Sökning: "Jacobian-free"

Hittade 4 uppsatser innehållade ordet Jacobian-free.

1. 1. Subgrid finite volume preconditioner for Discontinuous Galerkin implemented in the DUNE framework

   Master-uppsats, Lunds universitet/Matematik LTH

   Författare :Johannes Kasimir; [2021]
   Nyckelord :discontinuous galerkin spectral element method; dune; high performance computing; numerical analysis; numerical methods; fluid dynamics; simulation; multigrid; iterative methods; Technology and Engineering;

   Sammanfattning : A Jacobian free multigrid preconditioner for linear problems arising from Implicit Discontinuous Galerkin (DG) discretizations is implemented. The preconditioner is based on a multigrid method for a low order Finite volume (FV) discretization on a subcellgrid. L2-projections are introduced as a strategy to translate between the discretizations. LÄS MER

3. 2. Improving the Finite Difference Approximation in the Jacobian-Free Newton–Krylov Method

   Kandidat-uppsats, Lunds universitet/Matematik LTH

   Författare :Robert Van Heyningen; [2016]
   Nyckelord :GMRES; Jacobian-free; Fluid; Mathematics and Statistics;

   Sammanfattning : The Jacobian-free Newton–Krylov (JFNK) method is designed to solve a linear system of equations that appears in Newton’s method. It uses the generalized minimal residual (GMRES) method to solve the linear system and a simple function to approximate the matrix-vector multiplications required in GMRES. LÄS MER

4. 3. Parallelization of the SDIRK and Newton’s method and analysis of a weighted norm for error estimations

   Master-uppsats, Lunds universitet/Matematik LTH

   Författare :Matilda Hjälle; [2016]
   Nyckelord :Numerical analysis; Parallel programming; Mathematics and Statistics;

   Sammanfattning : Execution time is an important issue in the field of numerical analysis. Simulations are getting more and more complex and the execution times are rapidly increasing. In the scope of this thesis a time integration library is used to solve initial value problems. LÄS MER

5. 4. Numerical Implementations of the Generalized Minimal Residual Method (GMRES)

   Kandidat-uppsats, Lunds universitet/Matematik LTH

   Författare :Ivo Dravins; [2015]
   Nyckelord :Generalized Minimal Residual Method; Jacobian-free; GMRES; Householder; Givens rotations; Gram-Schmidt; Mathematics and Statistics;

   Sammanfattning : The generalized minimal residual method (GMRES) is an iterative method used to find numerical solutions to non-symmetric linear systems of equations. The method relies on constructing an orthonormal basis of the Krylov space and is thus vulnerable to an imperfect basis caused by computational errors. LÄS MER