RAND Lab@ FIU

RF, Analog, and Digital Laboratory for Advanced Signal Processing Circuits at Florida International University

Analog ACCESS

October 23, 2018  /  Arjuna Madanayake

Analog CMOS Computing Chips for Accelerating Linear and Non-Linear Partial Differential Equations (PDEs).

Team: Hasantha Malavipathirana, Nilan Udayanga, Jifu Liang, Yingying Wang, SI Hariharan, Soumyajit Mandal, Dale Mugler, and Arjuna Madanayake.

Analog computers (ACs) were the primary method of computation during 1930-1940. With the advent of digital computers (DCs), which were subsequently fueled by exponential technology scaling (Moore's Law) resulted in ACs being forgotten as a computing platform. However, with the limitations in technology scaling and the performance challenges of DCs, there has been significant interest in ACs as a method of alternative computing. In fact, applications of ACs are being investigated in domains such as machine learning (ML), artificial intelligence (AI), edge-cloud sensor processing and scientific computing.

This project is focused on the application of CMOS integrated circuit based ACs to perform complex physics-based simulations and scientific computing. In simple terms, scientific computing involves solving systems of partial differential equations (PDEs) that describe physical phenomena such as radiation from an antenna, formation of hurricanes or behavior of plasma. In general, PDEs are solved in DCs using finite difference time domain (FDTD) algorithms, which discretize the PDE in both space and time dimensions. However, the continuous time nature of PDEs allow them to be solved using continuous-time algorithms and analog circuits, achieving acceleration in the computing.

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We started with standard FDTD numerical methods and designed spatially discrete time continuous (SDTC) algorithms to solve linear and nonlinear PDEs. Then the algorithms are directly mapped with analog circuits to solve the equations. The time difference operator in FDTD method is replaced with an analog all-pass filter (designed using resistors and capacitors), which generates a continuous time delay. Primary building blocks of the AC are operational amplifiers (perform summing and scaling operations), all-pass filters (generate time delay), and analog multipliers (perform multiplication of sinusoidal signals). As a proof of concept, we designed an analog integrated circuit (IC) to solve the wave equation, which is a linear PDE widely applicable in computational electrodynamics. The IC was designed using TSMC 180 nm process and the measured results show a 420x speed-up compared to latest NVIDIA GPUs and 15x performance (in terms of computations per Watt) compared to state of the art FPGAs. while consuming only 200 mW of power. A second IC was designed to simulate acoustic wave propagation in a variable area duct, which has applications in modeling sound propagation in jet engine nozzles. This system is governed by two coupled nonlinear PDEs, which is a slightly complex variant of the Burger's equation in fluid dynamics. This IC was also designed using TSMC 180nm CMOS process and it is currently being assembled on a printed circuit board for testing.

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This research is sponsored by Ocius Technologies via an STTR Phase-2 award from DARPA Defense Science Office (DSO).


[ 1] N. Udayanga, A. Madanayake, S. I. Hariharan, J. Liang, S. Mandal, L. Belostotski, and L. T. Bruton, “A Radio Frequency Analog Computer for Computational Electromagnetics,” IEEE Journal of Solid-State Circuits (JSSC), pp. 1–1, 2020.

 

[2] N. Udayanga, S. I. Hariharan, S. Mandal, L. Belostotski, L. T. Bruton, and A. Madanayake, “Continuous-Time Algorithms for Solving Maxwell’s Equations Using Analog Circuits,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 66, no. 10, pp. 3941–3954, Oct. 2019.

 

[3] N. Udayanga, A. Madanayake, S. I. Hariharan, and N. Hawk, “Continuous-Time Analog Computing Circuits for Solving the Electromagnetic Wave Equation,” in Proc. IEEE Int. Symp. Circuits Syst. (ISCAS), May 2018, pp. 1–5.

 

[4] N. Udayanga, A. Madanayake, and S. I. Hariharan, “Continuous-Time Algorithms for Solving the Electromagnetic Wave Equation in Analog ICs,” in Proc. IEEE 60th Int. Midwest Symp. Circuits Syst. (MWSCAS), Aug. 2017, pp. 29–32.