Transient circuit simulations often necessitate the construction of linear system models

where the sequential solution of triangular matrices with multiple right-hand terms becomes a time-intensive process.To expedite the computational efficiency of back-substitution for these matrices in transient circuit simulations

this paper proposes a parallel computing method based on a heterogeneous platform.The method prioritizes the computation of multiplications relevant to the solution vector

exploiting the inherent parallelism of back-substitution calculations.The architecture features a core operation array with multiple floating-point calculation units and a control module employing a two-tiered master-slave state machine.Using the Zynq UltraScale series FPGA

specifically the XCZU15EG model

our architecture is compared to an Intel 24-core CPU platform utilizing the MKL solving library in linear matrix resolution experiments.The matrices used exhibit characteristics of being symmetric positive definite

diagonally dominant

and dense with a sparsity exceeding 50%.The proposed acceleration architecture achieves an average speedup factor of 22

with solution errors falling within the range of 10-17 to 10-14.The experiment results demonstrate the architecture's significant enhancement of matrix solution speed

especially suitable for forward and backward substitution resolution of high-dimensional linear matrices in transient circuit simulations.