相关论文: Localized RBF methods for modeling infiltration us…

Recently, the nonlinearity continuation method has been used to numerically solve boundary value problems for steady-state Richards equation. The method can be considered as a predictor-corrector procedure with the simplest form which has…

A major obstacle to the application of the standard Radial Basis Function-generated Finite Difference (RBF-FD) meshless method is constituted by its inability to accurately and consistently solve boundary value problems involving Neumann…

Orbital-free density functional theory (OF-DFT) for real-space systems has historically depended on Lagrange optimization techniques, primarily due to the inability of previously proposed electron density approaches to ensure the…

The Kirchhoff integral is a fundamental integral in scattering theory, appearing in both the Kirchhoff approximation, as well as the small slope approximation. In this work, a functional Taylor series approximation to…

In this article, we propose a linearized fully-discrete scheme for solving a time fractional nonlocal diffusion-wave equation of Kirchhoff type. The scheme is established by using the finite element method in space and the $L1$ scheme in…

This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…

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…

We present a novel framework inspired by the Immersed Boundary Method for predicting the fluid-structure interaction of complex structures immersed in flows with moderate to high Reynolds numbers. The main novelties of the proposed…

We present a computational framework for dimension reduction and surrogate modeling to accelerate uncertainty quantification in computationally intensive models with high-dimensional inputs and function-valued outputs. Our driving…

A general and easy-to-code numerical method based on radial basis functions (RBFs) collocation is proposed for the solution of delay differential equations (DDEs). It relies on the interpolation properties of infinitely smooth RBFs, which…

This paper presents a methodology to learn surrogate models of steady state fluid dynamics simulations on meshed domains, based on Implicit Neural Representations (INRs). The proposed models can be applied directly to unstructured domains…

We present a non-nested multilevel algorithm for solving the Poisson equation discretized at scattered points using polyharmonic radial basis function (PHS-RBF) interpolations. We append polynomials to the radial basis functions to achieve…

We introduce a novel numerical method, named the Robin Hood method, of solving electrostatic problems. The approach of the method is closest to the boundary element methods, although significant conceptual differences exist with respect to…

Many local integral methods are based on an integral formulation over small and heavilly overlapping stencils with local RBF interpolations. These functions have become an extremely effective tool for interpolation on scattered node sets,…

In this paper, we revisit the classical problem of solving over-determined systems of nonsmooth equations numerically. We suggest a nonsmooth Levenberg--Marquardt method for its solution which, in contrast to the existing literature, does…

This paper presents a new numerical model based on the highly nonlinear potential flow theory for simulating the propagation of water waves in variable depth. A new set of equations for estimating the surface vertical velocity is derived…

Accurate and efficient numerical simulation of unconventional reservoirs is challenging. Long periods of transient flow and steep potential gradients occur due to the extreme conductivity contrast between matrix and fracture. Detailed…

We present and analyze a series of benchmark tests regarding the application of the immersed boundary (IB) method to viscoelastic flows through and around non-trivial, stationary geometries. The IB method is widely used for the simulation…

A radial basis function (RBF) based sequential surrogate reliability method (SSRM) is proposed, in which a special optimization problem is solved to update the surrogate model of the limit state function (LSF) iteratively. The objective of…

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…