A spectral unit partitioning method applicable to local low-velocity medium models

Abstract

This invention discloses a spectral unit partitioning method suitable for local low-velocity medium models, comprising: determining simulation parameters of the simulation region; determining the element refinement factor and range based on the three-dimensional wave velocity structure of the simulation region; establishing a locally refined spectral unit model of the simulation region according to the simulation parameters, element refinement factor, and range; reducing the dimensionality of the locally refined spectral unit model into several sub-rectangles through vertical weighting and determining their weights; and performing long-side partitioning and short-side partitioning of the locally refined spectral unit model sequentially according to the weights of each sub-rectangle to obtain spectral unit partitioning results suitable for local low-velocity medium models. The partitioning obtained by the method of this invention has uniform load; under the condition of local element refinement, using the same spectral unit model and the same operating conditions as existing methods, the method of this invention is applied to spectral unit partitioning, and the results are stable and convergent.

Description

Technical Field

[0001] This invention belongs to the field of seismic motion simulation technology, specifically relating to a spectral unit partitioning method suitable for local low-velocity medium models. Background Technology

[0002] In seismic design of structures, reasonable seismic motion parameters are a prerequisite for ensuring the seismic safety of the structure. For important structures such as high dams, large reservoirs, and nuclear power facilities, seismic time histories are required as input for seismic calculations. However, for specific projects, it is usually difficult to obtain real records that meet the conditions for seismic geological similarity; therefore, artificial simulation methods are needed as a supplement. The spectral element method is a commonly used seismic motion simulation method.

[0003] In seismic motion simulation, the characteristic of the medium through which seismic waves propagate is that the wave velocity increases with depth. If a sedimentary basin exists, the wave velocity in the deep crust can be 2 to 5 times higher than that in the basin. To simulate the same frequency, lower wave velocity media require smaller element sizes. Therefore, modeling often requires refining the elements within a certain depth range from the surface, especially in basin areas; simultaneously, it is necessary to rationally partition the spectral element model, evenly distributing the load across multiple computer nodes to save simulation time for seismic wave propagation.

[0004] Existing techniques typically rely on open-source programs like Scotch and Metis to directly partition the spectral element model, decomposing the locally refined spectral element model into several parts for seismic wave simulation. This method is generally used to handle cases without local low-velocity media. However, when dealing with cases where local low-velocity media exist and element refinement is required, lower-quality elements may be located at the vertices of sub-partitions. The complex partition interfaces near low-quality elements can amplify high-frequency errors during the simulation, leading to non-convergence of the spectral element method simulation.

[0005] Therefore, when using the existing spectral element method to simulate higher frequencies (>5Hz), the complex spectral element partitioning contact surface will amplify the numerical error, causing the simulation process to fail to converge. Summary of the Invention

[0006] To address the aforementioned shortcomings in existing technologies, the spectral unit partitioning method for local low-velocity medium models provided by this invention solves the problem that existing simulation methods, when simulating higher frequencies, amplify numerical errors by obtaining complex partitioned contact surfaces, leading to non-convergence in the seismic wave simulation process.

[0007] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows: a spectral unit partitioning method suitable for local low-velocity medium models, comprising the following steps:

[0008] Determine the simulation parameters for the simulation region;

[0009] Based on the three-dimensional wave velocity structure of the simulated region, the element refinement factor and range are determined;

[0010] Based on the simulation parameters, element refinement factor, and range, a local refinement spectral element model of the simulation region is established;

[0011] The localized refined spectral unit model is reduced in dimensionality by vertical weighting into several sub-rectangles and their weights are determined.

[0012] Based on the weights of each sub-rectangle, the local refined spectral unit model is sequentially partitioned by long side and short side to obtain spectral unit partitioning results suitable for local low-velocity medium models.

[0013] Furthermore, the simulation parameters include simulation length, simulation width, simulation depth, and simulation height.

[0014] Furthermore, the horizontal range of the unit refinement range includes the discontinuous region range around the low wave velocity region where the wave velocity is less than the critical wave velocity.

