scispace - formally typeset
Search or ask a question
Topic

Meshfree methods

About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.


Papers
More filters
DOI
08 Sep 2021
TL;DR: In this article, the numerical properties of p-refined solutions were studied on a Poisson problem with a strong source within the domain, and the numerical performance was analyzed on poisson problems with strong sources.
Abstract: Local meshless methods obtain higher convergence rates when RBF approximations are augmented with monomials up to a given order. If the order of the approximation method is spatially variable, the numerical solution is said to be p-refined. In this work, we employ RBF-FD approximation method with polyharmonic splines augmented with monomials and study the numerical properties of p-refined solutions, such as convergence orders and execution time. To fully exploit the refinement advantages, the numerical performance is studied on a Poisson problem with a strong source within the domain.

4 citations

Journal ArticleDOI
TL;DR: In this paper, a new technique, the spiral weight, is introduced to increase the accuracy of the meshless approximations without increasing the nodal density, which is done by an appropriate modification of the weight function near crack tips.
Abstract: In the last decade several different approaches have been developed to study arbitrary static and dynamic cracks. Among these methods meshless techniques play an important role. These methods provide an accurate solution of a wide range of fracture mechanics problems while traditional methods such as finite element and boundary element have limitations. We wish to increase the accuracy of the meshless approximations without increasing the nodal density. This is done by an appropriate modification of the weight function near crack tips. Earlier attempts still had limitations that result in a lack of accuracy, especially in the case when a linear basis is used. In this work a new technique, the spiral weight, is introduced that minimizes the drawbacks of existing methods. Numerical examples show that the spiral weight method is more efficient than existing methods, when using a linear basis, for the solution of crack problems.

4 citations

Book ChapterDOI
01 Jan 2011
TL;DR: This work shows how to describe registration in purely mechanical terms, such as displacements, strains and stresses and perform it using established methods of continuum mechanics, and advocates the use of fully non-linear theory of continuum Mechanics.
Abstract: We present selected topics in the area of mathematical and numerical modelling of the brain biomechanics for brain image registration. We show how to describe registration in purely mechanical terms, such as displacements, strains and stresses and perform it using established methods of continuum mechanics. We advocate the use of fully non-linear theory of continuum mechanics. We discuss in some detail modelling geometry, boundary conditions, loading and material properties. We consider numerical problems such as the use of hexahedral and mixed hexahedral-tetrahedral meshes as well as meshless spatial discretisation schemes as well as the effects of model complexity on accuracy of brain deformation computation. We advocate the use of Total Lagrangian Formulation of both finite element and meshless methods together with explicit time-stepping procedures. We support our recommendations and conclusions with an example of the computation of the brain shift for intra-operative image registration.

4 citations

Journal ArticleDOI
TL;DR: In this paper, a direct collocation meshless method based on a moving least-squares approximation is presented to solve polarized radiative transfer in scattering media, and several classical cases are examined to verify the numerical performance of the method.
Abstract: A direct collocation meshless method based on a moving least-squares approximation is presented to solve polarized radiative transfer in scattering media. Contrasted with methods such as the finite volume and finite element methods that rely on mesh structures (e.g. elements, faces and sides), meshless methods utilize an approximation space based only on the scattered nodes, and no predefined nodal connectivity is required. Several classical cases are examined to verify the numerical performance of the method, including polarized radiative transfer in atmospheric aerosols and clouds with phase functions that are highly elongated in the forward direction. Numerical results show that the collocation meshless method is accurate, flexible and effective in solving one-dimensional polarized radiative transfer in scattering media. Finally, a two-dimensional case of polarized radiative transfer is investigated and analyzed.

4 citations

01 Jun 2009
TL;DR: In this article, a bridging transition algorithm is developed for the combination of the mesh-free method (MM) with the finite element method (FEM), where the MM domain and the FEM domain are connected by a transition (bridging) region.
Abstract: For certain continuum problems, it is desirable and beneficial to combine two different methods together in order to exploit their advantages while evading their disadvantages. In this paper, a bridging transition algorithm is developed for the combination of the meshfree method (MM) with the finite element method (FEM). In this coupled method, the meshfree method is used in the sub-domain where the MM is required to obtain high accuracy, and the finite element method is employed in other sub-domains where FEM is required to improve the computational efficiency. The MM domain and the FEM domain are connected by a transition (bridging) region. A modified variational formulation and the Lagrange multiplier method are used to ensure the compatibility of displacements and their gradients. To improve the computational efficiency and reduce the meshing cost in the transition region, regularly distributed transition particles, which are independent of either the meshfree nodes or the FE nodes, can be inserted into the transition region. The newly developed coupled method is applied to the stress analysis of 2D solids and structures in order to investigate its’ performance and study parameters. Numerical results show that the present coupled method is convergent, accurate and stable. The coupled method has a promising potential for practical applications, because it can take advantages of both the meshfree method and FEM when overcome their shortcomings.

4 citations


Network Information
Related Topics (5)
Finite element method
178.6K papers, 3M citations
89% related
Numerical analysis
52.2K papers, 1.2M citations
86% related
Discretization
53K papers, 1M citations
86% related
Boundary value problem
145.3K papers, 2.7M citations
82% related
Partial differential equation
70.8K papers, 1.6M citations
81% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202355
2022112
2021102
202092
201996
201897