Time parallel computing method, device, electronic device and storage medium of Biot model

Abstract

The present application relates to a time-parallel computing method, device, electronic device and storage medium for a Biot model. The time-parallel computing method comprises the following steps: S11, discretizing the Biot model to obtain a matrix expression of the Biot model; S12, designing a Schur complement type preprocessing matrix corresponding to the matrix after the Biot model is discretized; S13, performing an approximate replacement on the preprocessing matrix to obtain its approximate matrix; S14, solving the problem in a manner of first a time step cycle and then an iteration step cycle, using multiple processes corresponding to the number of iteration steps to perform calculations of all time steps on each iteration step, and each process only calculates the time step cycle once, thereby realizing parallel computing between iteration steps. Compared with existing algorithms, the time-parallel computing method of the present application is simple and computationally efficient.

Description

Technical Field

[0001] The present application relates to data processing technology, and more specifically, to a Biot model time parallel computing method, device, electronic device and storage medium. Background Art

[0002] The porous elastic model (i.e. Biot model) describes the interaction between the deformation of elastic porous media and the flow of viscous fluids. The model is widely used in biomechanics, earthquake engineering, environmental engineering, reservoir engineering and other fields. For example, in reservoir engineering, crude oil is continuously extracted, and the pore pressure in the soil will gradually decrease. The reduction in pore pressure in the soil will promote the movement of crude oil, causing the covering layer above the reservoir to gradually deform, causing the formation to collapse or sink. At this time, the Biot model can be used to simulate this process, thereby simulating and predicting this sedimentation process. Although this model has a very wide range of applications in many fields, it still has certain shortcomings when facing practical problem solving. At present, there are still great disadvantages in solving this model in actual engineering problems, which are mainly reflected in:

[0003] (1) The equation itself is relatively complex. The following formula (1) gives the expression of the Biot model:

[0004]

[0005] Among them, u represents the deformation, p represents the pressure, α represents the coefficient, f represents the external force or volume force, K represents the permeability coefficient, g is the source term, and t represents the time term. In addition, σ(u) represents the stress, and its expression is:

[0006] σ(u)=2με(u)+λdiv u I (2)

[0007]

[0008] Where λ, μ represent the Lame coefficients, and I represents the unit matrix. As can be seen from formula (1), the deformation of the porous elastic body is highly integrated with the pressure of the fluid in it, and it is difficult to solve them separately. In addition, a large number of studies have shown that when the standard finite element method or the central difference format on the same grid is used to solve the equation, the phenomenon of non-physical oscillation of pressure will occur, which greatly increases the difficulty of solving the problem.

[0009] (2) The solution area of ​​engineering problems is usually large and difficult to solve. Since engineering problems are relatively complex and the solution area is relatively large, in order to achieve accurate solutions to the problems, the number of grids is usually large, reaching tens of millions or even hundreds of millions. When the equation is discretely solved, the variables that need to be solved are three times the number of grid points. Such a large amount of calculation greatly increases the difficulty of solving and the efficiency of calculation.

[0010] (3) Engineering requires continuous iteration along the time step. In the actual application process, the Biot model also needs to be continuously iterated according to the time step, which means that the selection of the time step will also affect the calculation results. Too large a time step will also lead to a lack of calculation accuracy, resulting in deviations in the final results.

[0011] In order to overcome the difficulties in the application of the Biot model, a large number of researchers have conducted extensive research and proposed many algorithms for targeted modifications. In order to eliminate the pressure oscillation phenomenon in the process of solving the Biot model, the approximate space of the vector field and scalar field that satisfies the appropriate inf-sup condition is usually used. However, the numerical experiments of Gapar et al. show that even if the inf-sup condition is met, the difficulty of pressure oscillation may not be overcome. Only when some stability restrictions between the space and time discretization parameters are met, the vibration will disappear on a very fine grid. For this reason, Gapar et al. solved the physical phenomenon of pressure oscillation by adding a perturbation term (see: Aguilar G, Gaspar F, Lisbona F, et al. Numerical stabilization of Biot's consolidation model by a perturbation on the flow equation [J]. International journal for numerical methods in engineering, 2008, 75 (11): 1282-1300.)

