Solid Simulation Solving Method and Device Integrating Automatic Differentiation and Node Block Descent

Abstract

The present invention discloses a solid simulation solution method and device that integrates automatic differentiation and node block descent. The solid simulation model includes a mesh model, a material model, and boundary conditions of a solid object; a simulation solver that integrates automatic differentiation and node block descent is established, and the simulation solver is used to perform simulation calculations on the configured solid simulation model to obtain the node coordinates of the corresponding mesh model after the solid object is deformed by motion. The present invention integrates automatic differentiation and node block descent solution processing, reduces the solver R&D cost and the material model secondary development cost, improves the overall simulation solution speed, and can circumvent the numerical calculation defects of traditional finite element solvers, thereby improving the stability and robustness of the simulation calculation.

Description

Technical Field

[0001] The present invention mainly belongs to the field of physical simulation, involving the intersection of multiple disciplines such as computational mechanics, computer graphics, and artificial intelligence. Specifically, it relates to a solid simulation solution method and device that integrates automatic differentiation and node block descent, and is mainly used in traditional industrial and medical simulation technology fields. Background Art

[0002] Finite element simulation is currently the most widely used technology in solid structure simulation. The basic idea of this method is to discretize the continuous physical governing equations in space and time based on basic units of specific spatial geometry (such as 2D triangles or 3D tetrahedrons), construct large-scale linear systems, and finally perform numerical calculations using computers.

[0003] After years of development, the application of finite element simulation in the engineering field has achieved remarkable results. However, its inherent defects cannot well meet the development of digital industry, digital medicine and other fields. In particular, the disadvantages it has always shown in solving complex physical scenarios (such as timeliness and stability issues) and the closed nature of the inherent algorithm framework (which cannot be integrated with the machine learning framework) have greatly restricted technological breakthroughs in related fields.

[0004] Whether it is traditional computational solid mechanics or computer graphics deformable body simulation, it is a forward solution idea, which converts the solution of the equilibrium differential equation under known initial and boundary conditions into a potential energy variation problem or a potential energy minimization problem, and realizes the solution of the object's motion deformation by seeking the minimum state of solid potential energy.

[0005] The above technical route has the following defects:

[0006] (1) The derivation process of the strain energy density function is manual differentiation, which is time-consuming, complicated and error-prone. In addition, each new material constitutive model needs to be re-derived by differential operation and programming, which has poor versatility and flexibility.

[0007] (2) Traditional finite element solutions involve large-scale models. The assembly of global stiffness matrices and the solution of linear systems are very computer resource-intensive processes, which seriously affect the timeliness of actual engineering simulations.

[0008] (3) The properties of the global stiffness matrix (such as positive definiteness, singularity, condition number, etc.) directly determine the convergence of the Newton iteration and the solution effect of the global linear system. In complex situations, it is easy to produce an ill-conditioned stiffness matrix, which in turn easily leads to the failure of the simulation. Summary of the Invention

[0009] In order to solve the problems existing in the background technology, the present invention provides a solid simulation solution method, device and system that integrates automatic differentiation and node block descent.

[0010] The present invention mainly addresses three problems in the background technology, and provides better solid simulation algorithm processing based on the fusion of automatic differentiation and vertex block descent, making the development and engineering application of simulation solvers based on the underlying algorithm by computers efficient and easy to use.

[0011] The solid simulation algorithm framework proposed in this invention is based on the integration of two types of underlying technologies (automatic differentiation technology and node block descent solution technology). It aims to use their technical advantages to give more technical capabilities and practical value to the design, development and application of solid simulation solvers, focusing on improving the computational performance of solid finite element simulation solvers (including timeliness, convergence and stability) and reducing development costs (such as internal force and stiffness calculation module development, material model secondary development, etc.).

[0012] If the algorithm framework provided by the present invention is used to design a solid simulation solver, it can not only achieve the same engineering solution capabilities as traditional structural finite element simulation solvers, and be applicable to scenarios such as static and dynamic simulation of structures, but also have more advantages in computing performance and development costs.

[0013] The technical solution adopted in the present invention is:

[0014] The solid simulation of the present invention is a simulation process for the mechanics of a solid object, where the solid object refers to an object with physical solid properties inside and is deformable, such as a metal object, a cell wall, etc.

