Baluncore said:
False. For the same bandwidth technology, a digital processor will produce results more than 100 times faster than any analogue computer, with or without changes of parameters. A digital signal never has to settle to a fixed value, it need only be clear of the transition threshold. An analogue circuit requires more time and a lower noise environment. It is unlikely that the errors of an analogue computer at speed will be much less than 0.4%, equivalent to 8 bits. We can do a great many 16 bit digital computations, (with less than 0.004% error), in the time it takes one analogue signal to settle.A finite array of analogue computer elements is still FEM.You are correct, there are many problem dependent possibilities. Without specifications, or a set of equations, anything is possible. It seems like you are trying faithfully to maintain a belief in analogue computers, while all the evidence suggests they have been extinct for quite some time.
I no longer expect you to present specifications and equations, as to do that would threaten your faithfully held belief.
When one uses the word "simulation", it can be one of these:
1) Simulation of physics using a digital computer
2) Simulation of physics using an analog computer
3) Simulation of the analog computer of point 2) above, on a digital computer
One may note that points 1) to 3) are not one and same (although the results obtained using the three methods are expected to be practically the same). When I talk about analog simulations, it always refers to 2) above (not 3) above). I am interested to simulate certain physics, not certain analog computer. How one represents the physics depends on whether one uses a digital computer or an analog computer.
To give a simple example, if someone wants to find the circumference of a circle using a digital computer, he can just use the well known formula that can calculate the circumference if the radius is known. On the other hand, analog computer is something like actually drawing a circle with the specified radius on the ground, and then actually measuring the circumference using a thread. Now the point 3) above is like drawing the circle on a computer screen using an equation that describes the circle, and then "measuring the circumference" by counting the number of pixels on the circumference and by knowing the distance between individual pixels. Hence it is not fair to simply compare the speed of digital computers to analog computers because the problem to be solved itself are different (although the physics that needs to be simulated is the same, the analog model is different from the digital model).
Hence I do not understand your point that digital simulation should be at least 100 times faster than the corresponding analog simulation. I believe that the success of analog computers depend on the possibility of finding a good electrical analogy. Of course, when it comes to problems like the simulation of biological organs, it may turn out to be a very complicated task and the risk of failure may also be high, but this makes the problem interesting, challenging, and important. But no one would try to take up the challenge (and risk) if there is no possibility of being successful.
These three points are still of concern to me (thanks to many of the replies above, which helped me to get insight into the following points):
1) Time consumed for actively changing the connections and/or parameters
2) Time required for the oscillations to settle
3) Unpredictable and uncontrolled variation in parameters because of heating and drift over time
Constructing arrays of analog computing elements resembles more to the Finite Difference Method (not the Finite Element Method). The Finite Difference Method carries out simulations by replacing differential equations with difference equations.
There is a reason for not presenting the nonlinear differential equations. Available literature does not give the final form (which is required for our purpose) of these differential equations. This is like first defining a variable "a" as a function of the variables "b", "c", "d", then defining a variable "e" as a function of "a", then defining a variable "f" as a function of "e", then writing down the nonlinear differential equation in terms of "f". One may need to use a digital computer to get the final form of the differential equations. Moreover, some of the parameters (coefficients) in the differential equations will not be known beforehand. For example, the coefficients may depend on the position of the mouse pointer on the screen that is connected to a digital computer; the mouse pointer would be actively controlled by a human user (nobody can predict beforehand how the human user is going to move the mouse pointer); hence the digital computer would note down the position of the mouse pointer, then calculate the coefficients for the differential equations. Then the digital computer can issue commands (at appropriate times) to the analog computer to change the connections/parameters of the analog computer.
If I am going to use the Finite Element Method, I can tell the form of the final set of equations to be solved using an analog computer; that is, as I have already told, I need to solve just a set of simultaneous nonlinear algebraic equations (not nonlinear differential equations). As informed in the previous paragraph, I can get the numerical values of the coefficients only during run-time. As informed already, I have about 5000 equations in the set of simultaneous nonlinear algebraic equations (but if the number is too much, I am okay with 1000 equations also).
Finally, speed is more important for me than accuracy. I am okay with about 5% error also.
