Structural finite element stiffness matrix super-node parallel Cholesky numerical decomposition method

Abstract

The invention belongs to the field of aircraft structural stiffness design, and particularly relates to a structural finite element stiffness matrix super-node parallel Cholesky numerical decomposition method. The method comprises the following steps of: 1, acquiring a super node in a structural finite element stiffness matrix, and determining a numerical decomposition task of the super node; step 2, constructing a task pool; step 3, adding the numerical decomposition task into the task pool; and step 4, receiving the tasks from the task pool according to a preset task receiving principle and executing the tasks, and repeating the step 3 to the step 4 until all the numerical decomposition tasks are executed. According to the structural finite element stiffness matrix super-node parallel Cholesky numerical decomposition method, the parallel potential of numerical decomposition is explored to the maximum extent, and the solving efficiency of the structural finite element stiffness matrix is improved.

Description

Technical Field

[0001] The present application belongs to the field of aircraft structure stiffness design, and in particular relates to a super-node parallel Cholesky numerical decomposition method of a structural finite element stiffness matrix. Background Art

[0002] The structural finite element method is a digital model composed of basic units formed by meshing the continuous physical structure into spatial coordinate points, which are connected to each other by specific criteria. The digital model can be represented by the structural finite element stiffness matrix. The size of the matrix is ​​determined by the number of nodes, the number of node degrees of freedom, and constraints. By analyzing the structural finite element stiffness matrix, it is possible to evaluate the strength and stiffness of the aircraft structure, study the dynamic response, and optimize the structural design.

[0003] Numerical decomposition methods for structural finite element stiffness matrix usually include multi-wavefront method, super-node method and Gaussian elimination method, etc. However, traditional numerical decomposition methods all use single row and single column as the operation object for decomposition, which is inefficient.

[0004] Therefore, it is desired to have a technical solution to overcome or at least alleviate at least one of the above-mentioned defects of the prior art. Summary of the invention

[0005] The purpose of the present application is to provide a super-node parallel Cholesky numerical decomposition method for a structural finite element stiffness matrix to solve at least one problem existing in the prior art.

[0006] The technical solution of this application is: A super-node parallel Cholesky numerical decomposition method for structural finite element stiffness matrix, comprising: Step 1: Obtain a supernode in the structural finite element stiffness matrix and determine the numerical decomposition task of the supernode, including: Obtain super nodes in the structural finite element stiffness matrix; Determine the numerical decomposition task of the supernode according to the supernode relationship, wherein the numerical decomposition task of the supernode includes the internal decomposition task of the supernode, the external modification task of the descendant supernode to the supernode, and the external modification task of the supernode to the ancestor supernode; Screening out invalid tasks from the numerical decomposition tasks of the supernode and removing the invalid tasks; Step 2: Build a task pool; Step 3: Add the numerical decomposition task to the task pool; Step 4: According to the preset task collection principle, tasks are collected from the task pool and executed, and steps 3 to 4 are repeated until all the numerical decomposition tasks are completed.

[0007] In at least one embodiment of the present application, in step 1, filtering out invalid tasks in the numerical decomposition tasks of the supernode includes: If the diagonal matrix of the descendant supernode and the supernode do not have the same rows, the external modification task of the descendant supernode to the supernode is an invalid task; If the diagonal matrix of a supernode and its ancestor supernode do not have the same rows, the external modification task of the supernode to the ancestor supernode is an invalid task.

[0008] In at least one embodiment of the present application, in step 2, the task pool includes: Internal decomposition task pool, used to store the internal decomposition tasks of the super node; The external modification task pool is used to store the external modification tasks of descendant super nodes to super nodes and the external modification tasks of super nodes to ancestor super nodes.

[0009] In at least one embodiment of the present application, in step three, adding the numerical decomposition task to the task pool includes: When initializing the task pool, the internal decomposition tasks of all supernodes without descendant supernodes are added to the internal decomposition task pool; When the number of times that the descendant supernode executes the external modification task of the supernode is equal to the number of descendant supernodes, the internal decomposition task of the supernode is added to the internal decomposition task pool; When the internal decomposition tasks of a supernode are executed, the external modification tasks of the supernode to all ancestor supernodes are added to the external modification task pool.

[0010] In at least one embodiment of the present application, in step 4, the task receiving principle includes: Prioritize the internal decomposition tasks in the internal decomposition task pool. If there are no internal decomposition tasks in the internal decomposition task pool, then take the external modification tasks in the external modification task pool. In the internal decomposition task pool, firstly take the internal decomposition tasks added earlier; In the external modification task pool, the external modification tasks added earlier are given priority; At the same time, accept the external modification tasks of the same supernode to different ancestor supernodes; Multiple supernodes cannot simultaneously accept external modification tasks for the same ancestor node.

[0011] In at least one embodiment of the present application, multiple supernodes cannot simultaneously claim external modification tasks for the same ancestor node, including: When receiving the external modification task of a supernode to an ancestor supernode, the ancestor supernode is marked as being updated; When a supernode has completed the external modification task of an ancestor supernode, it marks the ancestor supernode as idle; When picking up tasks, skip the external modification tasks of the supernode to the ancestor supernode marked as being updated.

[0012] In at least one embodiment of the present application, the internal decomposition task execution process includes: Perform Cholesky decomposition on the diagonal matrix of the supernode to obtain the factor matrix L 1 : ; According to the factor matrix L 1 Update the following elements on the diagonal of the supernode: ; in, C1 is the diagonal matrix of supernodes, L 1 is the factor matrix obtained by decomposing the diagonal matrix, C2 , C3 , C4 , C5 , C6 The fragment pointer of the supernode.

[0013] In at least one embodiment of the present application, the external modification task execution process includes: The process of executing the external modification task of the descendant supernode on the supernode includes performing DGEMM operation on the supernode according to the descendant supernode: ; B= ( A1 ) T ; in, A1 , A2 , A3 , A4 It is the fragment pointer of the descendant supernode; The process of executing the external modification task of a supernode on an ancestor supernode includes performing a DGEMM operation on the ancestor supernode according to the supernode.

[0014] In at least one embodiment of the present application, when the number of times the internal decomposition tasks of a supernode are executed is equal to the number of supernodes, it indicates that all the numerical decomposition tasks are executed.

[0015] The invention has at least the following beneficial technical effects: The super-node parallel Cholesky numerical decomposition method of the structural finite element stiffness matrix of the present application maximizes the parallel potential of numerical decomposition and improves the efficiency of solving the structural finite element stiffness matrix. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is a flow chart of a method for super-node parallel Cholesky numerical decomposition of a structural finite element stiffness matrix according to an embodiment of the present application; Figure 2 is a schematic diagram of a supernode elimination tree according to an embodiment of the present application; Figure 3 This is a schematic diagram of the internal decomposition task execution of an implementation method of the present application; Figure 4 It is a schematic diagram of executing an external modification task according to one embodiment of the present application. DETAILED DESCRIPTION

[0017] In order to make the purpose, technical scheme and advantages of the implementation of this application clearer, the technical scheme in the embodiment of this application will be described in more detail below in conjunction with the drawings in the embodiment of this application. In the drawings, the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The described embodiments are part of the embodiments of this application, not all of them. The embodiments described below with reference to the drawings are exemplary and are intended to be used to explain this application, and should not be construed as limitations on this application. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application. The embodiments of this application are described in detail below in conjunction with the drawings.

[0018] In the description of the present application, it should be understood that the terms "center", "longitudinal", "lateral", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as limiting the scope of protection of the present application.

[0019] The following is combined with Figures 1 to 4 This application is described in further detail.

[0020] This application provides a super-node parallel Cholesky numerical decomposition method for structural finite element stiffness matrix, such as Figure 1 As shown, the following steps are included: Step 1: Obtain the supernode in the structural finite element stiffness matrix and determine the numerical decomposition task of the supernode, including: Obtain super nodes in the structural finite element stiffness matrix; Determine the numerical decomposition task of the supernode according to the supernode relationship. The numerical decomposition task of the supernode includes the internal decomposition task of the supernode, the external modification task of the descendant supernode to the supernode, and the external modification task of the supernode to the ancestor supernode; Filter out invalid tasks in the numerical decomposition tasks of the supernode and remove the invalid tasks; Step 2: Build a task pool; Step 3: Add the numerical decomposition task to the task pool; Step 4: Collect tasks from the task pool according to the preset task collection principles and execute them. Repeat steps 3 to 4 until all numerical decomposition tasks are completed.

[0021] In a preferred implementation of the present application, first, in step 1, the invalid tasks are screened in the following manner: If the diagonal matrix of the descendant supernode and the supernode do not have the same rows, the external modification task of the descendant supernode to the supernode is an invalid task; If the diagonal matrix of a supernode and its ancestor supernode do not have the same rows, the external modification task of the supernode to the ancestor supernode is an invalid task.

[0022] In a preferred embodiment of the present application, in step 2, the constructed task pool includes an internal decomposition task pool and an external modification task pool. The internal decomposition task pool is used to store the internal decomposition tasks of the supernode, and the external modification task pool is used to store the external modification tasks of the descendant supernode to the supernode and the external modification tasks of the supernode to the ancestor supernode.

[0023] The present invention discloses a parallel Cholesky numerical decomposition method for supernodes of structural finite element stiffness matrix. According to the division of supernodes in structural finite element stiffness matrix during symbolic decomposition, the adjacency matrix of supernodes is obtained. The elimination tree of supernodes is constructed according to the adjacency matrix. The supernode relationship is obtained through the elimination tree of supernodes. The supernode relationship includes all ancestor supernodes of supernodes and all descendant supernodes of supernodes. The numerical decomposition task of supernodes is determined according to the supernode relationship. After invalid tasks are removed, valid tasks are retained for numerical decomposition. By transferring matrix data to the memory space of the lower triangular matrix of the structural finite element stiffness matrix obtained by symbolic decomposition, preparation is made for formal numerical decomposition. Since there is no operation on matrix floating-point data in the symbolic decomposition stage, before the formal execution of numerical decomposition, the matrix data of structural finite element stiffness matrix needs to be transferred to the memory space of the lower triangular matrix. Since the row index of supernodes is saved in the form of fragments, when a certain data is put into the memory space, the row index of the value only needs to be compared with the fragment of the lower triangular matrix, and does not need to be compared with the row index of the lower triangular matrix, which greatly reduces the number of comparisons and improves the efficiency of the program.

[0024] The structural finite element stiffness matrix super-node parallel Cholesky numerical decomposition method of the present application, in step 3, adding the numerical decomposition task to the task pool, includes: When initializing the task pool, add the internal decomposition tasks of all supernodes that have no descendant supernodes to the internal decomposition task pool; When the number of times that the descendant supernode executes the external modification task of the supernode is equal to the number of descendant supernodes, the internal decomposition task of the supernode is added to the internal decomposition task pool; When the internal decomposition task of a supernode is completed, the external modification tasks of the supernode to all ancestor supernodes are added to the external modification task pool.

[0025] In the preferred implementation of the present application, in step 4, the task receiving principles include: Prioritize the internal decomposition tasks in the internal decomposition task pool. If there are no internal decomposition tasks in the internal decomposition task pool, then take the external modification tasks in the external modification task pool. In the internal decomposition task pool, the earlier added internal decomposition tasks will be given priority; Priority will be given to the external modification tasks that were added earlier in the external modification task pool; At the same time, accept the external modification tasks of the same supernode to different ancestor supernodes; Multiple supernodes cannot simultaneously accept external modification tasks for the same ancestor node.

[0026] Advantageously, in this embodiment, multiple supernodes cannot simultaneously receive external modification tasks for the same ancestor node, which is achieved in the following manner: When receiving the external modification task of a supernode to an ancestor supernode, the ancestor supernode is marked as being updated; When a supernode has completed the external modification task of an ancestor supernode, it marks the ancestor supernode as idle; When picking up tasks, skip the external modification tasks of the supernode to the ancestor supernode marked as being updated.

[0027] In this embodiment, when the number of times the internal decomposition tasks of a supernode are executed is equal to the number of supernodes, it indicates that all numerical decomposition tasks are executed.