[0015] 1. A solid simulation solution method integrating automatic differentiation and node block descent, the method specifically comprising:

[0016] 1) Configure the solid simulation model in the computer:

[0017] The solid simulation model includes a mesh model, a material model and boundary conditions of the solid object;

[0018] Configuring a solid simulation model involves assembling a mesh model, selecting a material model and setting its material parameters, and applying boundary and load conditions. The mesh model is a spatial geometric discretization model of the solid object, the material model is the elastic constitutive model of the solid object (required to be expressed as a strain energy density function), and the boundary conditions are the external constraints or loads applied to the solid object.

[0019] This step is the primary task of simulation pre-processing, aiming to obtain model data that can be used by the simulation solver to perform calculations. In addition to selecting the material model already developed by the simulation solver, users can also directly enter the material model analytical expression to implement more customized material models.

[0020] 2) Perform simulation calculations on a computer:

[0021] In a computer, a simulation solver integrating automatic differentiation and node block descent is established, and the configured solid simulation model is simulated and calculated using the simulation solver to obtain the node coordinates of the mesh model after the solid object moves and deforms, that is, the position and shape changes of the simulated solid object;

[0022] The core technical logic of the simulation solver calculation process is directly related to the innovative technical solution introduced in the present invention, mainly involving automatic differentiation calculation and node block descent processing. The following text will discuss in detail the fusion calculation framework and process based on the solution technical logic of the simulation solver.

[0023] The fusion technology solution provided by the present invention reduces the development cost of the simulation solver and improves the solver computing performance. Compared with the traditional finite element solver, it has obvious advantages in material model development and secondary development, computing speed, stability and convergence.

[0024] The simulation solver developed based on the technology of the present invention benefits from the technical advantages of automatic differentiation fusion processing. Users only need to input the analytical expression of the custom material model to complete the "secondary development" of different material models. In essence, no code development is required. Moreover, the material model is implemented through the automatic differentiation module, and there is no need for R&D personnel to manually develop the corresponding code. If it is a traditional finite element simulation solver, users can only perform secondary development of the material model based on the interface provided by the simulation solver according to the specified programming logic, and the strain energy function also needs to be manually derived before secondary development. And for different material models, R&D personnel need to develop corresponding code.

[0025] 3) Output:

[0026] The node coordinates of all nodes of the mesh model can be used as the basic data of the deformation field to perform conventional mechanical analysis to obtain mechanical parameters, and finally the mechanical parameters can be used for visualization and simulation prediction of solid modes.

[0027] The mechanical parameters mainly include displacement, stress, strain, etc. This step mainly belongs to simulation post-processing. The visualization effect and quantitative data of post-processing can be used to simulate and predict the release effect of TAVI stent implantation.

[0028] The grid model refers to a geometric topology model in a computer that is composed of grid meshes as basic units, such as a triangle grid model or a tetrahedron grid model.

[0029] The material model refers to an elastic constitutive model of a solid material represented by a strain energy density function in continuum mechanics, such as Saint Venant–Kirchhoff, Neo-Hookean, Mooney–Rivlin, etc.

[0030] The boundary conditions refer to the displacement constraints or load conditions on solid objects. In the simulation model, the displacement constraints are to apply a specific displacement amount (such as how many meters to move) on one or more nodes of the grid model, and the load conditions are to apply a specific load amount (such as how many Newtons of force) on one or more nodes of the grid model.

[0031] The solid simulation model is any deformable solid object model, and may be a solid object model formed by the association of a medical device and biological tissue, such as a model formed by a transcatheter aortic valve implantation (TAVI) stent and an aortic valve.

[0032] The above method processing process mainly demonstrates the connection between the actual simulation process and the simulation technology of the present invention, as well as the role and advantages of the present invention in actual simulation processes. Next, using the algorithmic logic of the simulation solver in the above process, we will explain how the fusion method of automatic differentiation and node block descent is implemented in the simulation solver algorithm.

[0033] In step 2), the core processing logic of the simulation solver is as follows:

[0034] The simulation solver divides the continuous motion deformation process of the mesh model of the solid object over time into discontinuous states at different moments with equal time intervals for simulation processing. Each moment is regarded as a time step, and the same logical solution process is executed on the mesh model under the limitation of the material model and boundary conditions. The different moments of the time sequence are iteratively processed to obtain the mesh model node coordinates at the end of the entire duration of the continuous motion deformation process.

