The filament approach is used to model essentially 1-D phenomena embedded in multi-D spaces. Filaments are long, slender objects whose transverse dimensions are much smaller than the typical length scales of the surrounding domains. Many diverse physical systems possess such multi-scale features including:

• microchannels in fluidic devices
• optical or electrical leads
• conducting paths in micro-chips
• high density wirebonds in packages
• waveguides and antennas in open spaces
• micro blood-vessels

Conventional numerical simulations on a domain containing disparate length scales requires simultaneous gridding of small geometrical features in an otherwise large-scale domain. Mesh generation difficulties and the need to maintain grid matching across the different domains can increase the total number of cells to prohibitive levels.

The filament approach solves this problem by allowing the filament structures to be gridded independently and subsequently embedding them in the surrounding 3-D mesh. The overall solution is fully coupled and internally handled by the solver: the user specifies only the grid systems and types of interactions to be modeled. The approach has been used to successfully model many diverse multi-scale systems.

Domain-Domain Interaction
Thermal Conduction Through Wirebonds on an Electronic Chip

Dynamic Growth and Configuration
Angiogenic Blood Vessel Propagation To a Tumor