Nonlinear continuous data assimilation
Adam Larios, Yuan Pei
Abstract
We introduce three new nonlinear continuous data assimilation algorithms. These models are compared with the linear continuous data assimilation algorithm introduced by Azouani, Olson, and Titi (AOT). As a proof-of-concept for these models, we computationally investigate these algorithms in the context of the 1D Kuramoto-Sivashinsky equations. We observe that the nonlinear models experience super-exponential convergence in time, and converge to machine precision significantly faster than the linear AOT algorithm in our tests. For both simplicity and completeness, we provide the key analysis of the exponential-in-time convergence in the linear case.
Topics & Concepts
Data assimilationNonlinear systemConvergence (economics)Exponential functionComputer scienceApplied mathematicsAlgorithmContext (archaeology)Completeness (order theory)MathematicsMathematical optimizationMathematical analysisPhysicsBiologyPaleontologyMeteorologyEconomic growthEconomicsQuantum mechanicsMeteorological Phenomena and SimulationsFluid Dynamics and Turbulent FlowsStochastic processes and financial applications