[0028] In one embodiment of the present application, Figure 2 As shown, the elimination tree shows the four super nodes in the structural finite element stiffness matrix S 1 , S 2 , J , K , where supernode S 1. S 2 non-zero element fragments and supernodes J There are common rows, supernodes J Non-zero element fragments and supernodes K There are common rows. The supernode relationship is obtained based on the elimination tree, where all ancestor node information of each supernode is: ; Through a two-dimensional array FJ Save the ancestor supernode number, FJ_N Saves the number of ancestor supernodes.

[0029] According to the information of all ancestor nodes of each supernode, whenever a supernode completes its internal decomposition task, its external modification tasks for all ancestor supernodes can be immediately added to the external modification task pool and be picked up and executed at the same time.

[0030] It should be noted that although the information of all ancestor supernodes of any supernode can be directly obtained from the elimination tree, these ancestor supernodes do not necessarily need to be externally updated by the supernode. K Although it is a supernode S 1's ancestor supernode, but the supernode S 1 pair of super nodes K However, there is no contribution relationship. S 1 and supernode KThe diagonal matrix of has no identical rows, so the supernode S 1 pair of super nodes K The external modification tasks are invalid tasks, so in order to remove these unnecessary external modification tasks, the ancestor super nodes of each super node are checked. If they are invalid super nodes, they can be directly removed. Therefore, after removing the invalid super nodes, the information of all ancestor nodes of each super node is: ; Similarly, the information of all descendant supernodes of each supernode is: ; Through a two-dimensional array SJ Save the descendant supernode number, SJ_N Save the number of descendant supernodes. All descendant supernode information of each supernode is available during back generation, and the number of descendant supernodes owned by a supernode can also be used to assist in determining whether it has completed all external modification tasks.

[0031] In order to complete the correct decomposition process, the numerical decomposition tasks of these four supernodes must be executed in a certain order. S 1 , S 2 There are no child supernodes, supernode S 1 , S 2 The internal decomposition tasks of a supernode can be executed simultaneously. S 1 , S 2 After the internal decomposition task is completed, three new external modification tasks are immediately generated, namely, supernode S 1 pair of super nodes J , Super Node S 2 pairs of super nodes J , Super Node S 2 pairs of super nodes K Among these three external modification tasks, the external modification tasks for the same ancestor super node cannot be executed at the same time, that is, the super node S 1 pair of super nodes J With SuperNode S 2 pairs of super nodes J The external modification tasks cannot be executed simultaneously. Because both tasks will modify the supernode J The modified area may have a common part, and simultaneous updates will cause data competition and result in wrong calculation results. However, external modification tasks for different ancestor nodes can be executed simultaneously, such as super nodes. S 2 pairs of super nodesJ With SuperNode S 2 pairs of super nodes K external modification tasks, thereby achieving parallel processing of numerical decomposition.

[0032] In a preferred embodiment of the present application, Figure 3 As shown in the figure, the internal decomposition task execution process includes: Perform Cholesky decomposition on the diagonal matrix of the supernode to obtain the factor matrix L 1: ; This process is completed by the LAPACK function dpotrf(); According to the factor matrix L 1 Update the following diagonal elements of the supernode: ; This process is completed by the BLAS function dtrsm(); in, C1 is the diagonal matrix of supernodes, L 1 is the factor matrix obtained by decomposing the diagonal matrix, C2 , C3 , C4 , C5 , C6 The fragment pointer of the supernode.

[0033] In this embodiment, the external modification task execution process includes: like Figure 3 As shown, the super node S 2 pairs of super nodes J Take the update of as an example. The execution process of the external modification task of the descendant supernode to the supernode includes performing DGEMM operation on the supernode according to the descendant supernode: ; B= ( A1 ) T ; This process is completed by the BLAS function dgemm(); in, A1 , A2 , A3 , A4 It is the fragment pointer of the descendant supernode; The process of executing the external modification task of the super node on the ancestor super node includes performing DGEMM operation on the ancestor super node according to the super node. For details, please refer to the process of executing the external modification task of the descendant super node on the super node, which will not be repeated here.