[0015] The depth of the refined unit range is the deepest unit depth corresponding to a wave velocity not exceeding the critical wave velocity.

[0016] Furthermore, methods for establishing locally refined spectral unit models include:

[0017] The simulation region is modeled using hexahedral elements based on the average shear wave velocity of the Earth's crust, and the horizontal coordinates of each node in the modeling region are located on the same node.

[0018] The number of cell layers in the statistical modeling region in three directions is determined, and the number of cell layers to be refined in the three directions is determined based on the depth of the cell refinement range.

[0019] Based on the number of unit layers to be refined, and combined with the unit refinement factor and range, the low wave velocity region units are refined to obtain a locally refined spectral unit model.

[0020] Furthermore, the method for reducing the dimensionality of the locally refined spectral unit model into several sub-rectangles through vertical weighting and determining their weights includes:

[0021] Based on the horizontal projection of the local refined spectral unit model, the local refined spectral unit model is discretized into several sub-rectangles;

[0022] The weight of each sub-rectangle is determined based on the number of refinement units in each sub-rectangle in different directions.

[0023] Furthermore, the weight w of the i-th sub-rectangle in the x-direction and the j-th sub-rectangle in the y-direction... i,j for:

[0024]

[0025] In the formula, nz n is the number of cell layers in the z-direction. z,r Let z be the number of element layers to be refined in the z-direction. Let be the number of refinement units for the i-th sub-rectangle in the x-direction and the j-th sub-rectangle in the y-direction, expressed as:

[0026]

[0027] In the formula, n r The refinement factor for the unit.

[0028] Furthermore, methods for partitioning the local refined spectral unit model along its long side include:

[0029] T1. Based on the hardware parameters, determine the number of partitions N = N for the local refinement spectral unit model. x ×N y N x and N y These are the number of partitions in the x and y directions, respectively;

[0030] T2. Determine the long-side direction of the partitions in the local refined spectral unit model and their corresponding parameters, including the number of partitions along the long-side direction, the number of sub-rectangles along the long-side direction, the target weight along the long-side direction, and the weight of each layer of sub-rectangles along the long-side direction; where the long-side direction is N. x and N y The direction corresponding to the larger value in the middle;

[0031] T3. Divide the long side into sections starting from the first layer of sub-rectangles along the long side.

[0032] T4. During the long-side partitioning process, determine whether the current long-side partition weight is greater than the target weight in the long-side direction;

[0033] If so, proceed to step T5;

[0034] If not, proceed to step T6;

[0035] T5. Determine the ending layer of the current long-side partition and the final weight of the current long-side partition, then proceed to step T7.

[0036] T6. Overlay the next layer of sub-rectangles onto the current long side partition, and return to step T4;

[0037] T7. Repeat steps T4 to T6 to obtain the long-side partitioning result.

[0038] Furthermore, the starting layer of the current long-side partition is the layer below the ending layer of the previous long-side partition;

[0039] The ending layer of the current long side partition is the layer corresponding to the smaller value of the absolute difference between the weight of the current long side partition and the target weight in the long side direction, and the layer corresponding to the smaller value of the absolute difference between the weight of the long side partition and the target weight in the long side direction of the previous sub-rectangle.

[0040] The final weight of the current long side partition is the sum of the weights of each sub-rectangle from the start layer to the end layer of the current long side partition.

[0041] Furthermore, methods for short-side partitioning of the locally refined spectral unit model include:

[0042] M1. Determine the short-side direction of the partitions in the local refined spectral unit model and their corresponding parameters, including the number of partitions in the short-side direction and the number of sub-rectangles in the short-side direction.

[0043] M2. Under each long-side partition, determine the target weight of each short-side partition, and sort the sub-rectangles in each long-side partition in order according to the principle of short-side priority, and then determine the total number of sub-rectangles in the long-side partition.

[0044] M3. Starting from the first sub-rectangle within the current long-side partition, perform short-side partitioning;

[0045] M4. During the short-side partitioning process, determine whether the current short-side partition weight is greater than the corresponding short-side partition target weight.

[0046] If so, proceed to step M5;

[0047] If not, proceed to step M6;

[0048] M5. Determine the ending sub-rectangle of the current short side partition and the final weight of the current short side partition, then proceed to step M7.

[0049] M6. Overlay the next sub-rectangle onto the current short side partition and return to step M4;

[0050] M7. Repeat steps S4 to M6 to divide each long side partition into corresponding short side partitions, and calculate the corresponding polygon range based on its starting and ending sub-rectangles to obtain the short side partitioning results.

[0051] Furthermore, the starting layer of the current short side partition is the next sub-rectangle of the ending sub-rectangle of the previous short side partition;

[0052] The ending sub-rectangle of the current short side partition is the sub-rectangle corresponding to the smaller of the absolute value of the difference between the current short side partition weight and the target weight of the short side partition, and the absolute value of the difference between the short side partition weight and the target weight of the short side partition corresponding to the previous sub-rectangle.

[0053] The final weight of the current short side partition is the sum of the weights of all sub-rectangles from the beginning to the end of the current long side partition.

[0054] The beneficial effects of this invention are as follows:

[0055] (1) The partition load obtained by the method of the present invention is uniform, and the partition non-uniformity obtained by the method of the present invention is 14%, which can distribute the load approximately uniformly to each computing node.

[0056] (2) Under the condition of local unit refinement, the same spectral unit model and the same working conditions as the existing methods are used. When partitioning the spectral units, the method of this invention is used to obtain stable convergence results. Attached Figure Description

[0057] Figure 1 The flowchart shows the spectral unit partitioning method for local low-velocity medium models provided by this invention.

[0058] Figure 2 A schematic diagram of the modeling region obtained by modeling the simulated region provided by the present invention.

[0059] Figure 3 This is a schematic diagram of the localized refined spectral unit model provided by the present invention.

[0060] Figure 4 This is a cross-sectional view of the locally refined spectral unit model provided by the present invention.

[0061] Figure 5 This is a schematic diagram of the sub-rectangle obtained by discretizing the locally refined spectral unit model according to the present invention.

[0062] Figure 6 This invention provides a sub-rectangular refinement partition map obtained by discretizing a local refinement spectral unit model.

[0063] Figure 7 This is a schematic diagram of the long-side partitioning result provided by the present invention.

[0064] Figure 8 This is a schematic diagram of a short-side partition under a long-side partition provided by the present invention.

[0065] Figure 9 The final partitioning result diagram of the spectral units provided by this invention.

[0066] Figure 10 The simulation convergence diagram obtained using the method of this invention is provided for this invention. Detailed Implementation

[0067] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0068] This invention provides a spectral unit partitioning method suitable for local low-velocity medium models, such as... Figure 1 As shown, it includes the following steps:

[0069] Determine the simulation parameters for the simulation region;

[0070] Based on the three-dimensional wave velocity structure of the simulated region, the element refinement factor and range are determined;

[0071] Based on the simulation parameters, element refinement factor, and range, a local refinement spectral element model of the simulation region is established;

[0072] The localized refined spectral unit model is reduced in dimensionality by vertical weighting into several sub-rectangles and their weights are determined.

[0073] Based on the weights of each sub-rectangle, the local refined spectral unit model is sequentially partitioned by long side and short side to obtain spectral unit partitioning results suitable for local low-velocity medium models.

[0074] The method provided in this embodiment of the invention is applicable to the spectral unit partitioning of local low-velocity medium models, and can uniformly distribute the load to any number of computer cores while ensuring the convergence of the spectral element method for seismic wave simulation.

[0075] In this embodiment of the invention, the simulation parameters of the simulation area are determined according to the simulation requirements, including the simulation length and simulation width; the simulation depth and simulation height are determined according to the maximum seismic depth of the simulation area.

