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