Related papers: Meshfree Local Radial Basis Function Collocation M…
In this paper we develop a discrete Hierarchical Basis (HB) to efficiently solve the Radial Basis Function (RBF) interpolation problem with variable polynomial order. The HB forms an orthogonal set and is adapted to the kernel seed function…
We aim to improve the Inverted Neural Radiance Fields (iNeRF) algorithm which defines the image pose estimation problem as a NeRF based iterative linear optimization. NeRFs are novel neural space representation models that can synthesize…
The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
Problems with localized nonhomogeneous material properties arise frequently in many applications and are a well-known source of difficulty in numerical simulations. In certain applications (including additive manufacturing), the physics of…
We develop an immersed-boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a…
The Partition of Unity (PU) method, performed with local Radial Basis Function (RBF) approximants, has been proved to be an effective tool for solving large scattered data interpolation problems. However, in order to achieve a good…
We consider the problem of reconstructing 3D objects via meshfree interpolation methods. In this framework, we usually deal with large data sets and thus we develop an efficient local scheme via the well-known Partition of Unity (PU)…
Archetypal scenarios for change detection generally consider two images acquired through sensors of the same modality. However, in some specific cases such as emergency situations, the only images available may be those acquired through…
In this paper, we solve nonlinear conservation laws using the radial basis function generated finite difference (RBF-FD) method. Nonlinear conservation laws have solutions that entail strong discontinuities and shocks, which give rise to…
This paper applies meshless method of lines, which uses radial basis functions (RBFs) as a spatial collocation scheme to solve the Coupled Drinfeld's-Sokolov-Wilson System. Runge-Kutta method is used for time integration of the system of…
We propose a novel meshless method to achieve super resolution from scattered data obtained from sparse, randomly positioned sensors such as the particle tracers of particle tracking velocimetry. The method combines K Nearest Neighbor…
We describe the optimization algorithm implemented in the open-source derivative-free solver RBFOpt. The algorithm is based on the radial basis function method of Gutmann and the metric stochastic response surface method of Regis and…
In this research work, let us focus on the construction of numerical scheme based on radial basis functions finite difference (RBF-FD) method combined with the Laplace transform for the solution of fractional order dispersive wave…
This paper presents an evaluation of efficient radial basis function mesh deformation for complex iced geometries. Given the high computational cost of mesh deformation, state-of-the-art radial basis function techniques are used for data…
We present a new method for the solution of PDEs on manifolds $\mathbb{M} \subset \mathbb{R}^d$ of co-dimension one using stable scale-free radial basis function (RBF) interpolation. Our method involves augmenting polyharmonic spline (PHS)…
The time-fractional diffusion equation is considered, where the time derivative is either of Caputo or Riemann-Liouville type. The solution of a general initial-boundary value problem with time-dependent boundary conditions over bounded and…
There are plenty of applications and analysis for time-independent elliptic partial differential equations in the literature hinting at the benefits of overtesting by using more collocation conditions than the number of basis functions.…
Can graded meshes yield more accurate numerical solution than uniform meshes? A time-dependent nonlocal diffusion problem with a weakly singular kernel is considered using collocation method. For its steady-state counterpart, under the…
We present and study techniques for investigating the spectra of linear differential operators on surfaces and flat domains using symmetric meshfree methods: meshfree methods that arise from finding norm-minimizing Hermite-Birkhoff…