Zhen Zhuang

Chenghan Wang, Zhen Zhuang, Shui Jiang et al.

Coarse-grained thermal simulation tends to underestimate localized thermal issues, potentially missing critical hotspots. Accurate analysis, therefore, demands fine-grained information, which dramatically increases grid resolution and thus computational workload. Fortunately, the coefficient matrices are often sparse with regular sparsity patterns, offering optimization opportunities. However, existing general-purpose matrix solvers on GPUs rarely exploit these domain-specific properties, thereby encountering bottlenecks in data storage, memory access, parallelism, computational efficiency, and hardware utilization. Therefore, we propose CUTh-Solver, a co-designed GPU-accelerated Preconditioned Conjugate Gradient (PCG)-based sparse solver framework for Symmetric Positive Definite (SPD) systems arising from high-resolution steady-state and transient 3D IC thermal simulation. For data storage, CUTh-Solver condenses the Diagonal (DIA) storage format to remove redundancy. To optimize the memory access, CUTh-Solver employs diagonal-wise SpMV to achieve coalesced memory access. We further observe a critical conflict between parallelism and preconditioning quality and thus adopt a high-parallelism preconditioning strategy. To improve computational efficiency and hardware utilization, we employ an adaptive fine-grained mixed-precision strategy that leverages diverse floating-point units to avoid resource contention, enhancing throughput without compromising numerical stability. Experimental results show that CUTh-Solver achieves up to 25.8x speedup over GPU-accelerated COMSOL Multiphysics 6.4 and over 3x speedup over NVIDIA's native general-purpose libraries (AmgX, cuSPARSE, cuDSS). Ablation studies validate the individual contribution of each optimization. The code is available at: https://github.com/Chenghan-Wang/CUTh-Solver

Genggeng Liu, Zhen Zhuang, Wenzhong Guo et al.

As the basic model for very large scale integration (VLSI) routing, the Steiner minimal tree (SMT) can be used in various practical problems, such as wire length optimization, congestion, and time delay estimation. In this paper, a novel particle swarm optimization (PSO) algorithm based on multi-stage transformation and genetic operation is presented to construct two types of SMT, including non-Manhattan SMT and Manhattan SMT. Firstly, in order to be able to handle two types of SMT problems at the same time, an effective edge-vertex encoding strategy is proposed. Secondly, a multi-stage transformation strategy is proposed to both expand the algorithm search space and ensure the effective convergence. We have tested three types from two to four stages and various combinations under each type to highlight the best combination. Thirdly, the genetic operators combined with union-find partition are designed to construct the discrete particle update formula for discrete VLSI routing. Moreover, in order to introduce uncertainty and diversity into the search of PSO algorithm, we propose an improved mutation operation with edge transformation. Experimental results show that our algorithm from a global perspective of multilayer structure can achieve the best solution quality among the existing algorithms. Finally, to our best knowledge, it is the first work to address both manhattan and non-manhattan routing at the same time.