Related papers: Meshfree Local Radial Basis Function Collocation M…
Numerical simulation of the laser powder bed fusion (LPBF) procedure for additive manufacturing (AM) is difficult due to the presence of multiple scales in both time and space, ranging from the part scale (order of millimeters/seconds) to…
In this paper, we propose a hybrid collocation method based on finite difference and Haar wavelets to solve nonlocal hyperbolic partial differential equations. Developing an efficient and accurate numerical method to solve such problem is a…
Because physical phenomena on Earth's surface occur on many different length scales, it makes sense when seeking an efficient approximation to start with a crude global approximation, and then make a sequence of corrections on finer and…
Optical sensor applications have become popular through digital transformation. Linking observed data to real-world locations and combining different image sensors is essential to make the applications practical and efficient. However, data…
Diffusion bridge models establish probabilistic paths between arbitrary paired distributions and exhibit great potential for universal image restoration. Most existing methods merely treat them as simple variants of stochastic interpolants,…
The problem of supervised classification of the satellite image is considered to be the task of grouping pixels into a number of homogeneous regions in space intensity. This paper proposes a novel approach that combines a radial basic…
A meshless method is presented to solve the radiative transfer equation in the even parity formulation of the discrete ordinates method in complex 2D and 3D geometries. Prediction results of radiative heat transfer problems obtained by the…
Camera pose estimation is a long-standing computer vision problem that to date often relies on classical methods, such as handcrafted keypoint matching, RANSAC and bundle adjustment. In this paper, we propose to formulate the Structure from…
Steady and unsteady Poisson and Stokes equations are solved using mesh dependent Finite Element Method and meshless Radial Basis Function Collocation Method to compare the performances of these two numerical techniques across several…
We propose algorithms for solving convective-diffusion partial differential equations (PDEs), which model surfactant concentration and heat transport on evolving surfaces, based on intrinsic kernel-based meshless collocation methods. The…
The variable-order fractional Laplacian plays an important role in the study of heterogeneous systems. In this paper, we propose the first numerical methods for the variable-order Laplacian $(-\Delta)^{\alpha({\bf x})/2}$ with $0 <…
Fractional Laplace equations are becoming important tools for mathematical modeling and prediction. Recent years have shown much progress in developing accurate and robust algorithms to numerically solve such problems, yet most solvers for…
In this article, we introduce a new class of coupled fractional Lane-Emden boundary value problems. We employ a novel approach, the fractional Haar wavelet collocation method with the Newton-Raphson method. We analyze the conditions in two…
In this paper we present a new fast and accurate method for Radial Basis Function (RBF) approximation, including interpolation as a special case, which enables us to effectively find the optimal value of the RBF shape parameter. In…
We present a parallelized optimization method based on fast Neural Radiance Fields (NeRF) for estimating 6-DoF pose of a camera with respect to an object or scene. Given a single observed RGB image of the target, we can predict the…
We show how the Stefan type free boundary problem with random diffusion in one space dimension can be approximated by the corresponding free boundary problem with nonlocal diffusion. The approximation problem is a slightly modified version…
Diffusion probabilistic models have achieved remarkable success in generative tasks across diverse data types. While recent studies have explored alternative degradation processes beyond Gaussian noise, this paper bridges two key diffusion…
Neural Radiance Fields (NeRF) recently emerged as a new paradigm for object representation from multi-view (MV) images. Yet, it cannot handle multi-scale (MS) images and camera pose estimation errors, which generally is the case with…
Mesh-free methods have significant potential for simulations of flows in complex geometries, with the difficulties of domain discretisation greatly reduced. However, many mesh-free methods are limited to low order accuracy. In order to…
In this paper we propose a new efficient interpolation tool, extremely suitable for large scattered data sets. The partition of unity method is used and performed by blending Radial Basis Functions (RBFs) as local approximants and using…