A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion...

The lattice Boltzmann method (LBM) has two key steps: collision and streaming. In a conventional LBM, the streaming is exact, where each distribution function perfectly shifted to neighbor node on uniform mesh arrangement. This advantage may curtail applicability of problems with complex geometries. To overcome this issue, high-order meshless interpolation-based approach proposed handle step. O...

We present a new approach to simultaneously denoise and parameterize unorganized point cloud data. This is achieved by minimizing an appropriate energy function defined on the point cloud and its parameterization. An iterative algorithm to minimize the energy is described. The key ingredient of our approach is an “as-rigid-as-possible” meshless parameterization to map a point cloud with disk to...

We present an exponentially convergent semi-implicit meshless algorithm for the solution of Navier-Stokes equations in complex domains. The discretizes partial derivatives at scattered points using radial basis functions (RBF) as interpolants. Higher-order polynomials are appended to polyharmonic splines (PHS-RBF) and a collocation method is used derive interpolation coefficients. interpolating...

This paper proposes a novel meshless boundary method called the singular boundary method (SBM). This method is mathematically simple, easy-to-program, and truly meshless. Like the method of fundamental solutions (MFS), the SBM employs the singular fundamental solution of the governing equation of interest as the interpolation basis function. However, unlike the MFS, the source and collocation p...

A Meshless Radial Basis Function Method for Fluid Flow with Heat Transfer K Nagamani Devi1, D.W. Pepper2 Summary Over the past few years, efforts have been made to solve fluid flow and heat transfer problems using radial basis functions. This approach is meshless, easy to understand, and simple to implement. Preliminary results indicate accuracies on the order of finely meshed conventional tech...

Under very mild additional assumptions, translates of conditionally positive definite radial basis functions allow unique interpolation to scattered multivariate data, because the interpolation matrices have a symmetric and positive definite dominant part. In many applications, the data density varies locally, and then the translates should get different scalings that match the local data densi...

In landmark-based registration, radial basis function-based transformation play an important role. The compact support radial basis function based on thin-plate splines (CSTPS) is an effective function which has been used to perform interpolation in elastic registration of medical images. In this paper, the positive definite property of CSTPS is theoretically proved. Thus, the solvability of th...