the use of pde centres in the local rbf hermitian method for 3d convective diffusion problems in this work an extension is proposed to the local hermitian interpolation lhi method a meshless numerical method based on interpolation with small and heavily overlapping radial basis function rbf systems this extension to the lhi method uses interpolation functions which themselves satisfy the partial differential equation pde to be solved in this way a much improved reconstruction of partial derivatives can be obtained resulting in significantly improved accuracy in many cases the implementation algorithm is described and is validated via three convection diffusion reaction problems for steady and transient situations a crank nicolson implicit time stepping technique is used for the time dependent problems in the proposed approach a form of analytical upwinding is implicitly implemented by the use of the partial differential operator of the governing equation in the interpolation function which includes the desired information about the convective velocity field the implicit upwinding scheme intrinsic to the proposed numerical approach is tested by solving a one dimensional travelling front problem at peclet numbers of 500 1000 2000 5000 and infinity which corresponds to a shock front in the case of infinity in addition the accuracy of the numerical scheme is validated against a one dimensional steady state solution exhibiting strong boundary layer effects and also against a steady and a transient three dimensional convection diffusion problem on irregular datasets all the test cases are validated against the corresponding analytical solutions finally the effect of various interpolation stencil configurations is investigated and some important limitations on local data centre distribution are identified

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

a new cloud based hp finite element method a hybrid computational method for solving boundary value problems is introduced which combines features of the meshless hp cloud methods with features of conventional finite elements the method admits straightforward nonuniform hp type approximations easy implementation of essential boundary conditions is robust under severe distortions of the mesh and can deliver exponential rates of convergence results of numerical experiments are presented

a green s discrete transformation meshfree method for simulating transient diffusion problems this manuscript presents the formulation and application of the green s discrete transformation method gdtm for the meshfree simulation of transient diffusion problems including those with moving boundaries the gdtm implements a linear combination of time dependent green s basis functions defined on a set of source points to approximate the field in the form of a solution series a discrete transformation is implemented to evaluate unknown coefficients of this series which eliminates the need to use time integration schemes we will study the optimal number and location of the gdtm source points that yield the highest level of accuracy while maintaining a manageable condition number for the resulting linear system of equations the optimal values of these parameters which are inherently independent of the domain geometry are determined such that the basis functions have appropriate features for approximating the field a comprehensive convergence study is presented to show the precision and convergence rate of the gdtm for modeling various diffusion problems we also demonstrate the application of this method for simulating three diffusion problems with complex and evolving morphologies heat transfer in a turbine blade thermal response of a porous material and localized pitting corrosion in stainless steel copyright c 2015 john wiley sons ltd

local radial basis function based gridfree scheme for unsteady incompressible viscous flows a local radial basic function rbf based gridfree scheme has been developed to solve unsteady incompressible navier stokes equations in primitive variables the velocity pressure decoupling is obtained by making use of a fractional step algorithm the scheme is validated over a variety of benchmark problems and found a very good agreement with the existing results comparisons with the benchmark solutions show that the developed local rbf gridfree scheme is stable and produces accurate results on domains discretized even with non uniform distribution of nodal points

multi level meshless methods based on direct multi elliptic interpolation a short overview on the direct multi elliptic interpolation and the related meshless methods for solving partial differential equations is given a new technique is proposed which produces a biharmonic interpolation along the boundary and solves the original problem inside the domain an error estimation is also derived to implement the method quadtree based multi level methods are used the approach avoids the use of large dense and ill conditioned matrices and significantly reduces the computational cost

rbf fd formulas and convergence properties the local rbf is becoming increasingly popular as an alternative to the global version that suffers from ill conditioning in this paper we study analytically the convergence behavior of the local rbf method as a function of the number of nodes employed in the scheme the nodal distance and the shape parameter we derive exact formulas for the first and second derivatives in one dimension and for the laplacian in two dimensions using these formulas we compute taylor expansions for the error from this analysis we find that there is an optimal value of the shape parameter for which the error is minimum this optimal parameter is independent of the nodal distance our theoretical results are corroborated by numerical experiments

