Essays about: "Sum-factorization"

Found 2 essays containing the word Sum-factorization.

1. 1. Discussion of Python Implementation Techniques for Discontinuous Galerkin Methods

   University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

   Author : Ulf Vestberg; [2023]
   Keywords : Best approximation; Orthogonal polynomials; Legendre polynomials; Integration; Full tensor product; Sum-factorization; Dune; Mathematics and Statistics;

   Abstract : This paper discusses implementation techniques for integration methods within the Discontinuous Galerkin Methods. These methods are used to approximate solutions for differential equations. To do so, one must compute a polynomial, which is an approximation of the used function. READ MORE

3. 2. High-performance implementation of H(div)-conforming elements for incompressible flows

   University essay from Uppsala universitet/Avdelningen för beräkningsvetenskap

   Author : Niklas Wik; [2022]
   Keywords : Finite elements; H div -conforming; incompressible flows; incompressible Navier-Stokes equations; high-performance; matrix-free; Raviart-Thomas;

   Abstract : In this thesis, evaluation of H(div)-conforming finite elements is implemented in a high-performance setting and used to solve the incompressible Navier-Stokes equation, obtaining an exactly point-wise divergence-free velocity field. In particular, the anisotropic Raviart-Thomas tensor-product polynomial space is considered, where the finite element operators are evaluated with quadrature in a matrix-free fashion using sum-factorization on tensor-product meshes. READ MORE