BI-domain Finite Element Toolkit
BIFET is a deal.ii based interface for solving PDEs living in high-dimension (by high-dimension we mean dimension larger than three) space. Finite element triangulation of a domain with dimension larger than three is not feasible, which is a technical bottleneck for high-dimension problems. Particularly, physicists prefer phase-space description for analyzing systems with micro processes portrayed by macro properties, e.g., fluid dynamics. In order to free scientists from the trade-off between simulation precision and programming complexity, a general framework which enables users to describe and solve high-dimension problem is required.
Driven by such motivation, BIFET is designed to decompose high-dimension problems into two sub-domains, e.g., expressing phase-space distribution with spatial and momentum coordinates. Triangulation in each sub-domain can thus be carried out independently, and as well for other mathematical quantities like finite-elements and sparsity pattern. The methods invented for assembling high-dimension linear algebra from two sub-domains root deeply in deal.ii library.