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

comparison of finite element techniques for solidification problems the accuracies of the computed temperatures of a liquid in a corner region under freezing conditions are compared for various fixed grid finite element techniques using the analytical solution for this problem as a reference in the finite element formulation of the problem different time stepping schemes are compared the implicit euler backward algorithm combined with an iterative scheme and two three time level methods the lees algorithm and a dupont algorithm which are both applied as non iterative schemes furthermore different methods for handling the evolution of latent heat are examined an approximation method suggested by lemmon and one suggested by del giudice both using the enthalpy formulation as well as a fictitious heat flow method presented by rolph and bathe results of calculations performed with the consistent heat capacity matrix are compared with those performed with a lumped heat capacity matrix

a scalable and implicit meshless rbf method for the 3d unsteady nonlinear richards equation with single and multi zone domains the local hermitian interpolation lhi method is a strong form meshless numerical technique which uses radial basis function rbf interpolants to satisfy linear and nonlinear governing equations and boundary operators recent developments have shown that for linear transport problems applying the pde governing equation directly to the basis functions can greatly improve the accuracy and stability of the resulting solutions in this work the lhi formulation with local pde interpolation is extended to the nonlinear gravity driven richards equation in order to solve unsteady problems involving flow in unsaturated porous media the application of the linearised pde operator to the basis functions incorporates information such as the effective velocity field directly into the solution construction this results in a form of analytical upwinding which helps to stabilise the solution in addition the local interpolation itself satisfies the linearised governing equation allowing for more accurate reconstruction of partial derivatives and hence a more accurate solution the procedure is tested using a 3d infiltration problem with a known analytical solution the performance of the lhi method both with and without local pde interpolation is compared to the finite element method via the femwater software the lhi formulation with pde data centres shows consistent improvement over the femwater solutions reducing errors by several orders of magnitude in addition a procedure is introduced to model strongly heterogeneous and layered soils the physically correct matching conditions are applied over layer interfaces i e continuity of pressure and mass flux the double collocation property of the hermitian rbf method is exploited to enforce both matching conditions at the same set of locations on the layer interface this procedure allows the accurate capture of solutions across such interfaces replicating the required discontinuities in the first derivatives of the pressure profile the multi layer formulation is validated using a transient two layer infiltration problem with the analytical solution replicated to a high precision in a variety of configurations copyright 2010 john wiley sons ltd

inference based on imputed failure times for the proportional hazards model with interval censored data abstract we propose an approach to the proportional hazards model for interval censored data in which parameter estimates are obtained by solving estimating equations that are the partial likelihood score equations for the full data proportional hazards model averaged over all rankings of imputed failure times consistent with the observed censoring intervals imputed failure times are generated using a parametric estimate of the baseline distribution the parameters of the baseline distribution are estimated simultaneously with the proportional hazards regression parameters although a parametric form for the baseline distribution must be specified simulation studies show that the method performs well even when the baseline distribution is misspecified the estimating equations are solved using monte carlo techniques we present a recursive stochastic approximation scheme that converges to the zero of the estimating equations the solution has a random error that is asymptotically normally distributed w

a hybrid boundary node method a new variational formulation for boundary node method bnm using a hybrid displacement functional is presented here the formulation is expressed in terms of domain and boundary variables and the domain variables are interpolated by classical fundamental solution while the boundary variables are interpolated by moving least squares mls the main idea is to retain the dimensionality advantages of the bnm and get a truly meshless method which does not require a boundary element mesh either for the purpose of interpolation of the solution variables or for the integration of the energy all integrals can be easily evaluated over regular shaped domains in general semi sphere in the 3 d problem and their boundaries numerical examples presented in this paper for the solution of laplace s equation in 2 d show that high rates of convergence with mesh refinement are achievable and the computational results for unknown variables are most accurate no further integrations are required to compute the unknown variables inside the domain as in the conventional bem and bnm copyright 2001 john wiley sons ltd

a new method for evaluating options based on multiquadric rbf fd method abstract in this paper a new local meshless approach based on radial basis functions rbfs is presented to price the options under the black scholes model the global rbf approximations derived from the conventional global collocation method usually lead to ill conditioned matrices employing the idea of local approximants of the finite difference fd method and combining it with the radial basis function rbf method can result in a local meshless approach such as rbf fd it removes the difficulty of ill conditionness of the original method the new proposed approach is unconditionally stable as it is shown by von neumann stability analysis it is fast and produces high accurate results as shown in numerical experiments moreover we took into account the variation of shape parameter and analyzed numerically the behavior of the rbf fd method

quaternionic differential operators motivated by a quaternionic formulation of quantum mechanics we discuss quaternionic and complex linear differential equations we touch only a few aspects of the mathematical theory namely the resolution of the second order differential equations with constant coefficients we overcome the problems coming out from the loss of the fundamental theorem of the algebra for quaternions and propose a practical method to solve quaternionic and complex linear second order differential equations with constant coefficients the resolution of the complex linear schrodinger equation in the presence of quaternionic potentials represents an interesting application of the mathematical material discussed in this paper

