Related papers: Hybrid GFD-RBF Method for Convection-Diffusion Pro…
Accurate numerical simulations of interaction between fluid and solid play an important role in applications. The task is challenging in practical scenarios as the media are usually highly heterogeneous with very large contrast. To overcome…
Multi-Robot Motion Planning (MRMP) involves generating collision-free trajectories for multiple robots operating in a shared continuous workspace. While discrete multi-agent path finding (MAPF) methods are broadly adopted due to their…
We propose a finite volume method on general meshes for the discretization of a degenerate parabolic convection-reaction-diffusion equation. Equations of this type arise in many contexts, such as the modeling of contaminant transport in…
Based on the radial basis function (RBF), non-singular general solution and dual reciprocity principle (DRM), this paper presents an inheretnly meshless, exponential convergence, integration-free, boundary-only collocation techniques for…
In this manuscript we present a novel and efficient numerical method for the compressible viscous and resistive MHD equations for all Mach number regimes. The time-integration strategy is a semi-implicit splitting, combined with a hybrid…
In this work, we propose an adaptive radial basis function (RBF) approach for the efficient solution of multidimensional spatiotemporal integrodifferential equations. Our approach can automatically adjust the shape of RBFs and provide an…
In this work we develop a class of high-order finite difference weighted essentially non-oscillatory (FD-WENO) schemes for solving the ideal magnetohydrodynamic (MHD) equations in 2D and 3D. The philosophy of this work is to use efficient…
This paper presents a general framework of high-order finite difference (HFD) schemes for the tempered fractional Laplacian (TFL) based on new generating functions obtained from the discrete symbols. Specifically, for sufficiently smooth…
Solving high-dimensional parabolic partial differential equations (PDEs) with deep learning methods is often computationally and memory intensive, primarily due to the need for automatic differentiation (AD) to compute large Hessian…
We propose a method to obtain superresolution of turbulent statistics for three-dimensional ensemble particle tracking velocimetry (EPTV). The method is ''meshless'' because it does not require the definition of a grid for computing…
In this article, we develop a systematic approach of the invariant subspace method combined with variable transformation to find the generalized separable exact solutions of the nonlinear two-component system of time-fractional PDEs…
The physics-informed neural network (PINN) is effective in solving the partial differential equation (PDE) by capturing the physics constraints as a part of the training loss function through the Automatic Differentiation (AD). This study…
This paper introduces a novel, robust, and computationally efficient framework for high-quality quadrilateral mesh generation on general two-dimensional domains. The core of the proposed approach is a novel method for computing cross fields…
Coupled nonlinear system of reaction-diffusion equations describing multi-component (species) interactions with heterogeneous coefficients is considered. Finite volume method based approximation for the space is used to construct…
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…
The finite difference time domain method is one of the simplest and most popular methods in computational electromagnetics. This work considers two possible ways of generalising it to a meshless setting by employing local radial basis…
A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…
Finite Difference methods (FD) are one of the oldest and simplest methods for solving partial differential equations (PDE). Block Finite Difference methods (BFD) are FD methods in which the domain is divided into blocks, or cells,…
Finite Difference methods (FD) are one of the oldest and simplest methods for solving partial differential equations (PDE). Block Finite Difference methods (BFD) are FD methods in which the domain is divided into blocks, or cells,…
The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied…