Multi-core CPU parallel acceleration parameterization horizontal heat collection conduction topological optimization method based on implicit identification and Flood Fill algorithm

Abstract

The invention belongs to the technical field of high-performance design of high-precision advanced engineering structures, and discloses a multi-core CPU parallel acceleration parameterization horizontal heat collection conduction topological optimization method and system based on implicit identification and a Flood Fill algorithm. The invention aims to solve thermal management challenges in industries such as semiconductor manufacturing and the like and the defects of a traditional design method in the aspects of time consumption of grid division, isolated structure generation, slow convergence speed and the like. According to the method, a symbol distance field is automatically constructed through an implicit identification model, a tip isolated structure is eliminated in combination with a Flood Fill algorithm, convergence of a globally optimal solution is accelerated by adopting a multi-stage volume relaxation strategy, and integration of thermal performance evaluation and parameter updating is realized based on parallel sensitivity analysis. A numerical experiment of a radiator structure verifies that the framework is excellent in global optimal approximation and calculation efficiency, and has a wide engineering application prospect.

Description

Technical Field

[0001] The present invention belongs to, but is not limited to, the field of high-performance design technology for high-precision engineering structures, and in particular relates to a multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization method based on implicit identification and Flood Fill algorithm. Background Art

[0002] With the rapid development of aerospace integration and hypersonic technologies, modern aircraft face unprecedented challenges in achieving ultra-lightweight, high-strength, and high-heat dissipation performance in structures subjected to extreme heat, high loads, and complex vibration environments. However, existing structural topology optimization methods face multiple shortcomings in meeting these comprehensive requirements. First, most topology optimization methods rely on manual meshing and simplification, resulting in a significant information disconnect between the CAD geometry model and the optimization process, inefficient design, and difficult to directly apply to engineering applications. Second, the lack of effective connectivity monitoring and global approximation strategies during parameterized level set thermal conductivity topology optimization often leads to isolated structures or local optima, which compromise thermal performance and reduce manufacturing feasibility. Finally, faced with 3D meshes of millions or even larger, traditional serial computing architectures based on advanced platforms such as MATLAB struggle to meet the stringent requirements of rapid iteration and high-precision design in aircraft development, both in terms of computational resource consumption and solution time.

[0003] Given these shortcomings, there is an urgent need for an efficient 3D topology optimization technique that can seamlessly integrate with complex CAD models, maintain structural connectivity, and achieve near-global optimality during heat transfer optimization. Furthermore, this technique should fully leverage multi-core parallel computing platforms and high-resolution solver strategies to significantly improve computational efficiency and accuracy for large-scale meshes. Only by addressing the challenges of CAD-CAE collaboration, monitoring structural integrity in real time, introducing multi-stage volume relaxation and domain decomposition techniques, and accelerating the computational process can the diverse structural design requirements of hypersonic vehicles be truly met.

[0004] The development of this high-resolution, high-performance 3D structural topology optimization technology is crucial for overcoming bottlenecks in my country's aircraft structural design. It not only helps shorten the entire process from conceptual design to engineering implementation, improving the frequency and reliability of design iterations, but also plays a key supporting role in the innovative manufacturing of key aircraft components operating in extremely high temperatures, providing a strong foundation for the technological advancement and industrial competitiveness of my country's aerospace equipment.

[0005] In view of the above analysis, the technical problems that need to be solved urgently in the existing technology are:

[0006] The existing technology has problems such as the disconnection between the geometric information of the CAD model and the optimization solution process, the proneness of island structures in the parametric level set heat conduction topology optimization, the long serial calculation time for large-scale problems, the proneness of heat conduction topology optimization to "tree-like" local solutions, and the large number of convergence iteration steps. Summary of the Invention

[0007] In response to the problems existing in the prior art, the present invention provides a multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization method and system based on implicit identification and Flood Fill algorithm.

[0008] The present invention is achieved by providing a multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization method based on implicit identification and Flood Fill algorithm, characterized in that the multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization method based on implicit identification and Flood Fill algorithm specifically includes:

[0009] S1: Automatically construct signed distance fields through implicit recognition models;

[0010] S2: The computational domain is divided into private and shared areas, the concepts of local domain and ghost domain are introduced, and the heat conduction finite element solution is deployed in parallel on multi-core CPUs;

[0011] S3: Combining parameterization with the level set method, different topological configurations are generated by adjusting parameters. The level set method is used to describe the boundaries of the structure and optimize the topology of the structure by gradually evolving these boundaries.