[0035] The grid model is mainly composed of nodes and grids. Each node has spatial position information, and the spatial position information consists of the coordinate x of the node.

[0036] The simulation solver is processed according to the following process:

[0037] S1. Start the current time step t: input the node coordinates x(t-△t) and node velocity v(t-△t) at the time t-△t of the previous time step;

[0038] S2, calculate the initial iteration coordinate x of the node at the current time step t according to the node coordinate x(t-△t) and the node velocity v(t-△t) t0 :

[0039] S3. Perform iterative loop processing for the current time step:

[0040] S31, start the current iteration step i, use the node coordinate x of the previous iteration step i-1 t(i-1) Calculate the internal force and stiffness information, and then solve the linear system based on the internal force and stiffness information. Specifically, traverse each node in the following way:

[0041] S31.1. Calculate the internal force vector f at each node n n and the stiffness matrix k n :

[0042] Each node is shared by e grids. Traverse all e grids that share the node and use the material model to calculate the strain energy of each grid for each node coordinate x by automatic differentiation. t(i-1) The derivative of the material model is to use the automatic differentiation process to process the node iteration coordinate x of each node in the current i-th iteration step. ti Calculate and process to obtain the internal force vector f of each grid on the node e and the stiffness matrix k e , and then assemble the internal force vector f of all e grids corresponding to the node according to the following formula e and the stiffness matrix k e Get the internal force vector F of node n n and the stiffness matrix K n :

[0043] F n =∑ e f e , K n =∑ e k e

[0044] S31.2, then according to the boundary conditions the internal force vector F n and the stiffness matrix K n Perform correction processing to obtain the corrected internal force vector F n ' and stiffness matrix K n ', then according to the modified internal force vector F n ' and stiffness matrix K n 'Calculate the coordinate increment △x of the current node n using the linear system according to the following formula n :

[0045] △x n =K n ' -1 ×F n '

[0046] S32. Merge the coordinate increments of all nodes n to obtain the coordinate increment vector of the global system. Update the global coordinates of the current iteration step i according to the coordinate increment vector of the global system according to the following formula:

[0047] x t(i) = x t(i-1) +△x

[0048] △x=(△x 0、 △x1,…,△x n )

[0049] Among them, △x is the global coordinate increment vector;

[0050] Here, the coordinate increment of each node is △x n Merging them sequentially can be written as a large vector △x (described as the global coordinate increment vector). The above addition operation uses the global coordinate vector x of the previous iteration step. t(i-1) Add the global coordinate increment vector △x to get the global coordinate vector x of the current iteration step t(i) If a 3D model has only 4 nodes, then the coordinate vector of each node is a 3*1 vector. If the vectors of these 4 nodes are combined into a large global coordinate vector representation, it becomes a 12*1 vector.

[0051] S33. Make a convergence judgment and calculate the infinite norm of the global coordinate increment vector △x‖△x‖ ∞ , and then judge and process it as follows:

[0052] If ‖△x‖ ∞ >ε and i max , then the global coordinate x of the current iteration step i is obtained t(i) Return to S31 to start the loop processing of the next iteration step;

[0053] If ‖△x‖ ∞ ≤ε and i≤i max , the iterative calculation converges and proceeds to step S4;

[0054] If ‖△x‖ ∞ >ε and i=i max , the calculation does not converge, the processing is stopped directly, and an error message is given;

[0055] The above ε represents the preset convergence tolerance, and imax represents the upper limit of the number of iteration cycles;

[0056] S4, the global coordinate x obtained at the last iteration of S3 tI Update the node coordinates of the current time step according to the formula x(t)=x t(I) ​, proceed to the next step of the current time step;

[0057] S5. End the current time step: Update the node velocity of the current step according to the following formula:

[0058] v(t)=(x(t)-x(t-△t)) / △t

[0059] Finally, the node coordinates x(t) and node velocity v(t) of the current time step are output.

[0060] All nodes are traversed to obtain the node coordinates and node velocity of each node, and the node coordinates and node velocities of all nodes constitute the deformation field.

