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Helical Organization of Blood Coagulation Factor VIII on Lipid Nanotubes
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A FAST ITERATIVE METHOD FOR SOLVING THE EIKONAL EQUATION ON TRIANGULATED SURFACES.

Zhisong Fu1, Won-Ki Jeong, Yongsheng Pan

  • 1The Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84112.

SIAM Journal on Scientific Computing : a Publication of the Society for Industrial and Applied Mathematics
|May 30, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces an efficient parallel algorithm for solving the Eikonal equation on triangular meshes. The novel method extends the fast iterative method (FIM) for improved performance on various parallel architectures.

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Area of Science:

  • Computational Mathematics
  • Numerical Analysis
  • Scientific Computing

Background:

  • The Eikonal equation, a type of Hamilton-Jacobi equation, is crucial in fields like geometric optics, seismology, and image analysis.
  • Solving these equations efficiently is vital for parameter space exploration and inverse problems.
  • Existing parallel algorithms often require new approaches tailored for synchronous updates on modern hardware.

Purpose of the Study:

  • To extend the Fast Iterative Method (FIM) for efficient Eikonal equation solving on triangular meshes.
  • To develop a fine-grained parallel algorithm suitable for CPUs and graphics processors.
  • To enable accurate and efficient solutions for complex computational problems.

Main Methods:

  • Extension of the Fast Iterative Method (FIM) to triangulated domains.
  • Development of a new local update scheme for first-order accuracy.
  • Introduction of a novel triangle-based update scheme and data structure for SIMD processors.

Main Results:

  • An efficient, fine-grained parallel algorithm for solving the Eikonal equation on triangular meshes.
  • First-order accuracy achieved through a new local update scheme on CPUs and GPUs.
  • Demonstrated efficient irregular data mapping to parallel SIMD architectures.

Conclusions:

  • The extended FIM offers an efficient solution for Eikonal equations on triangular meshes across diverse parallel architectures.
  • The proposed methods provide a foundation for advanced computational modeling and analysis.
  • This work advances the capabilities for solving inverse problems and visualizing complex data.