Sparse direct solvers are critical building blocks in a range of scientific applications on heterogeneous supercomputers. However, existing sparse direct solvers have not been able to well leverage the high bandwidth and floating-point performance of modern GPUs. The primary challenges are twofold: (1) the absence of a mechanism for aggregating small tasks to saturate the GPU, and (2) the lack of a mechanism for executing a diverse set of small tasks in batch mode on a single GPU.

We in this paper propose a strategy called Trojan Horse, which significantly enhances the execution efficiency of sparse direct solvers on GPU clusters. This mechanism divides each process's work into two stages: Aggregate (with two modules Prioritizer and Container) and Batch (with two modules Collector and Executor). In the Aggregate stage, a process first assesses the urgency of the input tasks through the Prioritizer module, and based on their priority, sends them to the Collector module or the Container module. In the batch stage, the Collector module receives high-priority heterogeneous tasks from the Prioritizer module and retrieves enough tasks from the Container module to send them to the Executor module for batch execution on GPU.In addition, our strategy is independent of solver libraries, and is integrated into SuperLU_DIST and PanguLU.

In the scale-up evaluation on a single NVIDIA A100 GPU, the Trojan Horse strategy delivers speedups of up to 418.79x (5.47x on average) for SuperLU_DIST and up to 5.59x (2.84x on average) for PanguLU. In the scale-out evaluation on two 16-GPU clusters from NVIDIA and AMD, respectively, Trojan Horse continues to deliver strong performance gains for both SuperLU_DIST and PanguLU across different GPU counts.