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
DissertationDOI
01 Jan 2010
TL;DR: Pasupuleti et al. as discussed by the authors developed improved computational tools like 1D integration and modification of distance fields for analysis of diffusion concentration in heterogeneous material with high contrast of physical and geometrical properties.
Abstract: OF THE THESIS DEVELOPMENT OF MESHFREE METHOD FOR CERTAIN ENGINEERING ANALYSIS PROBLEM by Sunil Kumar Pasupuleti Florida International University, 2010 Miami, Florida Professor Igor Tsukanov, Major Professor This study presents a numerical technique that enables exact treatment of all boundary conditions including those that are given on the interface boundary of two distinct media. This interface boundary conditions for Poisson equation are formulated as equality of the physical field and fluxes across the interface boundary. In this work first, the range of physical and geometric parameters which allow the applicability of the meshfree method with distance fields are tested and compared with analytical solution. Second, it investigates how the solution error depends on the ratio of B-spline support and thickness of the interface layer. Further, this study also concentrates on developing improved computational tools like 1D integration and modification of distance fields for analysis of diffusion concentration in heterogeneous material with high contrast of physical and geometrical properties. These improved computational tools for meshfree method with distance fields improves the accuracy of solution and decreases the computational time. Finally, these improved tools are used to solve a 2D problem for analysis of diffusion concentration and the results are compared to FEM solution to show that the improved tools yield computationally better results.
Posted ContentDOI
11 Jun 2022
TL;DR: In this article , a node control domains-based meshless method is proposed to handle porous flow problems with singular source terms by virtually constructing the node control domain, which only focuses on the volume of the vertex control domain rather than the specific shape.
Abstract: In this paper, a novel meshless method that can handle porous flow problems with singular source terms is developed by virtually constructing the node control domains. By defining the connectable node cloud, this novel meshless method uses the integral of the diffusion term and generalized difference operators to derive overdetermined equations of the node control volumes. An empirical method of calculating reliable node control volumes and a triangulation-based method to determine the connectable point cloud are developed. NCDMM only focuses on the volume of the node control domain rather than the specific shape, so the construction of node control domains is called virtual, which will not increase the computational cost. To our knowledge, this is the first time to construct node control volumes in the meshless framework, so this novel method is named a node control domains-based meshless method, abbreviated as NCDMM, which can also be regarded as an extended finite volume method (EFVM). Taking two-phase porous flow problems as an example, the NCDMM discrete schemes meeting local mass conservation are derived by integrating the generalized finite difference schemes of governing equations on each node control domain. Finally, existing commonly used low-order finite volume method (FVM) based nonlinear solvers for various porous flow models can be directly employed in the proposed NCDMM, significantly facilitating the general-purpose applications of the NCDMM. Four numerical cases are implemented to test the computational accuracy, efficiency, convergence, and good adaptability to the calculation domain with complex geometry and various boundary conditions.
Book ChapterDOI
01 Jan 2022
TL;DR: In this paper , a method based on the localized radial basis function (RBF) and the Kirchhoff transformation technique was developed to solve the Richards equation in one and two-dimensional homogeneous medium.
Abstract: In this study, we focus on the modelling of infiltration process in porous media. We use the meshless techniques for efficiently solving the Richards equation which describes unsaturated water flow through soils. The design of approximate numerical methods for the Richards equation remains computationally challenging and requires the development of efficient numerical techniques. This difficulty is mainly due to the nonlinearity of the unsaturated hydraulic conductivity and the capillary pressure function. In this study, we develop a new method based on the localized radial basis function (RBF) and the Kirchhoff transformation technique in order to solve Richards equation in one and two-dimensional homogeneous medium. Our approach using the multiquadric radial basis function allows us to reduce the computational time and provide accurate numerical solutions. The proposed method does not require mesh generation. Picard's iterations are used to linearize the resulting nonlinear problem obtained using the Kirchhoff transformation technique. The numerical simulations show the capability of the proposed numerical techniques in predicting the dynamics of water through unsaturated soils.
Posted ContentDOI
23 May 2023
TL;DR: In this paper , an Interface-Modified Reproducing Kernel Particle Method (IM-RKPM) is proposed for appropriate approximations of weak discontinuities across material interfaces.
Abstract: This work presents an approach for automating the discretization and approximation procedures in constructing digital representations of composites from Micro-CT images featuring intricate microstructures. The proposed method is guided by the Support Vector Machine (SVM) classification, offering an effective approach for discretizing microstructural images. An SVM soft margin training process is introduced as a classification of heterogeneous material points, and image segmentation is accomplished by identifying support vectors through a local regularized optimization problem. In addition, an Interface-Modified Reproducing Kernel Particle Method (IM-RKPM) is proposed for appropriate approximations of weak discontinuities across material interfaces. The proposed method modifies the smooth kernel functions with a regularized heavy-side function concerning the material interfaces to alleviate Gibb's oscillations. This IM-RKPM is formulated without introducing duplicated degrees of freedom associated with the interface nodes commonly needed in the conventional treatments of weak discontinuities in the meshfree methods. Moreover, IM-RKPM can be implemented with various domain integration techniques, such as Stabilized Conforming Nodal Integration (SCNI). The extension of the proposed method to 3-dimension is straightforward, and the effectiveness of the proposed method is validated through the image-based modeling of polymer-ceramic composite microstructures.
01 Jan 2007
TL;DR: Central dierence scheme for 2D meshless gas dynamics is presented and the corresponding meshless method, called FuzzyGrid, is presented, a natural generalization of meshless methods, based on Free-points method and SPH methods ideas.
Abstract: Central dierence scheme for 2D meshless gas dynamics is presented. The corresponding meshless method, called FuzzyGrid has been presented earlier [1]. The method is a natural generalization of meshless methods, based on Free-points method and SPH methods ideas. The main idea of the method is based on the approximation of the surface and volume integrals of the unknown functions in a particle as sums of these functions values in the points (particles), which are in the nearest vicinity to the given one.

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