[0012] S4: A multi-stage volume relaxation strategy (M-VRS) is used to gradually approximate the volume constraint in stages, giving priority to improving thermal performance in the early stages of the optimization process, improving the Lagrange multiplier update mechanism, and accelerating the convergence process of topology optimization.

[0013] S5: Flood Fill algorithm is used to traverse and mark all structures connected to the heat source using breadth-first search (BFS), and a secondary traversal is performed on the unvisited areas to identify all isolated material points that are not connected to the column structure and delete them, thereby eliminating the tip isolated structure.

[0014] Furthermore, the S1 performs geometric scaling and translation operations on an arbitrary shape CAD model stored in an STL file format; calculates a signed distance field value for each node in the background grid, and initializes a level set function based on the signed distance field, specifically including:

[0015] (1) the scaling operation comprises: traversing all vertices in the STL file, obtaining the maximum and minimum values of the model in x, y and z directions, calculating the size of each direction, dividing the background grid size by the corresponding model size in each direction, and taking the minimum scaling factor to proportionally scale all vertex coordinates;

[0016] (2) the translation operation comprises: after scaling is completed, traversing all vertex coordinates, and subtracting the minimum value in each direction to make the geometric center of the model coincide with the origin of the background grid;

[0017] (3) the calculation of the signed distance field value comprises: judging the distance of each node in the background grid relative to the model surface and assigning a positive (internal) or negative (external) sign, calculating the node level set function value through the compactly supported radial basis function (CSRBF), and intercepting the zero isosurface as the initial boundary.

[0018] Further, the S2, the local region is composed of the private area and the shared area of the current processor core, and includes all grid units and the corresponding CSRBF compact support and internal units of the processor core, so that the processor has all the necessary node information when performing CSRBF calculation.

[0019] Further, the S4, the M-VRS comprises: dividing the volume constraint into multiple volume relaxation stages, gradually tightening with the progress of the topology optimization iteration, switching to the next stage only when the current volume fraction is close to the constraint value of the stage, improving the optimization efficiency and reducing unnecessary iterations, and avoiding falling into a "tree-like" local optimal solution.

[0020] Another object of the present application is to provide a multi-core CPU parallel acceleration parameterized level set heat conduction topology optimization system based on implicit recognition and Flood Fill algorithm, which specifically comprises:

[0021] an implicit recognition model for constructing a signed distance field;

[0022] a CPU parallel finite element analysis module for realizing multi-core parallel acceleration;

[0023] a Flood Fill algorithm module for eliminating sharp isolated structures;

[0024] an M-VRS module for reducing the number of convergence iterations, so that the final structure has better performance and manufacturability.

[0025] In combination with the above technical solutions and the technical problems solved, the technical solution to be protected by the present application has the following advantages and positive effects:

[0026] First, the heat conduction topology optimization calculation framework proposed in this invention significantly improves the automation level, thermal performance and computational efficiency of the topology optimization process by introducing an implicit recognition model, the FloodFill algorithm, M-VRS and multi-core CPU parallel computing. The framework can automatically convert STL geometric models of any shape into level set functions, avoiding tedious meshing work and achieving seamless integration of CAD and optimization processes. At the same time, the FloodFill algorithm is used to effectively eliminate isolated island structures, and M-VRS is used to reduce the number of convergence iterations, so that the final structure has better performance and manufacturability. Combined with multi-core parallel acceleration, it significantly reduces the computational cost of large-scale optimization tasks, providing an efficient, stable and scalable optimization tool for the design of complex heat conduction structures, with broad engineering application prospects.

