High-performance matrix operation acceleration method and system based on parallel computing

Abstract

The invention discloses a parallel computing-based high-performance matrix operation acceleration method and system, and relates to the technical field of matrix operation, and the method comprises the following steps: matrix multi-scale decomposition: carrying out multi-scale decomposition on a to-be-processed matrix to obtain a plurality of sub-matrixes under different resolutions, including coarse-scale sub-matrixes and fine-scale sub-matrixes; according to the method, the to-be-processed matrix is divided into the sub-matrixes with different resolutions through multi-scale decomposition, and the sub-matrixes are distributed to the parallel processing sub-units to be processed at the same time by combining the parallel computing technology, so that the processing efficiency is improved, and the processing efficiency is improved. Meanwhile, a cross-scale information transfer mechanism is designed, coarse and fine scale sub-matrixes are subjected to collaborative iteration, the coarse scale sub-matrixes adopt an improved block Krylov subspace method and a matrix precondition technology, the fine scale sub-matrixes are introduced into an adaptive step length conjugate gradient algorithm, and an inter-scale constraint relation is established to realize bidirectional feedback.

Description

Technical Field

[0001] The present invention relates to the field of matrix operation technology, and in particular to a high-performance matrix operation acceleration method and system based on parallel computing. Background Art

[0002] In today's era of rapid technological development, scientific computing, engineering simulation, data analysis and many other fields have increasingly stringent requirements for computing technology. Matrix operations, as the core supporting technology in these fields, are becoming increasingly important. With the explosive growth of data scale and the increasing complexity of problems, traditional matrix operation methods face huge challenges when processing large-scale matrices. New technologies are urgently needed to improve the performance and efficiency of matrix operations.

[0003] Traditional matrix operation iterative algorithms have gradually exposed many serious defects when facing large-scale complex problems. On the one hand, their convergence speed is extremely slow. When processing large-scale matrices, it often takes a large number of iterations to achieve acceptable accuracy, which not only leads to a significant increase in computing time, but also makes the utilization efficiency of computing resources low, and cannot meet application scenarios with high real-time requirements. On the other hand, traditional algorithms are prone to falling into local optimal solutions and it is difficult to find the global optimal solution, which affects the accuracy and reliability of the calculation results. Although the introduction of parallel computing technology has brought new opportunities to improve the efficiency of matrix operations, by allocating computing tasks to multiple processing sub-units, Parallel execution shortens the computing time to a certain extent. However, when processing matrix operations, existing parallel computing methods have too simple a processing strategy for sub-matrices, lacking flexibility and specificity. Sub-matrices of different scales have different characteristics and computing requirements, but existing methods fail to fully consider these differences, resulting in a lack of effective coordination mechanism between sub-matrices of different scales. This lack of coordination makes the information exchange between the processing sub-units in the parallel computing process poor, and the inherent connection between sub-matrices of different scales cannot be fully utilized, which in turn limits the further improvement of overall computing efficiency and accuracy, and makes it difficult to meet the urgent demand for high-performance matrix operations in large-scale computing scenarios. Summary of the Invention

[0004] The purpose of the present invention is to make up for the shortcomings of the existing technology and provide a high-performance matrix operation acceleration method and system based on parallel computing. It can decompose the matrix into sub-matrices of different resolutions through multi-scale decomposition, design a cross-scale information transmission mechanism to realize the collaborative iteration of coarse and fine-scale sub-matrices, adopt the improved block Krylov subspace method and matrix preconditioning technology for the coarse-scale sub-matrix, introduce the adaptive step-size conjugate gradient algorithm for the fine-scale sub-matrix, and establish an inter-scale constraint relationship to realize two-way feedback. Finally, the final operation result is obtained by fusion of the results, realizing efficient matrix operation and effectively improving the operation efficiency and accuracy.