local method of approximate particular solutions for two dimensional unsteady burgers equations the local method of approximate particular solutions lmaps is first proposed to solve burgers equations in avoiding the ill conditioning problem the weight coefficients of linear combination with respect to the function values and its derivatives can be obtained by solving low order linear systems within the local supporting domain then the global solutions can be obtained by reformulating the local matrix in the global and sparse matrix the obtained large sparse linear systems are directly solved instead of using more complicated iterative method the numerical experiments have shown that the proposed method is suitable for solving the two dimensional unsteady burgers equations with high accuracy and efficiency

quaternionic symmetry groups and particle multiplets we consider the quaternionic complete symmetry group of a massive physical system obtained extending the connected poincare group and the internal symmetry group by means of the cpt and the generalized parity operators we classify the irreducible q representations of this group crossing the generalized wigner and frobenius schur classifications and obtain 14 different cases some novelties arise in this context such as the failure of the statement that only irreducible representations must be associated with particle multiplets and a suggestion on the possible forms of a parity violating hamiltonian

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

dual reciprocity hybrid boundary node method for free vibration analysis abstract as a truly meshless method of boundary type the hybrid boundary node method hbnm has the advantages of both boundary element method bem and meshless method the main problem is that it is only suitable for the homogeneous problems now the dual reciprocity method drm is introduced into hbnm to deal with the integral for the inhomogeneous terms of the governing equations and the rigid body motion approach is employed to solve the hyper singular integrations a new meshless method named dual reciprocity hybrid boundary node method drhbnm is proposed and applied to solve free vibration problems in this method the solution composes into two parts i e the general solution and the particular solution the general solution is solved by hbnm and the particular one is obtained by drm drhbnm is a true boundary type meshless method it does not require the boundary element mesh either for the purpose of interpolation of the variables or for the integration of energy the points in the domain are only used to interpolate particular solution by the radial basis function finally the boundary variables are interpolated by the independent smooth boundary segments the q r algorithm and householder algorithm are applied to solve the eigenvalues and eigenvectors of the transformed matrix numerical examples for free vibration problems show that a good convergence with mesh refinement is achievable and the computational results for the natural circular frequencies and free vibration modes are very accurate furthermore the computation parameters have little influence on the results and can be chosen in a wide range it is shown that the present method is effective and can be widely applied in practical engineering

alternative descriptions in quaternionic quantum mechanics we characterize the quasianti hermitian quaternionic operators in quaternionic quantum mechanics by means of their spectra moreover we state a necessary and sufficient condition for a set of quasianti hermitian quaternionic operators to be anti hermitian with respect to a uniquely defined positive scalar product in a infinite dimensional right quaternionic hilbert space according to such results we obtain two alternative descriptions of a quantum optical physical system in the realm of quaternionic quantum mechanics while no alternative can exist in complex quantum mechanics and we discuss some differences between them

pseudoanti hermitian operators in quaternionic quantum mechanics we introduce the concept of pseudoanti hermitian operators in quaternionic quantum mechanics and give a complete characterization of their spectra we highlight some physical properties related to time reversal symmetry of the pseudoanti hermitian quaternionic hamiltonians

generalized fs w versus dyson s classification of irreducible representations we study the characterization of the 13 cases obtained in the classification of the irreducible linear antilinear representations of semigroups in a finite dimensional vector space x over an algebraically closed field k with a conjugation j generalized frobenius schur wigner or fs w classification it has already been shown that each case can be characterized by various equivalent properties some of which can be endowed with a physical interpretation we show here that whenever k is the complex field c each case can be characterized by the structure in the sense specified by the weyl theorem on the structure of the matrix algebras and their commutators of a pair of suitable operator algebras over the real field r this characterization coincides with the one given by dyson for each case of his classification of symmetry groups thus the latter classification is recovered under more general assumptions and in a generalized framework and its one to one correspondence with the generalized fs w cla

efficient computation of subset selection probabilities with application to cox regression summary an efficient method is presented to compute the probability of selection of a specified subset from the set of all subsets of a fixed size where the subsets are taken from a population whose units have varying individual probabilities of selection the problem is motivated by the computation of the exact marginal likelihood for the cox proportional hazards model

