Optimizing the decay rate in the damped wave equation: a numerical study

We present a numerical study of optimizing the rate of decay of solutions of the linear damped wave equation. This optimal damping design is formulated as finding a damping term that would optimize the spectral abscissa of the related differential operator. The problem is discretized to a finite-dimensional problem by a Legendre pseudospectral method. The supremum of the real part of the spectrum of the finite-dimensional operator is optimized for the constant and non-constant damping terms. Numerical experiments yield results in excellent agreement with analytical or prior numerical work. They also show that this approach provides an accurate and flexible framework for future optimal damping design studies.