ParILUT - A Parallel Threshold ILU for GPUs. architectures. The proposed ParILUT-GPU algorithm is based on interleaving parallel fixed-point iterations that approximate the incomplete factors for an existing nonzero pattern with a strategy that dynamically adapts the nonzero pattern to the problem characteristics. This requires the efficient selection of thresholds that separate the values to be dropped from the incomplete factors, and we design a novel selection algorithm tailored towards GPUs. All components of the ParILUT-GPU algorithm make heavy use of the features available in the latest NVIDIA GPU generations, and outperform existing multithreaded CPU implementations.