Related papers: A Radial Basis Function (RBF)-Finite Difference (F…

The meshless/meshfree radial basis function (RBF) method is a powerful technique for interpolating scattered data. But, solving large RBF interpolation problems without fast summation methods is computationally expensive. For RBF…

In this paper, we propose an efficient numerical scheme for the approximate solution of the time fractional diffusion-wave equation with reaction term based on cubic trigonometric basis functions. The time fractional derivative is…

Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…

We propose a novel efficient and robust Wavelet-based Edge Multiscale Finite Element Method (WEMsFEM) motivated by \cite{MR3980476,GL18} to solve the singularly perturbed convection-diffusion equations. The main idea is to first establish a…

In this paper we consider a class of unfitted finite element methods for discretization of partial differential equations on surfaces. In this class of methods known as the Trace Finite Element Method (TraceFEM), restrictions or traces of…

In this paper, we investigate the application of radial basis functions (RBFs) for the approximation with collocation of the Stokes problem. The approximate solution is constructed in a multi-level fashion, each level using compactly…

We demonstrate that we can carry over the strategy of Finite Element Exterior Calculus (FEEC) to Summation-by-Parts (SBP) Finite Difference (FD) methods to achieve divergence- and curl-free discretizations. This is not obvious at first…

In this work, we develop a high-order collocation method using radial basis function (RBF) for the incompressible Navier-Stokes equation (NSE) on the rotating sphere. The method is based on solving the projection of the NSE on the space of…

We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…

Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…

In this paper, a mixed high order finite difference scheme-Pad\'{e} approximation method is applied to obtain numerical solution of the Riesz fractional advection-dispersion equation. This method is based on the high order finite difference…

We present fast, spatially dispersionless and unconditionally stable high-order solvers for Partial Differential Equations (PDEs) with variable coefficients in general smooth domains. Our solvers, which are based on (i) A certain "Fourier…

In this paper, we approximate the solution and also discuss the periodic behavior termed as eventual periodicity of solutions of (IBVPs) for some dispersive wave equations on a bounded domain corresponding to periodic forcing. The…

Analytical expressions for radial distribution function (RDF) are of critical importance for various applications, such as development of the perturbation theories for equilibrium properties. Theoretically, RDF expressions for…

In this paper, a higher order finite difference scheme is proposed for Generalized Fractional Diffusion Equations (GFDEs). The fractional diffusion equation is considered in terms of the generalized fractional derivatives (GFDs) which uses…

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…

We derive stability estimates for three commonly used radial basis function (RBF) methods to solve hyperbolic time-dependent PDEs: the RBF generated finite difference (RBF-FD) method, the RBF partition of unity method (RBF-PUM) and Kansa's…

In this paper, we introduce a superconvergent approximation method that employs radial basis functions (RBFs) in the numerical solution of conservation laws. The use of RBFs for interpolation and approximation is a well developed area of…

In this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on Generalized Multiscale Finite Element Method (GMsFEM), where we represent the fracture effects on a coarse grid via…

We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical…