CN115222870A

CN115222870A - Unstructured grid implicit LUSGS (Lusgs) balanced coloring method, equipment and medium

Info

Publication number: CN115222870A
Application number: CN202211119764.3A
Authority: CN
Inventors: 代喆; 邓亮; 王岳青; 张健; 赵丹
Original assignee: Computational Aerodynamics Institute of China Aerodynamics Research and Development Center
Current assignee: Computational Aerodynamics Institute of China Aerodynamics Research and Development Center
Priority date: 2022-09-15
Filing date: 2022-09-15
Publication date: 2022-10-21
Anticipated expiration: 2042-09-15
Also published as: CN115222870B

Abstract

The invention discloses a method, equipment and a medium for implicit LUSGS (LuSGS) balanced coloring of an unstructured grid, belonging to the technical field of computational fluid mechanics and comprising the following steps of: and obtaining the grid coloring number by utilizing the topological structure of the computational grid, completing the balanced division of grid units by combining a non-greedy coloring method, and then utilizing a multi-core/many-core processor to run an LUSGS algorithm program which is used for executing the grids with different colors after the balanced division in series and executing the grids with the same color in parallel. The invention can effectively utilize the existing multi-core/many-core processor to obtain higher computing performance.

Description

Unstructured grid implicit LUSGS (Lusgs) balanced coloring method, equipment and medium

Technical Field

The invention relates to the technical field of computational fluid mechanics, in particular to a method, equipment and a medium for implicit LUSGS balanced coloring of an unstructured grid.

Background

The current CFD computing method comprises a structural grid and an unstructured grid, the unstructured grid has the advantages of automation, high fitness, high efficiency and the like, and various problems of an aircraft with a complex shape in grid generation can be well solved, so that the related technology of the unstructured grid is paid more and more attention. The unstructured grid implicit LUSGS method is a high-precision and high-efficiency solving (precondition) means, has good convergence robustness and calculation precision, and is widely applied to CFD engineering software. However, the algorithm has strong data dependency and cannot directly realize data parallel, and the existing method adopts serial execution or grid data decoupling to realize data parallel. Although the serial execution mode can avoid data conflict, the computation efficiency is low, and the computation potential of a multi-core and many-core processor on a high-performance computing platform cannot be fully exploited, so that a parallel technology of an implicit LUSGS method of a non-structural grid needs to be researched to further improve the computation performance.

There is currently a parallel approach that can decouple LUSGS data dependencies. The method focuses on the greedy coloring partition of the unstructured grid and the data parallel method. The algorithm comprises the following steps: setting the initial coloring number to be zero, detecting the coloring condition of the adjacent grid unit in the current grid unit, then selecting a color different from the adjacent grid unit in the existing color library to color the current grid unit, if the color library has no color or no color meeting the condition, adding a new color in the color library, coloring the current grid unit by using the new color, and moving to the next grid unit after coloring is finished until the grid unit is traversed and calculated. And after the grid coloring is finished, parallel execution is carried out according to the same color, and the LUSGS parallel algorithm is finished according to the standard of serial execution of different colors.

The main problem of the greedy coloring algorithm used by the method is that the coloring of grid cells is not uniform. The number of grid cells of each color cannot be determined, and the difference between the numbers of grid cells of different colors is 3,4 orders of magnitude, so for the color with less grid cells, the parallel overhead is even greater than the parallel profit, resulting in imbalance of data level parallelism. Rendering colors also does not guarantee a minimum, and thus may create additional parallel overhead.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provides a method, equipment and a medium for implicit LUSGS balanced coloring of an unstructured grid, which can effectively utilize the existing multi-core/many-core processor to obtain higher computing performance.

The purpose of the invention is realized by the following scheme:

an unstructured grid implicit LUSGS balanced coloring method comprises the following steps:

and obtaining the grid coloring number by utilizing the topological structure of the computational grid, completing the balanced division of grid units by combining a non-greedy coloring method, and then utilizing a multi-core/many-core processor to run an LUSGS algorithm program which is used for executing the grids with different colors after the balanced division in series and executing the grids with the same color in parallel.

Further, the calculating the topology structure of the grid to obtain the grid coloring number comprises the following sub-steps:

mapping the computational grid into an undirected graph, wherein the volume between adjacent surfaces is represented by adjacent points of the undirected graph;

after the calculation grid is mapped to the undirected graph, obtaining the minimum coloring number of the undirected graph according to the Vizing theorem of the graph theory;

firstly, assuming that the computational grid is a first type graph, if the coloring color is insufficient, the computational grid is a second type graph, adding 1 to the coloring number, and coloring from the initial grid unit.

Further, the method for balanced partitioning of grid cells in combination with non-greedy coloring comprises the sub-steps of:

step A: initializing a color library by using the grid coloring number;

and B: setting the number of grid cells divided into different colors to be 0;

step C: traversing the grid unit, and checking the coloring condition of the adjacent grid unit of each grid unit, wherein the coloring condition comprises the following three conditions: when there is one optional non-conflict color, selecting the color as the coloring of the current grid; when two or more non-conflicting selectable colors exist, selecting the color with the least number of grids in the current selectable colors; and when the selectable color is 0, the undirected graph corresponding to the grid is shown as a second class of graph, the coloring number is set to be the maximum number plus 1, and the step A is skipped to restart the division of the grid units.

Further, the elements of the computational grid include points, faces, and volumes.

Further, the undirected graph is topologically equivalent to a computational mesh.

Further, the maximum degree of the undirected graph is obtained by solving through a vertex traversal algorithm.

Furthermore, grid cells with the same color in the colored grid have no dependency relationship, and grid cells with different colors are dependent on each other.

Further, the step of completing the balanced partition of the grid cells by combining the non-greedy coloring method utilizes bit operation and is performed only once in the computer process to complete the balanced partition of the grid cells.

A computer device comprising a processor and a memory, the memory having stored therein a computer program which, when loaded by the processor, carries out the method of any of the preceding claims.

A readable storage medium, in which a computer program is stored, which computer program is loaded by a processor and executes a method according to any of the above.

The beneficial effects of the invention include:

compared with the existing parallel method capable of decoupling LUSGS data dependent items, the technical scheme provided by the invention has the following advantages:

the two-stage hybrid parallel of the embodiment of the invention has a more efficient hybrid parallel strategy, the data stage parallel cost is lower, and the parallel performance is higher.

The embodiment of the invention utilizes the optimal solution which is theoretically given and uses the coloring algorithm to eliminate the parallel dependency of the unstructured grid LUSGS data to perform the balanced coloring treatment, is suitable for the two-dimensional/three-dimensional computational grid with all the appearances, and has good interpretability and robustness.

The embodiment of the invention utilizes the theoretical optimal solution, and combines the improved non-greedy coloring method and the LUSGS data-level parallel method, realizes the LUSGS data-level balanced parallel of the non-structural grid, reduces the parallel overhead, improves the parallel performance, effectively utilizes the existing multi-core/many-core processor, and obtains higher computing performance.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.

FIG. 1 is a mapping of a computational grid to an undirected graph;

FIG. 2 is a flow diagram of a non-greedy coloring method for an unstructured grid;

FIG. 3 is a data dependency diagram of an implicit LUSGS of an unstructured grid;

fig. 4 is a diagram of LUSGS equalization data parallelism; fig. 4, (a) is a diagram illustrating serial execution of LUSGS, and (b) is a diagram illustrating parallel execution of LUSGS after uniform coloring;

in the figure, c1-c10 represent the body numbers of the unstructured grid schematic.

Detailed Description

The invention is further described with reference to the following figures and examples. All features disclosed in all embodiments in this specification, or all methods or process steps implicitly disclosed, may be combined and/or expanded, or substituted, in any way, except for mutually exclusive features and/or steps.

In seeking to solve the problems in the background, the present invention finds the following technical problems: the unstructured grid implicit LUSGS algorithm is a high-precision and high-efficiency solving (precondition) means, but the algorithm has strong data dependency, a serial execution mode cannot effectively utilize an existing multi-core/many-core processor, and high computing performance cannot be obtained, so that a data dependency decoupling method of the unstructured grid implicit LUSGS is urgently needed to be researched. The existing greedy coloring-based unstructured grid LUSGS parallel method can eliminate data dependence to a certain extent, but has the technical problems of unbalanced grid unit division, high parallel overhead and low parallel performance.

In order to solve the technical problem, the technical idea of the invention is as follows: by the method of grid area decomposition and grid partition internal equilibrium division, the prior information of grid coloring number is obtained by utilizing a computational grid topological structure, and the equilibrium division of grid units is completed by combining a non-greedy coloring method, so that the parallel overhead is reduced, the parallel performance is improved, the equilibrium data parallel of the non-structural grid implicit LUSGS is finally realized, and the parallel computational performance is further improved.

In a specific implementation manner, an implicit LUSGS balanced coloring method for an unstructured grid is provided in the embodiments of the present invention, where a non-greedy coloring method with prior information is used to divide the grid in a balanced manner, and then a data dependent item of a decoupling LUSGS algorithm is decoupled, so as to finally implement balanced data parallel, and provide a technical scheme of an efficient and fast parallel method for pre-condition solution.

In a specific implementation manner, the main process of the method of the embodiment of the present invention includes three steps of solving a grid coloring number, grid division of non-greedy coloring and a LUSGS data-level parallel method in a grid region, and the specific steps are as follows:

step (1): firstly, solving a grid coloring number of a topological structure of a computational grid, wherein the grid coloring number is directly related to parallel overhead, and the increase of the coloring number can cause the increase of the parallel overhead and weaken the parallel acceleration performance, so that the coloring number as small as possible needs to be found in the first step to reduce the parallel overhead, and the detailed implementation flow is as follows:

elements of the computational mesh comprise points, surfaces and volumes, and are mapped into an undirected graph, as shown in fig. 1, the volumes between adjacent surfaces are represented by adjacent points of the undirected graph, and the undirected graph is topologically equivalent to the computational mesh.

After the grid is mapped to the undirected graph, according to the Vizing theorem of graph theory, the minimum coloring number of the undirected graph can be obtained, wherein the minimum coloring number of the graph is related to the graph degree (namely the number of adjacent edges of the top points on the graph), and if the grid unit is the first type of graph, the coloring number is the maximum number; if the grid cell is of the second type, the shading number is the maximum number plus 1. Since the determination of the two types of graphs is an NP-hard problem and there is no general determination algorithm with low overhead, it is assumed that the number of colors is set to the maximum number of degrees for the first type of graph.

First, assuming a first type of graph, if the coloring color is insufficient, the grid is a second type of graph, the coloring number is increased by 1, and coloring is started from the initial grid cell. And solving the maximum degree of the undirected graph by using a vertex traversal algorithm.

Step (2): under the prior condition of calculating the grid coloring number, the non-greedy coloring method is shown in fig. 2, and specifically comprises the following steps:

a) Initializing a color library by using a grid coloring number condition;

b) The number of grid cells divided into different colors is set to be 0;

c) Traversing the grid cells, checking the coloring condition of the adjacent grid cells of each grid cell, wherein the coloring condition comprises the following 3 conditions: (a) If there is one and only one optional non-conflicting color, selecting the color as the coloring of the current grid; (b) If 2 or more non-conflicting selectable colors exist, selecting the color with the least number of grids in the current selectable colors; (c) The optional color is 0, the undirected graph corresponding to the grid is shown as a second class of graph, the coloring number is set to be the maximum number of degrees plus 1, and the step A is skipped to restart the division of the grid units.

The non-greedy coloring method provided by the embodiment of the invention utilizes the information of the topological structure of the computational grid, takes the global coloring condition of the grid into consideration, and completely eliminates the conditions of unbalanced grid division and the like in the traditional greedy coloring algorithm because the quantity difference of grid units with different colors is not more than 1. In addition, in order to reduce the algorithm overhead, the method of the embodiment utilizes bit operation and is only executed once in the process, so that the additional overhead is very small, and the whole calculation acceleration effect is not influenced.

And (3): according to the LUSGS data level parallel method, grid units with the same color in a grid after coloring have no dependency relationship, and grid units with different colors are mutually dependent, so that a balanced data parallel method is designed, namely a LUSGS algorithm which is executed in series by grids with different colors and is executed in parallel by grids with the same color, and the flow of the LUSGS algorithm is shown as the following formula.

A linear equation set Ax = b is taken as an example, where a is a coefficient matrix, x is a vector set to be solved, and b is a calculation result of the coefficient matrix a and the vector set to be solved x. First, the coefficient matrix a is decomposed into the following form:

（1）

where D is the diagonal matrix and L and U are the lower and upper triangular matrices, respectively. Replacing matrix a with D + L + U, the system of linear equations can be rewritten as:

（2）

then, the LU decomposition is approximated, and a is expressed as the product of the lower triangular part, the diagonal inverse part, and the upper triangular part:

（3）

wherein, I is a unit matrix,

is that

Defines:

（4）

the final system of linear equations can be written as:

（5）

b, D, L, U, D are known ^-1 Combining the formula (4) and the formula (5), the method can be solved by one-time forward scanning

Then, a forward scanning is performed again to obtain

This is the LUSGS method. The specific process and the data therein depend as shown in fig. 3. The calculation of the grid point i consists of forward and backward scanning, and when scanning forward, the current grid node and the lower triangular part

There is data dependency when only the upper triangle part data is utilized

Calculating; the reverse is true for the backward scan, which uses only the lower triangular portion data

And (6) performing calculation.

Due to the existence of data dependency in forward and backward scanning, the original LUSGS method can only serially traverse the computational grids, such as (a) the non-colored grid in fig. 4, and all grids are executed serially; as shown in fig. 4 (b), after the grid cells are divided by non-greedy coloring, the grids are divided into groups having no dependency relationship with each other, where circles, triangles, quadrilaterals, and pentagons represent different grid cell groups, and the grids in each group have no dependency relationship, and the number of the grid cells in each group is equivalent, which is close to the minimum coloring number of the theoretical extreme value, thereby ensuring the balance of parallel execution, avoiding the coloring number of the grid cells with the maximum or minimum number, reducing the calculation overhead, improving the calculation performance, and achieving better performance.

