An AI-based CAE simulation model meshing method

Abstract

This invention discloses an AI-based mesh generation method for CAE simulation models, comprising the following steps: acquiring CAD data, loads, and boundaries; generating an initial mesh; the AI ​​provides the density field, metric tensor, uncertainty, and sets an upper limit; joint scheduling and spectral trimming based on uncertainty; calibrating interfaces and guard zones; constructing an anisotropic Monge-Ampère boundary value problem by interface piecewise division and applying boundary and interface constraints; solving using monotonic discretization and filtering schemes combined with convex projection to obtain piecewise convex potentials and displacement candidates; iterating with error and mass fixed points, performing equal distribution and smoothing, and projecting to the feasible region to obtain the target displacement; selecting a refinement region within the upper limit using submodulus utility and metric consistency TV, and refining the size, order, and relocation; performing topology updates based on the target displacement and refinement region, and outputting the target mesh. This invention improves anisotropic control, interface continuity, and efficiency.

Description

Technical Field

[0001] This invention relates to the field of computer-aided engineering analysis technology, and in particular to an AI-based method for mesh generation in CAE simulation models. Background Technology

[0002] Current CAE mesh generation and adaptation mainly employ error posterior estimation-driven h-refinement, p-order increase, and r-smoothing, combined with metric space-based anisotropic mesh generation and boundary layer refinement strategies. Common implementations use gradient, curvature, residual, or ZZ-type recovery stress as indicators to transform into a target size field, and then call Delaunay, front advance, or local reconstruction to complete refinement and topology update. To address coupling issues, some methods use artificially weighted isotropic buffers near material boundaries and contact surfaces, or use simple limiters to suppress element distortion. In recent years, mesh migration frameworks based on optimal transport and the Monge-Ampère concept have also emerged, but these are mostly for isotropic or weakly anisotropic scenarios, with limited handling of interface conditions and global constraints.

[0003] Existing processes generally use a linear chain of "estimation-size field-grider," lacking a unified scheduling mechanism for the target density field and anisotropy metric tensor. This makes it difficult to simultaneously control directionality and density distribution. Data-driven uncertainty handling often remains at the level of empirical thresholds, failing to incorporate the predicted uncertainty field into scheduling and spectral boundary trimming. This results in over- or under-refinement in areas such as load abrupt changes, geometric details, and sparse observation regions. Cross-interface consistency largely relies on heuristic rules from the gridder, lacking explicit boundary consistency and interface normal flux continuity constraints at the mathematical model level. Protective strips are usually approximated with a fixed width, which easily introduces penetration and twisting.

[0004] At the numerical solution level, most existing Monge-Ampère-based mesh migrations employ standard discretization and conventional Newton iterations, making it difficult to maintain convexity stably. The lower bound of the element Jacobian and the upper bound of the mesh growth rate lack explicit feasible region projection guarantees. The combination of monotonic discretization and filtering schemes is insufficient, and the trade-off between higher-order consistency and stability is not robust. Interface splicing is often handled by interpolation or averaging, resulting in insufficient consistency of node displacements. The selection of refinement regions often relies on thresholds or greedy criteria. There is a lack of global submodular utility optimization and metric consistency total variation regularization under the constraint of the upper limit of the number of new elements, making it difficult to obtain a refined set that is oriented in a consistent and connected manner.

[0005] Therefore, how to provide an AI-based method for mesh generation in CAE simulation models is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] One objective of this invention is to propose an AI-based mesh generation method for CAE simulation models. This invention utilizes an artificial intelligence model to generate the target cell density field, anisotropic metric tensor, and predicted uncertainty field. It combines uncertainty-driven joint scheduling and spectral boundary clipping, solving the piecewise anisotropic Monge-Ampère second boundary value problem, monotonic discretization and filtering scheme fusion with convex projection, error and quality fixed-point iteration, and refinement region selection under submodulus utility and metric consistency total variation constraints. This completes node displacement calculation, mesh size refinement, node relocation, and topology update. It has the advantages of high anisotropic control accuracy, controllable refinement budget, strong interface continuity, stable mesh quality, and applicability to complex multiphysics simulations.

[0007] A mesh generation method for an AI-based CAE simulation model according to an embodiment of the present invention includes the following steps:

[0008] The system acquires CAD geometry, loads, and boundary conditions, generates an initial mesh, and outputs the target element density field, anisotropy metric tensor, and prediction uncertainty field from the AI ​​model, while setting an upper limit on the number of new elements.

[0009] Based on the predicted uncertainty field, the density field and anisotropy metric tensor of the target unit are jointly scheduled and spectral boundary clipped, and the multi-material and contact interface set is calibrated and a protective band constraint is set.

[0010] The interface set is divided into pieces, and an anisotropic Monge-Ampère second boundary value problem is established in each piece, with boundary consistency, interface normal flux continuity and cross-boundary barrier conditions applied.

[0011] The piecewise problem is solved by using a monotonic discretization and filtering scheme combined with convex projection to generate piecewise convex potential functions, and candidate fields of nodal displacements are calculated based on gradient mapping.

[0012] By employing error and mass fixed-point iteration, alternating between equal distribution mapping and mass smoothing, the candidate field of nodal displacements is projected onto a feasible region that satisfies the lower bound of the Jacobian and the upper bound of the growth rate, thus obtaining the target nodal displacement field.

[0013] Under the constraint of the upper limit of the number of new elements, the refinement region is selected based on the total variation of submodular utility and metric consistency. The mesh size refinement, basis function order lifting and node relocation are performed by combining the target node displacement field and the target element density field.

[0014] The target mesh is updated based on the target node displacement field and the refined region, a topology update is performed while adhering to the guard zone constraint, and the target mesh is output.

[0015] Optionally, the initial mesh generation, artificial intelligence model output, and upper limit setting of the number of newly added units specifically include:

[0016] Import CAD geometry and establish a computational domain, which is then analyzed into a set of surfaces, edges, and vertices, with unified units and coordinate systems.

[0017] Enter the loads and boundary conditions, generate load fields and boundary identification diagrams, and locate the boundary of the computational domain;

[0018] Set the mesh parameters, including cell type, size range, and growth rate;

[0019] An initial grid is generated in the computational domain based on the grid parameters, and node and cell indices are established.

