d and 3d for an arbitrary number of nodes these forms are especially useful for comparing finite element and mls approximations finally we present a general architecture of an mls program copyright 2000 john wiley sons ltd

a finite point method in computational mechanics applications to convective transport and fluid flow the paper presents a fully meshless procedure fo solving partial differential equations the approach termed generically the finite point method is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals some examples showing the accuracy of the method for solution of adjoint and non self adjoint equations typical of convective diffusive transport and also to the analysis of compressible fluid mechanics problem are presented

a meshless integral method based on regularized boundary integral equation a meshless integral method based on the regularized boundary integral equation is developed and applied to two dimensional linear elasticity the governing integral equation is obtained from the weak form of elasticity over a local sub domain and the moving least squares approximation is used for meshless function approximation the method is built on the lbie method proposed by atluri and co workers and several key improvements are introduced in this work that significantly enhance the accuracy and robustness of the method the most critical improvement is the use of the subtraction technique to remove the strong singularity that results in a regularized governing integral equation the technique is straightforward and efficient and is much simpler and easier compared to other singularity removal techniques a special numerical integration is employed for the calculation of integrals with weak singularity which further improves accuracy the collocation method is employed to enforce the essential boundary conditions exactly which is simple and computationally efficient the natural boundary conditions are incorporated in the system governing equation and require no special handling numerical tests show that the meshless integral method is accurate and robust the effects of weight function support domain sub domain and monomial basis are investigated and discussed

variance asymptotics and scaling limits for random polytopes abstract let k be a convex set in r d and let k be the convex hull of a homogeneous poisson point process p of intensity on k when k is a simple polytope we establish scaling limits as for the boundary of k in a vicinity of a vertex of k and we give variance asymptotics for the volume and k face functional of k k 0 1 d 1 resolving an open question posed in 17 the scaling limit of the boundary of k and the variance asymptotics are described in terms of a germ grain model consisting of cone like grains pinned to the extreme points of a poisson point process on r d 1 r having intensity d e d h d h d v

fast alternating bidirectional preconditioner for the 2d high frequency lippmann schwinger equation this paper presents a fast iterative solver for the lippmann schwinger equation for high frequency waves scattered by a smooth medium with a compactly supported inhomogeneity the solver is based on the sparsifying preconditioner l ying multiscale model simul 13 2015 pp 644 660 and a domain decomposition approach similar to the method of polarized traces l zepeda nunez and l demanet j comput phys 308 2016 pp 347 388 the iterative solver has two levels the outer level in which a sparsifying preconditioner for the lippmann schwinger equation is constructed and the inner level in which the resulting sparsified system is solved quickly using an iterative solver preconditioned with a bidirectional matrix free variant of the method of polarized traces the complexity of the construction and application of the preconditioner is cal o n and cal o n log n respectively where n is the number of degrees of freedom numerical experiments in 2 dimensions indicate that t

moving particle finite element method with global smoothness we describe a new version of the moving particle finite element method mpfem that provides solutions within a c 0 finite element framework the finite elements determine the weighting for the moving partition of unity a concept of general shape function is proposed which extends regular finite element shape functions to a larger domain these are combined with shepard functions to obtain a smooth approximation the moving particle finite element method combines desirable features of finite element and meshfree methods the proposed approach in fact can be interpreted as a moving partition of unity finite element method or moving kernel finite element method this method possesses the robustness and efficiency of the c 0 finite element method while providing at least c 1 continuity

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

applications of point interpolation method for spatial general shells structures the meshfree point interpolation method pim based on polynomial function is presented for the static analysis of spatial general shell structures the formulation of the discrete system equations is derived from stress resultant geometrically exact shell theory of shear flexible shells based on the cosserat surface the pim technique constructs its interpolation functions through a set of arbitrarily distributed points in the problem domain and its shape function has the delta function property hence the implementation of essential boundary conditions can be imposed with ease as in conventional finite element method an improved matrix triangularization algorithm mta is proposed to obtain proper node enclosure and basis selection in order to overcome the singularity problem in the point interpolation method using a polynomial basis it is found that the shape functions are generally not compatible to ensure the compatibility of the solution and lead to non conforming pim npim when the energy principles are used to formulate pim to obtain compatible shape functions the enforcement of compatibility is needed along the common edges of the background cells in the problem domain and a background cell based nodal selection is utilized which lead to conforming pim cpim both npim and cpim are evaluated in the paper several benchmark problems for shells are analyzed to demonstrate the validity and efficiency of the npim and cpim the phenomena of shear locking and membrane locking are illustrated by showing the membrane and shear energies as fractions of the total energy the convergences and performances are investigated for both conforming and non conforming pims it is also shown that the npim and cpim with the improved mta are very easy to implement and very efficient in constructing shape functions in comparison with the element free galerkin method

