Stable and accurate difference methods for wave propagation

• Date: 14. 4. 2016
• Time: 14:00 - 15:30
• Address:
  Sokolovská 83, Praha
• Room: K3
• Speaker: Anna Nissen (University of Bergen)

Abstract: High-order and stable discretizations are essential for many applications involving wave propagation, such as earthquake rupture dynamics and numerical quantum dynamics. Imposing boundary conditions for high-order finite difference methods in a numerically stable way can be challenging, and the accuracy order of the numerical stencil is typically reduced close to boundaries in favor of stability. Energy estimates can be used to show time-stability for spatial discretizations, but the accuracy estimates that follow are not always sharp. Normal mode analysis on the other hand provides a general accuracy analysis framework that lead to sharp estimates, although working out the details may be challenging. In this talk I will discuss how energy estimates and normal mode analysis can be combined to obtain estimates for stability and accuracy for finite difference discretizations of wave propagation problems.