[0020] The boundary marker map is mapped to the initial mesh to form a set of mesh constraints, and the load field is mapped to the specified elements and surfaces;

[0021] Organize the input features of the artificial intelligence model, and construct the input data according to the node order, cell order and coordinate system order. The input features include CAD geometric features, load fields, boundary identification diagrams and initial mesh statistics.

[0022] An artificial intelligence model is invoked to generate three fields. The artificial intelligence model consists of an input encoder, a feature extraction backbone, and three output heads. The input encoder performs scale unification and feature embedding, the feature extraction backbone performs joint geometric and topological representation, and the three output heads generate a target cell density field, an anisotropic metric tensor, and a prediction uncertainty field, respectively. The target cell density field is defined as a non-negative scalar on the cell and corresponds one-to-one with the cell index. The anisotropic metric tensor is defined as a symmetric second-order tensor on the node and corresponds one-to-one with the node index. The prediction uncertainty field is defined as a non-negative scalar on the node and corresponds one-to-one with the node index.

[0023] Set an upper limit on the number of new elements, and register the CAD geometry, initial mesh, target element density field, anisotropy metric tensor, prediction uncertainty field, load field, boundary marker map, and upper limit on the number of new elements into the data storage.

[0024] Optionally, the joint scheduling, spectral boundary trimming, interface set calibration, and guard band constraint setting specifically include:

[0025] Establish a joint scheduling parameter set, including density adjustment ratio, lower limit of main scale of metric, upper limit of main scale of metric, and smoothing window length;

[0026] Based on the distribution of density adjustment coefficients generated from the predicted uncertainty field, increase or decrease operations are performed on the density field of the target cell in each grid cell to form a scheduling density field;

[0027] On each grid cell, the principal direction and principal scale of the anisotropic metric tensor are calculated. The lower limit and upper limit of the principal scale are set according to the prediction uncertainty field. The principal scale is pruned while keeping the principal direction unchanged to obtain the pruned anisotropic metric tensor.

[0028] Based on CAD geometry and mesh topology, material boundaries and contact boundaries are identified, and a set of interfaces is formed. The correspondence between interfaces and mesh entities is established.

[0029] Generate a protective zone around the interface set, set the half-width of the protective zone, the normal displacement limit and the rule to prohibit crossing, and bind it to the corresponding mesh entity;

[0030] Within the protection zone, amplitude limiting rules are applied to the scheduling density field and the clipped anisotropic metric tensor to constrain the increase or decrease in density and the change in principal scale within a preset range.

[0031] Optionally, the fragmentation construction and the establishment of the anisotropic Monge-Ampère second boundary value problem specifically include:

[0032] The computation domain is divided into segments based on the set of interfaces. A segment index is established, and the set of segment boundaries and adjacent set of interfaces are recorded.

[0033] In each slice, load the scheduling density field, the clipped anisotropic metric tensor, and the guard band region parameters;

[0034] In each piece, a piecewise convex potential function is defined. The gradient mapping is given by the gradient of the piecewise convex potential function. The mapping target includes points inside the piecewise part and points on the piecewise boundary.

[0035] Anisotropic Monge-Ampère master equations are established for each piece, and the metric transformation is performed using the principal square root of the metric tensor. The master equations are obtained based on the metric conservation and variable substitution formulas in optimal transport, and are written as:

[0036] ;

[0037] in, For spatial coordinates, For piecewise convex potential functions, It is a Hessian matrix. For determinant, For the clipped anisotropic metric tensor, It is a symmetric positive definite principal square root. For the partitioned scheduling density field, This is the partitioning normalization coefficient;

[0038] Apply a boundary consistency condition to each partition boundary so that the gradient mapping maps the partition boundary points to the corresponding set of boundary points;

[0039] Apply the interface normal flux continuity condition to each interface so that the gradient mapping of adjacent pieces takes the same value on the normal component.

[0040] Apply cross-boundary barrier conditions to the protection zone area to restrict the normal displacement of gradient mapping from crossing the interface, and set displacement limits according to the protection zone parameters;

[0041] The master equation, boundary consistency, interface normal flux continuity, and cross-boundary barrier conditions are combined into a set of piecewise coupled anisotropic Monge-Ampère second boundary value problems.

[0042] Optionally, the generation of the piecewise convex potential function and the calculation of the nodal displacement candidate field specifically include:

[0043] In each partition, a set of discrete nodes and an adjacency template are established, and a monotonic discrete operator index and a higher-order candidate discrete operator index are generated.

[0044] The assembly boundary consistency discrete constraint, the interface normal flux continuous discrete constraint, and the guard band constraint are combined to form a constraint matrix;

[0045] Initialize the discrete vector of the piecewise convex potential function, and set the convergence threshold, step size control parameters and linearization iteration strategy;

[0046] Calculate the monotonic discrete residuals and higher-order candidate residuals to generate a filter control parameter field;

[0047] By employing a filtering scheme to fuse monotonic discrete operators and higher-order candidate discrete operators, the discrete master equation is written as:

[0048] ;

[0049] This formula, based on the theory of viscous solution consistency and filtering schemes, is used for adaptive switching between monotonic consistency and higher-order consistency. For piecewise convex potential functions, discrete vectors For monotone discrete Monge-Ampère operators, For higher-order candidate discrete operators, For the filtered discrete operator, A positive threshold The truncation function is mapped to the interval [0,1].

[0050] Linearization is performed based on the discrete master equation and constraint matrix. The Newton-Krylov method is used to solve the linear subproblem and update the discrete vector of the piecewise convex potential function. The Newton-Krylov method consists of outer Newton linearization and inner Krylov subspace iteration. It only relies on the calculation of Jacobi and vector product and constructs Jacobi-vector product by difference approximation. There is no need to explicitly construct the Jacobi matrix and perform matrix inversion.

[0051] Perform convex projection, prune according to the characteristic spectrum of discrete Hessian to maintain positive semidefiniteness, and apply constraint corrections to boundary nodes and interface nodes;

[0052] Determine whether the residual and step size meet the convergence threshold. If they do, output the piecewise convex potential function, calculate the gradient mapping according to the discrete gradient operator, and uniformly stitch them together at shared edges and shared points to generate a candidate field of node displacements.

