Consistency on Domain Boundaries for Linear PDAE Systems
Jens Neumann, Constantinos C. Pantelides · SIAM Journal on Scientific Computing · 2008
This paper considers the determination of consistent variations of the dependent variables over the boundary of the domain of definition of a linear system of partial differential and algebraic equations (PDAEs). Particular emphasis is placed on the specifications (“boundary conditions”) imposed on different parts of the boundary and their consistency with the underlying PDAE system and with each other. Specifications imposed on overlapping parts of the boundary (e.g., faces with common edges, or edges with common vertices) often lead to inconsistencies (corner singularities) that are not trivial to detect, especially in PDAEs involving three or more dimensions. A symbolic/numerical algorithm is proposed for the analysis of PDAE systems defined over finite hyperrectangular domains of arbitrary dimensions.