a sub domain smoothed galerkin method for solid mechanics problems summary a sub domain smoothed galerkin method is proposed to integrate the advantages of mesh free galerkin method and fem arbitrarily shaped sub domains are predefined in problems domain with mesh free nodes in each sub domain based on mesh free galerkin weak formulation the local discrete equation can be obtained by using the moving kriging interpolation which is similar to the discretization of the high order finite elements strain smoothing technique is subsequently applied to the nodal integration of sub domain by dividing the sub domain into several smoothing cells moreover condensation of dof can also be introduced into the local discrete equations to improve the computational efficiency the global governing equations of present method are obtained on the basis of the scheme of fem by assembling all local discrete equations of the sub domains the mesh free properties of galerkin method are retained in each sub domain several 2d elastic problems have been solved on the basis of this newly proposed method to validate its computational performance these numerical examples proved that the newly proposed sub domain smoothed galerkin method is a robust technique to solve solid mechanics problems based on its characteristics of high computational efficiency good accuracy and convergence copyright 2014 john wiley sons ltd

perfectly matched layer boundary integral equation method for wave scattering in a layered medium for scattering problems of time harmonic waves the boundary integral equation bie methods are highly competitive since they are formulated on lower dimension boundaries or interfaces and can automatically satisfy outgoing radiation conditions for scattering problems in a layered medium standard bie methods based on green s function of the background medium need to evaluate the expensive sommerfeld integrals alternative bie methods based on the free space green s function give rise to integral equations on unbounded interfaces which are not easy to truncate since the wave fields on these interfaces decay very slowly we develop a bie method based on the perfectly matched layer pml technique the pmls are widely used to suppress outgoing waves in numerical methods that directly discretize the physical space our pml based bie method uses the pml transformed free space green s function to define the boundary integral operators the method is efficient since the pml transformed free space green s func

elastoplastic meshless integral method abstract in this paper the meshless integral method based on regularized boundary integral equation a bodin j ma x j xin p krishnaswami a meshless integral method based on regularized boundary integral equation comput methods appl mech engrg 195 2006 6258 6286 has been extended to elastoplastic materials in the formulation the domain of interest is populated with a set of nodes using an automatic node generation algorithm the sub domain and support domain associated with each node are also generated automatically using algorithms that have been developed for this purpose the governing integral equation is obtained from the weak form of elastoplasticity over a local sub domain and the moving least squares approximation is used for meshless function approximation the constitutive law is the small deformation rate independent flow theory based on von mises yielding criterion with isotropic hardening the generalized collocation method is employed to enforce the essential boundary conditions exactly which is simple and computationally efficient natural boundary conditions are incorporated in the system governing equation and require no special handling the solution algorithm for elastoplastic analysis is discussed in detail the proposed method can handle any prescribed loading profile including unloading and reversed loading numerical examples show that the elastoplastic integral meshless method is accurate and robust

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

linearized state based peridynamics for 2 d problems summary in this work the authors formulate a 2 d linearized ordinary state based peridynamic model of elastic deformations and compute the stiffness matrix for 2 d plane stress strain conditions this model is then verified by testing the recovery of elastic properties for given poisson s ratios in the range 0 1 0 45 the convergence behavior of peridynamic solutions in terms of the size of the nonlocal region by comparison with the classical local mechanics model is also discussed the degree to which the peridynamic surface effect influences the recovery of elastic properties is examined and stress strain recovery values are found to have a definite influence on the results the technique used here can provide the basis for applying 2 d peridynamic models to the study of fatigue failure and quasi static fracture problems copyright 2016 john wiley sons ltd

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

a new implementation of the element free galerkin method abstract element free galerkin methods efg are methods for solving partial differential equations with moving least squares interpolants efg methods require only nodal data no element connectivity is needed in a previous implementation of the efg method lagrange multipliers were used to enforce the essential boundary condition however the use of lagrange multipliers increases the cost of solving the linear algebraic equations a new implementation is developed based on a modified variational principle in which the lagrange multipliers are replaced at the outset by their physical meaning so that the discrete equations are banded in addition weighted orthogonal basis functions are constructed so the need for solving equations at each quadrature point is eliminated numerical examples show that the present implementation effectively computes stress concentrations and stress intensity factors at cracks with very irregular arrangements of nodes the latter makes it very advantageous for modelling progressive cracking

