SU608165A1 - Digital network model computing unit for solving partial differential equations - Google Patents

Description

the input of the node and the output of the node, and the second inputs of the elements of the group of elements And are connected to the third control input of the node 3,

The disadvantage of the computational node is that when it solves three-dimensional problems of mathematical physics, equipment costs and computation time increase significantly.

The purpose of the invention is to reduce the equipment and computation time.

This is achieved by the fact that the computational node contains a multiplication unit, a serial input, parallel inputs and an output of which are connected respectively to the output of the my-input adder, with a group of code inputs of the node and a serial input of the shift register.

In addition, in the computational node, the multiplication unit contains an n-bit adder with memory transfers and elements, And, the first, second inputs and outputs of the elements And are connected respectively to the parallel inputs of the block, with the serial input of the block and the inputs of the n-bit adder C memory transfers, in which the output of the sum of 1 bit is connected to the input of the next least significant bit, the output of the transfer of the bit is connected to the bit input, and the output of the lower half of the adder is connected to the output of the multiplication unit.

FIG. Figure 1 shows the block diagram of the computational node of the digital mesh model; in fig. 2 is a block multiplication circuit; in fig. 3 is a diagram of a portion of a computational digital grid model node for solving the Laplace equations; in fig. 4, 5 are diagrams of a part of the computational node of the digital grid model for solving the Poisson equation.

The computational node of the digital grid model for solving partial differential equations contains (see Fig. 1) a multi-input adder 1, a shift register 2, an element 3, a group of 4 elements AND, a multiplication unit 5, control inputs 6-8, information inputs 9, outputs 10, code inputs 11. Position 12 designates the output of the adder. The multiplication unit contains (see Fig. 2) an adder 13 with memory transfers, elements AND 14, serial input 15, parallel inputs 16, output 17.

The computational node of the digital grid model for solving the Laplace equations (see FIG. 3) contains memory elements 18, and the multi-input adder has inputs 19 and outputs 20. Other symbols are similar to those in FIG. one.

The computational node of the digital grid model for solving the Poisson equations (ime. Fig. 4 contains memory elements 21, 22, 23, and the multi-input adder has inputs 2-i and outputs 25. Other indications are similar to those indicated in Fig. 1.

One of the fastest variants of the computational node of the digital mesh model for solving the Poisson equation contains see FIG. 5) function register 26 with inputs 27. Other indications are similar to those of FIG. 14.

Computing node of a digital mesh model for solving partial differential equations. derivative works as follows.

When solving three-dimensional problems, J needs to sum up six or seven numbers specified by a sequential code, and the result should be six. The division operation is performed by multiplying by a factor of 1/6. The inputs of the adder I are supplied with a sequential code of summable numbers. The result of the sum is fed to the output 12 of the combinational adder 1, and the transfers are memorized for one clock cycle on the memory elements 18 (see Fig. 3) when the Laplace equation is solved or on one, two, and three clock cycles on the memory elements 21, 22, and 23 ( cm.

FIG. 4) respectively, for the Poisson equation. When solving the Poisson equations, one of the inputs of the adder 1 receives the sequential code of the right side of the solved equation Fyv. To perform the online input of the function Fly and increase the speed

node at peaieHHH Poisson’s equation, it is necessary to enable function register 26 on one of the inputs of adder 1 (see Fig. 5), inputs 27 of which are connected to the receiving inputs of the node, and the output of the lower order; and register 26 of the function is connected to the input of its resulting bit Yes . In the function register 26, the function of the right-hand part F is entered; the sequential code of which at each iteration of the solution is entered into the adder 1.

From the output of multiplier 5, the result of summation divided by a factor of six is entered into register 2. The code of the value of the function sought in register 2 on the previous iteration is shifted on each clock cycle under the control of the signal fed to the first control input 6 of the node and gives s - at the output of the node through an AND element, which is opened by a signal arriving at the second control input 7 of the node. After passing the p-cycles (p-width), the And 3 ' element closes and the subsequent bits of the function sought are calculated in the subsequent p-cycles. Similar calculations are performed at subsequent iterations. When signals are received at the third control input 8 of the node, group 4 is opened by element I. through which the result is output from register 2 on

S outs 10 knots.