[0005] To solve the above technical problems, the present invention provides the following technical solutions: On the one hand, a high-performance matrix operation acceleration method based on parallel computing, the method comprising: Matrix multi-scale decomposition: Perform multi-scale decomposition on the matrix to be processed to obtain multiple sub-matrices at different resolutions, including coarse-scale sub-matrices and fine-scale sub-matrices; Parallel computing task allocation: The decomposed sub-matrices of different scales are allocated to multiple parallel processing sub-units. Each processing sub-unit is responsible for processing at least one sub-matrix. During the allocation process, load balancing is performed based on the size and complexity of the sub-matrices and the performance of the processing sub-units. Submatrix collaborative iterative processing: A cross-scale information transmission mechanism is designed. Each parallel processing sub-unit adopts a corresponding iterative strategy for collaborative processing of the assigned sub-matrix, and implements the inter-scale constraint relationship by establishing a solution space mapping function. Result fusion: The sub-matrix results obtained by each parallel processing sub-unit are fused. The fusion process combines the sub-matrix results according to the inverse process of multi-scale decomposition to obtain the final calculation result of the matrix to be processed.

[0006] Furthermore, in the matrix multi-scale decomposition step, wavelet basis functions are selected from a preset wavelet basis function library or a multi-resolution analysis method is adopted according to the characteristics of the matrix to be processed, and the number of decomposition layers and the scale parameters for dividing different scale ranges are set according to the matrix size and calculation accuracy requirements. According to the set method and parameters, a coarse-scale sub-matrix that retains low-frequency features is generated by filtering and downsampling, and a fine-scale sub-matrix that retains high-frequency detail features is generated by filtering and upsampling, so that each sub-matrix reflects the characteristics of the corresponding scale of the original matrix.

[0007] Furthermore, in the parallel computing task allocation step, the size, non-zero element ratio and complexity of the sub-matrix are extracted, and the number of floating-point operations per second, memory capacity and cache size indicators of each parallel processing sub-unit are monitored in real time. Based on the sub-matrix characteristics and the performance of the processing sub-unit, a dynamic allocation strategy based on task complexity is adopted, and the sub-matrix is ​​mapped to different parallel processing sub-units through a load balancing algorithm, and each processing sub-unit processes at least one sub-matrix.

[0008] Furthermore, in the parallel computing task allocation step, the sub-matrices are mapped to different parallel processing sub-units through a load balancing algorithm, and the algorithm formula is: ,in For the The amount of tasks assigned to the parallel processing sub-units, is the number of sub-matrices assigned to the processing sub-unit, For the The complexity coefficient of the submatrix, For the The processing subunit The processing capacity adaptation coefficient of the sub-matrix.

[0009] Furthermore, in the submatrix collaborative iterative processing step, cross-scale information transmission is achieved through shared memory or message passing interface. For the coarse-scale submatrix, an improved block Krylov subspace method is used, combined with matrix preconditioning technology for processing. Specifically, on the basis of the traditional block Krylov subspace method, the number of dimensions of the subspace is increased to improve the approximation degree of the subspace to the matrix characteristics. The matrix preconditioning technology uses incomplete LU decomposition preprocessing to decompose the original matrix to obtain incomplete lower triangular matrix and upper triangular matrix, thereby reducing the condition number of the matrix. The iterative process follows the formula ,in is the coarse-scale submatrix in the The solution vector of the iteration, is the coarse-scale submatrix The solution vector of the iteration, is the iteration step coefficient of the coarse-scale submatrix, Based on the Improved block Krylov subspace operator of the iterative solution, is the preconditioning matrix of the coarse-scale submatrix.

[0010] Furthermore, in the sub-matrix collaborative iterative processing step, for the fine-scale sub-matrix, an adaptive step-size conjugate gradient algorithm is introduced to monitor the norm change of the local residual in real time, adjust the iteration step size and convergence criterion according to the preset threshold, use the solution range determined by the coarse-scale sub-matrix as the initial value and fine-tune it according to its own characteristics, and the iterative process satisfies the formula ,in is the fine-scale submatrix in the The solution vector of the iteration, For the The solution vector of the iteration, Based on the Iteration local residual The adaptive step size function, is the conjugate gradient operator.

[0011] Furthermore, in the sub-matrix collaborative iterative processing step, the inter-scale constraint relationship is realized by establishing a solution space mapping function to satisfy the cross-scale constraint formula ,in is the scale feedback coefficient, For fine-scale solution The coarse-scale reference solution is mapped, and the coarse-scale solution generates the fine-scale physical constraint boundary through interpolation operation. The fine-scale solution is fed back to the coarse-scale model through filtering processing.