[0012] When faced with actual engineering problems, the most time-consuming part of solving the Biot model is solving the large linear equations generated by discretization. Due to the large scale of the actual problem, each iteration of the discretized matrix takes a long time to solve, which makes the problem solving usually more time-consuming. In order to alleviate this problem, the common method is to design an effective preprocessing matrix to accelerate the convergence of the Krylov subspace method and to accelerate its solution based on a multi-grid framework.

[0013] All the algorithms mentioned above are based on the time-marching method, in which each time step is solved one by one in a sequential manner, so they do not allow parallelization of the time variable. However, as the scale of calculations increases, only accelerating the iteration of the matrix can no longer meet the needs of solving large-scale problems. At the same time, due to the emergence of large-scale parallel systems with thousands of threads, time-parallel integration methods have received widespread attention, and more and more scholars have begun to consider introducing concurrency along the time dimension. The most famous time parallelization methods include the space-time parallel full approximation method (see: Emmett M, Minion M. Toward an efficient parallel in time method for partialdifferential equations[J]. Communications in Applied Mathematics and Computational Science, 2012, 7(1): 105-132.), the multigrid reduction algorithm in time (MGRIT) (see: Falgout RD, Friedhoff S, Kolev TV, et al. Parallel time integration with multigrid[J]. SIAM Journal on Scientific Computing, 2014, 36(6): C635-C661.), the space-time multigrid method (see: Gander MJ, Vandewalle S. Analysis of the parareal time-parallel time-integration method[J]. SIAM Journal on Scientific Computing, 2007, 29(2): 556-578.), etc. However, due to the elliptic-parabolic hybrid structure of the Biot problem, the development of existing time parallel algorithms is not optimistic. There are still defects such as complex algorithms, complex proofs, and low computational efficiency. Summary of the invention

[0014] The technical problem to be solved by the present application is to provide a simple and computationally efficient time parallel calculation method and device for the Biot model, as well as an electronic device and a computer-readable storage medium for implementing the method, in view of the above-mentioned defects of the prior art.

[0015] In order to solve the technical problem, the present application proposes a time parallel calculation method of a Biot model in the first aspect, the method comprising the following steps:

[0016] S11, discretize the Biot model to obtain a matrix expression of the Biot model;

[0017] S12, design a Schur complement type preprocessing matrix corresponding to the matrix after the Biot model is discretized;

[0018] S13, performing approximate replacement on the preprocessing matrix to obtain its approximate matrix;

[0019] S14. Solve the problem in a time step cycle followed by an iteration step cycle. Use multiple processes corresponding to the number of iteration steps to perform calculations of all time steps on each iteration step, and each process only calculates the time step cycle once, thereby achieving parallel calculations between iteration steps.

[0020] According to an embodiment of the first aspect of the present application, the step S11 further includes:

[0021] Add a disturbance term to the Biot model to obtain the transformed Biot model;

[0022] The transformed Biot model is discretized to obtain its matrix expression.

[0023] According to an embodiment of the first aspect of the present application, the Biot model is discretized in step S11 using a finite element method, a finite difference method or a finite volume method.

[0024] According to an embodiment of the first aspect of the present application, step S12 further includes: based on the Schur complement theory, designing a corresponding Schur complement type preprocessing matrix for the matrix after the Biot model is discretized.

[0025] According to an embodiment of the first aspect of the present application, step S13 further includes: deleting the inverse terms in the Schur complement matrix to obtain an approximate matrix of the Schur complement matrix, and replacing the preprocessing matrix with the approximate matrix of the Schur complement matrix to obtain an approximate matrix of the preprocessing matrix.

[0026] According to an embodiment of the first aspect of the present application, the step S14 of solving the problem in a time step cycle followed by an iteration step cycle specifically includes:

[0027] Assign n processes. When the first process calculates the first time step, it sends the calculation result to the second process. The second process calculates the iteration of the second step. Meanwhile, the first process continues to calculate the second time step until the mth time step is calculated. When the second process calculates the first time step, it sends the calculation result to the third process. The third process further calculates the iteration of the third step. Meanwhile, the second process continues to calculate the second time step until the mth time step is calculated. And so on, parallel calculation between iteration steps is realized, where n is the number of iteration steps and m is the number of time step steps.

[0028] According to an embodiment of the first aspect of the present application, the iterative calculation in step S14 adopts GMRES or QMR iterative algorithm.

