Transient Conduction with Internal Heat Generation

Analyzing the temperature rise process of heat-generating bodies. Predicting transient temperatures for batteries, electronic components, and nuclear fuel rods.

We use spatial discretization by the Finite Element Method (FEM). We assemble the element stiffness matrix and construct the global stiffness equation.

We perform a transformation to the weak form (variational form) and use formulation by the Galerkin method using test functions and shape functions. The choice of element type (low-order elements vs. high-order elements, full integration vs. reduced integration) directly affects the trade-off between solution accuracy and computational cost.

We solve the simultaneous equations using direct methods (LU decomposition, Cholesky decomposition) or iterative methods (CG method, GMRES method). For large-scale problems, preconditioned iterative methods are effective.

Developed in 1970 by Swanson Analysis Systems Inc. (SASI). APDL (Ansys Parametric Design Language) based.

Current affiliation: Ansys Inc.

Developed in 1978 by HKS (Hibbitt, Karlsson & Sorensen). Acquired by Dassault Systèmes in 2005 and integrated into the SIMULIA brand.

Current affiliation: Dassault Systèmes SIMULIA

Founded in Sweden in 1986. Started as FEMLAB with MATLAB integration, later renamed to COMSOL. Strong in multiphysics.

Current affiliation: COMSOL AB

When converting models between different solvers, attention must be paid to the correspondence of element types, compatibility of material models, and differences in the representation of loads and boundary conditions. In particular, high-order elements and special elements (cohesive elements, user-defined elements, etc.) often cannot be directly converted between solvers.