Essays about: "Summation By Parts"

Showing result 6 - 10 of 27 essays containing the words Summation By Parts.

  1. 6. Numerical simulation of acoustic wave propagation with a focus on modeling sediment layers and large domains

    University essay from Uppsala universitet/Avdelningen för beräkningsvetenskap

    Author : Elias Estensen; [2022]
    Keywords : Helmholtz; wave equation; acoustics; ocean acoustics; numerical analysis; computational science; finite differences; summation by parts; sbp; waveholtz; cylindrical coordinates; sediment layers; interface; super-grid; super grid; absorbing layer; Helmholtz; vågekvationen; akustik; undervattensakustik; numerisk analys; beräkningsvetenskap; finita differenser; summation by parts; sbp; cylindriska koordinater; waveholtz; sedimentskikt; interface; super-grid; absorberande lager;

    Abstract : In this report, we study how finite differences can be used to simulate acoustic wave propagation originating from a point source in the ocean using the Helmholtz equation. How to model sediment layers and the vast size of the ocean is studied in particular. READ MORE

  3. 7. An exploration of classical SBP-SAT operators and their minimal size

    University essay from Linnéuniversitetet/Institutionen för matematik (MA)

    Author : Jesper Nilsson; [2021]
    Keywords : Finite differences; summation by parts; simultaneous approximation term; SBP-SAT; discretization matrix inverses;

    Abstract : We consider diagonal-norm classical summation-by-parts (SBP) operators us-ing the simultaneous approximation term (SAT) method of imposing boundaryconditions. We derive a formula for the inverse of these SBP-SAT discretizationmatrices. READ MORE

  4. 8. Numerical simulations of the Dynamic Beam Equation in discontinuous media

    University essay from Uppsala universitet/Avdelningen för beräkningsvetenskap

    Author : Niklas Wik; David Niemelä; Valter Wagner Zethrin; [2020]
    Keywords : Dynamic beam equation; DBE; SAT; projection; SBP;

    Abstract : The study examines the Projection method and the simultaneousapproximation-term (SAT) method as boundary treatment for the dynamic beam equation using summation-by-parts (SBP) operators for handling the inner domain. The methods are examined for both the homogeneous constant coefficient case, and the inhomogeneous piecewise constant coefficient case with a coupled interface. READ MORE

  5. 9. Numerical Simulation of Soliton Tunneling

    University essay from

    Author : Matilda Tiberg; Elias Estensen; Amanda Seger; [2020]
    Keywords : soliton; GPE; gross pitaevskii; Schrödinger; step potential; summation by parts; SBP-SAT; Simultaneous approximation term; SAT; Projection; SBP-Projection; finite differences; boundary treatment; interface treatment;

    Abstract : This project studied two different ways of imposing boundary conditions weakly with the finite difference summation-by-parts (SBP) operators. These operators were combined with the boundary handling methods of simultaneous-approximation-terms (SAT) and the Projection to impose homogeneous Neumann and Dirichlet boundary conditions. READ MORE

  6. 10. Simulation of Viscosity-Stratified Flow

    University essay from

    Author : Victor Carlsson; Philip Isaac; Persson Adina; [2020]
    Keywords : Burgers equation; flow; SAT; projection method; boundary treatment;

    Abstract : The aim of this project is to study the viscous Burgers' equation for the case where the viscosity is constant, but also when it contains a jump in viscosity. In the first case where the viscosity is constant, Burgers' is simply solved on a singular domain. READ MORE