相关论文: Boundary knot method: A meshless, exponential conv…

The boundary element method (BEM) provides an efficient numerical framework for solving multiple scattering problems in unbounded homogeneous domains, since it reduces the discretization to the domain boundaries, thereby condensing the…

This paper treats the inverse problem of retrieving the electrical conductivity of a material starting from boundary measurements in the framework of Electrical Resistance Tomography (ERT). In particular, the focus is on non-iterative…

Scattered data interpolation schemes using kriging and radial basis functions (RBFs) have the advantage of being meshless and dimensional independent, however, for the data sets having insufficient observations, RBFs have the advantage over…

This article describes a numerical method based on the dual reciprocity boundary elements method (DRBEM) for solving some well-known nonlinear parabolic partial differential equations (PDEs). The equations include the classic and…

A fourth-order finite volume embedded boundary (EB) method is presented for the unsteady Stokes equations. The algorithm represents complex geometries on a Cartesian grid using EB, employing a technique to mitigate the "small cut-cell"…

In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…

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…

The Random Batch Method (RBM) is an effective technique to reduce the computational complexity when solving certain stochastic differential problems (SDEs) involving interacting particles. It can transform the computational complexity from…

The context of this paper is the simulation of parameter-dependent partial differential equations (PDEs). When the aim is to solve such PDEs for a large number of parameter values, Reduced Basis Methods (RBM) are often used to reduce…

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…

Deep Ritz methods (DRM) have been proven numerically to be efficient in solving partial differential equations. In this paper, we present a convergence rate in $H^{1}$ norm for deep Ritz methods for Laplace equations with Dirichlet boundary…

Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…

Computationally solving the equations of elasticity is a key component in many materials science and mechanics simulations. Phenomena such as deformation-induced microstructure evolution, microfracture, and microvoid nucleation are examples…

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…

Recently, collocation based radial basis function (RBF) partition of unity methods (PUM) for solving partial differential equations have been formulated and investigated numerically and theoretically. When combined with stable evaluation…

The method of fundamental solution (MFS) is an efficient meshless method for solving a boundary value problem in an exterior unbounded domain. The numerical solution obtained by the MFS is accurate, while the corresponding matrix equation…

An efficient and easy-to-implement method is proposed to regularize integral equations in the 3D boundary element method (BEM). The method takes advantage of an assumed three-noded triangle discretization of the boundary surfaces. The…

Many applications like subseismic fault modeling, fractured reservoir modeling and interpretation/validation of fault connectivity involve the solution to an elliptic boundary value problem in a background medium perturbed by the presence…

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…

The Boundary Element Method (BEM) is implemented using piecewise linear elements to solve the two-dimensional Dirichlet problem for Laplace's equation posed on a disk. A benefit of the BEM as opposed to many other numerical solution…