[0053] Optionally, the generation of the target node displacement field specifically includes:

[0054] Error monitoring quantity and quality monitoring quantity are calculated on the grid based on the candidate field of node displacement and the piecewise convex potential function. The error monitoring quantity is based on the scheduling density field, and the quality monitoring quantity is based on the cell Jacobian determinant and the grid growth rate.

[0055] Establish an equally distributed mapping operator to generate displacement increments for node positions according to the scheduling density field and form an equally distributed update.

[0056] Establish a quality smoothing operator, generate smoothing increments based on the quality monitoring quantity as the node position, and form a quality update;

[0057] Define a feasible region, including the lower bound threshold of the cell Jacobian determinant and the upper bound threshold of the grid growth rate, and register the two thresholds at the cell level;

[0058] Set iteration control parameters, including step size factor sequence, termination threshold and maximum number of iterations, and initialize the nodal displacement field as a nodal displacement candidate field;

[0059] Perform fixed-point iteration, and in each round, perform the following steps in sequence: apply the equal distribution mapping operator to update the node position, apply the quality smoothing operator to update the node position, and project the updated node position onto the feasible region to simultaneously satisfy the lower bound threshold of the cell Jacobian determinant and the upper bound threshold of the grid growth rate.

[0060] After projection is completed, new error monitoring quantities and quality monitoring quantities are calculated. The step size factor is adjusted according to the changes in the monitoring quantities, while maintaining boundary consistency, interface normal flux continuity and guard band constraints.

[0061] When the iteration increment is lower than the termination threshold and all elements satisfy the feasible region, the target node displacement field is determined.

[0062] Optionally, the refinement region selection, mesh size refinement, basis function order lifting, and node relocation under the constraint of the upper limit of the number of newly added cells specifically include:

[0063] The target node displacement field, target element density field, clipped anisotropic metric tensor, and upper limit of the number of new elements are collected. The element utility gain is calculated by element index and a unit utility sequence is formed.

[0064] Construct a sub-modular utility objective, establish an objective function based on the unit utility sequence, superimpose a metric consistent total variation regularization, and use a pruned anisotropic metric tensor to determine the total variation weights;

[0065] Solve the region selection problem under the constraint of the upper limit of the number of new units, obtain the refined region, and fix the unit index of the refined region;

[0066] In the refined region, mesh size refinement, basis function order lifting and node relocation are performed. Node relocation uses the target node displacement field as the positioning reference, and mesh size refinement uses the target element density field as the size reference.

[0067] Within the protection zone constraints, the no-crossing rule and normal displacement limiting parameters are applied to maintain boundary consistency and interface normal flux continuity.

[0068] Optionally, the generation of the target mesh specifically includes:

[0069] Locate nodes based on the target node displacement field, maintaining boundary consistency, interface normal flux continuity, and protective zone constraints;

[0070] Perform mesh size refinement based on the refined region and the target cell density field, count the number of newly added cells and limit it to not exceed the upper limit of the number of newly added cells;

[0071] Perform topology updates, implement edge folding and edge flipping, and update cell connectivity;

[0072] Perform quality checks by calculating the unit Jacobian determinant, mesh growth rate, aspect ratio, and first layer thickness, and mark unqualified units and nodes according to the threshold.

[0073] Perform quality smoothing, node relocation, edge folding and edge flipping on the marked object in sequence until the feasible region is satisfied;

[0074] Apply no-crossing rules and normal displacement limiting parameters in the protected zone area to maintain boundary consistency and interface normal flux continuity.

[0075] Update unit connectivity, node index and boundary association, update interface set index and guard band identifier.

[0076] The beneficial effects of this invention are:

[0077] This invention generates the target cell density field, anisotropic metric tensor, and predicted uncertainty field through an artificial intelligence model. It then uses uncertainty-driven joint scheduling and spectral boundary clipping to enter the piecewise anisotropic Monge-Ampère second boundary value problem. Combined with monotonic discretization, filtering schemes, and convex projection, it establishes an integrated constraint link from density and orientation to nodal displacement and mesh shape function, achieving boundary consistency and interface normal flux continuity, maintaining the Jacobian lower bound and the growth rate upper bound, and obtaining the target nodal displacement field and target mesh.

[0078] This invention selects the refinement region by using submodal utility and metric consistency total variation within the upper limit of the number of newly added elements, and ensures the coordination of node relocation and size refinement by using equally distributed mapping and quality smoothing error-quality fixed point iteration, thereby reducing the occurrence rate of over-refinement and under-refinement, reducing the number of distortion and flipped elements, improving convergence stability and mesh independence, and maintaining a consistent, connected and quality-controlled mesh configuration under multi-material and contact interface scenarios, strong anisotropic load scenarios, and limited budget constraints. Attached Figure Description

[0079] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0080] Figure 1 This is a flowchart of an AI-based CAE simulation model mesh generation method proposed in this invention;

[0081] Figure 2 This is a schematic diagram of the piecewise anisotropic Monge–Ampère second boundary value problem of a mesh generation method for a CAE simulation model based on AI proposed in this invention.

[0082] Figure 3 This is a schematic diagram illustrating the refinement region selection and protection zone constraint of an AI-based CAE simulation model mesh generation method proposed in this invention. Detailed Implementation

[0083] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0084] refer to Figure 1-3 A mesh generation method for CAE simulation models based on AI, comprising the following steps:

[0085] The system acquires CAD geometry, loads, and boundary conditions, generates an initial mesh, and outputs the target element density field, anisotropy metric tensor, and prediction uncertainty field from the AI ​​model, while setting an upper limit on the number of new elements.

[0086] Based on the predicted uncertainty field, the density field and anisotropy metric tensor of the target unit are jointly scheduled and spectral boundary clipped, and the multi-material and contact interface set is calibrated and a protective band constraint is set.

[0087] The interface set is divided into pieces, and an anisotropic Monge-Ampère second boundary value problem is established in each piece, with boundary consistency, interface normal flux continuity and cross-boundary barrier conditions applied.

