Application of an RBF-FD solver for the Helmholtz equation to full-waveform inversion

三维亥姆霍兹方程的多二次径向基函数离散化的高效克雷洛夫正则化求解器

Efficient Krylov-Regularization Solvers for Multiquadric RBF Discretizations of the 3D Helmholtz Equation

针对三维亥姆霍兹方程MQ-RBF无网格配点法产生的稠密病态系统，提出三种嵌入正则化的克雷洛夫投影方法，经测试HKT精度优且效率高，低成本TSVD在仅需主导模态时最快，为复杂场景提供鲁棒可扩展方案。

A stabilized local integral method using RBFs for the Helmholtz equation with applications to wave chaos and dielectric microresonators

Most problems in electrodynamics do not have an analytical solution so much effort has been put in the development of numerical schemes, such as the finite-difference method, volume element methods, boundary element methods, and related methods based on boundary integral equations. In this paper we introduce a local integral boundary domain method with a stable calculation based on Radial Basis Functions (RBF) approximations, in the context of wave chaos in acoustics and dielectric microresonator problems. RBFs have been gaining popularity recently for solving partial differential equations nu…

A High-Order Radial Basis Function (RBF) Leray Projection Method for the Solution of the Incompressible Unsteady Stokes Equations

A new projection method based on radial basis functions (RBFs) is presented for discretizing the incompressible unsteady Stokes equations in irregular geometries. The novelty of the method comes from the application of a new technique for computing the Leray-Helmholtz projection of a vector field using generalized interpolation with divergence-free and curl-free RBFs. Unlike traditional projection methods, this new method enables matching both tangential and normal components of divergence-free vector fields on the domain boundary. This allows incompressibility of the velocity field to be enfo…

An investigation of global radial basis function collocation methods applied to Helmholtz problems

Global radial basis function (RBF) collocation methods with inifinitely smooth basis functions for partial differential equations (PDEs) work in general geometries, and can have exponential convergence properties for smooth solution functions. At the same time, the linear systems that arise are dense and severely ill-conditioned for large numbers of unknowns and small values of the shape parameter that determines how flat the basis functions are. We use Helmholtz equation as an application problem for the theoretical analysis and numerical experiments. We analyse and characterise the convergen…

无网格RBF基伪谱解声波方程

Meshless RBF based pseudospectral solution of acoustic wave equation

本文提出基于RBF-PS方法的无网格算法，用于求解非齐次亥姆霍兹方程，通过误差分析比较RBF与多项式基函数的优劣，并解决典型频域声波传播问题。

径向基函数生成的有限差分法结合贝塞尔权重用于二维亥姆霍兹方程

Radial basis function-generated finite differences with Bessel weights for the 2D Helmholtz equation

本文利用径向基函数生成的有限差分法（RBF-FD）结合贝塞尔函数定义的振荡径向基函数，对二维亥姆霍兹方程进行近似数值求解，通过正则化插值矩阵来解决局部插值获得权重时的病态问题，并通过不同数值测试验证了色散和污染效应的缓解。