Skeletal reduction of boundary value problems

Boundary value problems posed over thin solids are amenable to a dimensional reduction in that one or more spatial variables may be eliminated from the governing equation, resulting in significant computational gains with minimal loss in accuracy. Extant dimensional reduction techniques rely on representing the solid as a hypothetical mid-surface plus a possibly varying thickness. Such techniques are however hard to automate since the mid-surface is often ill-defined and ambiguous. We propose here a skeletal representation based dimensional reduction of boundary value problems. The proposed technique has the computational advantages of mid-surface reduction, but can be easily automated. A systematic methodology is presented for reducing boundary value problems to lowerdimensional problems over the skeleton of a solid. The theoretical properties of the proposed method are derived, and supported by representative numerical experiments