The proposed device has a considerably smaller amount of equipment as compared with the known devices intended for solving a similar task.

Three-dimensional problems of mathematical physics by methods known in the literature can be reduced to two-dimensional problems. Moreover, to obtain one iteration of the solution of a three-dimensional (spatial) problem, it is necessary to solve K-two-dimensional (plane) problems,

5 where K is the number of cross sections of the space problem of the planes.

Claims (3)

In this case, due to the absence of connections between the planes, to obtain a solution to an equivalent single iteration, the solution of a three-dimensional problem requires an iterative process, which usually requires t-small iterations, each of which consists of 8 solving K-two-dimensional problems. Let us compare the positions of equipment and time for solving with the same number of nodes solving three-dimensional problems of mathematical physics on three-dimensional digital models of x-grids of dimension KK. in which the invention is used as a node, and on K-two-dimensional digital models of x-grids of dimension KK, in which a known computational node is used as a node. If we take the cost of equipment for one node of a two-dimensional digital grid model per unit, then the cost of equipment for implementing K-two-dimensional digital model grids with a gap of K-K nodes is 3 K equipment units. The cost of equipment per one node of a three-dimensional digital grid model is about 2 times the amount of equipment per node of a two-dimensional digital model grid. Consequently, the cost of equipment for the implementation of a three-dimensional digital grid model is 3-3K units of equipment. The time spent on working out one value in a two-dimensional digital grid model is t2, and in a three-dimensional digital model grid. To obtain a two-dimensional digital model-grid solution, equivalent to one iteration of solving a three-dimensional problem on a three-dimensional digital grid model, it is necessary to perform t-small iterations, each of which requires time t. Then the total time of a large iteration on a two-dimensional digital grid model is Tg m-ta. On a three-dimensional digital grid model, a result equivalent to m-small iterations of the two-dimensional digital grid model is obtained during the processing of one value in the grid-model nodes, t. e. in time Tz, Then the ratio of the cost of equipment and time on a two-dimensional digital grid model to the corresponding product for a three-dimensional digital grid model is K y t g. The value of m varies from 20 to 50 iterations depending on the task. Consequently, the benefit from the application of the invention in three-dimensional digital models, as compared with similar two-dimensional digital models, is 2fir52 5 - 2.5 times. Formula 1-shadow 1. Computing node of a digital model grid for solving partial differential equations, containing a multi-input adder, the inputs of which are connected to information inputs of the node, the shift register, the control input and the serial output of which are connected respectively to the first control input of the node and with the first input of the element I. the group of elements is And, the first inlets and outputs of which are connected respectively to the parallel outputs of the shift register and to the group of outputs of the node, the first, second The input and output of the element I are connected respectively with the serial output of the shift register, with the second control input of the node and with the output of the node, and the second inputs of the elements of the group of elements And are connected with the third control input of the node, characterized in that and computation time, it contains a multiplication unit, a serial input, parallel inputs and an output of which are connected respectively to the output of a multi-input adder, a group of code inputs of the node and a serial input of the shift register. 2. A computing node according to claim I, characterized in that in it the multiplication unit contains an n-bit adder with memory of transfers and elements AND, the first, second inputs and outputs of elements AND are connected respectively to parallel inputs of the block, with a serial input block and inputs of the n-bit adder with memory hyphenation, in which the output of the sum of each bit is connected to the input of the next least significant bit, the bit transfer output is connected to the bit's input, and the low-bit output of the adder is connected to the output of the multiplier. Sources of information taken into account in the examination: 1. Evreinov, E. V., Kosarev, Yu.G. Uniform high performance universal computing systems. “Science, Novoibirsk, 1966, p. 40, fig. eight. 2.Katkov A.F., Romantsov V.P. Kombin-. National Digital Grid for solving equations of mathematical physics, coll. "Math modeling. Theories and methods of hybrid calculations. IV All-Union Conference, Allin, April 1973, Abstracts of reports. M., 1973, p. 37. 3. Forward M “2114222/24, on which the decision was made on January 28, 1997 to issue the author's certificate. -H AO./ in J i IN iai r, .....-, Ф R La.4 I