A Dynamic-Precision Bit-Serial Computing Hardware Accelerator for Solving Partial Differential Equations Using Finite Difference Method

This article presents an all-digital hardware accelerator for solving partial differential equations using the finite difference method (FDM) with dynamically reconfigurable computing bit precision. The proposed accelerator consists of 21
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21 bit-serial processing elements (PEs) to compute 2-D grid solutions with massive parallelism. The 21
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21 bit-serial PEs are connected in a lattice structure, and a PE communicates with four neighboring PEs to update the grid solutions. A PE comprises four key building blocks: a bit-serial adder, a shift register, 4:1 multiplexers, and an accumulator. The proposed hardware accelerator minimizes data movement based on its array architecture that directly maps a 2-D grid of the FDM. Besides, the proposed residue-based bit-serial computation method lowers energy consumption and latency. The checkerboard update method further improves the performance by updating the solutions in two cycles regardless of the grid size. A test chip is fabricated using 65 nm, and a 21
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21 PE array occupies 0.462 mm2. The measured energy consumption is 1.59 nJ per iteration at 16 bit, 1 V, and 25.6 MHz.