[0027] Second, the technical solution of the present invention fills the technical gap in the industry at home and abroad:

[0028] Existing heat conduction topology optimization methods often rely on manual meshing or simplification operations when processing complex CAD models, resulting in a disconnect between the design process and geometric information, and the inability to realize the engineering application of high-resolution components; at the same time, traditional parametric level set optimization lacks connectivity monitoring and global approximation strategies, and is prone to generating isolated island structures or falling into local "tree-like" optimal solutions, affecting thermal performance and manufacturing feasibility; furthermore, large-scale three-dimensional mesh solution architectures based on serial computing platforms such as MATLAB are difficult to meet the needs of rapid iteration and high-precision design in extremely high temperature and high load environments. To address the above technical difficulties, the present invention proposes a high-resolution three-dimensional parallel topology optimization method based on parameterized level sets. By automatically extracting CAD geometric information and dynamically generating refined meshes, it achieves integrated collaboration between CAD and CAE. In the optimization process, it introduces real-time connectivity monitoring and global approximation strategies such as multi-stage volume relaxation and domain decomposition to effectively suppress the generation of islands and avoid the local optimal dilemma. In addition, combined with the MPI / OpenMP parallel computing architecture, the present invention fully utilizes multi-core resources to accelerate the solution of meshes of millions of scale and above, significantly shortening the calculation time and reducing resource consumption, thus meeting the integrated design requirements of hypersonic aircraft for lightweight structure, high strength and high heat dissipation performance. Through the above innovations, the present invention not only breaks through the collaborative barriers between complex geometric models and high-precision thermal conductivity optimization, but also achieves a qualitative leap in connectivity assurance, global search capability and computational efficiency, providing important technical support for breaking through bottlenecks in the field of aircraft structure design in my country.

[0029] The technical solution of the present invention solves the technical problems that people have been eager to solve but have never been able to solve successfully: First, to address the problem of disconnection between complex geometric models and topology optimization processes, implicit recognition technology is used to automatically and accurately map CAD geometry of any shape to a high-resolution background grid, fundamentally eliminating the information loss and inefficiency caused by manual gridding; second, to address the problem that isolated island structures are difficult to avoid in heat conduction topology optimization and are prone to falling into "tree-like" local optimal solutions, Flood The Fill algorithm monitors connectivity in real time and automatically eliminates isolated materials that are not connected to the heat source during the optimization iteration process. At the same time, it combines the multi-stage volume relaxation strategy (M-VRS) to adaptively adjust the volume constraints, effectively breaking the dilemma of local stagnation of traditional level set methods in the early iteration stage due to volume constraints; thirdly, in response to the problem of huge computing resources consumption and slow iteration speed of three-dimensional grids of millions or even larger scales under serial architecture, the innovative use of multi-core CPU parallel finite element analysis and domain decomposition technology achieves significant acceleration of intensive computing tasks, so that complex heat conduction topology optimization can achieve rapid convergence while ensuring accuracy and connectivity, thereby truly meeting the integrated design requirements of hypersonic aircraft for lightweight structure, high strength and high heat dissipation performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a technical solution flow chart of a multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization method based on implicit identification and Flood Fill algorithm provided by an embodiment of the present invention;

[0031] Figure 2 This is a schematic diagram of the signed distance field synthesis of a multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization method based on implicit identification and Flood Fill algorithm provided by an embodiment of the present invention;

[0032] Figure 3 Schematic diagram of level set Boolean operations of a multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization method based on implicit identification and Flood Fill algorithm provided by an embodiment of the present invention;

[0033] Figure 4 This is a flowchart of implicit level set generation for a multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization method based on implicit identification and Flood Fill algorithm provided by an embodiment of the present invention;

[0034] Figure 5 This is a CPU finite element parallel flow chart of a multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization method based on implicit identification and Flood Fill algorithm provided by an embodiment of the present invention;

[0035] Figure 6 Schematic diagram of implicit boundary description of a level set heat conduction topology optimization method based on implicit identification and Flood Fill algorithm provided by a multi-core CPU parallel acceleration parameterized level set provided by an embodiment of the present invention;

[0036] Figure 7 Schematic diagram of an island structure of a multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization method based on implicit identification and Flood Fill algorithm provided by an embodiment of the present invention;

[0037] Figure 8 This is a flow chart of a Flood Fill algorithm for a multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization method based on implicit identification and the Flood Fill algorithm provided by an embodiment of the present invention;

[0038] Figure 9 This is a comparison chart between L-VRS and M-VRS of a multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization method based on implicit identification and Flood Fill algorithm provided by an embodiment of the present invention;

[0039] Figure 10 This is a module diagram of a multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization system based on implicit identification and Flood Fill algorithm provided by an embodiment of the present invention;

[0040] Figure 11 These are the pseudo-two-dimensional heat sink topology optimization results under three volume constraint strategies of a multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization method based on implicit identification and Flood Fill algorithm provided by an embodiment of the present invention;