[0061] The resulting nodal coordinates x(t) are the nodal coordinates of the mesh model corresponding to the solid object's deformation at the current time t. These nodal coordinates can be used for visualization (such as rendering the mesh model's shape at the current time) or for related mechanical analysis.

[0062] In step S2, the estimation process is performed according to the following formula:

[0063] x t0 = x(t-△t)+ v(t-△t)×△t +△t 2 ×a ext

[0064] Among them, △t is the time step, that is, the interval between adjacent moments; x(t-△t) represents the node coordinates at the moment t-△t of the previous time step, v(t-△t) represents the node velocity at the moment t-△t of the previous time step, and a ext Represents the external acceleration of the continuous motion deformation process of the solid object simulation; x t0 Represents the initial iteration coordinates of the node at the current time step t.

[0065] 2. A computer device comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the above method when executing the computer program.

[0066] 3. A computer-readable storage medium having a computer program stored thereon, wherein the computer program implements the steps of the above method when executed by a processor.

[0067] The advantages and features of the fusion framework are further explained here. For traditional finite element technology, whether it is the development of a simulation solver or the subsequent secondary development, a lot of time and cost are required in the work related to formula derivation and code development. The present invention calculates the internal force and stiffness in the above step S31 by automatic differentiation processing, which is one of the main differences from the traditional finite element algorithm framework. In this way, in the initial development of the simulation solver or the secondary development of subsequent materials, there is no need to worry about any derivative formula derivation and related code development, which greatly reduces the difficulty of research and development and saves program development costs.

[0068] In terms of solution, the above step S31 adopts the node block descent solution idea, which is a local linear system solution starting from the node. For this local small-scale linear system, the direct inversion analytical method can be used to calculate it, that is, △x n =K n ' -1 ×F n Compared with the traditional finite element algorithm that constructs a global large-scale linear system solution from the unit, it completely avoids the numerical problems brought about by the solution of large-scale linear systems, such as convergence and stability problems, and also has more advantages in computational efficiency and parallel computing performance.

[0069] In a specific implementation, the automatic differentiation module under the algorithm framework of the present invention is directly implemented using open source tools, such as TensorFlow, Pytorch, Tai Chi language, etc.

[0070] The present invention utilizes the advantages of automatic differentiation to reduce the threshold and cost of research and development of solid simulation solvers and related developments.

[0071] As described in the background art, when faced with complex problems, traditional solid finite element simulation technology has computational performance issues, such as timeliness, convergence, and stability. From the perspective of overcoming these technical shortcomings, the solution of the present invention can provide a possibility for improving the computational performance of solid simulation solvers from the underlying algorithm level by utilizing the advantages of node block descent. It can not only ensure the reduction of global energy at a rate comparable to Newton's method, but also help improve the positivity and condition number of the Hessian matrix, ultimately achieving the effect of improving the convergence and stability of the algorithm.

[0072] The present invention may include technical solutions according to the relationship from application layer to algorithm layer to principle layer.

[0073] First, from the application level, the relationship and role of the method of the present invention in the actual simulation process, as well as the advantages of automatic differentiation and node block descent solution, are introduced.

[0074] Starting from the algorithm logic of the simulation solver, the fusion calculation framework based on automatic differentiation and node block descent is the most important part of the technical solution of the present invention. The calculation framework can be used as the basic framework for the development of actual simulation solver algorithms.

[0075] Finally, starting from the basic principles, automatic differentiation and its practical processing, the basic formulas of node block descent and the corresponding solution steps of each formula are introduced.

[0076] The simulation solution processing based on automatic differentiation and node block descent fusion provided by the present invention has the following advantages and beneficial effects:

[0077] 1. The present invention adopts automatic differentiation processing to improve the efficiency of forward simulation analysis algorithm development and the versatility and flexibility of simulation solver development.

[0078] 2. The present invention also uses node block descent solving technology to improve the computational efficiency and performance of the solid simulation solver.

[0079] 3. The overall solution of the present invention is applicable to parallel technologies (such as shader algorithms, CUDA programming, etc.), which improves the solution speed of the overall simulation, and can avoid the numerical calculation defects of the global algorithm in traditional finite element methods, thereby improving the stability and robustness of the simulation calculation.