[0088] The piecewise problem is solved by using a monotonic discretization and filtering scheme combined with convex projection to generate piecewise convex potential functions, and candidate fields of nodal displacements are calculated based on gradient mapping.

[0089] By employing error and mass fixed-point iteration, alternating between equal distribution mapping and mass smoothing, the candidate field of nodal displacements is projected onto a feasible region that satisfies the lower bound of the Jacobian and the upper bound of the growth rate, thus obtaining the target nodal displacement field.

[0090] Under the constraint of the upper limit of the number of new elements, the refinement region is selected based on the total variation of submodular utility and metric consistency. The mesh size refinement, basis function order lifting and node relocation are performed by combining the target node displacement field and the target element density field.

[0091] The target mesh is updated based on the target node displacement field and the refined region, a topology update is performed while adhering to the guard zone constraint, and the target mesh is output.

[0092] This invention generates density fields, anisotropy metrics, and uncertainties using AI and sets an upper limit for new cells. It combines uncertainty-driven scheduling and spectral boundary clipping, piecewise anisotropic Monge-Ampère boundary value solving, monotonic discretization and filtering schemes with convex projection, fixed-point iteration with equidistributed mapping and quality smoothing, and refinement region selection and topology update based on submodal utility and metric consistency total variation under budget constraints. This achieves integrated control of density, orientation, and budget, maintains boundary consistency and interface normal flux continuity, significantly reduces low comparability and distorted cells, suppresses over-refinement and under-refinement, reduces convergence steps, and shortens mesh generation and simulation time.

[0093] In this embodiment, the initial mesh generation, artificial intelligence model output, and setting of the upper limit for the number of newly added units specifically include:

[0094] Import CAD geometry and establish a computational domain, which is then analyzed into a set of surfaces, edges, and vertices, with unified units and coordinate systems.

[0095] Enter the loads and boundary conditions, generate load fields and boundary identification diagrams, and locate the boundary of the computational domain;

[0096] Set the mesh parameters, including cell type, size range, and growth rate;

[0097] An initial grid is generated in the computational domain based on the grid parameters, and node and cell indices are established.

[0098] The boundary marker map is mapped to the initial mesh to form a set of mesh constraints, and the load field is mapped to the specified elements and surfaces;

[0099] Organize the input features of the artificial intelligence model, and construct the input data according to the node order, cell order and coordinate system order. The input features include CAD geometric features, load fields, boundary identification diagrams and initial mesh statistics.

[0100] An artificial intelligence model is invoked to generate three fields. The artificial intelligence model consists of an input encoder, a feature extraction backbone, and three output heads. The input encoder performs scale unification and feature embedding, the feature extraction backbone performs joint geometric and topological representation, and the three output heads generate a target cell density field, an anisotropic metric tensor, and a prediction uncertainty field, respectively. The target cell density field is defined as a non-negative scalar on the cell and corresponds one-to-one with the cell index. The anisotropic metric tensor is defined as a symmetric second-order tensor on the node and corresponds one-to-one with the node index. The prediction uncertainty field is defined as a non-negative scalar on the node and corresponds one-to-one with the node index.

[0101] Set an upper limit on the number of new elements, and register the CAD geometry, initial mesh, target element density field, anisotropy metric tensor, prediction uncertainty field, load field, boundary marker map, and upper limit on the number of new elements into the data storage.

[0102] Based on the unification of the computational domain and unit coordinates, this invention accurately maps the load field and boundary identifier to the initial mesh to form a set of mesh constraints. It organizes AI input according to the sequential indexing of nodes and elements to generate a target element density field, anisotropic metric tensor, and prediction uncertainty field that correspond one-to-one with the index. At the same time, it registers the upper limit of the number of newly added elements and the full input and output data, ensuring the consistent expression of density, direction, and constraints from the source. This reduces manual tuning and multiple mesher trials, reduces quality problems caused by mapping deviation and index misalignment, and shortens the preprocessing cycle.

[0103] In this embodiment, the joint scheduling, spectral boundary trimming, interface set calibration, and guard band constraint setting specifically include:

[0104] Establish a joint scheduling parameter set, including density adjustment ratio, lower limit of main scale of metric, upper limit of main scale of metric, and smoothing window length;

[0105] Based on the distribution of density adjustment coefficients generated from the predicted uncertainty field, increase or decrease operations are performed on the density field of the target cell in each grid cell to form a scheduling density field;

[0106] On each grid cell, the principal direction and principal scale of the anisotropic metric tensor are calculated. The lower limit and upper limit of the principal scale are set according to the prediction uncertainty field. The principal scale is pruned while keeping the principal direction unchanged to obtain the pruned anisotropic metric tensor.

[0107] Based on CAD geometry and mesh topology, material boundaries and contact boundaries are identified, and a set of interfaces is formed. The correspondence between interfaces and mesh entities is established.

[0108] Generate a protective zone around the interface set, set the half-width of the protective zone, the normal displacement limit and the rule to prohibit crossing, and bind it to the corresponding mesh entity;

[0109] Within the protection zone, amplitude limiting rules are applied to the scheduling density field and the clipped anisotropic metric tensor to constrain the increase or decrease in density and the change in principal scale within a preset range.

[0110] This invention unifies the joint scheduling parameter set and uses prediction uncertainty to drive the addition, subtraction and principal scale trimming of the target unit density field and anisotropy metric tensor. At the same time, it calibrates the material and contact interface and sets protection zones and amplitude limiting rules, so that the refinement intensity and direction are controlled in the high-risk area and smoothed in the stable area, reducing the probability of over-refinement and under-refinement, suppressing interface crossing and mismatch, and stabilizing the continuity of interface normal flux.

[0111] In this embodiment, the piecewise construction and the establishment of the anisotropic Monge-Ampère second boundary value problem specifically include:

[0112] The computation domain is divided into segments based on the set of interfaces. A segment index is established, and the set of segment boundaries and adjacent set of interfaces are recorded.

[0113] In each slice, load the scheduling density field, the clipped anisotropic metric tensor, and the guard band region parameters;

[0114] In each piece, a piecewise convex potential function is defined. The gradient mapping is given by the gradient of the piecewise convex potential function. The mapping target includes points inside the piecewise part and points on the piecewise boundary.

