<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Time-dependent problems modeled by hyperbolic partial differential equations can be reformulated in terms of boundary integral equations and solved via the boundary element method. In this context, the analysis of damping phenomena that occur in many physics and engineering problems is a novelty. Starting from a recently developed energetic space-time weak formulation for 1D damped wave propagation problems rewritten in terms of boundary integral equations, we develop here an extension of the so-called energetic boundary element method for the 2D case. Several numerical benchmarks, whose numerical results confirm accuracy and stability of the proposed technique, already proved for the numerical treatment of undamped wave propagation problems in several dimensions and for the 1D damped case, are illustrated and discussed. </p></abstract>

Time-dependent problems modeled by hyperbolic partial differential equations can be reformulated in terms of boundary integral equations and solved via the boundary element method. In this context, the analysis of damping phenomena that occur in many physics and engineering problems is a novelty. Starting from a recently developed energetic space-time weak formulation for 1D damped wave propagation problems rewritten in terms of boundary integral equations, we develop here an extension of the so-called energetic boundary element method for the 2D case. Several numerical benchmarks, whose numerical results confirm accuracy and stability of the proposed technique, already proved for the numerical treatment of undamped wave propagation problems in several dimensions and for the 1D damped case, are illustrated and discussed.

Energetic BEM for the numerical analysis of 2D Dirichlet damped wave propagation exterior problems

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Time-dependent problems modeled by hyperbolic partial differential equations can be reformulated in terms of boundary integral equations and solved via the...

Energetic BEM for the numerical analysis of 2D Dirichlet damped wave propagation exterior problems

Published Online: Jul 20, 2017

Page range: 103 - 127

Received: Nov 07, 2016

Accepted: May 02, 2017

DOI: https://doi.org/10.1515/caim-2017-0006

Keywords
Damped wave equation, energy, boundary element method

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Energetic BEM for the numerical analysis of 2D Dirichlet damped wave propagation exterior problems

Published Online: Jul 20, 2017

Page range: 103 - 127

Received: Nov 07, 2016

Accepted: May 02, 2017

DOI: https://doi.org/10.1515/caim-2017-0006

KeywordsDamped wave equation, energy, boundary element method

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Damped wave equation, energy, boundary element method