High-fidelity numerical simulation of the dynamic beam equation

Abstract

PostprintThis is the accepted version of a paper published in Journal of Computational Physics. This paper has been peer-reviewed but does not include the final publisher proof-corrections or journal pagination.Citation for the original published paper (version of record):Mattsson, K., Stiernström, V. (2015) High-fidelity numerical simulation of the dynamic beam equation. Journal of Computational Physics

Exponential Integrators for Second-Order in Time Partial Differential Equations

“…We consider the product space X = H 1 0 ( ) × L 2 ( ) and rewrite (25) in abstract form ẏ(t) = Ay(t) + F (y(t)), y(0) = ( p, q) , where A : D(A) → X is the operator defined by…”

“…Example 4.10 Adding all damping terms into the nonlinear part. Another common approach for solving (25) consists in merging the damping terms with the nonlinear terms and then For a wave equation. For a beam equation.…”

“…These types of equations have been studied extensively in many fields of mathematics. For damped wave equations, see [4,5,13,20,27,30]; for Euler-Bernoulli beam equations, see [1,2,10,11,21,23,25,26,28,29] and references therein. The time discretization of these equations, to the best of our knowledge, is usually carried out by standard integration schemes such as Runge-Kutta methods or multistep methods.…”