The increasing complexity of high-frequency circuits calls for efficient and accurate passive macromodeling techniques. Existing passivity enforcement methods, including those in commercial tools, often encounter convergence issues or compromise accuracy. The Domain-Alternated Optimization (DAO) framework seeks to restore accuracy through an additional optimization step but is hampered by high memory consumption and slow convergence, particularly for large-scale problems. This paper presents G-SpNN, a novel GPU-accelerated framework that recasts the passivity-enforced macromodeling problem as a neural network training task. This approach significantly enhances both the speed and scalability of passivity enforcement. Experimental results show that G-SpNN achieves an average speedup of $7.63 \times$ in convergence compared to DAO, while reducing memory usage by two orders of magnitude. This enables G-SpNN to handle complex, high-port-count circuits with greater accuracy and efficiency, paving the way for robust high-frequency circuit simulations.

Solving sparse linear systems dominates the simulation time for nonlinear integrated circuits. Developing an effective preconditioner is crucial for accelerating the iterative solver when dealing with large-scale circuit matrices, yet this remains a challenging task. In this paper, we introduce an efficient sparsification-based preconditioner method that significantly reduces the number of iterations needed in iterative solvers. Our method transforms nonlinear components into symmetric Laplacian matrices, enabling the inclusion of both nonlinear and linear elements in the sparsification process. We then intersect the generated sparsifier with the original Modified Nodal Analysis (MNA) matrix to further reduce the sparsity, thereby decreasing preconditioner factorization time. Furthermore, we enhance the parallelization of the spectral sparsification strategy by integrating block RMQ and point exclusivity algorithms, which substantially speeds up preprocessing. Experiment results demonstrate acceleration of 2.50x, 13.46x, 2.18x on average in serial, 3.72x, 24.23x, 3.86x on average in parallel, and memory reduction of 21.3%, 21.7%, 88.0% on average when solving nonlinear circuit matrices compared to the state-of-the-art solver GPSCP, feGRASS, and direct solver KLU, respectively.

Algebraic multigrid (AMG) methods are particularly efficient to solve a wide range of sparse linear systems, due to their good flexibility and adaptability. Even though modern parallel devices, such as GPUs, brought massive parallelism to AMG, the latest major hardware features, i.e., tensor core units and their low precision compute power, have not been exploited to accelerate AMG. This paper proposes AmgT, a new AMG solver that utilizes the tensor core and mixed precision ability of the latest GPUs during multiple phases of the AMG algorithm. Considering that the sparse general matrix-matrix multiplication (SpGEMM) and sparse matrix-vector multiplication (SpMV) are extensively used in the setup and solve phases, respectively, we propose a novel method based on a new unified sparse storage format that leverages tensor cores and their variable precision. Our method improves both the performance of GPU kernels, and also reduces the cost of format conversion in the whole data flow of AMG. To better utilize the algorithm components in existing libraries, the data format and compute kernels of the AmgT solver are incorporated into the HYPRE library. The experimental results on NVIDIA A100, H100 and AMD MI210 GPUs show that our AmgT outperforms the original GPU version of HYPRE by a factor of on geomean $1.46 \times, 1.32 \times$ and $2.24 \times$ (up to $2.10 \times, 2.06 \times$ and $3.67 \times$), respectively.