[0012] Furthermore, in the result fusion step, the sub-matrix results obtained by each parallel processing sub-unit are fused, and a multi-scale reconstruction algorithm is used to perform weighted combination of the sub-matrix results according to the inverse process of multi-scale decomposition. Specifically, the result of the fine-scale sub-matrix is ​​upsampled and filtered, and then superimposed with the coarse-scale sub-matrix result according to the set weight coefficient to obtain a preliminary fusion result. The final fusion result satisfies the formula ,in is the final matrix operation result, For the The result after iterative processing of the sub-matrices is For the The fusion weight coefficient corresponding to the sub-matrix result is, is the number of all sub-matrices.

[0013] On the other hand, a high-performance matrix operation acceleration system based on parallel computing comprises: Matrix multi-scale decomposition module: used to perform multi-scale decomposition on the matrix to be processed to obtain multiple sub-matrices at different resolutions, including coarse-scale sub-matrices and fine-scale sub-matrices; Task allocation module: used to allocate the sub-matrices of different scales obtained by decomposition to multiple parallel processing sub-units, and perform load balancing based on the size and complexity of the sub-matrices and the performance of the processing sub-units; Cross-scale information transfer module: used to realize information transfer between coarse-scale and fine-scale sub-matrices, and establish inter-scale constraint relationships, so that the coarse-scale solution provides physical constraints for the fine scale, and the fine-scale solution feeds back to correct the coarse-scale model; Result fusion module: used to fuse the sub-matrix results obtained by each parallel processing sub-unit to obtain the final calculation result of the matrix to be processed.

[0014] Compared with the existing technology, this high-performance matrix operation acceleration method and system based on parallel computing has the following beneficial effects: 1. The present invention divides the matrix to be processed into sub-matrices of different resolutions through multi-scale decomposition. Combined with parallel computing technology, the sub-matrices are assigned to multiple parallel processing sub-units for simultaneous processing. At the same time, a cross-scale information transmission mechanism is designed to allow coarse-scale and fine-scale sub-matrices to iterate collaboratively. The coarse-scale sub-matrix adopts an improved block Krylov subspace method and matrix preconditioning technology, and the fine-scale sub-matrix introduces an adaptive step-size conjugate gradient algorithm. Inter-scale constraint relationships are established to achieve two-way feedback. This comprehensive processing method optimizes the matrix operation strategy, fully utilizes the advantages of parallel computing, significantly improves the coordination and processing efficiency of matrix operations, and can obtain operation results more quickly.

[0015] 2. By introducing the adaptive step-size conjugate gradient algorithm, the present invention can dynamically adjust the iterative parameters according to the changes in local residuals, better capture the detailed features of the matrix, and through the inter-scale constraint relationship, the coarse-scale solution provides physical constraints for the fine scale, and the fine-scale solution feedback corrects the coarse-scale model, making the final result fusion more accurate, enhancing the adaptability of the entire calculation process to matrices of different scales and complexities, and effectively improving the calculation accuracy.

[0016] Other advantages, objects and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art based on an examination of the following or may be learned from the practice of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. Those skilled in the art can also derive other drawings based on these drawings without inventive effort.

[0018] Figure 1 This is a flowchart of a high-performance matrix operation acceleration method based on parallel computing; Figure 2 This is a structural block diagram of a high-performance matrix operation acceleration system based on parallel computing. DETAILED DESCRIPTION

[0019] In order to further illustrate the technical means and effects adopted by the present invention to achieve the predetermined purpose of the invention, the specific implementation methods, structures, features and effects of the present invention are described in detail below in conjunction with the accompanying drawings and preferred embodiments.

[0020] Example 1 In the large sparse matrix operation scenarios in the field of scientific computing, such as Figure 1 As shown, first, a multi-scale matrix decomposition is performed. According to the element distribution law and sparsity of the large sparse matrix, a wavelet decomposition method is selected, and an adapted wavelet basis function is selected from a preset wavelet basis function library. According to the size of the matrix and the accuracy requirements of scientific calculations, the number of decomposition layers is set to 4, and the corresponding scale parameters are divided. Each scale corresponds to a specific resolution. According to the set decomposition method and parameters, the large sparse matrix is ​​decomposed. A coarse-scale sub-matrix is ​​generated through filtering and downsampling operations, and a fine-scale sub-matrix is ​​generated through filtering and upsampling operations. Each sub-matrix reflects the characteristics of the original matrix at the corresponding scale. The coarse-scale sub-matrix retains the low-frequency characteristics of the original matrix, and the fine-scale sub-matrix retains the high-frequency detail characteristics.

