On mathematical and numerical modelling of multiphysics wave propagation with polygonal Discontinuous Galerkin methods

Code:
66/2021
Title:
On mathematical and numerical modelling of multiphysics wave propagation with polygonal Discontinuous Galerkin methods
Date:
Wednesday 3rd November 2021
Author(s):
Antonietti, P.F.; Botti, M.; Mazzieri, I.
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Abstract:
In this work we present discontinuous Galerkin finite element methods on polytopal grids (PolydG) for the numerical simulation of multiphysics wave propagation phenomena in heterogeneous media. In particular, we address wave phenomena in elastic, poro-elastic, and poro-elasto-acoustic materials. Wave ropagation is modeled by using either the elastodyanmics equation, in the elastic domain, the acoustics equations in the acoustic domain and the low-frequency Biot’s equations in the poro-elastic one. The coupling between different models is realized by means of (physically consistent) transmission conditions, weakly imposed on the interface between the domains. For all models configuration, we introduce and analyse the PolydG semi-discrete formulation, which is then coupled with suitable time marching schemes. For the semi-discrete problem, we present the stability analysis and derive a-priori error estimates in a suitable energy norm. A wide set of verification tests with manufactured solutions are presented in order to validate the error analysis. Examples of physical interest are also shown to demonstrate the capability of the proposed methods.
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Vietnam Journal of Mathematics