Multiscale oscillatory problems

Goal: Computing effective behavior of a system that has highly oscillatory modes. Do so without the need to resolve oscillations everywhere in the domain

Time-parallel multiscale coupling of Gaussian Beams and wave equations

Refs: 

Ariel, Kim and Tsai, SIAM J. Sci. Comput., 38(6), 2016

Computation of constrained mechanical system via slow manifolds of an unconstrained highly oscillatory system. 

Example: 

the planar motion of two unit point masses: the first is joined to the origin through a stiff spring of elastic constant ω ≫ 1 and the second is joined to the first through a second stiff spring of elastic constant ω ≫ 1.

In the limit where ω→ ∞, the springs become rigid rods of unit length and the system becomes a double pendulum with no gravity. 

Ref: Ariel, Sanz-Serna and Tsai, Multiscale Model. Simul. Vol. 10, No. 4, 2012