[0041] Figure 12 These are the pseudo-two-dimensional heat sink topology optimization results under three Flood Fill strategies of the multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization method based on implicit identification and Flood Fill algorithm provided by an embodiment of the present invention;

[0042] Figure 13 The results of applying the multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization method based on implicit identification and Flood Fill algorithm provided by the embodiment of the present invention to the topology optimization of a three-dimensional heat sink are presented;

[0043] Figure 14 This paper compares different volume constraint strategies for a multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization method based on implicit identification and Flood Fill algorithm provided by an embodiment of the present invention.

[0044] Figure 15This is a comparison of the results of different volume relaxation strategies for a three-dimensional heat sink using a multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization method based on implicit identification and Flood Fill algorithm provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0046] In traditional heat conduction topology optimization, the level set method has good boundary evolution capabilities, but the initial level set function construction relies on manual definition or regular geometry generation, which is difficult to adapt to the input requirements of complex CAD models, limiting the wide range of practical engineering applications. The existing technology still lacks a distance field generation method that can automatically convert any complex structure into a suitable level set initialization method. This solution proposes to introduce an implicit recognition strategy based on STL models, combine it with compactly supported radial basis functions (CSRBFs) to construct a signed distance field, and automatically implement level set function initialization, so that complex CAD models can be directly embedded in the topology optimization process, improving modeling efficiency and versatility.

[0047] During the parallel computation phase of topology optimization, existing multi-core deployment methods often suffer from complex data dependencies between nodes, leading to reduced boundary computation accuracy or requiring global synchronization, significantly weakening the parallel acceleration effect. This paper constructs a dual-domain structure called "local domain + shadow domain" to clearly define the node coverage of the processor core's private area and the shared boundary area. This ensures that each core has sufficient CSRBF support domain for independent computation, thereby ensuring computational accuracy and parallel consistency, significantly reducing synchronization costs, and improving the parallel acceleration efficiency of heat conduction finite element solutions.

[0048] During topological evolution, traditional level set methods suffer from slow convergence rates and a tendency to fall into local structural dilemmas. This phenomenon, particularly under multi-objective trade-offs, often manifests as "structural branching," an impractical configuration characterized by branches connected by pointed, thin materials. This method combines parametric description with level set co-evolution, designing a set of adjustable shape parameters to guide boundary evolution. These parameters are embedded in the level set evolution equation, freeing structural evolution from complete reliance on gradient flow. This results in a regulated boundary update mechanism, enhancing the targeted direction of evolution and reducing the risk of poor local solutions.

[0049] To address the challenges of managing volume constraints in heat conduction optimization, particularly the problem of prematurely imposing global volume constraints, which can compress the search space and hinder the initial generation of high-quality structures, this method proposes a multi-stage volume relaxation strategy (M-VRS). This strategy divides the volume fraction target into multiple progressive threshold segments, advancing to the next stage of constraints only when the current optimized structure approaches a certain volume threshold. Combined with dynamically updated Lagrange multipliers, this strategy allows for gradual volume compression based on sufficient early structural evolution, achieving a balance between optimization accuracy and depth of search space exploration.

[0050] Traditional methods often use post-processing manual removal of isolated material points and dangling connectors in topological results, or rely on simple connectivity analysis, which can lead to erroneous or missed deletions. This solution introduces a Flood Fill algorithm, employing a breadth-first traversal within the grid domain. Starting from the heat source node, it marks all thermally connected areas, ensuring that the retained materials have a thermal conductivity path. Unvisited node areas are then identified and removed, systematically addressing the issue of isolated materials that cannot conduct heat in thermal structures and improving the engineering manufacturability and physical rationality of the final structure.

[0051] The present invention constructs a complete, collaborative and efficient heat conduction topology optimization framework by introducing a signed distance field automatic generation mechanism, a multi-core parallel computing domain optimization strategy, a parameterized-level set joint boundary evolution method, an M-VRS volume control mechanism and a Flood Fill isolated material removal algorithm. It systematically breaks through the bottlenecks of traditional methods in modeling flexibility, parallel performance, convergence efficiency and manufacturability, and has good practical engineering adaptability and promotion value.

