https://hal.inria.fr/hal-01316197Kern, MichelMichelKernINRIA Rocquencourt - Inria - Institut National de Recherche en Informatique et en AutomatiqueParallel Solution of the Wave Equation Using Higher Order Finite ElementsHAL CCSD1997 wave equation finite elementParallel computing[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA]Kern, MichelM.-O. BristeauG. EtgenW. FitzgibbonJ.-L. LionsJ. PĂ©riauxM. F. Wheeler2016-05-20 13:49:152022-02-04 03:18:442016-05-20 14:17:19enBook sectionsapplication/pdf1The time domain simulation of wave propagation phenomena is a computationally demanding task. The acoustic wave equation is the simplest such model and serves as a useful benchmark for more realistic situations (elastodynamics, or electromagnetism). This paper presents a parallel simulation code for such phenomena. The initial implementation is for 2D acoustics, but of course the method is general, and we are currently investigating more complex models.We use the higher order finite elements developed by Cohen et al.. These elements were designed to give a diagonal mass matrix, thus enabling an explicit solution, while retaining high accuracy. They are based on a modification of the classical degree 2 and 3 elements. We also recall how the modified equation technique leads to higher order methods in time. As the resulting method is explicit, it lends itself very naturally to a parallel implementation. We have chosen a coarse grain, domain splitting approach, using message passing, as this is known to be the most portable approach, likely to give the best efficiency on a wide range of parallel computers.