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

rank based inference in the proportional hazards model for interval censored data summary a marginal likelihood approach to fitting the proportional hazards model to interval censored or grouped data is proposed this approach maximises a likelihood that is the sum over all rankings of the data that are consistent with the observed censoring intervals as in the usual proportional hazards model the method does not require specification of the baseline hazard function the score equations determining the maximum marginal likelihood estimator can be written as the expected value of the score of the usual proportional hazards model with respect to a certain distribution of rankings a gibbs sampling scheme is given to generate rankings from this distribution and stochastic approximation is used to solve the score equations simulation results under various censoring schemes give point estimates that are close to estimates obtained using actual failure times

optimal variable shape parameter for multiquadric based rbf fd method in this follow up paper to our previous study in bayona et al 2011 2 we present a new technique to compute the solution of pdes with the multiquadric based rbf finite difference method rbf fd using an optimal node dependent variable value of the shape parameter this optimal value is chosen so that to leading order the local approximation error of the rbf fd formulas is zero in our previous paper bayona et al 2011 2 we considered the case of an optimal constant value of the shape parameter for all the nodes our new results show that if one allows the shape parameter to be different at each grid point of the domain one may obtain very significant accuracy improvements with a simple and inexpensive numerical technique we analyze the same examples studied in bayona et al 2011 2 both with structured and unstructured grids and compare our new results with those obtained previously we also find that if there are a significant number of nodes for which no optimal value of the shape parameter exists then the improvement in accuracy deteriorates significantly in those cases we use generalized multiquadrics as rbfs and choose the exponent of the multiquadric at each node to assure the existence of an optimal variable shape parameter

estimation of finite population properties when sampling is without replacement and proportional to magnitude abstract geologists often evaluate aggregate volumes of discovered plus undiscovered oil and or gas in a petroleum basin by use of geologic volumetric methods although sophisticated geological reasoning may be employed the essential idea behind these methods is simple estimate a the volume of hydrocarbon bearing sediment in the basin b the amount of hydrocarbons present per unit volume of sediment and c the fraction of hydrocarbons present per unit volume that is technologically recoverable the product of a and b is interpretable as a point estimate of the sum of amounts of oil and gas in place in individual oil and gas deposits fields in the basin the product of a b and c is a point estimate of amounts of oil and gas recoverable from all individual deposits in the basin

a comparison analysis between unsymmetric and symmetric radial basis function collocation methods for the numerical solution of partial differential equations abstract in this article we present a thorough numerical comparison between unsymmetric and symmetric radial basis function collocation methods for the numerical solution of boundary value problems for partial differential equations a series of test examples was solved with these two schemes different problems with different type of governing equations and boundary conditions particular emphasis was paid to the ability of these schemes to solve the steady state convection diffusion equation at high values of the peclet number from the examples tested in this work it was observed that the system of algebraic equations obtained with the symmetric method was in general simpler to solve than the one obtained with the unsymmetric method and that the resulting algorithm performs better however the unsymmetric method has the advantage of being simpler to implement two main features about the results obtained in this work are worthy of special attention first with the symmetric method it was possible to solve convection diffusion problems at a very high peclet number without the need of any artificial damping term and second with these two approaches symmetric and unsymmetric it is possible to impose free boundary conditions for problems in unbounded domains

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

t violation and quaternionic state oscillations we derive using the quaternionic group representation theory the possible forms of the t violating hamiltonians and consider time evolution in a two level system when a t violating term is added to a t preserving unperturbed hamiltonian transition probabilities are calculated moreover the time evolution of a complex state is determined analytically showing that a quaternionic component arises naturally in its evolution finally some properties of the time reversal observable are studied and a set of selection rules is obtained

irreducible linear antilinear representations and internal symmetries we reconsider a well known classification due to wigner of the unitary antiunitary finite dimensional irreducible group representations within a somewhat generalized mathematical framework where in particular any algebraically closed field k with an involutory automorphism j is considered in place of the complex field c we show that each case of the classification can be characterized by the set u l of the linear mappings that commute with the given set u which is now assumed to be an irreducible semigroup of linear and antilinear i e j semilinear mappings and explicitly exhibit u l then this classification is crossed with the classification of the sets of linear and antilinear mappings that has been obtained in some previous work and that generalizes the old classification of the unitary representations introduced by frobenius and schur we obtain a new classification in which every case can be characterized by the group uc of the invertible linear and antilinear mappings which commute with

meshless methods for one dimensional oscillatory fredholm integral equations abstract in this paper efficient and simple algorithms based on levin s quadrature theory and our earlier work involving local radial basis function rbf and chebyshev differentiation matrices are adopted for numerical solution of one dimensional highly oscillatory fredholm integral equations this work is focused on the comparative performance of local rbf meshless and pseudospectral procedures we have tested the proposed methods on phase functions with and without stationary phase point s both on uniform and chebyshev grid points the proposed procedures are shown accurate and efficient and therefore provide a reliable platform for the numerical solution of integral equations from the numerical results we draw some conclusions about accuracy efficiency and robustness of the proposed approaches