[0021] Then, parallel computing tasks are allocated, and the scale, non-zero element ratio and complexity of each sub-matrix obtained by decomposition are extracted. At the same time, the performance indicators such as the number of floating-point operations per second, memory capacity, cache size, etc. of the multiple parallel processing sub-units used are monitored in real time. Based on the extracted sub-matrix characteristics and the monitored processing sub-unit performance, a dynamic allocation strategy based on task complexity is adopted, and the sub-matrix is ​​mapped to different parallel processing sub-units through a load balancing algorithm to ensure that each processing sub-unit processes at least one sub-matrix, and the load of each processing sub-unit is balanced, and the amount of tasks allocated to each processing sub-unit meets the requirements. .

[0022] Then, the sub-matrix collaborative iterative processing is performed, and cross-scale information transmission is realized through shared memory or message passing interface. For the allocated coarse-scale sub-matrix, the processing sub-unit adopts the improved block Krylov subspace method to improve the calculation stability by expanding the subspace dimension. At the same time, combined with the matrix preconditioning technology, the coarse-scale sub-matrix is ​​processed by incomplete LU decomposition preprocessing. The iterative process follows For the fine-scale submatrix, the processing subunit introduces an adaptive step-size conjugate gradient algorithm to monitor the norm change of the local residual in real time, dynamically adjust the iteration step size and convergence criterion according to the preset threshold, use the solution range determined by the coarse-scale submatrix as the initial value, and make appropriate fine-tuning according to the characteristics of the fine-scale submatrix itself. The iterative process satisfies In the iterative process, the constraint relationship between scales is established and realized through the solution space mapping function. The coarse-scale solution generates the fine-scale physical constraint boundary through interpolation operation. The fine-scale solution is fed back to the coarse-scale model through filtering processing to realize the coordinated iteration of the coarse-scale and fine-scale sub-matrices. The constraint relationship satisfies .

[0023] Finally, the results are fused, the reconstruction parameters are set, and the fusion weight coefficient is set according to the scale resolution of each sub-matrix. The higher the resolution of the sub-matrix, the larger the corresponding fusion weight coefficient. The multi-scale reconstruction algorithm is used to perform weighted combination of the processing results of each sub-matrix according to the inverse process of multi-scale decomposition. The results of the fine-scale sub-matrix are first up-sampled and filtered, and then superimposed with the coarse-scale sub-matrix results according to the set weight coefficient to obtain the preliminary fusion result. The final fusion result satisfies ,in is the number of all sub-matrices. The initial fusion result is subjected to post-processing operations such as outlier removal and smoothing to obtain the final operation result of the large sparse matrix.

[0024] Example 2 In high-dimensional dense matrix operation scenarios in the field of engineering simulation, the high-performance matrix operation acceleration method and system based on parallel computing of the present invention are applied.

[0025] First, the matrix multi-scale decomposition step is performed. According to the scale of the high-dimensional dense matrix and the requirements of the engineering simulation for calculation accuracy, the multi-resolution analysis method is selected, the number of decomposition layers is set to 3, and the corresponding scale parameters are divided. Each scale corresponds to a specific resolution. According to the set multi-resolution analysis method and parameters, the high-dimensional dense matrix is ​​decomposed. Coarse-scale sub-matrices are generated through filtering and downsampling, and fine-scale sub-matrices are generated through filtering and upsampling. Each sub-matrix reflects the characteristics of the original matrix at the corresponding scale.

[0026] Next, parallel computing tasks are allocated, and the scale, non-zero element ratio and complexity of each sub-matrix are extracted. At the same time, the performance indicators of the parallel processing sub-units used are monitored in real time. Based on these sub-matrix characteristics and processing sub-unit performance, a dynamic allocation strategy based on task complexity is adopted, and the sub-matrices are reasonably allocated to different parallel processing sub-units through a load balancing algorithm, such as Figure 2 As shown, it is ensured that each processing sub-unit processes at least one sub-matrix, thereby achieving load balancing among the processing sub-units.

