A study of efficient concurrent integration methods of B-Spline basis functions in IGA-FEM

@article{Wozniak2022ASO,
  title={A study of efficient concurrent integration methods of B-Spline basis functions in IGA-FEM},
  author={Maciej Wo'zniak and Anna Szyszka and Sergio Rojas},
  journal={ArXiv},
  year={2022},
  volume={abs/2207.00280}
}
Based on trace theory, we study efficient methods for concurrent integration of B-spline basis functions in IGA-FEM. We consider several scenarios of parallelization for two standard integration methods; the classical one and sum factorization. We aim to efficiently utilize hybrid memory machines, such as modern clusters, by focusing on the non-obvious layer of the shared memory part of concurrency. We estimate the performance of computations on a GPU and provide a strategy for performing such… 

References

SHOWING 1-10 OF 36 REFERENCES

Optimal Kernel Design for Finite-Element Numerical Integration on GPUs

The design and optimization of the GPU kernels for numerical integration, as it is applied in the standard form in finite-element codes is presented, with the main emphasis on the placement of variables in the shared memory or registers.

Fast algorithms for setting up the stiffness matrix in hp-FEM: a comparison

A generalization of the Spectral Galerkin Algorithm of [7], where the shape functions are adapted to the quadrature formula, to the case of triangles/tetrahedra is presented.

Sum factorization techniques in Isogeometric Analysis

Package for calculating B-splines

Eight FORTRAN subprograms for dealing computationally with piecewise polynomial functions (of one variable) are presented. The package is built around an algorithm for the stable evaluation of

Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume II Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications

Volume II Frontiers: Three-Dimensional Elliptic and Maxwell Problems with Applications presents the theoretical foundations of the 3D hp algorithm and provides numerical results using the3Dhp code developed by the authors and their colleagues.

Spline Functions: Basic Theory

The material covered provides the reader with the necessary tools for understanding the many applications of splines in such diverse areas as approximation theory, computer-aided geometric design, curve and surface design and fitting, image processing, numerical solution of differential equations, and increasingly in business and the biosciences.