[0076] In this embodiment of the invention, the method for determining the element refinement factor and range includes:

[0077] Establish a three-dimensional model of the crustal wave velocity structure;

[0078] Based on the obtained minimum wave velocity V in the low wave velocity region s,min Calculation unit refinement factor Here, ceil() is the floor function. V s,c The mean shear wave velocity of the Earth's crust is typically taken as 2800 m / s. r It is usually 2 or 3;

[0079] By calculating the critical wave velocity Determine the scope of unit refinement.

[0080] Specifically, in this embodiment, the horizontal range of the element refinement range includes the area around the low wave velocity region where the wave velocity is less than the critical wave velocity V. s,r The discontinuous region range; the depth D of the element refinement range. r The wave speed is not greater than the critical wave speed V. s,r The corresponding deepest cell depth.

[0081] In this embodiment of the invention, the method for establishing a locally refined spectral unit model includes:

[0082] The simulation region is modeled using hexahedral elements based on the average shear wave velocity of the Earth's crust, and the horizontal coordinates of each node in the modeling region are located on the same node.

[0083] The number of cell layers in the statistical modeling region in three directions is determined, and the number of cell layers to be refined in the three directions is determined based on the depth of the cell refinement range.

[0084] Based on the number of unit layers to be refined, and combined with the unit refinement factor and range, the low wave velocity region units are refined to obtain a locally refined spectral unit model.

[0085] In this embodiment, as Figure 2 The image shows an example of a modeled region obtained by modeling a simulated region; where the number of unit layers in the three directions are n respectively. x n y n z Based on the depth D of the element refinement range r Determine the number of unit layers n to be refined. z,r The thickness of each layer is multiplied by the number of layers, and this value is greater than the depth D. r .

[0086] In this embodiment, for Figure 2 The modeling region shown is refined into low-velocity spectral element models, and the resulting locally refined spectral element models and their corresponding profiles are as follows. Figure 3 and Figure 4 As shown.

[0087] In this embodiment of the invention, the method for reducing the local refined spectral unit model into several sub-rectangles through vertical weighting and determining their weights includes:

[0088] Based on the horizontal projection of the local refined spectral unit model, the local refined spectral unit model is discretized into several sub-rectangles;

[0089] The weight of each sub-rectangle is determined based on the number of refinement units in each sub-rectangle in different directions.

[0090] Specifically, in this embodiment, according to the horizontal projection of the locally refined spectral unit model, such as Figure 5As shown, the locally refined spectral unit model is discretized into n x ×n y There are n sub-rectangles. x ,n y These represent the number of sub-rectangles in the x and y directions, respectively.

[0091] The weights of each sub-rectangle are determined based on the number of unit layers in each rectangular region. The weight w of the i-th sub-rectangle in the x-direction and the j-th sub-rectangle in the y-direction is... i,j for:

[0092]

[0093] In the formula, n z n is the number of cell layers in the z-direction. z,r Let z be the number of element layers to be refined in the z-direction. Let be the number of refinement units for the i-th sub-rectangle in the x-direction and the j-th sub-rectangle in the y-direction, expressed as:

[0094]

[0095] In the formula, n r The refinement factor for the unit.

[0096] In this embodiment, as Figure 6 As shown, the refinement area is a sub-rectangle where all elements are refined, as shown in the purple area in the figure; the edge of the refinement area is the transition area between the refined and non-refined areas, as shown in the green area in the figure; the corner of the refinement area is the corner of the transition area, as shown in the orange area in the figure.

[0097] In this embodiment of the invention, the method for partitioning a locally refined spectral unit model along its long side includes:

[0098] T1. Based on the hardware parameters, determine the number of partitions N = N for the local refinement spectral unit model. x ×N y N x and N y These are the number of partitions in the x and y directions, respectively;

[0099] T2. Determine the long-side direction of the partitions in the local refined spectral unit model and their corresponding parameters, including the number of partitions along the long-side direction, the number of sub-rectangles along the long-side direction, the target weight along the long-side direction, and the weight of each layer of sub-rectangles along the long-side direction; where the long-side direction is N. x and N y The direction corresponding to the larger value in the middle;

[0100] T3. Divide the long side into sections starting from the first layer of sub-rectangles along the long side.