[0027] Then, the sub-matrix collaborative iterative processing stage is entered. Cross-scale information transmission is implemented through shared memory. A shared memory area is set up, and each parallel processing sub-unit can perform read and write operations on this area. The relevant units of cross-scale information transmission ensure the consistency and timeliness of data transmission. For the coarse-scale sub-matrix, the processing sub-unit adopts an improved block Krylov subspace method to expand the subspace dimension to improve computational stability. At the same time, combined with matrix preconditioning technology, the coarse-scale sub-matrix is ​​processed by incomplete LU decomposition preprocessing. For the fine-scale sub-matrix, the processing sub-unit introduces an adaptive step-size conjugate gradient algorithm to dynamically adjust the iteration step size and convergence criterion according to the norm change of the local residual. The solution range determined by the coarse-scale sub-matrix is ​​used as the initial value, and fine-tuned according to the characteristics of the fine-scale sub-matrix itself, to establish an inter-scale constraint relationship. Through the solution space mapping function, the coarse-scale solution is interpolated to generate the fine-scale physical constraint boundary. The fine-scale solution is fed back to the coarse-scale model through filtering processing to achieve collaborative iteration of the two.

[0028] Finally, the results are fused, the reconstruction parameters are set, and the fusion weight coefficient is set according to the scale resolution of the sub-matrix. The multi-scale reconstruction algorithm is used, and the processing results of each sub-matrix are weighted and combined according to the inverse process of multi-scale decomposition. The results of the fine-scale sub-matrix are first upsampled and filtered, and then superimposed with the coarse-scale sub-matrix results according to the set weight coefficient to obtain the preliminary fusion result. The preliminary fusion result is post-processed to obtain the final calculation result of the high-dimensional dense matrix to meet the needs of engineering simulation.

[0029] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as above in terms of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art can, without departing from the scope of the technical solution of the present invention, make some changes or modifications to equivalent embodiments using the technical contents disclosed above. However, any brief modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A high-performance matrix operation acceleration method based on parallel computing, characterized in that: The method comprises the following specific steps: Matrix multi-scale decomposition: Perform multi-scale decomposition on the matrix to be processed to obtain multiple sub-matrices at different resolutions, including coarse-scale sub-matrices and fine-scale sub-matrices; Parallel computing task allocation: The decomposed sub-matrices of different scales are allocated to multiple parallel processing sub-units. Each processing sub-unit is responsible for processing at least one sub-matrix. During the allocation process, load balancing is performed based on the size and complexity of the sub-matrices and the performance of the processing sub-units. Submatrix collaborative iterative processing: A cross-scale information transmission mechanism is designed. Each parallel processing sub-unit adopts a corresponding iterative strategy for collaborative processing of the assigned sub-matrix, and implements the inter-scale constraint relationship by establishing a solution space mapping function. Result fusion: The sub-matrix results obtained by each parallel processing sub-unit are fused. The fusion process combines the sub-matrix results according to the inverse process of multi-scale decomposition to obtain the final calculation result of the matrix to be processed.

2. The high-performance matrix operation acceleration method based on parallel computing according to claim 1, characterized in that: In the matrix multi-scale decomposition step, wavelet basis functions are selected from a preset wavelet basis function library or a multi-resolution analysis method is adopted based on the characteristics of the matrix to be processed, and the number of decomposition layers and scale parameters for dividing different scale ranges are set according to the matrix size and calculation accuracy requirements. According to the set method and parameters, coarse-scale sub-matrices that retain low-frequency features are generated through filtering and downsampling, and fine-scale sub-matrices that retain high-frequency detail features are generated through filtering and upsampling, so that each sub-matrix reflects the characteristics of the corresponding scale of the original matrix.

3. The high-performance matrix operation acceleration method based on parallel computing according to claim 1 is characterized in that: In the parallel computing task allocation step, the size, non-zero element ratio and complexity of the sub-matrix are extracted, and the number of floating-point operations per second, memory capacity and cache size indicators of each parallel processing sub-unit are monitored in real time. Based on the sub-matrix characteristics and the performance of the processing sub-unit, a dynamic allocation strategy based on task complexity is adopted, and the sub-matrix is ​​mapped to different parallel processing sub-units through a load balancing algorithm, and each processing sub-unit processes at least one sub-matrix.