[0080] In addition, the present invention can further integrate differentiable programming technology to improve the training and optimization speed of artificial intelligence models, providing more possibilities for the deep integration of simulation and artificial intelligence. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 is a flow chart of the method of the present invention;

[0082] Figure 2 It is a detailed flow chart of the simulation solver of the present invention;

[0083] Figure 3 Schematic diagram of the cloth simulation effect based on the present invention. DETAILED DESCRIPTION

[0084] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0085] like Figure 1 As shown, the embodiments of the present invention are as follows.

[0086] Example 1:

[0087] In the specific implementation, a simulation scenario of a transcatheter aortic valve implantation (TAVI) device in the medical field is taken as an example. If a solid simulation solver is customized and developed based on the technology of the present invention for this physical scenario, the actual simulation process is basically as follows:

[0088] 1) Configure the solid simulation model in the computer:

[0089] Configuring a solid simulation model involves assembling mesh models of the TAVI stent and aortic valve, selecting a material model and setting its material parameters, and applying boundary and load conditions. In this embodiment, the mesh models of the TAVI stent and aortic valve utilize tetrahedral meshes. The material model for the TAVI stent is a linear elastic model, while the material model for the aortic valve is a Neo-Hookean model. Fixed displacement constraints are applied to the ends of the aortic valve model (with the position value set to 0).

[0090] The grid model is mainly composed of nodes and grids. Each corner point of the grid serves as a node. Adjacent grids share nodes. The node information of each node includes the node's coordinate x and may also include the node's velocity v.

[0091] 2) Perform simulation calculations on a computer:

[0092] The simulation calculations are primarily performed using a simulation solver to simulate the deployment of a TAVI stent on a configured solid simulation model. A simulation solver integrating automatic differentiation and node block descent is established on a computer. This solver is used to simulate the deployment of a TAVI stent on the configured solid simulation model, obtaining a deformation field for the solid object. This simulates the deployment of the TAVI stent within a blood vessel and its fit to the aortic valve.

[0093] like Figure 2 As shown, the core processing logic of the simulation solver is as follows:

[0094] Solid structure simulation solvers employ a spatial and temporal discretization approach to solving physical problems. Spatial discretization corresponds to the mesh model objects used in the actual solution process; temporal discretization involves dividing the continuous motion and deformation of an object over time into discrete states at a finite number of moments (also referred to as time steps t, as used herein). The time intervals between adjacent moments are either equal (also referred to as time step △t, as used herein herein) or unequal.

[0095] At each discrete time step, the simulation solver will execute the same logical solution process on the mesh model. The solution process at each time step is the core algorithm logic stated here.

[0096] Here we explain some of the symbols discussed later. The node coordinates and node velocities of the grid model are represented by x and v respectively, and the internal force vector and stiffness matrix are represented by f and stiffness matrix K respectively.

[0097] The simulation solver divides the continuous motion deformation process of the mesh model of the solid objects of the TAVI stent and the aortic valve into discontinuous states at different moments with equal time intervals for simulation processing. Each moment is used as a time step to perform the same logical solution process on the mesh model using the material model and boundary conditions, and iteratively and progressively processes the different moments in the time sequence to obtain the final node coordinates of the entire continuous motion deformation process. The node coordinates of all nodes constitute a deformation model / deformation field.

[0098] Each time step in the simulation solver is processed according to the following process (each time step contains an iteration step). For the fusion calculation framework of automatic differentiation and node block descent, the solution process and related descriptions for each time step are as follows:

[0099] S1, start time t of the current time step: input the node information of the previous time step at time t-△t, including node coordinates x(t-△t), node velocity v(t-△t), etc., and estimate the node information to obtain the initial iteration coordinate x of the node in the current time step. t0 ;

[0100] For any deformable solid, the following formula is used for estimation:

[0101] x t0 = x(t-△t)+ v(t-△t)×△t +△t 2 ×a ext

[0102] Among them, △t is the time step, that is, the interval between adjacent moments; x(t-△t) represents the node coordinates at time t of the previous time step, △t is the time step, v(t-△t) represents the node velocity at time t of the previous time step, a ext Represents the external acceleration (such as gravity acceleration) during the continuous motion deformation process of the solid object simulation; x t0 Represents the initial node iteration coordinates at time t+△t of the previous time step;

[0103] At the initial first time step, the node coordinates x(t) and initial node velocities v(t) of the nodes stored in the original mesh model (the initial node velocities can be directly defined when configuring the simulation model, such as setting all initial node velocities to 0) are used as the node information at time t of the previous time step.