[0101] T4. During the long-side partitioning process, determine whether the current long-side partition weight is greater than the target weight in the long-side direction;

[0102] If so, proceed to step T5;

[0103] If not, proceed to step T6;

[0104] T5. Determine the ending layer of the current long-side partition and the final weight of the current long-side partition, then proceed to step T7.

[0105] T6. Overlay the next layer of sub-rectangles onto the current long side partition, and return to step T4;

[0106] T7. Repeat steps T4 to T6 to obtain the long-side partitioning result.

[0107] In step T1 of this embodiment, the hardware parameters specifically refer to the computer core and memory configuration. Based on these parameters, the required number of partitions N is determined. If N is not a non-prime number, N can be divided into the product of partitions in the x and y directions, i.e., N = N x ×N y ; where N x and N y These are the number of partitions in the x and y directions, respectively.

[0108] In step T2 of this embodiment, the long side direction of the partition in the local refined spectral unit model is n. x and n y The direction corresponding to the larger value; the number of partitions is The number of sub-rectangles along the longer side is The target weight along the longer side is Weight of the l-th sub-rectangle along the long side

[0109] In this embodiment, during the process of performing long-side partitioning as described above, the starting layer of the current long-side partition is the layer below the ending layer of the previous long-side partition.

[0110] The ending layer of the current long side partition is the layer corresponding to the smaller value of the absolute difference between the weight of the current long side partition and the target weight in the long side direction, and the layer corresponding to the smaller value of the absolute difference between the weight of the long side partition and the target weight in the long side direction of the previous sub-rectangle.

[0111] The final weight of the current long side partition is the sum of the weights of each sub-rectangle from the start layer to the end layer of the current long side partition.

[0112] In this embodiment, the first layer of sub-rectangles along the long side is taken as the starting layer of the first long side partition. For example, the weight of the first longest side fraction. From the start layer to the current layer l c The total weight, i.e.:

[0113] when Greater than Calculate separately and and The absolute value of the difference, where the index corresponding to the smaller value is the end layer of the first long-side partition. Right now:

[0114]

[0115] Let the starting layer of the Lth partition on the long side be... It is the end layer of the previous partition L-1 + 1, that is Repeat steps T4 to T6 until l c =n l , obtain N L Each of the long-side partitions has its own starting layer. and end layer The final weight of the Lth long-side partition is:

[0116]

[0117] In this embodiment, based on the above-described long-side partitioning method, the long-side partitioning result is as follows: Figure 7 As shown.

[0118] In this embodiment of the invention, the method for short-side partitioning of a locally refined spectral unit model includes:

[0119] M1. Determine the short-side direction of the partitions in the local refined spectral unit model and their corresponding parameters, including the number of partitions in the short-side direction and the number of sub-rectangles in the short-side direction.

[0120] M2. Under each long-side partition, determine the target weight of each short-side partition, and sort the sub-rectangles in each long-side partition in order according to the principle of short-side priority, and then determine the total number of sub-rectangles in the long-side partition.

[0121] M3. Starting from the first sub-rectangle within the current long-side partition, perform short-side partitioning;

[0122] M4. During the short-side partitioning process, determine whether the current short-side partition weight is greater than the corresponding short-side partition target weight.

[0123] If so, proceed to step M5;

[0124] If not, proceed to step M6;

[0125] M5. Determine the ending sub-rectangle of the current short side partition and the final weight of the current short side partition, then proceed to step M7.

[0126] M6. Overlay the next sub-rectangle onto the current short side partition and return to step M4;

[0127] M7. Repeat steps S4 to M6 to divide each long side partition into corresponding short side partitions, and calculate the corresponding polygon range based on its starting and ending sub-rectangles to obtain the short side partitioning results.