[0029] In order to solve the technical problem, the present application proposes a time parallel computing device of a Biot model in the second aspect, which is characterized by comprising:

[0030] Discrete module, used to discretize the Biot model and obtain the matrix expression of the Biot model;

[0031] A preprocessing module is used to design a Schur complement type preprocessing matrix corresponding to the matrix after the Biot model is discretized;

[0032] An approximate processing module, used for performing approximate replacement on the preprocessing matrix to obtain its approximate matrix;

[0033] The parallel computing module is used to solve the problem in a time step cycle followed by an iteration step cycle. Multiple processes corresponding to the number of iteration steps are used to perform calculations of all time steps on each iteration step, and each process only calculates the time step cycle once, thereby achieving parallel computing between iteration steps.

[0034] In order to solve the technical problem, the present application proposes an electronic device in the third aspect, including a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, the time parallel calculation method of the Biot model as described above is implemented.

[0035] In order to solve the technical problem, the present application proposes a computer-readable storage medium in the fourth aspect, which stores a computer program. When the computer program is executed by a processor, the time-parallel calculation method of the Biot model as described above is implemented.

[0036] The time parallel calculation method, device, electronic device and computer-readable storage medium of the Biot model of the present application have the following beneficial effects: according to the time parallel calculation method of the Biot model of the embodiment of the present application, the Biot model is discretized and the corresponding preprocessing matrix is ​​designed, and then multi-process concurrent iteration is performed along the time direction for the designed preprocessing matrix to realize the time parallel calculation of the Biot model. Compared with the existing algorithms, the present application can use the preprocessing matrix to speed up the calculation process and greatly improve the efficiency of the calculation; compared with the existing algorithms, the time parallel calculation method of the present application is simple, and there is no need for complex proof. It only needs to design the corresponding preprocessing matrix, and the iterative process of the calculation is adjusted to realize the parallelism between the iterative steps, especially when the number of time steps is much larger than the number of iterative steps, the parallel efficiency is higher. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The present application will be further described below with reference to the accompanying drawings and embodiments, in which:

[0038] Figure 1 is a flow chart of a time parallel calculation method of a Biot model according to an embodiment of the present application;

[0039] Figure 2 It is a schematic diagram of the iterative calculation process of the traditional algorithm;

[0040] Figure 3 It is a schematic diagram of the iterative calculation process of the flipping algorithm;

[0041] Figure 4 is a schematic diagram of a time parallel computing method according to an embodiment of the present application;

[0042] Figure 5 It is a schematic diagram of the logical structure of a time parallel computing device of a Biot model according to an embodiment of the present application;

[0043] Figure 6 It is a schematic diagram of the logical structure of an electronic device according to an embodiment of the present application. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not intended to limit the present application. In addition, the embodiments in the present application and the features in the embodiments may be combined with each other in the absence of conflict.

[0045] This application proposes a time-parallel computing method for the Biot model, which discretizes the Biot model and designs a corresponding preprocessing matrix, and then performs multi-process concurrent iterations along the time direction for the designed preprocessing matrix to achieve its time parallelism, greatly improving the computing efficiency. Figure 1 The flowchart of the method 10 for time parallel calculation of the Biot model according to one embodiment of the present application is shown. The method 10 is based on the Biot model with added disturbance terms proposed by Gaspar et al., and implements time parallel calculation of the Biot model by performing finite element discretization on it, using a reasonable preprocessing matrix, and flipping the time and iterating process. Figure 1 As shown, the time parallel calculation method 10 of the Biot model includes the following steps:

[0046] Step S11, discretize the Biot model to obtain a matrix expression of the Biot model.

[0047] Since the original Biot model has a pressure oscillation problem, in order to overcome this problem, this application adopts the solution of Gaspar et al., adds a disturbance term to the original Biot model, and the expression of the converted two-field Biot model is as follows:

[0048]

[0049] Among them, β(Δp) t is the added disturbance term, where β = h 2 / (4(λ+2μ)), h is the size of the grid, and the meanings of the other variables remain unchanged, namely: u represents the deformation, p represents the pressure, α represents the coefficient, f represents the external force or volume force, K represents the permeability coefficient, g is the source term, t represents the time term, and σ(u) represents the stress.