[0052] An embodiment of the present invention provides a multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization method based on implicit identification and flood fill algorithm. The method specifically includes:

[0053] S1: Automatically construct signed distance fields through implicit recognition models;

[0054] S2: The computational domain is divided into private and shared areas, introducing the concepts of local and ghost domains. The heat conduction finite element solution is deployed in parallel on multi-core CPUs, significantly shortening the calculation time of a single iteration.

[0055] S3: Combining parameterization with the level set method, different topological configurations are generated by adjusting parameters. The level set method is used to describe the boundaries of the structure and to optimize the topology of the structure by gradually evolving these boundaries, thereby designing a high-performance structural solution.

[0056] S4: A multi-stage volume relaxation strategy (M-VRS) is used to gradually approximate the volume constraint in stages, prioritizing thermal performance improvement in the early stages of the optimization process to avoid prematurely falling into a local optimal solution. The Lagrange multiplier update mechanism is improved to maintain a reasonable convergence speed and further accelerate the convergence process of topology optimization.

[0057] S5: Flood Fill algorithm is used to traverse and mark all structures connected to the heat source using breadth-first search (BFS), and a secondary traversal is performed on the unvisited areas to identify all isolated material points that are not connected to the column structure and delete them, thereby eliminating the tip isolated structure.

[0058] like Figure 1 The figure shows a flowchart of a multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization method based on implicit identification and Flood Fill algorithm provided by this embodiment. By combining implicit identification models, CPU parallel finite element analysis and parameterized level set topology optimization, the present invention can achieve efficient, high-performance, and high-precision topology optimization design of complex feature structures.

[0059] 1. Implicit Recognition Model

[0060] The implicit recognition model plays a crucial role in the design process of this paper. It efficiently and accurately maps the complex geometry of the CAD model onto the background mesh, providing a rigorous geometric representation for subsequent topology optimization. This model primarily includes four key steps: model scaling and translation, generation of a signed distance field (SDF), sign correction and Boolean operations, and initialization of the level set function.

[0061] (1) Scaling and translation of the model

[0062] First, the present invention uses the STL format to import a CAD model. By traversing the coordinate information of each vertex in the STL file, the size range of the model in the x, y, and z directions is calculated. The size of the background grid in each direction is divided by the size of the model in the corresponding direction to obtain three scaling factors, and the minimum value is selected to perform geometric scaling on the model. Subsequently, the minimum value of all the model's vertices in each coordinate direction is obtained and subtracted from each vertex coordinate to achieve the overall translation of the model so that it is close to the origin of the background grid. This process ensures the reasonable matching of the model and the background grid, providing a basis for subsequent numerical calculations.

[0063] (2) Generation and correction of signed distance field

[0064] The scaled and translated model is used to construct a signed distance field, which is to calculate the shortest Euclidean distance from each node in the background mesh to the geometric boundary, and assign a positive or negative sign according to whether it is inside or outside the model. The generation process of the signed distance field includes the shortest distance optimization solution, which has global optimality and ensures that the distance value of each point is the minimum value in the mathematical sense. The final signed distance field is obtained by multiplying the sign field and the distance field, as shown in Figure 2 shown.

[0065] However, when dealing with complex geometric corners or areas with sudden normal changes, simple sign assignment based on the nearest triangle can lead to misjudgments. To address this, the present invention further introduces a detection algorithm based on axis-aligned bounding boxes to identify the voxel regions covered by boundary triangles. Subsequently, a flood fill algorithm is used to divide the entire mesh into an "external region," an "interior region," and a "boundary region." The sign value of each node is then corrected for consistency, ensuring that its domain label is consistent with the sign of the signed distance field, eliminating sign errors and improving the reliability of the geometric description.

[0066] (3) Implicit Boolean operations and composite geometric constructions

[0067] In order to handle complex boundary conditions and complex geometric structures, the present invention introduces a Boolean operation mechanism based on the signed distance field. By performing Boolean operations such as intersection and difference on the SDF generated by different CAD models, such as Figure 3 As shown, logical combinations of design domains, fixed domains, and non-design domains can be achieved. Intersection operations can be used to restrict boundary conditions to within the design domain, while difference operations can be used to eliminate invalid structures or interfering regions. This strategy not only enhances geometric modeling flexibility but also ensures the physical feasibility and boundary accuracy of the optimization problem.