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

generalized finite differences using fundamental solutions summary it is well known that solutions for linear partial differential equations may be given in terms of fundamental solutions the fundamental solutions solve the homogeneous equation exactly and are obtained from the solution of the inhomogeneous equation where the inhomogeneous term is described by a dirac delta distribution fundamental solutions are the building blocks of the boundary element method and of the method of fundamental solutions and are traditionally used to build boundary only global approximations in the domain of interest in this work the same characteristic of the fundamental solutions that of solving the homogeneous equation exactly is used but not to build a global approximation on the contrary local approximations are built in such a manner that it is possible to construct finite difference operators that are free from any form of structured grid copyright q 2009 john wiley sons ltd

multilevel compact radial functions based computational schemes for some elliptic problems abstract compactly supported radial basis functions cs rbfs have been recently introduced in the context of the dual reciprocity method as a possible cure of dense matrices and ill conditioning problems when using the classical radial basis functions however the support scaling factor and slow convergence rate of the cs rbfs have also raised issues on the effectiveness of the cs rbfs in this paper two multilevel schemes have been proposed to alleviate these problems

right eigenvalue equation in quaternionic quantum mechanics we study the right eigenvalue equation for quaternionic and complex linear matrix operators defined in n dimensional quaternionic vector spaces for quaternionic linear operators the eigenvalue spectrum consists of n complex values for these operators we give a necessary and sufficient condition for the diagonalization of their quaternionic matrix representations our discussion is also extended to complex linear operators whose spectrum is characterized by 2n complex eigenvalues we show that a consistent analysis of the eigenvalue problem for complex linear operators requires the choice of a complex geometry in defining inner products finally we introduce some examples of the left eigenvalue equations and highlight the main difficulties in their solution

two algorithms for fast 2d node generation application to rbf meshless discretization of diffusion problems and image halftoning abstract mesh generation techniques for traditional mesh based numerical approaches such as fem and fvm have now reached a good degree of maturity there is no such an acknowledged background when dealing with node generation techniques for meshless numerical approaches despite their theoretical simplicity and efficiency furthermore node generation can be put in connection with some well known image approximation techniques two node generation algorithms are here proposed and employed in the numerical solution of 2d steady state diffusion problems by means of a local radial basis function rbf meshless method finally such algorithms are also tested for grayscale image approximation through stippling

a boundary meshless method using chebyshev interpolation and trigonometric basis function for solving heat conduction problems a boundary meshless method has been developed to solve the heat conduction equations through the use of a newly established two stage approximation scheme and a trigonometric series expansion scheme to approximate the particular solution and fundamental solution respectively as a result no fundamental solution is required and the closed form of approximate particular solution is easy to obtain the effectiveness of the proposed computational scheme is demonstrated by several examples in 2d and 3d we also compare our proposed method with the finite difference method and the other meshless method showed in sarler and vertnik comput math appl 2006 51 1269 1282 excellent numerical results have been observed copyright 2007 john wiley sons ltd

meshless methods for two dimensional oscillatory fredholm integral equations abstract in this paper a meshless solution procedure incorporating delaminating quadrature method for two dimensional highly oscillatory fredholm integral equation is put forward the proposed method is an extension of our earlier findings of meshless methods for two dimensional oscillatory fredholm integral equation having kernel function free of stationary phase point s siraj ul islam et al 2015 the current method deals not only with the kernels having no stationary phase point s but also with the kernels having stationary phase point s in the context of highly oscillatory integral equations the new method is numerically stable and computationally fast numerical experiments are presented to testify the robustness and efficiency of the proposed method

localized radial basis functions based pseudo spectral method lrbf psm for nonlocal diffusion problems abstract spectral pseudo spectral methods based on high order polynomials have been successfully used for solving partial differential and integral equations in this paper we will present the use of a localized radial basis functions based pseudo spectral method lrbf psm for solving 2d nonlocal problems with radial nonlocal kernels the basic idea of the lrbf psm is to construct a set of orthogonal functions by rbfs on each overlapping sub domain from which the global solution can be obtained by extending the approximation on each sub domain to the entire domain numerical implementation indicates that the proposed lrbf psm is simple to use efficient and robust to solve various nonlocal problems