[0104] S2. Perform iterative loop processing for the current time step:

[0105] S21, start the current iteration step (i+1 iteration step), use the node global coordinate x of the previous i-1 iteration step tiCalculate the internal force and stiffness information, and then solve the linear system based on the internal force and stiffness information. Specifically, traverse each node in the following way:

[0106] Specifically, the following calculations are performed by traversing all nodes in parallel:

[0107] S21.1. In the current iteration step, calculate the internal force vector f of the current node n. n and the stiffness matrix k n :

[0108] Specifically, each node is shared by e grids, e is greater than or equal to 1, and all e grids that share the current node are traversed. The material model is used through the automatic differentiation processing module (developed based on the open source module) to calculate the strain energy of each grid for each node coordinate x t(i-1) The derivative of each grid is used to obtain the internal force vector f of the current node e and the stiffness matrix k e , and then assemble the internal force vector f of all e grids corresponding to the current node according to the following formula e and the stiffness matrix k e Get the internal force vector F of the current node n n and the stiffness matrix K n :

[0109] F n =∑ e f e , K n =∑ e k e

[0110] In the specific implementation, for 3D problems, F n is a 3*1 vector, K n It is a 3*3 symmetrical square matrix.

[0111] S21.2, then according to the boundary conditions the internal force vector F n and the stiffness matrix K n Perform correction processing to obtain the corrected internal force vector F n ' and stiffness matrix K n ', then according to the modified internal force vector F n ' and stiffness matrix K n 'Use the linear system to calculate the coordinate increment △x of the current node n in the current iteration step according to the following formula n :

[0112] △x n =K n ' -1 ×F n '

[0113] The above coordinate increment calculation for each node is solved by utilizing a local small-scale linear system and is calculated by a direct inversion analytical method.

[0114] S22. Construct a global coordinate increment vector from the coordinate increments of all nodes n. Update the global coordinates of the current node n at the next iteration step i+1 in the current time step according to the global coordinate increment vector using the following formula:

[0115] x t(i) = x t(i-1) +△x

[0116] △x=(△x0、△x1、…、△x n )

[0117] Among them, △x is the global coordinate increment vector, which is assembled by merging the coordinate increments △x of all nodes. n get;

[0118] S23. Perform convergence judgment, pre-set the convergence tolerance ε, the maximum time step is imax, and calculate the infinite norm ‖△x‖ of the global coordinate increment vector △x ∞ , and then judge and process it in the following way, the following three situations will occur:

[0119] If ‖△x‖ ∞ >ε and i max , then the global coordinate x of the next iteration step is obtained t(i+1) As the global coordinate x of the node in the current iteration step ti , return to S21 and start the loop processing of the next iteration step;

[0120] If ‖△x‖ ∞ ≤ε and i≤i max , the iterative calculation converges and proceeds to step S3;

[0121] If ‖△x‖ ∞ >ε and i=i max , the calculation does not converge, the processing is stopped directly, an error message is given, and the subsequent steps are not processed;

[0122] The above ε represents the preset convergence tolerance, i max Indicates the upper limit of the number of iterations.

[0123] S3, the global coordinate x obtained from the last iteration of S2 tI Update the node coordinates of the next time step according to the formula x(t+△t)=x tI , jump out of the iterative calculation of node coordinates of the current time step and proceed to the next step of the current time step;

[0124] ​S4. End the current time step: Update the node velocity of the current step according to the following formula:

[0125] v(t+△t)=(x(t+△t)-x(t)) / △t

[0126] Finally, the node coordinates x(t+△t) and node velocity v(t+△t) of the current time step are output;

[0127] S5. Traverse all nodes to obtain the node coordinates and node velocity of each node, and form a deformation field by the node coordinates and node velocities of all nodes.

[0128] In the calculation process of the above time steps, the fusion processing is mainly applied to 2.1 in the iterative loop calculation 2.