[0115] Anisotropic Monge-Ampère master equations are established for each piece, and the metric transformation is performed using the principal square root of the metric tensor. The master equations are obtained based on the metric conservation and variable substitution formulas in optimal transport, and are written as:

[0116] ;

[0117] in, For spatial coordinates, For piecewise convex potential functions, It is a Hessian matrix. For determinant, For the clipped anisotropic metric tensor, It is a symmetric positive definite principal square root. For the partitioned scheduling density field, This is the partitioning normalization coefficient;

[0118] Apply a boundary consistency condition to each partition boundary so that the gradient mapping maps the partition boundary points to the corresponding set of boundary points;

[0119] Apply the interface normal flux continuity condition to each interface so that the gradient mapping of adjacent pieces takes the same value on the normal component.

[0120] Apply cross-boundary barrier conditions to the protection zone area to restrict the normal displacement of gradient mapping from crossing the interface, and set displacement limits according to the protection zone parameters;

[0121] The master equation, boundary consistency, interface normal flux continuity, and cross-boundary barrier conditions are combined into a set of piecewise coupled anisotropic Monge-Ampère second boundary value problems.

[0122] This invention divides the interface set into pieces and loads the scheduling density field, the clipped anisotropic metric tensor, and the guard band parameters within each piece. It defines the piecewise convex potential and establishes the anisotropic Monge-Ampère master equation, along with boundary consistency, interface normal flux continuity, and cross-boundary barrier constraints. This ensures that the displacement mapping remains continuous and constrained at the pieces and interfaces, significantly reducing splicing errors and penetration risks, and improving the quality and orientation consistency of the interface neighborhood mesh.

[0123] In this embodiment, the generation of the piecewise convex potential function and the calculation of the nodal displacement candidate field specifically include:

[0124] In each partition, a set of discrete nodes and an adjacency template are established, and a monotonic discrete operator index and a higher-order candidate discrete operator index are generated.

[0125] The assembly boundary consistency discrete constraint, the interface normal flux continuous discrete constraint, and the guard band constraint are combined to form a constraint matrix;

[0126] Initialize the discrete vector of the piecewise convex potential function, and set the convergence threshold, step size control parameters and linearization iteration strategy;

[0127] Calculate the monotonic discrete residuals and higher-order candidate residuals to generate a filter control parameter field;

[0128] By employing a filtering scheme to fuse monotonic discrete operators and higher-order candidate discrete operators, the discrete master equation is written as:

[0129] ;

[0130] This formula, based on the theory of viscous solution consistency and filtering schemes, is used for adaptive switching between monotonic consistency and higher-order consistency. For piecewise convex potential functions, discrete vectors For monotone discrete Monge-Ampère operators, For higher-order candidate discrete operators, For the filtered discrete operator, A positive threshold The truncation function is mapped to the interval [0,1].

[0131] Linearization is performed based on the discrete master equation and constraint matrix. The Newton-Krylov method is used to solve the linear subproblem and update the discrete vector of the piecewise convex potential function. The Newton-Krylov method consists of outer Newton linearization and inner Krylov subspace iteration. It only relies on the calculation of Jacobi and vector product and constructs Jacobi-vector product by difference approximation. There is no need to explicitly construct the Jacobi matrix and perform matrix inversion.

[0132] Perform convex projection, prune according to the characteristic spectrum of discrete Hessian to maintain positive semidefiniteness, and apply constraint corrections to boundary nodes and interface nodes;

[0133] Determine whether the residual and step size meet the convergence threshold. If they do, output the piecewise convex potential function, calculate the gradient mapping according to the discrete gradient operator, and uniformly stitch them together at shared edges and shared points to generate a candidate field of node displacements.

[0134] This invention employs a combination of monotonic discretization and high-order candidate discretization filtering within the partitioned structure, along with a constraint matrix to uniformly apply boundary consistency, interface normal flux continuity, and guard band restrictions. It utilizes Newton-Krylov linearization, relying solely on the Jacobian vector product, and combines convex projection to maintain the discrete Hessian semi-definiteness. Simultaneously, it performs consistent splicing at shared edges and shared points, thereby improving the stability and scale adaptability of nonlinear solutions, reducing iterative divergence and pseudo-oscillations, lowering the proportion of low-Jacobi and distorted units, and improving the continuity of displacement mapping and topological splicing.

[0135] In this embodiment, the generation of the target node displacement field specifically includes:

[0136] Error monitoring quantity and quality monitoring quantity are calculated on the grid based on the candidate field of node displacement and the piecewise convex potential function. The error monitoring quantity is based on the scheduling density field, and the quality monitoring quantity is based on the cell Jacobian determinant and the grid growth rate.

[0137] Establish an equally distributed mapping operator to generate displacement increments for node positions according to the scheduling density field and form an equally distributed update.

[0138] Establish a quality smoothing operator, generate smoothing increments based on the quality monitoring quantity as the node position, and form a quality update;

[0139] Define a feasible region, including the lower bound threshold of the cell Jacobian determinant and the upper bound threshold of the grid growth rate, and register the two thresholds at the cell level;

[0140] Set iteration control parameters, including step size factor sequence, termination threshold and maximum number of iterations, and initialize the nodal displacement field as a nodal displacement candidate field;

[0141] Perform fixed-point iteration, and in each round, perform the following steps in sequence: apply the equal distribution mapping operator to update the node position, apply the quality smoothing operator to update the node position, and project the updated node position onto the feasible region to simultaneously satisfy the lower bound threshold of the cell Jacobian determinant and the upper bound threshold of the grid growth rate.

[0142] After projection is completed, new error monitoring quantities and quality monitoring quantities are calculated. The step size factor is adjusted according to the changes in the monitoring quantities, while maintaining boundary consistency, interface normal flux continuity and guard band constraints.

[0143] When the iteration increment is lower than the termination threshold and all elements satisfy the feasible region, the target node displacement field is determined.

[0144] This invention is driven by two indicators: error monitoring quantity and quality monitoring quantity. First, the equal distribution mapping operator is used to balance the allocation of unit volume according to the scheduling density field. Then, the quality smoothing operator is used to suppress deformation based on Jacobian and growth rate. The updated node position in each round is projected onto the feasible region containing the lower bound of Jacobian and the upper bound of growth rate. With the combination of step size adaptation and boundary consistency, continuous interface normal flux, and unchanged guard band constraint, it can stably converge to the target node displacement field without increasing the number of units and significantly reduce the proportion of low-quality units and local distortion.