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

biometrika centenary survival analysis although papers relating to survival analysis have appeared in biometrika since the very first issue the current emphasis on the topic in this journal is fairly new especially as it relates to applications in biostatistics this survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of biometrika focusing primarily on work published since 1980

the generalized finite difference method for long time dynamic modeling of three dimensional coupled thermoelasticity problems abstract in this study a new framework for the efficient and accurate solutions of three dimensional 3d dynamic coupled thermoelasticity problems is presented in our computations the krylov deferred correction kdc method a pseudo spectral type collocation technique is introduced to perform the large scale and long time temporal simulations the generalized finite difference method gfdm a relatively new meshless method is then adopted to solve the resulting boundary value problems the gfdm uses the taylor series expansions and the moving least squares approximation to derive explicit formulae for the required partial derivatives of unknown variables the method thus is truly meshless that can be applied for solving problems merely defined over irregular clouds of points for problem with complicated geometries this paper also examines a new distance criterion for adaptive selection of nodes in the gfdm simulations preliminary numerical experiments show that the kdc accelerated gfdm methods are very promising for accurate and efficient long time and large scale dynamic simulations

quaternionic representations of magnetic groups we study magnetic groups which contain a time inversion operator besides spatial symmetries in the framework of quaternionic group representation theory we obtain a classification of these groups depending on the reducibility of their spatial part and then we cross it with the generalized frobenius schur classification that has been obtained by ourselves elsewhere ten distinct cases arise but only five of them apply to factorizable groups i e groups in which the time inversion operator appears alone and not multiplied by a spatial symmetry we supply examples for these five cases and determine which of them apply to bosonic or fermionic systems respectively finally we discuss the degeneracy of energy levels in the presence of a time reversal symmetry kramers degeneracy in quaternionic quantum mechanics obtaining right values in all cases

relative risk estimation and inference using a generalized logrank statistic when comparing two survival distributions with proportional hazard functions the logrank test is optimal for testing the null hypothesis that the constant hazard ratio relative risk is one in this paper we focus on i testing for departures from a relative risk other than one and ii estimation of the relative risk the standard tool to address both i and ii is the cox proportional hazards model however the performance of the cox model can be less than optimal with small samples we show why this is the case and propose a simple alternative method of estimation and inference based on a generalized logrank glr statistic while the glr and cox model approaches are asymptotically similar empirical results reveal that the glr approach is notably more efficient than the cox model when the number of subjects is small 100 subjects per treatment group an example based on survival times of cervical cancer patients is used to illustrate the proposed methodology

central projective quaternionic representations we obtain all the irreducible not similar central quaternionic projective representations of a finite group g from the knowledge of the vector complex irreducible representations of suitable extensions of g and classify them according to a generalized frobenius schur classification finally a definition of equivalence of such representations is proposed

an adaptive rbf finite collocation approach to track transport processes across moving fronts we develop a radial basis function finite collocation method rbf fc that utilises an adaptive quadtree dataset to cluster nodes around critical features in the domain for the solution of transport processes occurring in moving front problems an adaptive quadtree dataset is used to generate an improved distribution of solution centres in the domain around which local hermitian collocation systems are formed in these local systems the governing pde and boundary operators of the problem are enforced by collocation globally the systems are linked via reconstruction of the solution variable in terms of the solution value at neighbouring nodes producing a sparse global matrix with a solution cost that scales linearly with the number of nodes in the domain by generating an adaptive set of nodal points with the quadtree dataset we can reduce the global solution error in the rbf fc method whilst maintaining low solution times the proposed method is validated on a steady state boundary layer capture problem and a transient advection problem infinite peclet number in a 2d domain we then couple the method with an interface tracking technique to solve the transient heat transfer in a hele shaw cell viscous fingering problem we demonstrate the effectiveness of the proposed method for the solution of convection dominated transport in problems across moving fronts

multicloud multigrid convergence with a meshless operator the primary objective of this work is to develop and test a new convergence acceleration technique we call multicloud multicloud is well founded in the mathematical basis of multigrid but relies on a meshless operator on coarse levels the meshless operator enables extremely simple and automatic coarsening procedures for arbitrary meshes using arbitrary fine level discretization schemes the performance of multicloud is compared with established multigrid techniques for structured and unstructured meshes for the euler equations on two dimensional test cases results indicate comparable convergence rates per unit work for multicloud and multigrid however because of its mesh and scheme transparency multicloud may be applied to a wide array of problems with no modification of fine level schemes as is often required with agglomeration techniques the implication is that multicloud can be implemented in a completely modular fashion allowing researchers to develop fine level algorithms independent of the convergence accelerator for complex three dimensional problems

