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 published on a yearly basis
Papers
More filters
TL;DR: In this paper, the cell-based maximum entropy (CME) approximants in E3 space are constructed by constructing the smooth approximation distance function to polyhedral surfaces. But the accuracy and efficiency of the method is assessed in several numerical examples in terms of computational time, accuracy in boundary conditions imposition and strain energy density error.
Abstract: We present the Cell-based Maximum Entropy (CME) approximants in E3 space by constructing the smooth approximation distance function to polyhedral surfaces. CME is a meshfree approximation method combining the properties of the Maximum Entropy approximants and the compact support of element-based interpolants. The method is evaluated in problems of large strain elastodynamics for three-dimensional (3D) continua using the well-established Meshless Total Lagrangian Explicit Dynamics (MTLED) method. The accuracy and efficiency of the method is assessed in several numerical examples in terms of computational time, accuracy in boundary conditions imposition, and strain energy density error. Due to the smoothness of CME basis functions, the numerical stability in explicit time integration is preserved for large time step. The challenging task of essential boundary conditions imposition in non-interpolating meshless methods (e.g., Moving Least Squares) is eliminated in CME due to the weak Kronecker-delta property. The essential boundary conditions are imposed directly, similar to the Finite Element Method. CME is proven a valuable alternative to other meshless and element-based methods for large-scale elastodynamics in 3D.
8 citations
TL;DR: In this paper, the authors proposed a fully coupled model of cardiac electromechanics based on Total Lagrangian Smoothed Particle Hydrodynamics (TL-SPH).
8 citations
TL;DR: In this paper, a strong meshless collocation technique was proposed to solve the Dirichlet problem for the Monge-Ampere equation with convergence rates up to exponential, depending on the smoothness of the true solution.
Abstract: This paper solves the two-dimensional Dirichlet problem for the Monge-Ampere equation by a strong meshless collocation technique that uses a polynomial trial space and collocation in the domain and on the boundary. Convergence rates may be up to exponential, depending on the smoothness of the true solution, and this is demonstrated numerically and proven theoretically, applying a sufficiently fine collocation discretization. A much more thorough investigation of meshless methods for fully nonlinear problems is in preparation.
8 citations
TL;DR: In this paper, the complex variable Galerkin boundary node method (CVGBNM) is developed for BIEs, potential problems and Stokes problems, and numerical examples are given to demonstrate the efficacy of the method.
Abstract: In this study, combining the boundary integral equations (BIEs) with the complex variable moving least squares (CVMLS) approximation, a symmetric and boundary-only meshless method, the complex variable Galerkin boundary node method (CVGBNM), is developed. Numerical applications and theoretical error estimates of the CVGBNM are derived for BIEs, potential problems and Stokes problems. Finally, numerical examples are given to demonstrate the efficacy of the method.
8 citations
TL;DR: In this article, two different mesh-free methods consisting of the Radial Basis Functions (RBFs) and the Moving Least Square Method (MLS) are applied to solve the Grad-Shafranov (GS) equation for the axisymmetric equilibrium of plasma in the tokamak.
Abstract: In this study, two different meshfree methods consisting of the Radial Basis Functions (RBFs) and the Moving Least Square Method (MLS) are applied to solve the Grad–Shafranov (GS) equation for the axisymmetric equilibrium of plasma in the tokamak. The validity and the effectiveness of the proposed schemes are studied by several test problems through absolute and Root Mean Squared (RMS) errors. Although, during the past few years, a meshfree method is normally applied in magnetohydrodynamic (MHD) studies to the numerical solution of partial differential equations (PDEs) but to the best of our knowledge, its application in MHD equilibrium of the tokamak plasma investigations is rare. The future more extensive studies regarding this numerical method would definitely have a significant impact on improving tokamak numerical tools.
8 citations