[0145] In this embodiment, the refinement region selection, mesh size refinement, basis function order enhancement, and node relocation under the constraint of the upper limit of the number of newly added cells specifically include:

[0146] The target node displacement field, target element density field, clipped anisotropic metric tensor, and upper limit of the number of new elements are collected. The element utility gain is calculated by element index and a unit utility sequence is formed.

[0147] Construct a sub-modular utility objective, establish an objective function based on the unit utility sequence, superimpose a metric consistent total variation regularization, and use a pruned anisotropic metric tensor to determine the total variation weights;

[0148] Solve the region selection problem under the constraint of the upper limit of the number of new units, obtain the refined region, and fix the unit index of the refined region;

[0149] In the refined region, mesh size refinement, basis function order lifting and node relocation are performed. Node relocation uses the target node displacement field as the positioning reference, and mesh size refinement uses the target element density field as the size reference.

[0150] Within the protection zone constraints, the no-crossing rule and normal displacement limiting parameters are applied to maintain boundary consistency and interface normal flux continuity.

[0151] This invention constructs a submodal utility objective based on the unit utility sequence under the constraint of the upper limit of the number of newly added units, and superimposes the metric consistency total variation regularization. Combining the target node displacement field and the target unit density field, it generates a refined region that is consistent with the anisotropic principal direction and connected only in the high sensitivity and high gradient regions. This controls the control unit scale to avoid fragmentation and densification, improves local resolution and global convergence stability, and maintains boundary consistency and interface normal flux continuity within the protection zone.

[0152] In this embodiment, the generation of the target mesh specifically includes:

[0153] Locate nodes based on the target node displacement field, maintaining boundary consistency, interface normal flux continuity, and protective zone constraints;

[0154] Perform mesh size refinement based on the refined region and the target cell density field, count the number of newly added cells and limit it to not exceed the upper limit of the number of newly added cells;

[0155] Perform topology updates, implement edge folding and edge flipping, and update cell connectivity;

[0156] Perform quality checks by calculating the unit Jacobian determinant, mesh growth rate, aspect ratio, and first layer thickness, and mark unqualified units and nodes according to the threshold.

[0157] Perform quality smoothing, node relocation, edge folding and edge flipping on the marked object in sequence until the feasible region is satisfied;

[0158] Apply no-crossing rules and normal displacement limiting parameters in the protected zone area to maintain boundary consistency and interface normal flux continuity.

[0159] Update unit connectivity, node index and boundary association, update interface set index and guard band identifier.

[0160] This invention locates nodes using the target node displacement field and performs size refinement and upper limit control of new elements in the refined region according to the target element density field. At the same time, it performs topology updates by folding and flipping the edges, and cooperates with quality verification and repair sequences to ensure that the element connectivity and index are consistent and meet the Jacobian, growth rate, aspect ratio and first layer thickness threshold. Under the protection zone rule, it maintains boundary consistency and interface normal flux continuity and outputs the target mesh stably.

[0161] Example 1:

[0162] To verify the feasibility of this invention in actual production scenarios in the manufacturing industry, it was applied to the mesh generation process of a CAE simulation model for injection molds. The tested mold was a one-piece plastic shell with a geometry including deep cavities, thin walls, chamfered draft surfaces, and complex conformal cooling channels. Significant thickness variations and surface transitions exist internally. Traditional heuristic dimensional field mesh generation methods often face two problems in such complex geometries: first, element distortion and flipping easily occur in regions of curvature variation, leading to a Jacobian determinant below a threshold; second, excessive mesh refinement and node discontinuity occur at the interface between the cooling channels and the cavity, causing instability in thermal flow analysis and stress distribution simulation. To solve these problems, this invention employs an adaptive mesh generation method based on artificial intelligence and the anisotropic Monge-Ampère equation, achieving fully automated generation from CAD geometry to high-quality meshes.

[0163] During implementation, the mold CAD geometric model is first imported, the coordinate system is unified, and the sets of surfaces, edges, and vertices are analyzed. Boundary conditions and thermal load distribution information are entered. Based on pre-trained sample data, the artificial intelligence model extracts features from the input geometric features, load fields, and initial mesh statistics, and automatically outputs the target element density field, anisotropic metric tensor, and prediction uncertainty field. The target element density field reflects the region refinement requirements, the anisotropic metric tensor characterizes the element shape and orientation, and the prediction uncertainty field is used to measure the model's confidence in the region judgment. The system uses the uncertainty field to perform joint scheduling and spectral boundary clipping on the density field and metric tensor, thereby achieving local refinement in high stress gradient and high heat flux regions, while maintaining a moderate element distribution in stable regions. The system also calibrates the protective zone constraint according to the contact surface and parting surface to avoid mesh crossing and boundary distortion.

[0164] Subsequently, the entire computational domain is partitioned according to the interface set, and an anisotropic Monge-Ampère second boundary value problem is established. In each partition, a pruned metric tensor and scheduling density field are loaded, and a partitioned convex potential function is constructed, with boundary consistency, normal flux continuity, and cross-boundary barrier conditions applied. The master equation is solved using monotonic discretization and a filtering scheme, and geometric consistency of the solution is maintained by combining convex projection. The solution is linearized using the Newton-Krylov method, which relies only on Jacobian vector products without explicitly constructing the Jacobian matrix, maintaining convergence stability and computational efficiency in large-scale nonlinear problems. After obtaining the partitioned convex potential function, candidate field of nodal displacements is obtained through gradient mapping and then stitched together to generate a global nodal displacement reference.

[0165] During the node position update phase, the system performs error and quality fixed point iteration, alternating between isodistribution mapping and quality smoothing processes. Isodistribution mapping adjusts node positions based on the scheduling density field to ensure that the cell distribution is consistent with the target density field. Quality smoothing balances node movement based on the cell Jacobian determinant and growth rate to improve mesh quality. After the iteration, the node displacement field is projected onto a feasible region that satisfies the lower bound of the Jacobian and the upper bound of the growth rate, thus obtaining the target node displacement field that satisfies geometric consistency and quality constraints. Subsequently, under the constraint of the upper limit of the number of new cells, the refinement region is determined by the submodular utility and the total variation of metric consistency. Refinement is only carried out on the cooling channel wall, sharp corner transition, and high thermal gradient region, while keeping the overall cell size under control.

