Sökning: "multigrid"

Visar resultat 1 - 5 av 13 uppsatser innehållade ordet multigrid.

  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. Pricing Put Options with Multilevel Monte Carlo Simulation

    Kandidat-uppsats, Mälardalens högskola/Akademin för utbildning, kultur och kommunikation

    Författare :Jonathan Schöön; [2021]
    Nyckelord :Multilevel Monte Carlo Simulation”; ”European Put Option Pricing” ”Stochastic Differential Equations;

    Sammanfattning : Monte Carlo path simulations are common in mathematical and computational finance as a way of estimating the expected values of a quantity such as a European put option, which is functional to the solution of a stochastic differential equation (SDE). The computational complexity of the standard Monte Carlo (MC) method grows quite large quickly, so in this thesis we focus on the Multilevel Monte Carlo (MLMC) method by Giles, which uses multigrid ideas to reduce the computational complexity. LÄS MER

  4. 3. Numerical Analysis of the Two Dimensional Wave Equation : Using Weighted Finite Differences for Homogeneous and Hetrogeneous Media

    Kandidat-uppsats, Uppsala universitet/Avdelningen för beräkningsvetenskap

    Författare :Christian Böhme; Anton Holmberg; Martin Nilsson Lind; [2020]
    Nyckelord :hetrogeneous media; variable wave speed; wave equation; finite differences; gamma method; multigrid; weighted central difference; numerical analysis; agmg; gamma discretisation; two dimensional wave equation;

    Sammanfattning : This thesis discusses properties arising when finite differences are implemented forsolving the two dimensional wave equation on media with various properties. Both homogeneous and heterogeneous surfaces are considered. LÄS MER

  5. 4. Optimizing multigrid smoothers using GLT theory

    Master-uppsats, Lunds universitet/Matematik LTH; Lunds universitet/Matematikcentrum

    Författare :Denhanh Huynh; [2020]
    Nyckelord :multigrid; smoothers; GLT; Mathematics and Statistics;

    Sammanfattning : Multigrid algorithms are algorithms used to find numerical solutions to differential equations using a hierarchy of grids of different coarseness. This exploits the fact that short-wavelength components of the solutions converges at a faster rate than the long-wavelength components when using some basic iterative methods, such as the Jacobi method or the Gauss-Seidel method. LÄS MER

  7. 5. Smoothed Aggregation for Nonsymmetric Linear Systems

    Master-uppsats, Lunds universitet/Matematik LTH; Lunds universitet/Matematikcentrum

    Författare :Siobhan Correnty; [2019]
    Nyckelord :Mathematics and Statistics;

    Sammanfattning : Smoothed Aggregation (SA) is a technique from algebraic multigrid methods (AMG) which has shown very promising results when solving systems of linear equations with symmetric system matrices, but suboptimal results for nonsymmetric system matrices. The purpose of this thesis is to investigate the method EMIN(r) and a closely related method EMIN proposed by Sala and Tuminaro. LÄS MER