Boundary element solution of heat conduction problems in multizone bodies of non-linear material

A novel algorithm for handling material non‐linearities in bodies consisting of subregions having different, temperature dependent heat conductivities is developed. The technique is based on Kirchhoff's transformation. The material non‐linearity is reduced to a solution dependent function of unified form added to unknown nodal Kirchhoff's transforms. Assembling of element contributions brings the non‐linearity to the right hand sides of the global set of equations. The first step of the solution of this set is the Gaussian pre‐elimination (condensation) of linear degrees of freedom. At this stage efficient block solvers can be used. Then, a set of non‐linear equations is extracted from the condensed one and solved employing the Newton‐Raphson technique. The iteratively solved set consists of the least possible number of equations and its Jacobian matrix is calculated efficiently by taking advantage of the specific form of the equations.