[0129] 3) Output:

[0130] The deformation field is subjected to conventional mechanical analysis to obtain mechanical parameters, which are finally used for visualization and simulation prediction of solid mechanical behavior and modes.

[0131] The output mechanical parameter results ultimately include displacement, stress, strain, etc., which can realize the simulation prediction of the release effect of TAVI stent implantation.

[0132] The advantages and features of the fusion framework are further explained here. For traditional finite element technology, whether it is simulation solver development or subsequent secondary development, a lot of time and cost are required in formula derivation and code development related work. The present invention calculates the internal force and stiffness in the above step S21 by automatic differential combination processing, which is one of the main differences from the traditional finite element algorithm framework. In this way, in the initial development of the simulation solver or the secondary development of subsequent materials, there is no need to worry about any derivative formula derivation and related code development, which greatly saves computer development time and improves efficiency.

[0133] In terms of solution, the above step S21 is a local linear system solution process starting from the node. For small-scale linear systems, it can be calculated by direct inversion analytical method, that is, △x=H -1 g. Compared with the traditional finite element algorithm that constructs a global large-scale linear system solution from the unit, it completely avoids the numerical problems brought about by the solution of large-scale linear systems, such as convergence and stability problems.

[0134] In a specific implementation, the automatic differentiation module under the algorithm framework of the present invention is directly implemented using open source tools, such as TensorFlow, Pytorch, Tai Chi language, etc.

[0135] Example 2:

[0136] Here, taking cloth simulation as an example, the mass-spring model is used to define the elastic potential energy model of the cloth.

[0137] Based on the mass-spring model, the potential energy function E in the local optimization model is j (x) (equivalent to the material model mentioned above) can be expressed as:

[0138] E j (x)=(k(||x i -x j ||-L0) 2 ) / 2

[0139] Among them, x j For x i For the adjacent j-th node, L0 is the distance between the two mass points at the initial moment, and k is the stiffness coefficient.

[0140] Then, for the above cloth simulation embodiment, a forward simulation process integrating automatic differentiation and node block descent solution as in embodiment 1 of the present invention is performed:

[0141] 1) Configure the solid simulation model in the computer:

[0142] Configuring the solid simulation model involves assembling a cloth mesh model, selecting a cloth material model and setting its material parameters, and applying boundary and load conditions to the cloth. In this embodiment, the cloth model has a square geometry, the mesh is a triangular mesh, the material model uses the potential energy function of the mass-spring model, and the boundary conditions are fixed constraints on the two endpoints of the cloth (i.e., displacement is zero).

[0143] 2) Perform simulation calculations on a computer:

[0144] In a computer, a simulation solver integrating automatic differentiation and node block descent is established, and the simulation solver is used to perform simulation calculations on the configured solid simulation model to obtain the node coordinates of the grid model after the solid object moves and deforms, that is, the position and shape changes of the simulated solid object. In this embodiment, the solution logic processing of the solver at each time step is the same as that in Example 1.

[0145] Based on the mesh model node coordinate data obtained at each time step, visual rendering can be performed to present the motion and deformation state of the cloth. Figure 3 In this embodiment, based on the node coordinate data at a certain time step, the deformation effect of the cloth at this moment under the constraints of the top two ends and the action of gravity is illustrated.

[0146] The above specific embodiments are used to illustrate the present invention rather than to limit the present invention. Any modifications and changes made to the present invention within the spirit of the present invention and the protection scope of the claims shall fall within the protection scope of the present invention.

[0147] The above description is only a preferred embodiment of the present invention. Therefore, any equivalent changes or modifications made according to the structure, characteristics and principles described in the scope of the patent application of the present invention are included in the scope of the patent application of the present invention.

Claims

1. A solid simulation solution method integrating automatic differentiation and node block descent, characterized by: The method is specifically as follows: 1) Configure the solid simulation model in the computer: The solid simulation model includes a mesh model, a material model and boundary conditions of the solid object; 2) Perform simulation calculations on a computer: Establishing a simulation solver that integrates automatic differentiation and node block descent, and using the simulation solver to simulate and calculate the configured solid simulation model to obtain the node coordinates of the mesh model after the solid object moves and deforms; The simulation solver is processed according to the following process: S1. Start the current time step t: input the node coordinates x(t-△t) and node velocity v(t-△t) at the time t-△t of the previous time step; S2. Calculate the initial iteration coordinate x of the node at the current time step t t0 : S3. Perform iterative loop processing for the current time step: S31, start the current iteration step, using the node coordinate x of the previous iteration step t(i-1) Calculate the internal force and stiffness information, and then solve the linear system based on the internal force and stiffness information. Specifically, traverse each node in the following way: S31.

