Stability issues in time-domain methods for unstructured block meshing using local time-steps

Abdelrahman Ijjeh (1, 2) , Michel Ney (3, 2)

1 LEAT - Laboratoire d'Electronique, Antennes et Télécommunications
2 IMT Atlantique - MO - Département Micro-Ondes
3 Lab-STICC_IMTA_MOM_PIM

To find a stable Time-Domain (TD) numerical scheme, that adopts a local time-step in unstructured meshing, is a real challenge in numerical methods. This article presents a theoretical investigation on the origins of such instabilities. New finding shows that using multiple time-steps in one computational domain with TD methods produces a systematic error that does not tend to zero as both the spatial and temporal steps go to zero. This mathematical formulation leads to a new approach to elaborate stable TD algorithms that use local timestep. Eventually, some correction terms are introduced into update equations for all cells adjacent to boundaries that separate different blocks with different time-steps.

Mots clés: Maxwell equations; finite difference time-domain analysis; mesh generation; numerical stability; computational domain; different time-steps; local time-step; local time-steps; multiple time-steps; numerical methods; spatial steps; stable Time-Domain numerical scheme; temporal steps; time-domain methods; unstructured block meshing; unstructured meshing; Algorithm design and analysis; Finite difference methods; Mathematical model; Numerical models; Stability analysis; Time-domain analysis

Domaines: Electronique

Abdelrahman Ijjeh, Michel Ney. Stability issues in time-domain methods for unstructured block meshing using local time-steps. ICEAA17: International conference on electromagnetics in advanced applications, Sep 2017, Verone, Italy. pp.1127-1130, ⟨10.1109/ICEAA.2017.8065464⟩. ⟨hal-01807314⟩