Certified Reduced Basis Method for the Damped Wave Equations on Networks

TL;DR

This paper introduces a reduced basis method for damped wave equations on networks that preserves structure and provides sharp, reliable error bounds based on energy decay, verified through numerical experiments.

Contribution

It presents a novel reduced basis approach that ensures structure preservation and tight error bounds for damped wave equations on networks, without regularization.

Findings

Fast convergence of reduced solutions demonstrated.

Tight a posteriori error bounds verified numerically.

Method effectively preserves system structure.

Abstract

In this paper we present a reduced basis method which yields structure-preservation and a tight a posteriori error bound for the simulation of the damped wave equations on networks. The error bound is based on the exponential decay of the energy inside the system and therefore allows for sharp bounds without the need of regularization parameters. The fast convergence of the reduced solution to the truth solution as well as the tightness of the error bound are verified numerically using an academic network as example.