Meshfree methods

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

Real-Time Nonlinear Finite Element Computations on GPU: Handling of Different Element Types

Abstract: Application of biomechanical modeling techniques in the area of medical image analysis and surgical simulation implies two conflicting requirements: accurate results and high solution speeds. Accurate results can be obtained only by using appropriate models and solution algorithms. In our previous papers, we have presented algorithms and solution methods for performing accurate nonlinear finite element analysis of brain shift (which includes mixed mesh, different nonlinear material models, finite deformations and brain–skull contacts) in less than 5 s on a personal computer using a Graphics Processing Unit (GPU) for models having up to 50,000 degrees of freedom. In this chapter, we compare several approaches for implementing different element types on the GPU using the NVIDIA Compute Unified Device Architecture. Our results can be used as a guideline for selecting the best GPU implementation approach for finite element algorithms which require mixed meshes or even for meshless methods.

A Multiscale Meshfree Method for Macroscopic Approximations of Interacting Particle Systems

Abstract: A multiscale meshfree particle method for macroscopic mean field approximations of interacting particle models is developed. The method is working for a large range of interaction parameters. The well resolved case for large interaction radius, as well as underresolved diffusive situations with small values of the interaction radius, are treated. There are various applications of the method to more complicated problems, for example, in swarming or pedestrian flow simulation.

On the use of meshfree methods and a geometry based surgical cutting algorithm in multimodal medical simulations

Abstract: In this paper, we present some of our recent advances in the simulation of surgical procedures including surgical cutting in multimodal virtual environments. Progressive cutting, without the generation of new primitives, is achieved by snapping the nearest nodes to the interaction point between the cutting tool and the underlying polygon edge. The realism of the simulation is enhanced by employing a local subdivision algorithm in the vicinity of the tool-tissue interaction region. A cutting gutter is constructed to display the interior of the cut surface as the cut opens up. A meshfree method is used to compute the deformation fields and interaction forces. Simulation examples involving the cutting of realistic organ models are presented.

Meshless RPIM modeling of open-structures using PMLs

Abstract: Meshless methods are emerging as a new class of numerical techniques for modeling complex electromagnetic problems with irregular geometries. To apply them to open structures, effective absorbing boundaries need to be developed. In this paper, the perfectly matched layer (PML) absorbing boundary condition is implemented into the meshless radial point interpolation method (RPIM) for accurate meshfree modeling of electromagnetic radiation problems in time-domain. Two benchmark radiating structures, a parallel waveguide and a conical unipole antenna, are presented to validate the effectiveness of the implementation. Comparisons are made between the numerically computed results and the measured results from previous reports and good agreements are found. In contrast to conventional FDTD technique, the RPIM modeling with the PML condition requires much less computational efforts for antenna radiation problems, thanks to its capability of conformal modeling and multi-scale solutions.

Parallel computations in nonlinear solid mechanics using adaptive finite element and meshless methods

Abstract: Purpose – A variety of meshless methods have been developed in the last 20 years with an intention to solve practical engineering problems, but are limited to small academic problems due to associated high computational cost as compared to the standard finite element methods (FEM). The purpose of this paper is to develop an efficient and accurate algorithms based on meshless methods for the solution of problems involving both material and geometrical nonlinearities. Design/methodology/approach – A parallel two-dimensional linear elastic computer code is presented for a maximum entropy basis functions based meshless method. The two-dimensional algorithm is subsequently extended to three-dimensional adaptive nonlinear and three-dimensional parallel nonlinear adaptively coupled finite element, meshless method cases. The Prandtl-Reuss constitutive model is used to model elasto-plasticity and total Lagrangian formulations are used to model finite deformation. Furthermore, Zienkiewicz and Zhu and Chung and Bely...