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Algorithms
Special Issues
Geometric Algorithms and Applications
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Geometric Algorithms and Applications

A special issue of Algorithms (ISSN 1999-4893). This special issue belongs to the section "Analysis of Algorithms and Complexity Theory".

Deadline for manuscript submissions: 30 September 2024 | Viewed by 529

Special Issue Editor

Dr. Antoine Vigneron

E-Mail Website
Guest Editor
Department of Computer Science and Engineering, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
Interests: computational geometry; algorithm design and analysis; data structures

Special Issue Information

Dear Colleagues,

Geometric algorithms deal with data represented by mathematical objects such as points, lines, curves, or polyhedral subdivisions. These algorithms find applications in various fields such as computer graphics, computer vision, geographic information systems, and robotics. We invite submissions of original results to the Special Issue of Algorithms on "Geometric Algorithms and Applications". Topics of interest may include, but are not limited to, the following:

  • Design and analysis of geometric algorithms;
  • Geometric data structures;
  • Geometric approximation algorithms;
  • Computational complexity of geometric problems;
  • Discrete geometry;
  • Algorithms for doubling spaces and hyperbolic spaces;
  • Experimental algorithmics of geometric problems;
  • Applications of computational geometry to any field.

Dr. Antoine Vigneron
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • computational geometry
  • algorithm design and analysis
  • data structures
  • discrete geometry
  • approximation algorithms

Published Papers (1 paper)

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Research

23 pages, 18462 KiB  
Article
Boundary SPH for Robust Particle–Mesh Interaction in Three Dimensions
by Ryan Kim and Paul M. Torrens
Algorithms 2024, 17(5), 218; https://doi.org/10.3390/a17050218 - 16 May 2024
Viewed by 315
Abstract
This paper introduces an algorithm to tackle the boundary condition (BC) problem, which has long persisted in the numerical and computational treatment of smoothed particle hydrodynamics (SPH). Central to the BC problem is a need for an effective method to reconcile a numerical [...] Read more.
This paper introduces an algorithm to tackle the boundary condition (BC) problem, which has long persisted in the numerical and computational treatment of smoothed particle hydrodynamics (SPH). Central to the BC problem is a need for an effective method to reconcile a numerical representation of particles with 2D or 3D geometry. We describe and evaluate an algorithmic solution—boundary SPH (BSPH)—drawn from a novel twist on the mesh-based boundary method, allowing SPH particles to interact (directly and implicitly) with either convex or concave 3D meshes. The method draws inspiration from existing works in graphics, particularly discrete signed distance fields, to determine whether particles are intersecting or submerged with mesh triangles. We evaluate the efficacy of BSPH through application to several simulation environments of varying mesh complexity, showing practical real-time implementation in Unity3D and its high-level shader language (HLSL), which we test in the parallelization of particle operations. To examine robustness, we portray slip and no-slip conditions in simulation, and we separately evaluate convex and concave meshes. To demonstrate empirical utility, we show pressure gradients as measured in simulated still water tank implementations of hydrodynamics. Our results identify that BSPH, despite producing irregular pressure values among particles close to the boundary manifolds of the meshes, successfully prevents particles from intersecting or submerging into the boundary manifold. Average FPS calculations for each simulation scenario show that the mesh boundary method can still be used effectively with simple simulation scenarios. We additionally point the reader to future works that could investigate the effect of simulation parameters and scene complexity on simulation performance, resolve abnormal pressure values along the mesh boundary, and test the method’s robustness on a wider variety of simulation environments. Full article
(This article belongs to the Special Issue Geometric Algorithms and Applications)
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