A revolution in sensor technology is introducing new problems that must be addressed by visualization research. These technologies will enable earthquake engineers to monitor tectonic plate activity, park rangers to respond more effectively to wildfires, and marine biologists to uncover mysteries from the ocean depths using a network of small, lightweight sensors collecting data in real-time. V...

in this paper, an effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (rbfs). we present an algorithm based on interpolation by radial basis functions including multiquadratics (mqs), using legendre-gauss-lobatto nodes and weights. also a theorem is proved for convergence of the algorithm. some numerical examples are presented...

The truly meshless local Petrov-Galerkin (MLPG) method holds a great promise in solving boundary value problems, using a local symmetric weak form as a natural approach. In the present paper, in the context of MLPG and the meshless interpolation of a moving least squares (MLS) type, a method which uses primary and secondary nodes in the domain and on the global boundary is introduced, in order ...

In this paper, a new partition of unity ± the synchronized reproducing kernel (SRK) interpolant ± is derived. It is a class of meshless shape functions that exhibit synchronized convergence phenomenon: the convergence rate of the interpolation error of the higher order derivatives of the shape function can be tuned to be that of the shape function itself. This newly designed synchronized reprod...

This paper introduces an effective H-adaptive upgrade to solution of the transport phenomena by the novel Local Radial Basis Function Collocation Method (LRBFCM). The transport variable is represented on overlapping 5-noded influence-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the variable are calculated from the ...

In the present work, the numerical solution of two-dimensional variable-order fractional cable (VOFC) equation using meshless collocation methods with thin plate spline radial basis functions is considered. In the proposed methods, we first use two schemes of order O(τ2) for the time derivatives and then meshless approach is applied to the space component. Numerical results obtained ...

Choosing data points is a common problem for researchers who employ various meshless methods for solving partial differential equations. On one hand, high accuracy is always desired; on the other, ill-conditioning problems of the resultant matrices, that may lead to unstable algorithms, prevent some researchers from using meshless methods. For example, the optimal placements of source points in...

In this paper, a numerical technique is presented for the solution of a parabolic partial differential equation with a time-dependent coefficient subject to an extra measurement. For solving the discussed inverse problem, at first we transform it into a nonlinear direct problem and then use the proposed method. This method is a combination of collocation method and radial basis functions. The r...

This paper deals with the dynamic analysis of stress field in cylindrically layeredstructures reinforced by carbon nanotube (CLSRCN) subjected to mechanical shock loading.Application of meshless local integral equations based on meshless local Petrov-Galerkin(MLPG) method is developed for dynamic stress analysis in this article. Analysis is carriedout in frequency domain by applying the Laplace...

Three different truly Meshless Local Petrov-Galerkin (MLPG) methods are developed for solving 3D elasto-static problems. Using the general MLPG concept, these methods are derived through the local weak forms of the equilibrium equations, by using different test functions, namely, the Heaviside function, the Dirac delta function, and the fundamental solutions. The one with the use of the fundame...