[0166] In the experimental comparison, using the same CAD geometry and boundary conditions, meshes were generated using both the traditional heuristic method and the method of this invention, and then subjected to co-thermal-structural simulations. The results show that the mesh generation time of this invention is reduced from approximately 42 minutes to 19 minutes, and the total number of elements is reduced from approximately 3.2 million to approximately 3 million; the proportion of low-quality elements (Jacobi < 0.2) decreases from 8.1% to 2.3%, and the average slenderness ratio decreases from 4.1 to 2.5. The root mean square error of the boundary normal flux decreases from 6.5% to 2.2%, and the discontinuity at the contact interface nodes is eliminated. In the thermal simulation calculations, the maximum deviation of the temperature field decreases from 18.3 K to 7.4 K, and the maximum deviation of the stress field decreases from 20.8 MPa to 8.6 MPa; the number of simulation convergence iterations decreases from 86 steps to 58 steps, and the total computation time is reduced by approximately 30%. In the mesh independence verification, the change in key physical quantities after further refinement by one level is less than 2%, indicating that the mesh meets the CAE accuracy requirements.

[0167] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A mesh generation method for CAE simulation models based on AI, characterized in that, Includes the following steps: The system acquires CAD geometry, loads, and boundary conditions, generates an initial mesh, and outputs the target element density field, anisotropy metric tensor, and prediction uncertainty field from the AI ​​model, while setting an upper limit on the number of new elements. Based on the predicted uncertainty field, the density field and anisotropy metric tensor of the target unit are jointly scheduled and spectral boundary clipped, and the multi-material and contact interface set is calibrated and a protective band constraint is set. The interface set is divided into pieces, and an anisotropic Monge-Ampère second boundary value problem is established in each piece, with boundary consistency, interface normal flux continuity and cross-boundary barrier conditions applied. The piecewise problem is solved by using a monotonic discretization and filtering scheme combined with convex projection to generate piecewise convex potential functions, and candidate fields of nodal displacements are calculated based on gradient mapping. By employing error and mass fixed-point iteration, alternating between equal distribution mapping and mass smoothing, the candidate field of nodal displacements is projected onto a feasible region that satisfies the lower bound of the Jacobian and the upper bound of the growth rate, thus obtaining the target nodal displacement field. Under the constraint of the upper limit of the number of new elements, the refinement region is selected based on the total variation of submodular utility and metric consistency. The mesh size refinement, basis function order lifting and node relocation are performed by combining the target node displacement field and the target element density field. The target mesh is updated based on the target node displacement field and the refined region, a topology update is performed while adhering to the guard zone constraint, and the target mesh is output.

2. The mesh generation method for an AI-based CAE simulation model according to claim 1, characterized in that, The initial mesh generation, AI model output, and upper limit setting for the number of new cells specifically include: Import CAD geometry and establish a computational domain, which is then analyzed into a set of surfaces, edges, and vertices, with unified units and coordinate systems. Enter the loads and boundary conditions, generate load fields and boundary identification diagrams, and locate the boundary of the computational domain; Set the mesh parameters, including cell type, size range, and growth rate; An initial grid is generated in the computational domain based on the grid parameters, and node and cell indices are established. The boundary marker map is mapped to the initial mesh to form a set of mesh constraints, and the load field is mapped to the specified elements and surfaces; Organize the input features of the artificial intelligence model, and construct the input data according to the node order, unit order and coordinate system order. The input features include CAD geometric features, load fields, boundary identification diagrams and initial mesh statistics. An artificial intelligence model is invoked to generate three fields. The artificial intelligence model consists of an input encoder, a feature extraction backbone, and three output heads. The input encoder performs scale unification and feature embedding, the feature extraction backbone performs joint geometric and topological representation, and the three output heads generate a target cell density field, an anisotropic metric tensor, and a prediction uncertainty field, respectively. The target cell density field is defined as a non-negative scalar on the cell and corresponds one-to-one with the cell index. The anisotropic metric tensor is defined as a symmetric second-order tensor on the node and corresponds one-to-one with the node index. The prediction uncertainty field is defined as a non-negative scalar on the node and corresponds one-to-one with the node index. Set an upper limit for the number of new elements, and register the CAD geometry, initial mesh, target element density field, anisotropy metric tensor, prediction uncertainty field, load field, boundary marker map, and upper limit for the number of new elements into the data storage.

3. The mesh generation method for an AI-based CAE simulation model according to claim 1, characterized in that, Joint scheduling, spectral boundary trimming, interface set calibration, and guard band constraint settings specifically include: Establish a joint scheduling parameter set, including density adjustment ratio, lower limit of main scale of metric, upper limit of main scale of metric, and smoothing window length; Based on the distribution of density adjustment coefficients generated from the predicted uncertainty field, increase or decrease operations are performed on the density field of the target cell in each grid cell to form a scheduling density field; On each grid cell, the principal direction and principal scale of the anisotropic metric tensor are calculated. The lower limit and upper limit of the principal scale are set according to the prediction uncertainty field. The principal scale is pruned while keeping the principal direction unchanged to obtain the pruned anisotropic metric tensor. Based on CAD geometry and mesh topology, material boundaries and contact boundaries are identified, and a set of interfaces is formed. The correspondence between interfaces and mesh entities is established. Generate a protective zone around the interface set, set the half-width of the protective zone, the normal displacement limit and the rule to prohibit crossing, and bind it to the corresponding mesh entity; Within the protection zone, amplitude limiting rules are applied to the scheduling density field and the clipped anisotropic metric tensor to constrain the increase or decrease in density and the change in principal scale within a preset range.