fully meshless solution of the one dimensional multigroup neutron transport equation with the radial basis function collocation method abstract in this paper a fully meshless method is proposed for the numerical solution of the one dimensional multigroup neutron transport equation with anisotropic scattering both first order and even parity forms of the transport equation are studied the radial basis function collocation method is chosen for the spatial treatment and legendre polynomials are used to approximate the angular variable the selection of the legendre polynomials instead of discrete ordinates approach resulted with a fully meshless algorithm in both independent variables multiquadric is utilized as the radial function seven problems are considered to evaluate the performance of the method the results show that the method converges exponentially and it is possible to obtain high levels of accuracies for the multiplication factor and neutron flux with a good stability in both spatial and angular domains for the one group isotropic benchmark problem discrete ordinates solutions employing discontinuous linear finite elements for the spatial variable are also provided and a comparison of the methods revealed that the fully meshless method produced more accurate results than the discrete ordinates finite element scheme when the shape parameter is properly chosen

local radial basis function based differential quadrature method and its application to solve two dimensional incompressible navier stokes equations local radial basis function based differential quadrature method is presented in detail in this paper the method is a natural mesh free approach like the conventional differential quadrature dq method it discretizes any derivative at a knot by a weighted linear sum of functional values at its neighbouring knots which may be distributed randomly however different from the conventional dq method the weighting coefficients in present method are determined by taking the radial basis functions rbfs instead of high order polynomials as the test functions the method works in a similar fashion as conventional finite difference schemes but with truly mesh free property in this paper we mainly concentrate on the multiquadric rbfs since they have exponential convergence the effects of shape parameter c on the accuracy of numerical solution of linear and nonlinear partial differential equations are studied and how the value of optimal c varies with the number of local support knots is also numerically demonstrated the proposed method is validated by its application to the simulation of natural convection in a square cavity excellent numerical results are obtained on an irregular knot distribution

the boundary collocation method with meshless concept for acoustic eigenanalysis of two dimensional cavities using radial basis function abstract in this paper a meshless method for the acoustic eigenfrequencies using radial basis function rbf is proposed the coefficients of influence matrices are easily determined by the two point functions in determining the diagonal elements of the influence matrices two techniques limiting approach and invariant method are employed based on the rbf in the imaginary part kernel the method results in spurious eigenvalues which can be separated by using the singular value decomposition svd technique in conjunction with the fredholm alternative theorem to understand why the spurious eigenvalues occur analytical study in the discrete system by discretizing the circular boundary is conducted by using circulants by using the svd updating terms and documents the true and spurious eigensolutions can be extracted out respectively several examples are demonstrated to see the validity of the present method

optimal constant shape parameter for multiquadric based rbf fd method radial basis functions rbfs have become a popular method for interpolation and solution of partial differential equations pdes many types of rbfs used in these problems contain a shape parameter and there is much experimental evidence showing that accuracy strongly depends on the value of this shape parameter in this paper we focus on pde problems solved with a multiquadric based rbf finite difference rbf fd method we propose an efficient algorithm to compute the optimal value of the shape parameter that minimizes the approximation error the algorithm is based on analytical approximations to the local rbf fd error derived in 1 we show through several examples in 1d and 2d both with structured and unstructured nodes that very accurate solutions compared to finite differences can be achieved using the optimal value of the constant shape parameter

a new structure preserving method for quaternion hermitian eigenvalue problems in this paper we propose a novel structure preserving algorithm for solving the right eigenvalue problem of quaternion hermitian matrices the algorithm is based on the structure preserving tridiagonalization of the real counterpart for quaternion hermitian matrices by applying orthogonal jrs symplectic matrices the algorithm is numerically stable because we use orthogonal transformations the algorithm is very efficient it costs about a quarter arithmetical operations and a quarter to one eighth cpu times comparing with standard general purpose algorithms numerical experiments are provided to demonstrate the efficiency of the structure preserving algorithm