[0034] Advantageously, by padding the upper triangle of the supernode diagonal matrix with zeros, the traditional trapezoidal supernode is padded with zeros to form a block supernode, which facilitates efficient use of high-performance multi-threaded three-level BLAS functions and LAPACK function subroutines for addressing in memory, reduces data transfer, and improves efficiency.

[0035] The structural finite element stiffness matrix supernode parallel Cholesky numerical decomposition method of the present application initializes the task pool and enters the OpenMP parallel region to complete the numerical decomposition in parallel. When initializing the task pool, all leaf supernodes without descendant supernodes need to be added to the task pool. During the formal parallel decomposition, when the internal decomposition task of a supernode is executed, its external modification tasks for all ancestor nodes are immediately added to the task pool to wait for collection and execution. When each thread task is collected, the internal modification task is given priority. When the external modification task is collected, if the ancestor supernode of a certain external modification task is being updated by another thread, the external modification task cannot be collected, so as to avoid data competition causing calculation errors. When the internal decomposition task of the last supernode is executed, the entire parallel decomposition process ends.

[0036] In one embodiment of the present application, a super-node parallel Cholesky numerical decomposition algorithm process of a structural finite element stiffness matrix is ​​provided:

[0037] In this algorithm, task_in Save the supernode number of the internal decomposition task. task_S Save the descendant supernode number of the external modification task. task_J Save the ancestor supernode number of the external modification task. Line 1 first initializes the arrays and variables used, and then puts all the supernode numbers that have no descendant supernodes into task_in The internal decomposition tasks are performed in parallel. At this time, simply, if SJ_N [ J ]=0, which means super node J Does not have any descendant supernodes.

[0038] After entering the parallel region, each loop will initialize the current task and task type to -1. Note that these variables are private variables of each thread. When receiving tasks, internal decomposition tasks are given priority. The current internal decomposition task is placed in the variable JIf there is no internal decomposition task, then the external modification task will be picked up. When picking up tasks, you can pick up from the beginning or the end of the array. Generally, the earlier the task is put in, the priority should be given. It should be noted that it has been pointed out that multiple external modification tasks cannot be performed on the same ancestor supernode at the same time, so an auxiliary array should be used to mark the ancestor supernode that is currently performing an external modification task, and the task should be skipped when picking up tasks. When using this auxiliary array, when an external modification task is received, the corresponding ancestor supernode will be marked as being updated, and marked as idle when the external modification task is completed. The operation of changing the content of the auxiliary array should be performed in the critical section. After the task is received, the corresponding task is executed according to the task type. When the internal decomposition task of a supernode is completed, the supernode number and all its ancestor supernode numbers are added to the external modification task pool. When the number of times the external modification task of a supernode is executed is equal to the number of its descendant supernodes, it is added to the internal decomposition task pool. When the number of times the internal decomposition task is executed is equal to the number of supernodes, it means that all supernodes have been decomposed and the while loop can be jumped out.

[0039] The super-node parallel Cholesky numerical decomposition method of the structural finite element stiffness matrix of the present application guides the parallel numerical decomposition process through the super-node relationship; The parallelization of numerical decomposition is achieved through the OpenMP task pool parallel template; numerical decomposition starts from all independent sub-leaf super nodes at the same time, and any idle thread can try to obtain valid update tasks from the task pool. Once the task is completed, the thread immediately adds a new task to the task pool to achieve multi-branch parallel numerical decomposition, which maximizes the parallel potential of numerical decomposition.

[0040] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A super-node parallel Cholesky numerical decomposition method for structural finite element stiffness matrix, characterized in that: include: Step 1: Obtain a supernode in the structural finite element stiffness matrix and determine the numerical decomposition task of the supernode, including: Obtain super nodes in the structural finite element stiffness matrix; Determine the numerical decomposition task of the supernode according to the supernode relationship, wherein the numerical decomposition task of the supernode includes the internal decomposition task of the supernode, the external modification task of the descendant supernode to the supernode, and the external modification task of the supernode to the ancestor supernode; Screening out invalid tasks from the numerical decomposition tasks of the supernode and removing the invalid tasks; Step 2: Build a task pool; Step 3: Add the numerical decomposition task to the task pool; Step 4: According to the preset task collection principle, tasks are collected from the task pool and executed, and steps 3 to 4 are repeated until all the numerical decomposition tasks are completed.