[0128] In step M1 of this embodiment, the direction of the shorter side is n. x and n y The direction corresponding to the smaller value in the middle, and its number of partitions N. S for Number of sub-rectangles n along the shorter side s for

[0129] In step M2 of this embodiment, taking the S-th short-side partition of the L-th long-side partition as an example, its target weight... for Within the Lth long-side partition, all sub-rectangles are arranged sequentially according to the principle of short-side priority. Then the total number of sub-rectangles n within this long-side partition is... L for The weight of the c-th sub-rectangle is The coordinates (i,j) of the sub-rectangle in the global coordinate system can be calculated, along with its corresponding weight w. i,j get.

[0130] In this embodiment, the starting layer of the current short side partition is the next sub-rectangle of the ending sub-rectangle of the previous short side partition;

[0131] The ending sub-rectangle of the current short side partition is the sub-rectangle corresponding to the smaller of the absolute value of the difference between the current short side partition weight and the target weight of the short side partition, and the absolute value of the difference between the short side partition weight and the target weight of the short side partition corresponding to the previous sub-rectangle.

[0132] The final weight of the current short side partition is the sum of the weights of all sub-rectangles from the beginning to the end of the current long side partition.

[0133] Specifically, taking the first sub-rectangle within the Lth long-side partition as the first short-side partition of that long-side partition as an example, its starting sub-rectangle... The weight of the first short side partition of the long side partition. From its starting subrectangle to the current subrectangle Total weight for

[0134] when Greater than Calculate separately and and The absolute values ​​of the differences, where the index corresponding to the smaller value is the ending sub-rectangle of the first sub-partition of the long-side partition. Right now:

[0135]

[0136] Let the starting sub-rectangle of the Lth long side partition and the Sth sub-partition be... It is the ending sub-rectangle of the previous sub-partition S-1 + 1, that is Repeat steps M4 through M6 until... Obtain the long-side partition N S Each of the short-side partitions has its own starting sub-rectangle. and the ending subrectangle The final weight of the short side partition in this long side partition is:

[0137]

[0138] Finally, based on the starting and ending sub-rectangles, calculate the polygon range P of the S-th sub-partition of the L-th long-side partition. L,S The subpartition result of one of the long-side partitions is as follows: Figure 8 As shown; for each long-side partition, the short-side partition is performed according to the above steps to obtain the final spectral unit partitioning result as shown. Figure 9 As shown.

[0139] like Figure 10 As shown, the maximum displacement when simulating using the partition obtained by the method of this invention is given. It can be seen that the maximum displacement of the model tends to be stable over time, completing the entire 15s simulation.

[0140] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

[0141] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A spectral unit partitioning method suitable for local low-velocity medium models, characterized in that, Includes the following steps: Determine the simulation parameters for the simulation region; Based on the three-dimensional wave velocity structure of the simulated region, the element refinement factor and element refinement range are determined; Based on the simulation parameters, element refinement factor, and range, a local refinement spectral element model of the simulation region is established; The localized refined spectral unit model is reduced in dimensionality by vertical weighting into several sub-rectangles and their weights are determined. Based on the weights of each sub-rectangle, the local refined spectral unit model is sequentially partitioned by long side and short side to obtain spectral unit partitioning results suitable for local low-velocity medium models; Methods for establishing locally refined spectral unit models include: The simulation region is modeled using hexahedral elements based on the average shear wave velocity of the Earth's crust, and the horizontal coordinates of each node in the modeling region are located on the same node. The number of cell layers in the statistical modeling region in three directions is determined, and the number of cell layers to be refined in the three directions is determined based on the depth of the cell refinement range. Based on the number of unit layers to be refined, and combined with the unit refinement factor and range, the low wave velocity region units are refined to obtain a locally refined spectral unit model.

2. The method according to claim 1, characterized in that, The simulation parameters include simulation length, simulation width, simulation depth, and simulation height.

3. The method according to claim 1, characterized in that, The horizontal range of the unit refinement range includes the discontinuous region range around the low wave velocity region where the wave velocity is less than the critical wave velocity. The depth of the refined unit range is the deepest unit depth corresponding to a wave velocity not exceeding the critical wave velocity.

