Event Detail

Event Type: 
M.Sc. Presentation
Friday, June 14, 2019 - 10:00 to 11:00
Valley Library Willamette West Room

In this expository paper we present the construction and analysis of Summation-By-Parts method for solving the first order form of the wave and Maxwell's Equations in one spatial dimension. Some of the most popular computational or numerical methods for wave propagation problems are high-order finite difference methods on staggered or dual grids. We study finite difference operators approximating first derivatives and satisfying a summation by parts (SBP) rule. We have derived second and fourth order SBP operators on staggered grids. The staggered grid operators when combined with weak boundary conditions, lead to an energy stable scheme. We use the SBP staggered grid operators to construct a stable, semi-discrete approximation of the wave equation and Maxwell equation in one dimension. Fully discrete scheme are constructed by using the ODE suite in MATLAB. Results of numerical simulations in MATLAB are presented that confirm the theoretical analysis.