4. The mesh generation method for an AI-based CAE simulation model according to claim 1, characterized in that, The specific steps of piecewise construction and the establishment of the anisotropic Monge-Ampère second boundary value problem include: The computation domain is divided into segments based on the set of interfaces. A segment index is established, and the set of segment boundaries and adjacent set of interfaces are recorded. In each slice, load the scheduling density field, the clipped anisotropic metric tensor, and the guard band region parameters; In each piece, a piecewise convex potential function is defined. The gradient mapping is given by the gradient of the piecewise convex potential function. The mapping target includes points inside the piecewise part and points on the piecewise boundary. An anisotropic Monge-Ampère master equation is established for each piece, and the metric transformation is performed using the principal square root of the metric tensor. The master equation is obtained based on the metric conservation and variable substitution formula in optimal transmission. Apply a boundary consistency condition to each partition boundary so that the gradient mapping maps the partition boundary points to the corresponding set of boundary points; Apply the interface normal flux continuity condition to each interface so that the gradient mapping of adjacent pieces takes the same value on the normal component. Apply cross-boundary barrier conditions to the protection zone area to restrict the normal displacement of gradient mapping from crossing the interface, and set displacement limits according to the protection zone parameters; The master equation, boundary consistency, interface normal flux continuity, and cross-boundary barrier conditions are combined into a set of piecewise coupled anisotropic Monge-Ampère second boundary value problems.

5. The mesh generation method for an AI-based CAE simulation model according to claim 1, characterized in that, The generation of piecewise convex potential functions and the calculation of candidate fields for nodal displacements specifically include: In each partition, a set of discrete nodes and an adjacency template are established, and a monotonic discrete operator index and a higher-order candidate discrete operator index are generated. The assembly boundary consistency discrete constraint, the interface normal flux continuous discrete constraint, and the guard band constraint are combined to form a constraint matrix; Initialize the discrete vector of the piecewise convex potential function, and set the convergence threshold, step size control parameters and linearization iteration strategy; Calculate the monotonic discrete residuals and higher-order candidate residuals to generate a filter control parameter field; A filtering scheme is adopted to fuse monotonic discrete operators and higher-order candidate discrete operators. The discrete master equation is obtained based on the theory of viscous solution consistency and filtering scheme, which is used to adaptively switch between monotonic consistency and higher-order consistency. Linearization is performed based on the discrete master equation and constraint matrix. The Newton-Krylov method is used to solve the linear subproblem and update the discrete vector of the piecewise convex potential function. Perform convex projection, prune according to the characteristic spectrum of discrete Hessian to maintain positive semidefiniteness, and apply constraint corrections to boundary nodes and interface nodes; Determine whether the residual and step size meet the convergence threshold. If they do, output the piecewise convex potential function, calculate the gradient mapping according to the discrete gradient operator, and uniformly stitch them together at shared edges and shared points to generate a candidate field of node displacements.

6. The mesh generation method for an AI-based CAE simulation model according to claim 1, characterized in that, The generation of the target nodal displacement field specifically includes: Error monitoring quantity and quality monitoring quantity are calculated on the grid based on the candidate field of node displacement and the piecewise convex potential function. The error monitoring quantity is based on the scheduling density field, and the quality monitoring quantity is based on the cell Jacobian determinant and the grid growth rate. Establish an equally distributed mapping operator to generate displacement increments for node positions according to the scheduling density field and form an equally distributed update. Establish a quality smoothing operator, generate smoothing increments based on the quality monitoring quantity as the node position, and form a quality update; Define a feasible region, including the lower bound threshold of the cell Jacobian determinant and the upper bound threshold of the grid growth rate, and register the two thresholds at the cell level; Set iteration control parameters, including step size factor sequence, termination threshold and maximum number of iterations, and initialize the nodal displacement field as a nodal displacement candidate field; Perform fixed-point iteration, and in each round, perform the following steps in sequence: apply the equal distribution mapping operator to update the node position, apply the quality smoothing operator to update the node position, and project the updated node position onto the feasible region to simultaneously satisfy the lower bound threshold of the cell Jacobian determinant and the upper bound threshold of the grid growth rate. After projection is completed, new error monitoring quantities and quality monitoring quantities are calculated. The step size factor is adjusted according to the changes in the monitoring quantities, while maintaining boundary consistency, interface normal flux continuity and guard band constraints. When the iteration increment is lower than the termination threshold and all elements satisfy the feasible region, the target node displacement field is determined.

7. The mesh generation method for an AI-based CAE simulation model according to claim 1, characterized in that, The specific steps for refining the region selection, mesh size refinement, basis function order lifting, and node relocation under the constraint of the upper limit on the number of new elements include: The target node displacement field, target element density field, clipped anisotropic metric tensor, and upper limit of the number of new elements are collected. The element utility gain is calculated by element index and a unit utility sequence is formed. Construct a sub-modular utility objective, establish an objective function based on the unit utility sequence, superimpose a metric consistent total variation regularization, and use a pruned anisotropic metric tensor to determine the total variation weights; Solve the region selection problem under the constraint of the upper limit of the number of new units, obtain the refined region, and fix the unit index of the refined region; In the refined region, mesh size refinement, basis function order lifting and node relocation are performed. Node relocation uses the target node displacement field as the positioning reference, and mesh size refinement uses the target element density field as the size reference. Within the protection zone constraints, the no-crossing rule and normal displacement limiting parameters are applied to maintain boundary consistency and interface normal flux continuity.

8. The mesh generation method for an AI-based CAE simulation model according to claim 1, characterized in that, The generation of the target mesh specifically includes: Locate nodes based on the target node displacement field, maintaining boundary consistency, interface normal flux continuity, and protective zone constraints; Perform mesh size refinement based on the refined region and the target cell density field, count the number of newly added cells and limit it to not exceed the upper limit of the number of newly added cells; Perform topology updates, implement edge folding and edge flipping, and update cell connectivity; Perform quality checks by calculating the unit Jacobian determinant, mesh growth rate, aspect ratio, and first layer thickness, and mark unqualified units and nodes according to the threshold. Perform quality smoothing, node relocation, edge folding and edge flipping on the marked object in sequence until the feasible region is satisfied; Apply no-crossing rules and normal displacement limiting parameters in the protected zone area to maintain boundary consistency and interface normal flux continuity. Update unit connectivity, node index and boundary association, update interface set index and guard band identifier.

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