[0050] By adding boundary conditions, the converted Biot model can be discretized. The Biot model can be discretized by using various existing discretization methods, such as finite element method, finite difference method, finite volume method, etc., which will not be described in detail here. This embodiment is based on the finite element method, by using backward Euler difference for the time term, and assuming that all boundary conditions are Dirichlet boundary conditions. The discretization process is as follows: Let

[0051] For the mth time instant, m ≥ 1, for any Make

[0052]

[0053]

[0054] Where τ is the time step, are the function spaces of deformation and pressure, v and q are test functions, and b is the function operator. After discretization using P1-P1 elements, the following linear equations can be obtained:

[0055]

[0056] in,

[0057]

[0058]

[0059]

[0060] F:=(f,v h ),

[0061] G: = τ(g, q h )

[0062] P1-P1 is a linear element, which is already well known to those skilled in the art, so it will not be described in detail here. m , P m With the known quantity U m-1 , P m-1 , F, and G, so we only need to solve the above thread equations (7) at each time step to get the true solution at the final moment.

[0063] Step S12, designing a Schur complement type preprocessing matrix corresponding to the matrix after the Biot model is discretized. In a specific embodiment, based on the Schur complement theory, a corresponding Schur complement preprocessing matrix can be designed for the matrix after the Biot model is discretized.

[0064] Specifically, solving the above formula (7) is equivalent to solving the following equation system shown in formula (8) at each time moment:

[0065]

[0066] By comparing formula (7), we can see that:

[0067]

[0068]

[0069] So, solve It is also equivalent to solving like If the eigenvalue of is greater than 1, then the above equation (7) is also equivalent to:

[0070] Xn+1 =X n +P -1 r n (9)

[0071] in, At this time, the initial value X can be given 0 Through continuous iteration, we can get the corresponding accuracy X, and thus get the numerical solution of the equation. Here P is the preprocessing matrix, also known as the preconditioner. Obviously, this problem is a saddle point problem. According to the Schur theory, the Schur complement matrix S of the saddle point problem can be obtained. p The expression is:

[0072] S p =(τK+β)C+αBA -1 B T (10)

[0073] Then, when the preprocessing matrix is:

[0074]

[0075] Theoretically, it only takes two iterations (n=2 in formula (9)) to converge to the true solution. Similarly, when the preprocessing matrix is:

[0076]

[0077] Similarly, it is theoretically proved that after the preprocessing matrix is ​​processed, there are four fixed condition numbers, which can also greatly improve the solution speed. The above two preprocessing matrices are simple in form and have clear condition numbers, which are important foundations for the design of preprocessing matrices in numerical calculations.

[0078] Step S13, performing approximate replacement on the preprocessing matrix to obtain its approximate matrix.

[0079] It is obvious to a person skilled in the art that S in formulas (11) and (12) is p It contains an inverse matrix. The process of matrix inversion is extremely cumbersome and time-consuming. At this time, the preprocessing matrix P1 or P2 cannot be used directly, so it is necessary to find a suitable approximation to replace S p A simple method is to directly delete the inverse term to obtain S p The approximate matrix Then use S p The preprocessing matrix is ​​replaced by the approximate matrix, and the preprocessing matrix becomes:

[0080]

[0081]

[0082] In addition, the present application may also adopt other more effective approximation methods, which are existing technologies well known to ordinary technicians in this field and will not be described in detail here.

[0083] Step S14, solving is performed in a manner of first a time step cycle and then an iteration step cycle, using multiple processes corresponding to the number of iteration steps to perform calculations of all time steps on each iteration step, and each process only calculates the time step cycle once, thereby achieving parallel calculations between iteration steps.

[0084] It is troublesome to calculate the number of iterations of the preprocessing matrix after approximate replacement through theoretical calculation. We can verify the number of iterations by using a smaller matrix. Assuming that the number of iterations after verification is n, the number of steps of the final time step is m, i represents the time step cycle, and j represents the iteration step cycle, then the traditional method for solving the Biot model can be expressed as the following algorithm:

[0085] Algorithm 1: Traditional algorithm

[0086]

[0087] It can be seen from the above algorithm 1 that parallelism cannot be achieved due to the dependencies between time items. Figure 2 The calculation process of Algorithm 1 is vividly demonstrated. Figure 2 It can be seen that the calculation process of the traditional algorithm is to first converge to the exact solution at each time moment, and then perform the calculation at the next time moment.

