关键词: 存内计算, 偏微分方程, 矩阵迭代算法

Abstract: To address the computational challenges of high-precision partial differential equation (PDE) solving in natural sciences and engineering,this paper proposes a novel PDE solver based on the computing-in-memory (CIM) architecture.Leveraging CIM technology,the solver embeds computational logic directly into memory,significantly reducing data transmission between the processor and memory.We thoroughly analyze the computational process of PDE solving,extract key computational flows,and transform them into matrix multiplication and accumulation operations suitable for CIM.By designing a parallel computing scheme and corresponding behavior-level model for the CIM architecture,we further develop and test the hardware implementation.The correctness and efficiency of the proposed design are verified by comparing results with traditional CPU computations.Experimental results show that when solving 2D Poisson equations,wave equations,and other PDEs,the solver achieves a solution accuracy of over 98% for 2D equations and 99.8% for 1D equations,with a solution speed 76 times faster than that of CPUs.

Key words: computing-in-memory, partial differential equation, matrix iteration algorithm