SU696473A1 - Device for solving partial differential equations - Google Patents

Description

the rational method applied to the difference scheme J.U О, where the Lrasonic analogue of the operator L. In particular, the known device implements the method of simple iteration:

CC.1 uk.i.u4eAU

where k is the iteration number; Q is an iterative parameter, the value of which is limited by the range of stability of the solution.

The operator is a linear combination with the coefficients ot of the values of the solution U at adjacent points xj in the coordinate k.

The disadvantage of the device is relatively low speed, due to the relatively slow convergence of the iteration process, due to the smallness of the value of the iteration parameter in, chosen before the start of the decision from the condition of stability of the iteration process 1.

The purpose of the invention is to increase speed.

To do this, the device also additionally includes n elements, whose information inputs are connected to the output of the multiplication unit, and the control inputs are connected to the control input of the device, the outputs of the And elements n are connected to the corresponding inputs of the adder, the output of the first register is connected to the second input of the adder, output The input unit is connected to the third input of the multiplication unit.

The block diagram of the proposed device is shown in the drawing, which contains the first register 1, the second register 2, the input block 3, the multiplication block 4, And 5 5jj elements, the adder 6.

The output 7 of the first register 1 is the information output of the device. The input 8 of the input unit 3 is the input of the device. The input conditions 9 are supplied with the initial conditions for the control stroke 10 — the control signals.

The proposed device works as follows.

Registers 1, 2 on the control signal to the input 10 from the input 9 are recorded initial conditions. The value and ° comes from the output of register 1 to the input of block 4 multiplication, the remaining inputs of which receive the values, and. from the outputs 7 of neighboring devices connected to the input 8 of the input unit 3, and the initial condition from the output of the register 2 in the case of solving the unsteady heat conduction equation. These values are multiplied in block 4 multiplied by the corresponding coefficients dtj. The resulting products, which are the components of a linear combination, representing the expression 6 L and °, arrive at the second input of the adder 6 and summed with the value coming from the output of the register 1 to the first input of the adder b, according to (1) the current solution and first iteration, From the output of the adder 6, the value of U | is written to the first register 1 and the iteration of the operation of the device is repeated, and the value U.J and so on is determined. At the same time, beginning with some of the -th iteration, the control signal at input 10 will open the element AND 5

g

and the value of Uj from the output of block 4 multiplies will go directly to the two inputs of adder b, the output of which forms the sum V + 29Di ,. After a certain number of iterations, or the same to-that iteration, the control signal at input 10 opens an element And 52 and at the output of the adder b equals 0 with the sum U | + 30AuS, where, etc. Finally, if all the elements 5-5 are open, then this corresponds to an increase in the iteration parameter 0 by n + .1 times, which, unlike the increase in S, before the beginning of the solution leads not to divergence, but to acceleration of the convergence of the iterative process (1) and . This solution, in the case of the unsteady thermal conductivity equation on the control signal on bus 10, will be overwritten from register 1 to register 2 as the initial condition for the next time layer, on which the iterative resolution process is repeated.

Use in the proposed device n elements And connecting the output of the multiplication unit to the inputs of the adder, and connecting to the input

The Q of the adder of the output of the first register allows accelerating the iterative process of solving the problem by multiplying the value of the iterative parameter.

Claims (2)

1. Kozlov E, S., Sergeev NP Nikolaev Y.S. Automating the process of solving boundary value problems using mesh AVMs. M ,, energy 1974. 2. USSR author's certificate number 373735, cl. Q06Q 7/56, 1973.