Compilation, performance testing, and optimization of the PETSc/TAO library on early access exascale systems for the Exascale Computing Project. Specific short-term tasks include: compile, pass make test, verify correct GPU usage, preliminary benchmarks focusing on vector and sparse matrix kernels, start improving GAMG support for GPUs, adding support for pinning memory for matrix kernels, and demonstrating our application / library accelerator support model. Long-term tasks include: complete performance benchmarks, implement performance enhancements, identify further performance enhancements based on profiles of application codes.