Essays about: "Simultaneous Approximation Terms"

Showing result 1 - 5 of 9 essays containing the words Simultaneous Approximation Terms.

  1. 1. Simulation of low frequency acoustic waves in small rooms : An SBP-SAT approach to solving the time dependent acoustic wave equation in three dimensions

    University essay from

    Author : Alva Fährlin; Olle Edgren Schüllerqvist; [2023]
    Keywords : room acoustics; numerical methods; SBP; SAT; acoustic wave equation.;

    Abstract : Low frequency acoustic room behaviour can be approximated using numerical methods. Traditionally, music studio control rooms are built with complex geometries, making their eigenmodes difficult to predict mathematically. READ MORE

  3. 2. Numerical Simulation of the Generalized Modified Benjamin-Bona-Mahony Equation Using SBP-SAT in Time

    University essay from Uppsala universitet/Avdelningen för beräkningsvetenskap

    Author : Vilma Kjelldahl; [2023]
    Keywords : Benjamin-Bona-Mahony equation; non-linear; initial boundary value problem; summation-by-parts; simultaneous-approximation-term; time integration; simulation;

    Abstract : This paper describes simulations of the generalized modified Benjamin-Bona-Mahony (BBM) equation, using finite difference methods (FDM). Well-posed boundary conditions (BCs) as well as stable semi-discrete approximations are derived using summations-by-parts (SBP) operators combined with the projection method. READ MORE

  4. 3. 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

  5. 4. 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. 5. Summation By Parts Finite Difference Methods with Simultaneous Approximation Terms for the Heat Equation with Discontinuous Coefficients

    University essay from Linnéuniversitetet/Institutionen för matematik (MA)

    Author : Niklas Kåhlman; [2019]
    Keywords : Finite Difference Method; FDM; Summation By Parts; Simultaneous Approximation Terms; SBP-SAT; Heat Equation; Poisson s Equation; Discontinuous Coefficients; Piecewise Constant Coefficients; Convergence; Dual Consistency; Stability;

    Abstract : In this thesis we will investigate how the SBP-SAT finite difference method behave with and without an interface. As model problem, we consider the heat equation with piecewise constant coefficients. The thesis is split in two main parts. READ MORE