meshfree explicit local radial basis function collocation method for diffusion problems this paper formulates a simple explicit local version of the classical meshless radial basis function collocation kansa method the formulation copes with the diffusion equation applicable in the solution of a broad spectrum of scientific and engineering problems the method is structured on multiquadrics radial basis functions instead of global the collocation is made locally over a set of overlapping domains of influence and the time stepping is performed in an explicit way only small systems of linear equations with the dimension of the number of nodes included in the domain of influence have to be solved for each node the computational effort thus grows roughly linearly with the number of the nodes the developed approach thus overcomes the principal large scale problem bottleneck of the original kansa method two test cases are elaborated the first is the boundary value problem nafems test associated with the steady temperature field with simultaneous involvement of the dirichlet neumann and robin boundary conditions on a rectangle the second is the initial value problem associated with the dirichlet jump problem on a square the accuracy of the method is assessed in terms of the average and maximum errors with respect to the density of nodes number of nodes in the domain of influence multiquadrics free parameter and timestep length on uniform and nonuniform node arrangements the developed meshless method outperforms the classical finite difference method in terms of accuracy in all situations except immediately after the dirichlet jump where the approximation properties appear similar

a localized approach for the method of approximate particular solutions the method of approximate particular solutions maps has been recently developed to solve various types of partial differential equations in the maps radial basis functions play an important role in approximating the forcing term coupled with the concept of particular solutions and radial basis functions a simple and effective numerical method for solving a large class of partial differential equations can be achieved one of the difficulties of globally applying maps is that this method results in a large dense matrix which in turn severely restricts the number of interpolation points thereby affecting our ability to solve large scale science and engineering problems in this paper we develop a localized scheme for the method of approximate particular solutions lmaps the new localized approach allows the use of a small neighborhood of points to find the approximate solution of the given partial differential equation in this paper this local numerical scheme is used for solving large scale problems up to one million interpolation points three numerical examples in two dimensions are used to validate the proposed numerical scheme

a new hybrid boundary node method based on taylor expansion and the shepard interpolation method summary a novel meshless method based on the shepard and taylor interpolation method stim and the hybrid boundary node method hbnm is proposed based on the shepard interpolation method and taylor expansion the stim is developed to construct the shape function of the hbnm in the stim the shepard shape function is used as the basic function which is the zero level shape function and the high power basic functions are constructed through taylor expansion four advantages of the stim are the interpolation property the arbitrarily high order consistency the absence of inversion for the whole process of shape function construction and the low computational expense these properties are desirable in the implementation of meshless methods by combining the stim and the hbnm a much more effective meshless method is proposed to solve the elasticity problems compared with the traditional hbnm the stim can improve accuracy because of the use of high power basic functions and can also improve the computational efficiency because there is no inversion for the shape function construction process numerical examples are given to demonstrate the accuracy and efficiency of the proposed method copyright 2015 john wiley sons ltd

circulant matrix and conformal mapping for solving partial differential equations in recent years a fast radial basis function rbf solver for surface interpolation has been developed by karageorghis et al 2007 in this paper we follow up their work by extending the idea of fast evaluation of the surface interpolation to efficiently solve various types of partial differential equations pdes we look into the possibility of solving pdes with conformal mapping to map the rbf circular points on a disk to the interior of an irregular domain we also compare the pros and cons for these two approaches in both approaches the circulant matrix formulation and the matrix decomposition method are the central ideas of fast computation in numerical experiments we test these two approaches for solving pdes using up to 160000 rbf interpolation points with greater accuracy and efficiency

an element free smoothed radial point interpolation method efs rpim for 2d and 3d solid mechanics problems abstract this paper presents a novel element free smoothed radial point interpolation method efs rpim for solving 2d and 3d solid mechanics problems the idea of the present technique is that field nodes and smoothing cells scs used for smoothing operations are created independently and without using a background grid which saves tedious mesh generation efforts and makes the pre process more flexible in the formulation we use the generalized smoothed galerkin gs galerkin weak form that requires only discrete values of shape functions that can be created using the rpim by varying the amount of nodes and scs as well as their ratio the accuracy can be improved and upper bound or lower bound solutions can be obtained by design the scs can be of regular or irregular polygons in this work we tested triangular quadrangle n sided polygon and tetrahedron as examples stability condition is examined and some criteria are found to avoid the presence of spurious zero energy modes this paper is the first time to create gs galerkin weak form models without using a background mesh that tied with nodes and hence the efs rpim is a true meshfree approach the proposed efs rpim is so far the only technique that can offer both upper and lower bound solutions numerical results show that the efs rpim gives accurate results and desirable convergence rate when comparing with the standard finite element method fem and the cell based smoothed fem cs fem