optimized schwarz methods for circular domain decompositions with overlap optimized schwarz methods are based on transmission conditions between subdo mains which are optimized for the problem class that is being solved such optimizations have been performed for many different types of partial differential equations but were almost exclusively based on the assumption of straight interfaces we study in this paper the influence of curvature on the optimization and we obtain four interesting new results first we show that the curvature does indeed enter the optimized parameters and the contraction factor estimates second we develop an asymptotically accurate approximation technique based on turan type inequalities in our case to solve the much harder optimization problem on the curved interface and this approximation tech nique will also be applicable to currently too complex best approximation problems in the area of optimized schwarz methods third we show that one can obtain transmission conditions from a simple circular model decomposition which have also been found using microlocal analysis but that these are not the best choices for the performance of the optimized schwarz method finally we find that in the case of curved interfaces optimized schwarz methods are not necessarily convergent for all admissible parameters our optimization leads however to parameter choices that give the same good performance for a circular decomposition as for a straight interface decomposition we illustrate our analysis with numerical experiments

the boundary node method for potential problems the element free galerkin efg method allows one to use a nodal data structure usually with an underlying cell structure within the domain of a body of arbitrary shape the usual efg combines moving least squares mls interpolants with a variational principle weak form and has been used to solve two dimensional 2 d boundary value problems in mechanics such as in potential theory elasticity and fracture this paper proposes a combination of mls interpolants with boundary integral equations bie in order to retain both the meshless attribute of the former and the dimensionality advantage of the latter this new method called the boundary node method bnm only requires a nodal data structure on the bounding surface of a body whose dimension is one less than that of the domain itself an underlying cell structure is again used for numerical integration in principle the bnm for 3 d problems should be extremely powerful since one would only need to put nodes points on the surface of a solid model for an object numerical results are presented in this paper for the solution of laplace s equation in 2 d dirichlet neumann and mixed problems have been solved some on bodies with piecewise straight and others with curved boundaries results from these numerical examples are extremely encouraging 1997 by john wiley sons ltd

central limit theorems for random polytopes in a smooth convex set let k be a smooth convex set with volume one in choose n random points in k independently according to the uniform distribution the convex hull of these points denoted by kn is called a random polytope we prove that several key functionals of kn satisfy the central limit theorem as n tends to infinity

on the variance of random polytopes abstract a random polytope is the convex hull of uniformly distributed random points in a convex body k a general lower bound on the variance of the volume and f vector of random polytopes is proved also an upper bound in the case when k is a polytope is given for polytopes as for smooth convex bodies the upper and lower bounds are of the same order of magnitude the results imply a law of large numbers for the volume and f vector of random polytopes when k is a polytope

element free galerkin method for deforming multiphase porous media in the proposed element free galerkin method for deforming multiphase porous media displacement of the porous solid skeleton is modelled by standard finite elements while wetting and non wetting fluid pore pressures are included as element free nodes the matrix formulation is derived from the variational formulation of the multiphase governing equations the case of a domain with a material or field discontinuity is handled by using lagrange multipliers one and two dimensional applications are presented for which the results compared with those obtained by either the closed form solution standard finite element approach or experimental tests show the efficiency of the proposed technique the necessity of taking air pore pressure into account for partially saturated soils is discussed free surface capturing is analysed and the problem of its intersection with outer boundaries so called seepage surface is studied 1998 john wiley sons ltd

meshfree iterative stabilized taylor galerkin and characteristic based split cbs algorithms for incompressible n s equations abstract this paper presents two stabilized schemes of the fractional step algorithm using characteristic based split and taylor galerkin like based split respectively in the meshfree context an iterative procedure which makes the convective term satisfy the momentum conservation equation in an implicit sense is introduced into the two schemes to allow much larger time step sizes a modified version of finite increment calculus process for incompressibility stabilization is developed to avoid the calculation of high order spatial derivatives numerical experiments demonstrate the capability and stability of the proposed schemes of the meshfree based fractional step method in the simulation of incompressible flows

finite element method and its analysis for a nonlinear helmholtz equation with high wave numbers the well posedness of a nonlinear helmholtz equation with an impedance boundary condition is established for high frequencies in two and three dimensions stability estimates are derived with expli

analysis of a cartesian pml approximation to acoustic scattering problems in r2 and r3 we consider the application of a perfectly matched layer pml technique applied in cartesian geometry to approximate solutions of the acoustic scattering problem in the frequency domain the pml is viewed as a complex coordinate shift stretching and leads to a variable complex coefficient equation for the acoustic wave posed on an infinite domain the complement of the bounded scatterer the use of cartesian geometry leads to a pml operator with simple coefficients although still complex symmetric non hermitian the pml reformulation results in a problem whose solution coincides with the original solution inside the pml layer while decaying exponentially outside the rapid decay of the pml solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation for the truncated problem this paper provides new stability estimates for the cartesian pml approximations both on the infinite and the truncated domain we first investigate the stability of the infinite pml approximation as a function of the pml strength s 0 this is done for pml methods which involve continuous piecewise smooth stretching as well as piecewise constant stretching functions we next introduce a truncation parameter m which determines the size of the pml layer our analysis shows that the truncated pml problem is stable provided that the product of email protected 0 is sufficiently large in which case the solution of the problem on the truncated domain converges exponentially to that of the original problem in the domain of interest near the scatterer this justifies the simple computational strategy of selecting a fixed pml layer and increasing s 0 to obtain the desired accuracy the results of numerical experiments varying m and s 0 are given which illustrate the theoretically predicted behavior

