Efficient time integration methods based on operator splitting and application to the Westervelt equation

摘要

Efficient time integration methods based on operator splitting are introducedfor the Westervelt equation, a nonlinear damped wave equation that arises innonlinear acoustics as mathematical model for the propagation of sound waves inhigh intensity ultrasound applications. For the first-order Lie-Trottersplitting method a global error estimate is deduced, confirming that thesplitting method remains stable and that the nonstiff convergence order isretained in situations where the problem data are sufficiently regular.Fundamental ingredients in the stability and error analysis are regularityresults for the Westervelt equation and related linear evolution equations ofhyperbolic and parabolic type. Numerical examples illustrate and complement thetheoretical investigations.