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Meshfree methods
About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.
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TL;DR: This paper introduces and analyzes a new class of methods, collectively called the reproducing kernel element method (RKEM), to combine the strengths of both finite element methods (FEM) and meshfree methods, and presents a rigorous error analysis and convergence study of the method.
165 citations
01 Jan 2003
TL;DR: A Meshfree Method for the Analysis of Planar Flows of Inviscid Fluids and Some Regularized Versions of the Method of Fundamental Solutions.
Abstract: ESPResSo 3.1 - Molecular Dynamics Software for Coarse-Grained Models: A. Arnold, O. Lenz, S. Kesselheim, R. Weeber, F. Fahrenberger, D. Roehm, P. Kosovan, C. Holm.- On the Rate of Convergence of the Hamiltonian Particle-Mesh Method Onno Bokhove, Vladimir Molchanov, Marcel Oliver, Bob Peeters.- Peridynamics: A Nonlocal Continuum Theory.- Etienne Emmrich, Richard B. Lehoucq, Dimitri Puhst.- Immersed Molecular Electrokinetic Finite Element Method for Nano-Devices in Biotechnology and Gene Delivery: Wing Kam Liu, Adrian M. Kopacz, Tae-Rin Lee, Hansung Kim, Paolo Decuzzi.- Corrected Stabilized Non-conforming Nodal Integration in Meshfree Methods: Marcus Ruter, Michael Hillman, Jiun-Shyan Chen.- Multilevel Partition of Unity Method for Elliptic Problems with strongly Discontinuous Coefficients: Marc Alexander Schweitzer.- HOLMES: Convergent Meshfree Approximation Schemes of Arbitrary Order and Smoothness: Agustin Bompadre, Luigi E. Perotti, Christian J. Cyron, Michael Ortiz.- A Meshfree Splitting Method for Soliton Dynamics in Nonlinear Schrodinger Equations: Marco Caliari, Alexander Ostermann, Stefan Rainer.- A Meshless Discretization Method for Markov State Models Applied to Explicit Water Peptide Folding Simulations: Konstantin Fackeldey, Alexander Bujotzek, Marcus Weber.- Kernel-based Collocation Methods versus Galerkin Finite Element Methods for Approximating Elliptic Stochastic Partial Differential Equations: Gregory E. Fasshauer, Qi Ye.- A Meshfree Method for the Analysis of Planar Flows of Inviscid Fluids: Vasily N. Govorukhin.- Some Regularized Versions of the Method of Fundamental Solutions: Csaba Gaspar.- A Characteristic Particle Method for Traffic Flow Simulations on Highway Networks: Yossi Farjoun, Benjamin Seibold.- Meshfree Modeling in Laminated Composites: Daniel C. Simkins, Jr., Nathan Collier, Joseph B. Alford
164 citations
Book•
01 Apr 2004
TL;DR: Various modern techniques from scattered data modelling, such as splines over triangulations and radial basis functions, are combined with customized adaptive strategies, which are developed individually in this work to design efficient, robust and reliable algorithms for the numerical simulation of multiscale phenomena.
Abstract: This application-oriented work concerns the design of efficient, robust and reliable algorithms for the numerical simulation of multiscale phenomena. To this end, various modern techniques from scattered data modelling, such as splines over triangulations and radial basis functions, are combined with customized adaptive strategies, which are developed individually in this work. The resulting multiresolution methods include thinning algorithms, multi- levelapproximation schemes, and meshfree discretizations for transport equa- tions. The utility of the proposed computational methods is supported by their wide range of applications, such as image compression, hierarchical sur- face visualization, and multiscale flow simulation. Special emphasis is placed on comparisons between the various numerical algorithms developed in this work and comparable state-of-the-art methods. To this end, extensive numerical examples, mainly arising from real-world applications, are provided. This research monograph is arranged in six chapters: 1. Introduction; 2. Algorithms and Data Structures; 3. Radial Basis Functions; 4. Thinning Algorithms; 5. Multilevel Approximation Schemes; 6. Meshfree Methods for Transport Equations. Chapter 1 provides a preliminary discussion on basic concepts, tools and principles of multiresolution methods, scattered data modelling, multilevel methods and adaptive irregular sampling. Relevant algorithms and data structures, such as triangulation methods, heaps, and quadtrees, are then introduced in Chapter 2.
161 citations
TL;DR: In this article, a node-based smoothed finite element method (NS-FEM) was proposed for the solid mechanics problems, which is further extended to more complicated visco-elastoplastic analyses of 2D and 3D solids using triangular and tetrahedral meshes.
159 citations
TL;DR: In this article, a simple methodology to model shear bands as strong displacement discontinuities in an adaptive mesh-free method is presented, where the shear band is represented by a displacement jump at discrete particle positions.
157 citations