Essays about: "boundary summation equation"

Showing result 1 - 5 of 15 essays containing the words boundary summation equation.

  1. 1. Numerical simulation of the non-linear Schrödinger equation A comparative study based on the summation-by-parts method in space and time

    University essay from Uppsala universitet/Institutionen för informationsteknologi

    Author : Ibrohim Hamoud; [2023]
    Keywords : ;

    Abstract : In this work, we present the numerical implementation of various time marching methods based on the summation-by-parts (SBP) method for the time integration of nonlinear dispersive systems. More specifically, we consider the nonlinear Schrödinger (NLS) equation that accepts soliton or soliton-like solution as a primary case study. READ MORE

  3. 2. 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

  4. 3. 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

  5. 4. 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

  6. 5. 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