[0068] (4) Initialization and reinitialization of the level set function

[0069] After the signed distance field is sign-corrected and Boolean-combined, the present invention smoothly interpolates the discrete field through the compactly supported radial basis function (CSRBF) to construct a high-order continuous level set function. 2 The continuous Wendland type CSRBF not only ensures the smoothness of the function at the boundary, but also can adapt to the corner approximation error under the condition of sparse background grid. Finally, the zero isosurface of the function is extracted, such as Figure 4 As shown, high-precision implicit modeling of arbitrarily complex geometric structures is achieved.

[0070] To improve numerical stability, the level set function is periodically reinitialized during the topology optimization iteration process so that it re-satisfies the characteristics of the signed distance function, ensuring the consistency of the geometric description during the evolution process and the stability of the calculation process.

[0071] Through this process, the implicit recognition model achieves efficient conversion from CAD geometry data to numerical representations for topology optimization, providing a solid foundation for subsequent parametric level set evolution, sensitivity analysis, and structural updates. Compared to traditional methods that require multiple manual conversions and modeling, the implicit modeling framework proposed in this paper significantly simplifies the design process, improves automation and geometric accuracy, and significantly enhances optimization efficiency and engineering applicability.

[0072] 2. CPU parallel finite element analysis

[0073] This paper proposes a finite element analysis method based on CPU-based distributed parallel computing. By fully leveraging the characteristics of a distributed memory architecture, the computational domain is divided into subdomains and distributed across multiple processors. Each processor independently performs finite element calculations in its local memory, while performing necessary data exchange and synchronization via an explicit communication network. This method linearly scales overall memory and computing resources as the number of processors increases, avoiding the cache coherence overhead associated with a global address space and achieving efficient and low-cost parallel computing.

[0074] In its implementation, this paper leverages the PETSc library's DMDA module to automatically manage grid distribution and MPI communication, and incorporates preprocessing multigrid (PCMG) techniques to improve linear equation solving efficiency. Furthermore, through a carefully designed parallel strategy, the division of private and shared regions, and the partitioning of local and ghost domains, it achieves efficient parallel solution of finite element problems in large-scale distributed systems.

[0075] (1) Parallel strategy

[0076] The parallel strategy of the present invention is based on the classic four-stage model of partitioning, communication, aggregation and mapping. Figure 5 As shown in the figure, the overall computational grid is divided into several subdomains and rationally assigned to each CPU core. Second, the MPI explicit communication mechanism is used to exchange boundary data between subdomains to ensure computational continuity. Then, the grid information of adjacent subdomains is locally merged to reduce the number of communications. Finally, load mapping is performed based on processor performance and network topology to balance computation and communication overhead and optimize overall runtime.

[0077] (2) The concepts of private and shared areas in grid division

[0078] During the subdomain division process, each subdomain consists of a private area and a shared area. The private area refers to the computing units within the subdomain, whose data is only accessible to the processor itself. The shared area refers to the computing units at the subdomain boundary that connect to adjacent subdomains, whose data is shared with adjacent processors. By clearly distinguishing between these two areas, only data in the shared area is packaged and transmitted during the communication phase, significantly reducing communication volume and improving parallel efficiency.

[0079] (3) Division and application of local domain and ghost domain

[0080] To meet the cross-domain node information requirements of the compactly supported radial basis function (CSRBF), we further divide the shared domain into a local domain and a ghost domain. The local domain covers all real node data in the subdomain; the ghost domain contains replicated information of adjacent subdomain boundary nodes outside the local domain, which is read during cross-domain calculations. This technology allows boundary nodes to obtain complete neighborhood data during the finite element assembly and solution process without the need for frequent communication requests.

[0081] In summary, the CPU-based parallel finite element analysis method proposed in this paper achieves efficient solution of finite element problems in large-scale distributed environments through a rationally designed parallel strategy, refined mesh region division, and flexible local and ghost domain management. This method exhibits excellent scalability and stability, making it suitable for a variety of engineering simulation tasks on high-performance computing platforms.

[0082] 3. Parameterized Level Set Topology Optimization

[0083] In this patent, we conduct topology optimization research based on a parameterized level set method to achieve accurate representation and efficient evolution of material boundaries. This method uses implicit functions to embed structural boundaries into a scalar field. Through parameterized basis function expansion, the partial differential equations for level set evolution can be transformed into a series of ordinary differential equations, significantly reducing computational complexity and improving convergence stability.