1. Calculate the internal force vector f at each node n n and the stiffness matrix k n : Each node is shared by e grids. Traverse all e grids that share the node and use the material model to automatically differentiate the node coordinates x of each node in the current iteration step. ti Calculate and process to obtain the internal force vector f of each grid on the node e and the stiffness matrix k e , and then assemble the internal force vector f of all e grids corresponding to the node according to the following formula e and the stiffness matrix k e Get the internal force vector F of the node n and the stiffness matrix K n : F n =∑ e f e ,K n =∑ e k e S31.2, then according to the boundary conditions the internal force vector F n and the stiffness matrix K n Perform correction processing to obtain the corrected internal force vector F n ' and stiffness matrix K n ', then according to the modified internal force vector F n ' and stiffness matrix K n 'Calculate the coordinate increment △x of the current node using the linear system according to the following formula n : △x n =K n ' -1 ×F n ' S32. Merge the coordinate increments of all nodes n to obtain the coordinate increment vector of the global system. Update the global coordinates of the current iteration step i according to the coordinate increment vector of the global system according to the following formula: x t(i) = x t(i-1) +△x △x=(△x 0、 △x1、…、△x n ) Among them, △x is the global coordinate increment vector; S33. Make a convergence judgment and calculate the infinite norm of the global coordinate increment vector △x‖△x‖ ∞ , and then judge and process it as follows: If ‖△x‖ ∞ > ε and i < imax, then use the global coordinate x at the current iteration step i t(i) to return to S31 to start the loop processing for the next iteration step; If ‖△x‖ ∞ ≤ε and i≤imax, the iterative calculation converges and proceed to step S4; If ‖△x‖ ∞ >ε and i=imax, the calculation does not converge, the processing is stopped directly, and an error message is reported; The above ε represents the preset convergence tolerance, and imax represents the upper limit of the number of iteration cycles; S4, the global coordinate x obtained at the last iteration of S3 tI Update the node coordinates of the current time step according to the formula x(t)=x tI , proceed to the next step of the current time step; S5. End the current time step: Update the node velocity of the current step according to the following formula: v(t)=(x(t)-x(t-△t)) / △t Finally, the node coordinates x(t) of the current time step are output; 3) Output: The node coordinates of all nodes in the mesh model can be used as the basic data of the deformation field to perform mechanical analysis to obtain mechanical parameters, and finally the mechanical parameters can be used for visualization and simulation prediction.

2. The solid simulation solution method integrating automatic differentiation and node block descent according to claim 1, characterized in that: The solid simulation model is any deformable solid object model.

3. The solid simulation solution method integrating automatic differentiation and node block descent according to claim 1 is characterized in that: In step 2), the simulation solver divides the continuous motion deformation process of the mesh model of the solid object over time into discontinuous states at different moments with equal time intervals for simulation processing. Each moment is used as a time step to execute the same logical solution process on the mesh model, and iteratively and progressively processes the different moments in the time series to obtain the final mesh model node coordinates of the entire time length.

4. The solid simulation solution method integrating automatic differentiation and node block descent according to claim 1 is characterized in that: The grid model is mainly composed of nodes and grids. Each node has spatial position information, and the spatial position information consists of the coordinate x of the node.

5. The solid simulation solution method integrating automatic differentiation and node block descent according to claim 1 is characterized in that: In step S2, the estimation process is performed according to the following formula: x t0 = x(t-△t)+ v(t-△t)×△t +△t 2 ×a ext Among them, △t is the time step, that is, the interval between adjacent moments; x(t-△t) represents the node coordinates at the moment t-△t of the previous time step, v(t-△t) represents the node velocity at the moment t-△t of the previous time step, and a ext Represents the external acceleration of the continuous motion deformation process of the solid object simulation; x t0 Represents the initial iteration coordinates of the node at the current time step t.

6. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 5 are implemented.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

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