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Abstract: “This dissertation investigates the utility of a programmable VLSI analog com- puter for the solution of differential equations. To investigate the capability of analog computing in a modern context, a large VLSI circuit (100 mm^2) was designed and fabricated in a standard mixed-signal CMOS technology. It contains 416 analog functional blocks, switches for their interconnection, and circuitry for the system’s program and control. This chip is controlled and programmed by a PC via a data acquisition card. This arrangement has been used to solve differential equations with acceptable accuracy, as much as 400x faster than a modern workstation.

The utility of a VLSI analog computer has been demonstrated by solving stochastic differential equations, partial differential equations, and ordinary differential equations (ODEs). Additionally, techniques for using the digital computer to refine the solution from the analog computer are presented. Solutions from the analog computer have been used to accelerate a digital computer’s solution of the periodic steadystate of an ODE by more than an order of magnitude.

An analysis has been done showing that the analog computer dissipates 0.02 % to 1 % of the energy of a digital general purpose microprocessor and about 2 % to 20 % of the energy of a digital signal processor, when solving the same differential equation.”