Investigate when established CPU-oriented numerical methods should be reformulated or replaced for GPU architectures, including new approaches to synchronization-avoiding Krylov methods, GPU-native multigrid and domain decomposition, matrix-free implicit methods, mixed-precision algorithms, and sparse direct/iterative hybrids. Experience with industrial simulation, EDA, semiconductor, CAE, or CAD ecosystems, including Ansys, Abaqus, LS-DYNA, Siemens Simcenter, Dassault SIMULIA, Altair, Cadence, Synopsys, COMSOL, MathWorks, or comparable internal solver and design platforms.