A new approach for analyzing cracked problems in 2D orthotropic materials using the well-known element free Galerkin method and orthotropic enrichment functions is proposed. The element free Galerkin method is a meshfree method which enables discontinuous problems to be modeled efficiently. In this study, element free Galerkin is extrinsically enriched by the recently developed crack-tip orthot...

A comparison study of the efficiency and accuracy of a variety of meshless trial and test functions is presented in this paper, based on the general concept of the meshless local Petrov-Galerkin (MLPG) method. 5 types of trial functions, and 6 types of test functions are explored. Different test functions result in different MLPG methods, and six such MLPG methods are presented in this paper. I...

We examine the e ect of constraining the number of hidden units For one hidden layer networks with fairly general type of units including perceptrons with any bounded activation function and radial basis function units we show that when also the size of parameters is bounded the best approximation property is satis ed which means that there always exists a parameterization achieving the global ...

By the sometimes so-called Main Theorem of Recursive Analysis, every computable real function is necessarily continuous. We wonder whether and which kinds of hypercomputation allow for the effective evaluation of also discontinuous f : R → R. More precisely the present work considers the following three super-Turing notions of real function computability: – relativized computation; specifically...

Abstract. In this paper we propose a variant of the level set formulation for identifying curves separating regions into different phases. In classical level set approaches, the sign of n level set functions are utilized to identify up to 2n phases. The novelty in our approach is to introduce a piecewise constant level set function and use each constant value to represent a unique phase. If 2n ...

An extended approach is developed by blending isogeometric analysis and the first-order local maximum entropy for standard enhanced fields, respectively. Isogeometric facilitates accurate parametrization of geometry in general, particularly exact geometric conic curves quadratic surfaces using NURBS. On other hand, leads to an improved estimate part due its infinite continuity. Moreover, paves ...

We introduce a general method, based on a mapping onto quantum mechanics, for investigating the large-T limit of the distribution P(r,T) of the nonlinear functional r[V]=(1/T)integral(T)(0)dT' V[X(T')], where V(X) is an arbitrary function of the stationary Gaussian Markov process X(T). For T-->infinity at fixed r we obtain P(r,T) approximately exp[-theta(r)T], where theta(r) is a large-deviatio...

We show that point-neuron models with a Heaviside firing rate function can be ill posed. More specifically, the initial-condition-to-solution map might become discontinuous in finite time. Consequently, if finite precision arithmetic is used, then it is virtually impossible to guarantee the accurate numerical solution of such models. If a smooth firing rate function is employed, then standard O...