The Dual Cell Method in NGSolve

The Dual Cell Method in NGSolve#

by M. Wess, J. Schöberl

TU Wien, Institute of Analysis and Scientific Computing,

based on joint work with B. Kapidani and L. Codecasa


This book is designed to provide an introduction and examples to the implementation of the Dual Cell Method in the high-order finite element library NGSolve.

The Dual Cell Method (DCM) is a Galerkin Method for the simulation of time-domain waves (e.g., electromagnetic or acoustiv waves) in mixed formulation. It is a Disconitinuous Galerkin variant where the two wave-fields are approximated by conforming functions on meshes dual to each other. Thus the respective ansatz functions feature discontinuities on different element boundaries.

For a full mathematical introduction to the method we refer to [KCSchoberl21, WKCS24].


Table of Contents#


References#

[KCSchoberl21]

Bernard Kapidani, Lorenzo Codecasa, and Joachim Schöberl. An arbitrary-order cell method with block-diagonal mass-matrices for the time-dependent 2D Maxwell equations. J. Comput. Phys., 433:Paper No. 110184, 20, 2021. doi:10.1016/j.jcp.2021.110184.

[WKCS24]

Markus Wess, Bernard Kapidani, Lorenzo Codecasa, and Joachim Schöberl. Mass lumping the dual cell method to arbitrary polynomial degree for acoustic and electromagnetic waves. Journal of Computational Physics, pages 113196, 2024. doi:https://doi.org/10.1016/j.jcp.2024.113196.