Tensor-Core-Optimized Strategies for BLR × Tall-Skinny Matrix Multiplication in BEM

Recent AI-oriented accelerators, such as Tensor Cores embedded on NVIDIA GPUs, provide substantially higher throughput for matrix operations than conventional HPC units. This paper presents strategies to exploit Tensor Cores for accelerating a key kernel in the boundary element method (BEM): the multiplication of a Block Low-Rank (BLR) matrix, which approximates a dense matrix through blockwise low-rank representations, by a tall–skinny dense matrix. While a dense matrix derived from conventional BEM requires O(N2) memory, BLR reduces this to O(N1.5) by compressing far-field interactions, but its irregular block sizes and varying ranks hinder efficient Tensor Core utilization. To address this challenge, we introduce Full-Depth Tree with Equal Division (FDE) to generate uniform block shapes compatible with batched GEMM operations, and Sliced Rank Alignment (SRA) to minimize zero-padding overhead along the rank dimension while satisfying Tensor Core alignment constraints. Numerical experiments on NVIDIA A100 GPUs demonstrate that the proposed FDE+SRA approach achieves up to three times faster performance than a straightforward BLR implementation and more than twice as fast as dense matrix multiplication, while significantly reducing memory usage. For large-scale problems and multiple righthand sides, the method reaches nearly 75% of the Tensor Core’s peak performance, demonstrating the effectiveness of AI-oriented hardware for BLR-based computations.