MASS-LUMPING NUMERICAL MODELS OF THREE-DIMENSIONAL HEAT CONDUCTION

Abstract

Abstract A variable mass-lumping numerical model (nodal domain integration) of three-dimensional heat conduction in an inhomogeneous continuum is developed The domain is discretized by tetrahedron-shaped elements and the state variable is approximated by linear trial functions. The resulting model represents the Galerkin finite-element, subdomain intergration, and integrated finite-difference methods as special cases and accommodates both Dirichlet and Neumann boundary conditions similar to a Galerkin finite-element model Consequently, a unified domain numerical model is developed that readily represents each of the abovementioned domain numerical methods and an infinity of finite-element mass-lumping schemes by the specification of a single constant model parameter. Application of the nodal domain integration model to linear heat conduction problems indicates that the degree of model mass lumping must vary to minimize the approximation error.