Accelerating finite element modeling of heat sinks with parallel processing using FEniCSx

Abstract

When designing machine elements and electronics, a detailed heat conduction analysis gives valuable insight into volumetric strains, displacements, and stress because they depend on temperature. Thermal problems involving complex geometries and boundary conditions take a long time to solve due to the unavailability of high-performance computing due to license restrictions. This study demonstrates a complete open-source framework to reduce the computational time required to perform these steady-state analyses. The work illustrates steady heat conduction in two brackets and a circuit with a heat sink. The Python-based open-source package FEniCSx is used to formulate the problem. The open-source solvers used are from PETSc and Gmsh acts as the mesh generator. The program was executed in parallel across four processors using preconditioned Krylov solvers, reducing computation time and memory consumption by 92%. Higher-order function spaces give more precise solutions but are more computationally intensive and take more time. Parallel processing and Krylov solvers can reduce the time required for higher-order function spaces while providing accurate results. To demonstrate the efficacy of the suggested approach, the time it took to solve for each order of the function space for various geometries in different solver configurations was recorded and presented. In the case of order 5, the proposed framework is 137 times faster than the conventional approach using only direct solvers.

Keywords

• Steady heat conduction
• Parallel processing
• Krylov subspace method
• Finite element method
• FEniCSx