Efficient searching in meshfree methods

  • James Olliff
  • Brad Alford
  • Daniel C. SimkinsJr.
Original Paper


Meshfree methods such as the Reproducing Kernel Particle Method and the Element Free Galerkin method have proven to be excellent choices for problems involving complex geometry, evolving topology, and large deformation, owing to their ability to model the problem domain without the constraints imposed on the Finite Element Method (FEM) meshes. However, meshfree methods have an added computational cost over FEM that come from at least two sources: increased cost of shape function evaluation and the determination of adjacency or connectivity. The focus of this paper is to formally address the types of adjacency information that arises in various uses of meshfree methods; a discussion of available techniques for computing the various adjacency graphs; propose a new search algorithm and data structure; and finally compare the memory and run time performance of the methods.


Meshfree Reproducing Kernel Particle Method Acceleration data structure Nearest neighbour Adjacency Connectivity 



The authors would like to thank and acknowledge Dr. Jen Bright for the data provided for the Scarlet Macaw bird skull. The author’s would also like to thank Formerics, LLC for the use of their software.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • James Olliff
    • 1
  • Brad Alford
    • 1
  • Daniel C. SimkinsJr.
    • 1
  1. 1.Department of Civil and Environmental EngineeringUniversity of South FloridaTampaUSA

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