analysis of 3d solids using the natural neighbour radial point interpolation method abstract in this work an improved meshless method is proposed based on the combination of the natural neighbour finite element method with the radial point interpolation method the natural neighbour radial point interpolation method nnrpim the nodal connectivity and the node dependent integration background mesh are constructed resorting to the voronoi tessellation and to the delaunay triangulation within nnrpim the obtained shape functions pass through all nodes inside the influence cell providing shape functions with the delta kronecker property optimization tests and examples of well known 2d and 3d problems are solved in order to prove the high accuracy and convergence rate of the proposed method

an adaptive perfectly matched layer technique for time harmonic scattering problems we develop an adaptive perfectly matched layer pml technique for solving the time harmonic scattering problems the pml parameters such as the thickness of the layer and the fictitious medium property are determined through sharp a posteriori error estimates the derived finite element a posteriori estimate for adapting meshes has the nice feature that it decays exponentially away from the boundary of the fixed domain where the pml layer is placed this property makes the total computational costs insensitive to the thickness of the pml absorbing layers numerical experiments are included to illustrate the competitive behavior of the proposed adaptive method

implementation of boundary conditions for meshless methods abstract boundaries and boundary conditions are an aspect of the numerical solution of partial differential equations where meshless methods have had to surmount many initial difficulties due to the lack of a finite element like kronecker delta condition furthermore it is frequently desirable especially in fluid mechanics to impose general nonlinear boundary and interface constraints this paper describes a computationally efficient algorithm based on d alembert s principle that can be used for general constraints both in meshless methods and finite elements first a method of partitioning meshless shape functions suitable for imposing linear boundary conditions is developed subsequently an analogous method is developed for nonlinear constraints special attention is given to imposing general boundary and fluid structure interface conditions on the navier stokes equations in terms of conservative variables numerical results using d alembert s principle with the reproducing kernel particle method rkpm including viscous supersonic flow past a naca 7012 airfoil are shown

natural domain decomposition algorithms for the solution of time harmonic elastic waves we study for the first time schwarz domain decomposition methods for the solution of the navier equations modeling the propagation of elastic waves these equations in the time harmonic regime are

an efficient rpim for simulating wave motions in saturated porous media an efficient meshless technique for simulating wave motions in saturated porous media is introduced in this paper using radial point interpolation method rpim and considering the precision requirement in wave motion simulation a lumped mass rpim for saturated porous media with clear physical concepts is derived combining explicit time integration with the lumped mass rpim leads to a decoupled radial point interpolation method decoupled rpim for dynamic analysis without solving algebra equation set a two dimensional problem is calculated by the proposed decoupled rpim the ordinary rpim and the finite element method fem the accuracy and efficiency of these methods are compared which demonstrate that the proposed decoupled rpim has comparable accuracy with the ordinary rpim and the finite element method but has high efficiency in simulating wave motions in saturated porous media

superconvergence analysis of linear fem based on polynomial preserving recovery for helmholtz equation with high wave number abstract although superconvergence properties of the polynomial preserving recovery ppr for finite element methods fem for coercive elliptic problems are well understood the superconvergence behavior of ppr for the helmholtz equation with high wave number still remains unclear we study the superconvergence property of the linear fem with ppr for the two dimensional helmholtz equation on triangulations satisfying the o h 1 approximate parallelogram property for some constant 0 we prove the supercloseness on the h 1 seminorm between the finite element solution and the linear interpolant of the exact solution under k k h 2 c 0 where k is the wave number and h is the mesh size then we obtain the superconvergence result based on the ppr technique which says that the ppr improves only the interpolation error but keeps the pollution error unchanged finally we provide numerical tests to verify the superconvergence property and to demonstrate that the ppr combining with the continuous interior penalty technique is much effective for improving both the interpolation error and the pollution error

limit theorems for convex hulls it is shown that the process of vertices of the convex hull of a uniform sample from the interior of a convex polygon converges locally after rescaling to a strongly mixing markov process as the sample size tends to infinity the structure of the limiting markov process is determined explicitly and from this a central limit theorem for the number of vertices of the convex hull is derived similar results are given for uniform samples from the unit disk