[0088] In order to achieve parallelism, this application flips the calculation process of the iterative algorithm. After the flip, i is used to represent the time step cycle and j is used to represent the iteration step cycle. The algorithm is expressed as follows:

[0089] Algorithm 2: Flipping Algorithm

[0090]

[0091] Figure 3 The calculation process of Algorithm 2 is vividly demonstrated. Figure 3 As can be seen from the figure, the calculation process of the flipping algorithm is to first calculate all time steps in each iteration step, and then move forward in the iteration step.

[0092] Therefore, this application uses n processes corresponding to the number of iteration steps to perform calculations of all time steps on each iteration step, realizing multi-process concurrent iteration, and each process only calculates one time step cycle, thereby realizing time parallel calculation of the Biot model. After the iterative algorithm is flipped, the time can be calculated from time 0 to the last time mτ on each iteration step. At this time, n processes can be allocated. After the first process calculates the first time step, the calculation result is sent to the second process. The second process calculates the iteration of the second step, and the first process continues to calculate the second time step until the mth time step is calculated; after the second process calculates the first time step, the calculation result is sent to the third process. The third process further calculates the iteration of the third step, and the second process continues to calculate the second time step until the mth time step is calculated; and so on, to realize parallel calculation between iteration steps. Assuming that only 8 steps are needed to complete the convergence of each time step, Figure 4 A schematic diagram of the time parallel computing method according to the present application is shown, where P1 to P8 represent processes, and iterative computing can adopt different existing iterative algorithms such as GMRES (generalized minimum residual method) or QMR (quasi minimum residual method).

[0093] The time parallel calculation method of the Biot model in the above embodiment of the present application flips the traditional method of first iterative step loop and then time step loop into the method of first time step loop and then iterative step loop to solve, so as to realize parallel calculation between iterative steps. It can be seen from the above description that the method has higher parallel efficiency when the number of time step steps m is much larger than the number of iterative steps n. If the preprocessing matrix chooses to solve the matrix itself, time parallelism cannot be realized at this time because the number of iterative steps n=1.

[0094] The time parallel calculation method of the Biot model in the above embodiment of the present application only needs to make a small change to the existing iterative algorithm to achieve parallelism in the time dimension. Since parallelism can be achieved in the process of iterating using the preprocessing matrix, the difference between iterating one step and iterating multiple steps is greatly reduced. When the resources of the cluster are sufficient, the number of iterations of the designed preprocessing matrix in each time step no longer becomes a factor affecting the total time, which also reduces the design pressure of the preprocessing matrix to a certain extent.

[0095] Based on the time-parallel computing method of the Biot model introduced above, the present application also proposes a time-parallel computing device of the Biot model. Figure 5 FIG. 2 shows a schematic diagram of the logical structure of a time parallel computing device 20 of a Biot model according to an embodiment of the present application. Figure 5As shown, the time parallel computing device 20 includes a discrete module 21, a preprocessing module 22, an approximate processing module 23 and a parallel computing module 24. Among them, the discrete module 21 is used to discretize the Biot model to obtain the matrix expression of the Biot model. The preprocessing module 22 is used to design a Schur complement type preprocessing matrix corresponding to the matrix after the Biot model is discretized. The approximate processing module 23 is used to perform an approximate replacement on the preprocessing matrix to obtain its approximate matrix. The parallel computing module 24 is used to solve in a manner of first a time step cycle and then an iteration step cycle, using multiple processes corresponding to the number of iteration steps to perform calculations of all time steps on each iteration step, and each process only calculates the time step cycle once, thereby realizing parallel computing between iteration steps. For the specific implementation of each module, please refer to the specific description of each step of the time parallel computing method 10 for the Biot model mentioned above, which will not be repeated here.

[0096] Based on the aforementioned Biot model time parallel computing method 10 of the present application, the present application also proposes an electronic device 30. Figure 6 As shown, the electronic device 30 includes a processor 31 and a memory 32, and the processor 31 and the memory 32 are in communication connection. The memory 32 stores a computer program, and when the computer program is executed by the processor 31, the processor 31 implements the time parallel calculation method 10 of the Biot model of the aforementioned embodiment of the present application.

[0097] The present application also proposes a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the time-parallel calculation method 10 of the Biot model of the aforementioned embodiment of the present application.

