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Everything about Regularized meshless method
In numerical mathematics, the regularized meshless method (RMM), also known as the singular meshless method or desingularized meshless method, is a meshless boundary collocation method designed to solve certain partial differential equations whose fundamental solution is explicitly known. The RMM is a strong-form collocation method with merits being meshless, integration-free, easy-to-implement, and high stability. Until now this method has been successfully applied to some typical problems, such as potential, acoustics, water wave, and inverse problems of bounded and unbounded domains. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Regularized meshless methodA 5-minute orientation
- Skim a recent paper: A meshless regularized method of fundamental solution for electromagnetic scattering problems of three-dimensional perfect electric conductor targetsInfluential work since 2022
- Pick up a classic book: Meshfree Methods for Partial Differential Equations VIThe most-reprinted book on the subject
- Read the landmark paper: A meshless method using the radial basis functions for numerical solution of the regularized long wave equationCited 76 times
- Go sideways: Singular boundary methodA closely related topic
- Go sideways: Method of fundamental solutionsA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
A meshless method using the radial basis functions for numerical solution of the regularized long wave equation
Regularized meshless method for multiply-connected-domain Laplace problems
A meshless method for the nonlinear generalized regularized long wave equation
Single layer regularized meshless method for three dimensional exterior acoustic problem
A new formulation of regularized meshless method applied to interior and exterior anisotropic potential problems
Regularized meshless method for antiplane shear problems with multiple inclusions
Boundary reconstruction in two-dimensional steady state anisotropic heat conduction using a regularized meshless method
Regularized meshless method for nonhomogeneous problems
🆕 Influential since 2022
A meshless regularized method of fundamental solution for electromagnetic scattering problems of three-dimensional perfect electric conductor targets
A hybrid wavelet-meshless method for variable-order fractional regularized long-wave equation
Application of Regularized Meshless Method with Error Estimation Technique for Water–Wave Scattering by Multiple Cylinders
A high-order regularized hybrid BEM–meshless method for electromagnetic scattering: Algorithm, stability analysis, and convergence proofs
Regularized moving least squares meshless method for solving three-dimensional Fredholm integral equations on 3D irregular domain
📚 Books worth reading
Meshfree Methods for Partial Differential Equations VIMichael Griebel · 2013
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Singular boundary method In numerical analysis, the singular boundary method (SBM) belongs to a family of meshless boundary collocation techniques which include the method of fundamenta…
- Method of fundamental solutions In scientific computation and simulation, the method of fundamental solutions (MFS) is a technique for solving partial differential equations based on…
- Boundary particle method In applied mathematics, the boundary particle method (BPM) is a boundary-only meshless (meshfree) collocation technique, in the sense that none of inner…
- Boundary knot method In numerical mathematics, the boundary knot method (BKM) is proposed as an alternative boundary-type meshfree distance function collocation scheme. Recent…
- Kansa method The Kansa method (also known as the unsymmetric radial basis function collocation method) is a meshless numerical method for solving partial differential…
- Meshfree methods In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but…
- Boundary element method The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations (PDEs) arising in engineering and…
- Discrete least squares meshless method In mathematics the discrete least squares meshless (DLSM) method is a meshless method based on the least squares concept. The method is based on the minimizatio…