Speaker
Description
We present a novel, fast solver for the numerical approximation of linear, time-dependent partial differential equations, leveraging model order reduction techniques and the Laplace transform. Specifically, we consider the application of this method to the linear, second-order wave equation.
We begin by applying the Laplace transform to the evolution problem, which results in a time-independent boundary value problem depending solely on the complex Laplace parameter and the problem’s data. During an offline stage, we carefully sample the Laplace parameter and solve the associated collection of high-fidelity problems. Subsequently, we apply proper orthogonal decomposition (POD) to this collection of solutions to obtain a reduced basis. The linear evolution problem is then projected onto this basis and solved using any suitable time-stepping method.
Numerical experiments demonstrate the method’s performance in terms of accuracy and, particularly, speed-up when compared to standard approaches.