[0098] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims

1. A time parallel computing method for a Biot model, characterized in that: The method comprises the following steps: S11, discretize the Biot model to obtain a matrix expression of the Biot model; S12, design a Schur complement type preprocessing matrix corresponding to the matrix after the Biot model is discretized; S13, performing approximate replacement on the Schur complement type preprocessing matrix to obtain its approximate matrix; S14, solving the problem in a manner of first a time step cycle and then an iteration step cycle, using a plurality of processes corresponding to the number of iteration steps to respectively perform calculations of all time steps on each iteration step, and each process only calculates the time step cycle once, thereby realizing parallel calculations between iteration steps; Wherein, the step S12 further comprises: based on the Schur complement theory, designing a corresponding Schur complement type preprocessing matrix for the matrix after the Biot model is discretized; The step S13 further comprises: deleting the inverse term of the Shure complement matrix in the Shure complement type preprocessing matrix to obtain an approximate matrix of the Shure complement matrix, and replacing the Shure complement type preprocessing matrix with the approximate matrix of the Shure complement matrix to obtain an approximate matrix of the Shure complement type preprocessing matrix; The step S14 of solving the problem in a time step cycle followed by an iteration step cycle specifically includes: Assign n processes. When the first process calculates the first time step, it sends the calculation result to the second process. The second process calculates the iteration of the second step. Meanwhile, the first process continues to calculate the second time step until the mth time step is calculated. When the second process calculates the first time step, it sends the calculation result to the third process. The third process further calculates the iteration of the third step. Meanwhile, the second process continues to calculate the second time step until the mth time step is calculated. And so on, parallel calculation between iteration steps is realized, where n is the number of iteration steps and m is the number of time step steps.

2. The time parallel computing method of the Biot model according to claim 1, characterized in that: The step S11 further comprises: Add a disturbance term to the Biot model to obtain the transformed Biot model; The transformed Biot model is discretized to obtain its matrix expression.

3. The time parallel computing method of the Biot model according to claim 1, characterized in that: In the step S11, the Biot model is discretized by using a finite element method, a finite difference method or a finite volume method.

4. The time parallel computing method of the Biot model according to claim 1, characterized in that: The iterative calculation in step S14 adopts GMRES or QMR iterative algorithm.

5. A time parallel computing device for a Biot model, characterized in that: include: Discrete module, used to discretize the Biot model and obtain the matrix expression of the Biot model; A preprocessing module is used to design a Schur complement type preprocessing matrix corresponding to the matrix after the Biot model is discretized; An approximate processing module, used for performing approximate replacement on the Schur complement type preprocessing matrix to obtain its approximate matrix; The parallel computing module is used to solve the problem in a time step cycle followed by an iteration step cycle. Multiple processes corresponding to the number of iteration steps are used to perform calculations of all time steps on each iteration step, and each process only calculates the time step cycle once, thereby realizing parallel computing between iteration steps. The preprocessing module is further used to design a corresponding Schur complement type preprocessing matrix for the matrix discretized by the Biot model based on the Schur complement theory; The approximate processing module is further used to delete the inverse term of the Shure complement matrix in the Shure complement type preprocessing matrix to obtain an approximate matrix of the Shure complement matrix, and replace the Shure complement type preprocessing matrix with the approximate matrix of the Shure complement matrix to obtain an approximate matrix of the Shure complement type preprocessing matrix; The parallel computing module solves the problem in a manner of first time step cycle and then iteration step cycle, specifically including: Assign n processes. When the first process calculates the first time step, it sends the calculation result to the second process. The second process calculates the iteration of the second step. Meanwhile, the first process continues to calculate the second time step until the mth time step is calculated. When the second process calculates the first time step, it sends the calculation result to the third process. The third process further calculates the iteration of the third step. Meanwhile, the second process continues to calculate the second time step until the mth time step is calculated. And so on, parallel calculation between iteration steps is realized, where n is the number of iteration steps and m is the number of time step steps.

6. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, the time parallel calculation method of the Biot model according to any one of claims 1 to 4 is implemented.

7. A computer-readable storage medium, characterized in that: A computer program is stored, and when the computer program is executed by a processor, the time parallel calculation method of the Biot model according to any one of claims 1 to 4 is implemented.

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