Example 1

Example 2

On the basis of the embodiment 1, the calculating the topology structure of the grid to obtain the grid coloring number includes the sub-steps of:

first, assuming that the computational grid is a first-class graph, if the coloring color is insufficient, the computational grid is a second-class graph, the coloring number is increased by 1, and coloring is started from an initial grid cell.

Example 3

On the basis of the embodiment 1, the method for completing the balanced division of the grid unit by combining the non-greedy coloring method comprises the following sub-steps:

step A: initializing a color library by using the grid coloring number;

and B: setting the number of grid cells divided into different colors to be 0;

and C: traversing the grid unit, and checking the coloring condition of the adjacent grid unit of each grid unit, wherein the coloring condition comprises the following three conditions: when there is one optional non-conflict color, selecting the color as the coloring of the current grid; when two or more non-conflicting selectable colors exist, selecting the color with the least number of grids in the current selectable colors; and when the selectable color is 0, the undirected graph corresponding to the grid is shown as a second class of graph, the coloring number is set to be the maximum number plus 1, and the step A is skipped to restart the division of the grid units.

Example 4

On the basis of embodiment 2, the elements of the computational grid include points, faces, and volumes.

Example 5

On the basis of embodiment 2, the undirected graph is topologically equivalent to a computational grid.

Example 6

On the basis of the embodiment 2, the maximum degree of the undirected graph is obtained by solving through a vertex traversal algorithm.

Example 7

On the basis of embodiment 2, grid cells of the same color in the colored grid have no dependency relationship, and grid cells of different colors are dependent on each other.

Example 8

On the basis of the embodiment 1, the step of completing the balanced division of the grid cells by combining the non-greedy coloring method utilizes bit operation and is performed only once in the computer process, so that the balanced division of the grid cells is completed.

Example 9

A computer device comprising a processor and a memory, the memory having stored therein a computer program that, when loaded by the processor, performs the method of any of embodiments 1 to 8.

Example 10

A readable storage medium, in which a computer program is stored, which computer program is loaded by a processor and executes a method according to any of embodiments 1-8.

The parts not involved in the present invention are the same as or can be implemented using the prior art.

The above-described embodiment is only one embodiment of the present invention, and it will be apparent to those skilled in the art that various modifications and variations can be easily made based on the application and principle of the present invention disclosed in the present application, and the present invention is not limited to the method described in the above-described embodiment of the present invention, so that the above-described embodiment is only preferred, and not restrictive.

Other embodiments than the above examples may be devised by those skilled in the art based on the foregoing disclosure, or by adapting and using knowledge or techniques of the relevant art, and features of various embodiments may be interchanged or substituted and such modifications and variations that may be made by those skilled in the art without departing from the spirit and scope of the present invention are intended to be within the scope of the following claims.

Claims

1. An unstructured grid implicit LUSGS balanced coloring method is characterized by comprising the following steps:

2. The implicit LUSGS balanced coloring method for unstructured grids according to claim 1, wherein the deriving the grid coloring number by using the topology of the computational grid comprises the substeps of:

3. The implicit LUSGS balanced coloring method for unstructured grids according to claim 1, wherein said balanced partitioning of grid cells is accomplished in combination with a non-greedy coloring method comprising the substeps of:

step A: initializing a color library by using the grid coloring number;

and B: setting the number of grid cells divided into different colors to be 0;

4. The implicit LUSGS balanced coloring method for unstructured grids according to claim 2, characterized in that the elements of the computational grid comprise points, faces and volumes.

5. The method of implicit LUSGS balanced coloring of an unstructured grid according to claim 2, wherein the undirected graph is topologically equivalent to a computational grid.

6. The implicit LUSGS balanced coloring method for unstructured grids according to claim 2, characterized in that the maximum degree of the undirected graph is solved by using a vertex traversal algorithm.

7. The implicit LUSGS equalization rendering method for unstructured grids according to claim 2, wherein the same color grid cells in the rendered grids have no dependency relationship, and the different color grid cells are dependent on each other.

8. The implicit LUSGS balancing coloring method for unstructured grids according to claim 1, wherein the step of performing balancing partitioning of grid cells in conjunction with the non-greedy coloring method performs balancing partitioning of grid cells by bit manipulation and only once in a computer process.

9. A computer device comprising a processor and a memory, the memory having stored therein a computer program which, when loaded by the processor, performs the method of any of claims 1~8.

10. A readable storage medium, in which a computer program is stored which, when loaded by a processor and executed, performs the method of any one of claims 1~8.