Parallel benchmarking of Krylov solvers and preconditioners for three-dimensional welding thermal simulation using FEniCSx/PETSc

Large-scale three-dimensional transient thermal analyses are widely encountered in manufacturing and thermo-mechanical engineering, where the solution of sparse linear systems often dominates the overall computational cost. This study presents a reproducible parallel benchmark of Krylov solvers and preconditioners for three-dimensional transient thermal simulation using FEniCSx and the Portable, Extensible Toolkit for Scientific Computation (PETSc). A moving Gaussian volumetric heat source, temperature-dependent thermophysical properties, and Robin-type surface heat losses are incorporated into a unified heat-conduction framework, which is validated against a gas tungsten arc welding case on 304 stainless steel. The predicted peak temperatures at the monitoring points show engineering-level agreement with the reference experimental thermocouple data, with all relative errors remaining within approximately 10%; meanwhile, the deviations from the reference volumetric heat-source FE results at the symmetric near-center points are below 4%, providing a physically meaningful baseline for performance comparison. Under fixed physical, discretization, and solver-control settings, 17 combinations of Generalized Minimal Residual (GMRES), BiConjugate Gradient Stabilized (BiCGSTAB), Transpose-Free Quasi-Minimal Residual (TFQMR), and Conjugate Gradient (CG) methods with representative preconditioners, including Jacobi, incomplete LU (ILU), algebraic multigrid (AMG), and LU factorization, are assessed on 1–16 CPU cores. The results show that end-to-end runtime is primarily governed by the trade-off between convergence rate and per-iteration cost rather than by iteration count alone. Lightweight preconditioning strategies provide the best overall efficiency, with GMRES + Jacobi and BiCGSTAB + ILU reducing total runtime by 11–16% relative to LU- and AMG-based configurations on 16 cores. Additional scale-up tests up to approximately 1.6 × 10 6 degrees of freedom confirm the robustness of these solver-selection trends. The study provides practical guidance for solver configuration in parallel transient thermal analyses and establishes a reproducible benchmark for moving heat-source problems.