4. The method according to claim 1, characterized in that, Methods for reducing the dimensionality of a locally refined spectral unit model into several sub-rectangles using vertical weights and determining their weights include: Based on the horizontal projection of the local refined spectral unit model, the local refined spectral unit model is discretized into several sub-rectangles; The weight of each sub-rectangle is determined based on the number of refinement units in each sub-rectangle in different directions.

5. The method according to claim 4, characterized in that, The weight of the i-th sub-rectangle in the x-direction and the j-th sub-rectangle in the y-direction for: In the formula, Let z be the number of cell layers in the z-direction. Let z be the number of element layers to be refined in the z-direction. Let be the number of refinement units for the i-th sub-rectangle in the x-direction and the j-th sub-rectangle in the y-direction, expressed as: In the formula, The refinement factor for the unit.

6. The method according to claim 1, characterized in that, Methods for partitioning the local refined spectral unit model along its long side include: T1. Determine the number of partitions for the localized refined spectral unit model based on the hardware parameters. , and These are the number of partitions in the x and y directions, respectively; T2. Determine the long-side direction of the partitions in the local refined spectral unit model and their corresponding parameters, including the number of partitions along the long-side direction, the number of sub-rectangles along the long-side direction, the target weight along the long-side direction, and the weight of each layer of sub-rectangles along the long-side direction; where the long-side direction is... and The direction corresponding to the larger value in the middle; T3. Divide the long side into sections starting from the first layer of sub-rectangles along the long side. T4. During the long-side partitioning process, determine whether the current long-side partition weight is greater than the target weight in the long-side direction; If so, proceed to step T5; If not, proceed to step T6; T5. Determine the ending layer of the current long-side partition and the final weight of the current long-side partition, then proceed to step T7. T6. Overlay the next layer of sub-rectangles onto the current long side partition, and return to step T4; T7. Repeat steps T4 to T6 to obtain the long-side partitioning result.

7. The method according to claim 6, characterized in that, The starting layer of the current long-side partition is the layer below the ending layer of the previous long-side partition; The ending layer of the current long side partition is the layer corresponding to the smaller value of the absolute difference between the weight of the current long side partition and the target weight in the long side direction, and the layer corresponding to the smaller value of the absolute difference between the weight of the long side partition and the target weight in the long side direction of the previous sub-rectangle. The final weight of the current long side partition is the sum of the weights of each sub-rectangle from the start layer to the end layer of the current long side partition.

8. The method according to claim 6, characterized in that, Methods for partitioning the local refined spectral unit model into short-side partitions include: M1. Determine the short-side direction of the partitions in the local refined spectral unit model and their corresponding parameters, including the number of partitions in the short-side direction and the number of sub-rectangles in the short-side direction. M2. Under each long-side partition, determine the target weight of each short-side partition, and sort the sub-rectangles in each long-side partition in order according to the principle of short-side priority, and then determine the total number of sub-rectangles in the long-side partition. M3. Starting from the first sub-rectangle within the current long-side partition, perform short-side partitioning; M4. During the short-side partitioning process, determine whether the current short-side partition weight is greater than the corresponding short-side partition target weight. If so, proceed to step M5; If not, proceed to step M6; M5. Determine the ending sub-rectangle of the current short side partition and the final weight of the current short side partition, then proceed to step M7. M6. Overlay the next sub-rectangle onto the current short side partition and return to step M4; M7. Repeat steps S4 to M6 to divide each long side partition into corresponding short side partitions, and calculate the corresponding polygon range based on its starting and ending sub-rectangles to obtain the short side partitioning results.

9. The method according to claim 8, characterized in that, The starting layer of the current short side partition is the next sub-rectangle of the ending sub-rectangle of the previous short side partition; The ending sub-rectangle of the current short side partition is the sub-rectangle corresponding to the smaller of the absolute value of the difference between the current short side partition weight and the target weight of the short side partition, and the absolute value of the difference between the short side partition weight and the target weight of the short side partition corresponding to the previous sub-rectangle. The final weight of the current short side partition is the sum of the weights of all sub-rectangles from the beginning to the end of the current long side partition.

Images