2. The method for super-node parallel Cholesky numerical decomposition of structural finite element stiffness matrix according to claim 1, characterized in that: In step 1, invalid tasks in the numerical decomposition tasks of the supernode are screened out, including: If the diagonal matrix of the descendant supernode and the supernode do not have the same rows, the external modification task of the descendant supernode to the supernode is an invalid task; If the diagonal matrix of a supernode and its ancestor supernode do not have the same rows, the external modification task of the supernode to the ancestor supernode is an invalid task.

3. The method for super-node parallel Cholesky numerical decomposition of structural finite element stiffness matrix according to claim 2 is characterized in that: In step 2, the task pool includes: Internal decomposition task pool, used to store the internal decomposition tasks of the super node; The external modification task pool is used to store the external modification tasks of descendant super nodes to super nodes and the external modification tasks of super nodes to ancestor super nodes.

4. The method for super-node parallel Cholesky numerical decomposition of structural finite element stiffness matrix according to claim 3 is characterized in that: In step three, adding the numerical decomposition task to the task pool includes: When initializing the task pool, the internal decomposition tasks of all supernodes without descendant supernodes are added to the internal decomposition task pool; When the number of times that the descendant supernode executes the external modification task of the supernode is equal to the number of descendant supernodes, the internal decomposition task of the supernode is added to the internal decomposition task pool; When the internal decomposition tasks of a supernode are executed, the external modification tasks of the supernode to all ancestor supernodes are added to the external modification task pool.

5. The method for super-node parallel Cholesky numerical decomposition of structural finite element stiffness matrix according to claim 4 is characterized in that: In step 4, the task collection principles include: Prioritize the internal decomposition tasks in the internal decomposition task pool. If there are no internal decomposition tasks in the internal decomposition task pool, then take the external modification tasks in the external modification task pool. In the internal decomposition task pool, firstly take the internal decomposition tasks added earlier; In the external modification task pool, the external modification tasks added earlier are given priority; At the same time, accept the external modification tasks of the same supernode to different ancestor supernodes; Multiple supernodes cannot simultaneously accept external modification tasks for the same ancestor node.

6. The method for super-node parallel Cholesky numerical decomposition of structural finite element stiffness matrix according to claim 5, characterized in that: You cannot accept multiple supernodes' external modification tasks for the same ancestor node at the same time, including: When receiving the external modification task of a supernode to an ancestor supernode, the ancestor supernode is marked as being updated; When a supernode has completed the external modification task of an ancestor supernode, it marks the ancestor supernode as idle; When picking up tasks, skip the external modification tasks of the supernode to the ancestor supernode marked as being updated.

7. The method for super-node parallel Cholesky numerical decomposition of structural finite element stiffness matrix according to claim 6, characterized in that: The internal decomposition task execution process includes: Perform Cholesky decomposition on the diagonal matrix of the supernode to obtain the factor matrix L 1 : ； According to the factor matrix L 1 Update the following elements on the diagonal of the supernode: ； in, C1 is the diagonal matrix of supernodes, L 1 is the factor matrix obtained by decomposing the diagonal matrix, C2 , C3 , C4 , C5 , C6 The fragment pointer of the supernode.

8. The method for super-node parallel Cholesky numerical decomposition of structural finite element stiffness matrix according to claim 7, characterized in that: The external modification task execution process includes: The process of executing the external modification task of the descendant supernode on the supernode includes performing DGEMM operation on the supernode according to the descendant supernode: ； B= ( A1 ) T ； in, A1 , A2 , A3 , A4 It is the fragment pointer of the descendant supernode; The process of executing the external modification task of a supernode on an ancestor supernode includes performing a DGEMM operation on the ancestor supernode according to the supernode.

9. The method for super-node parallel Cholesky numerical decomposition of structural finite element stiffness matrix according to claim 8, characterized in that: When the number of times the internal decomposition tasks of a supernode are executed is equal to the number of supernodes, it indicates that all the numerical decomposition tasks are executed.

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