4. The high-performance matrix operation acceleration method based on parallel computing according to claim 3 is characterized in that: In the parallel computing task allocation step, the sub-matrices are mapped to different parallel processing sub-units through a load balancing algorithm, and the algorithm formula is: ,in For the The amount of tasks assigned to the parallel processing sub-units, is the number of sub-matrices assigned to the processing sub-unit, For the The complexity coefficient of the submatrix, For the The processing subunit The processing capacity adaptation coefficient of the sub-matrix.

5. The high-performance matrix operation acceleration method based on parallel computing according to claim 1 is characterized in that: In the submatrix collaborative iterative processing step, cross-scale information transmission is achieved through shared memory or message passing interface. For the coarse-scale submatrix, an improved block Krylov subspace method is used in combination with matrix preconditioning technology for processing. Specifically, on the basis of the traditional block Krylov subspace method, the number of dimensions of the subspace is increased to improve the approximation degree of the subspace to the matrix characteristics. The matrix preconditioning technology uses incomplete LU decomposition preprocessing to decompose the original matrix to obtain incomplete lower triangular matrix and upper triangular matrix, thereby reducing the condition number of the matrix. The iterative process follows the formula ,in is the coarse-scale submatrix in the The solution vector of the iteration, is the coarse-scale submatrix The solution vector of the iteration, is the iteration step coefficient of the coarse-scale submatrix, Based on the Improved block Krylov subspace operator of the iterative solution, is the preconditioning matrix of the coarse-scale submatrix.

6. The high-performance matrix operation acceleration method based on parallel computing according to claim 1, characterized in that: In the sub-matrix collaborative iterative processing step, an adaptive step-size conjugate gradient algorithm is introduced for the fine-scale sub-matrix, the norm change of the local residual is monitored in real time, the iteration step size and the convergence criterion are adjusted according to the preset threshold, the solution range determined by the coarse-scale sub-matrix is ​​used as the initial value and fine-tuned according to its own characteristics, and the iterative process satisfies the formula ,in is the fine-scale submatrix in the The solution vector of the iteration, For the The solution vector of the iteration, Based on the Iteration local residual The adaptive step size function, is the conjugate gradient operator.

7. The high-performance matrix operation acceleration method based on parallel computing according to claim 6, characterized in that: In the sub-matrix collaborative iterative processing step, the inter-scale constraint relationship is realized by establishing a solution space mapping function to satisfy the cross-scale constraint formula ,in is the scale feedback coefficient, For fine-scale solution The coarse-scale reference solution is mapped, and the coarse-scale solution generates the fine-scale physical constraint boundary through interpolation operation. The fine-scale solution is fed back to the coarse-scale model through filtering processing.

8. The high-performance matrix operation acceleration method based on parallel computing according to claim 1 is characterized in that: In the result fusion step, the sub-matrix results obtained by each parallel processing sub-unit are fused, and the multi-scale reconstruction algorithm is used to perform weighted combination of the sub-matrix results according to the inverse process of multi-scale decomposition. Specifically, the result of the fine-scale sub-matrix is ​​upsampled and filtered, and then superimposed with the coarse-scale sub-matrix result according to the set weight coefficient to obtain a preliminary fusion result. The final fusion result satisfies the formula ,in is the final matrix operation result, For the The result after iterative processing of the sub-matrices is For the The fusion weight coefficient corresponding to the sub-matrix result is, is the number of all sub-matrices.

9. A high-performance matrix operation acceleration system based on parallel computing, the system being applicable to the high-performance matrix operation acceleration method based on parallel computing according to any one of claims 1 to 8, characterized in that: The system comprises: Matrix multi-scale decomposition module: used to perform multi-scale decomposition on the matrix to be processed to obtain multiple sub-matrices at different resolutions, including coarse-scale sub-matrices and fine-scale sub-matrices; Task allocation module: used to allocate the sub-matrices of different scales obtained by decomposition to multiple parallel processing sub-units, and perform load balancing based on the size and complexity of the sub-matrices and the performance of the processing sub-units; Cross-scale information transfer module: used to realize information transfer between coarse-scale and fine-scale sub-matrices, and establish inter-scale constraint relationships, so that the coarse-scale solution provides physical constraints for the fine scale, and the fine-scale solution feeds back to correct the coarse-scale model; Result fusion module: used to fuse the sub-matrix results obtained by each parallel processing sub-unit to obtain the final calculation result of the matrix to be processed.

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