Symmetric boundary integral formulations of transient heat conduction: saddle-point theorems for BE analysis and BE-FE coupling

Abstract

The linear problem of transient heat conduction over a bounded time interval in a homogeneous domain with boundary conditions for temperature and flux is formulated in terms of boundary integral equations with an integral operator which is shown to be symmetric with respect to a bilinear form (convolutive in time). This form generates a functional characterizing the solution by its stationarity. Making recourse to a suitable integral transform and to another special bilinear form, it is shown that the boundary solution over the unbounded time interval 0 ≤ t < ∞, is characterized by a saddle-point property with separation of variables. Separation means that the solution corresponds to a maximum with respect to the time history of temperatures on the Neumann boundary, and by a minimum with respect to the time history of fluxes on the Dirichlet boundary. Subsequently a domain decomposition is assumed in view of coupled BE-FE discretization and a variational basis to such heterogeneous multifield modelling is provided.