[0084] Furthermore, to balance topology, shape, and size optimization, the present invention introduces constraints on a parameterized basis to ensure the reconfigurability and numerical stability of the level set function. By constructing a suitable set of radial basis functions and their expansion coefficients, the scale of design variables can be flexibly controlled, and coupled with the optimizer to achieve efficient iteration.

[0085] (1) Parameterization: During the parameterization phase, we use a series of compactly supported basis functions to represent the level set implicit function, transforming the traditional node value description into the form of basis function coefficients. This way, the design variables of the optimization problem are only the parameterized coefficients, significantly reducing the number of variables. Furthermore, the local nature of the basis functions ensures that boundary changes only affect the corresponding region, improving computational efficiency.

[0086] (2) Level set method: The level set method describes the boundary between solid and cavity through implicit scalar field, such as Figure 6 As shown, this achieves a natural evolution of topological changes. Compared to explicit mesh movement, implicit representation does not need to track changes in boundary topology and can automatically handle merging and splitting. Based on parameterization, this invention retains the applicability of the level set method to complex boundary evolution while simplifying the solution of the evolution equation by utilizing parameter updates.

[0087] (3) Topology optimization: In the topology optimization process, we combine parameterized level set analysis with structural performance evaluation, obtain the sensitivity of each parameter to the objective function (thermal flexibility) through parallel finite element analysis, and iteratively update the parameters based on the gradient information. The optimization process includes:

[0088] a. Initial parameter setting: set basis function coefficients according to the initial design domain;

[0089] b. Parallel solution: Utilize CPU distributed parallel finite element analysis to calculate performance indicators and sensitivity;

[0090] c. Parameter update: adjust the basis function coefficients according to the sensitivity information;

[0091] d. Reconstruct the boundary: Generate a new level set boundary based on the updated coefficients;

[0092] e. Convergence judgment: If the performance indicators or parameter changes meet the stopping conditions, the optimization ends.

[0093] The proposed parameterized level set topology optimization method combines the flexibility of implicit boundary representation with the efficiency of parametric expression. By reducing the number of design variables and accelerating parallel computation, it enables rapid optimization of complex structures. This method significantly improves convergence speed, numerical stability, and scalability, making it suitable for topology design tasks in a wide range of engineering fields.

[0094] 4.Flood Fill Algorithm

[0095] When generating optimized structures, traditional LSM relies on boundary evolution to optimize the structural morphology, making it difficult to generate hole features inside the structure, thus limiting the design scheme's performance in topological complexity. To solve this problem, the parameterized level set topology optimization method adopts the CSRBF parameterization strategy, which overcomes the shortcomings of traditional methods in hole generation to a certain extent. However, when PLSM is used for thermal conduction topology optimization in practical applications, it is easy to produce isolated materials in the end areas of the structure. These isolated island structures are not only unable to conduct heat effectively, but also cannot be manufactured. To verify the universality of this phenomenon, this section uses the open source level set code provided by Liu et al. to conduct numerical experiments and obtain Figure 7 The topology optimization results are shown in Figure 2. The experimental results show that during the entire optimization iteration process, there are several isolated island structures in the end area of ​​the structure, which do not disappear even after the algorithm converges. Figure 7 This is highlighted in blue at step 200 (the last iteration). This phenomenon occurs because the PLSM method, when generating material distributions, does not rely on the dynamic evolution of the boundary. Instead, it controls the shape of the implicit function using an expansion coefficient and then intercepts the implicit function at the zero level (in two-dimensional problems) to obtain the material boundary. This interception at the zero level can easily lead to material disconnection.

[0096] To address this problem, this paper introduces the Flood Fill algorithm into the thermal topology optimization framework. Inspired by the diffusion process of water flow, the Flood Fill algorithm can rapidly identify all areas connected to a source point. Conceptually, heat sources and water sources share the fundamental property of continuous flow propagation, making the Flood Fill algorithm naturally applicable to this problem.

[0097] Figure 8 The whole process of identifying and eliminating isolated island structures using the Flood Fill algorithm is demonstrated. The basic principle of this algorithm is to use a pre-selected source point as the starting point and search for all pixels that are similar to the source point in terms of material existence, thermal conductivity, etc., to determine the effective heat transfer area inside the structure. Specifically, first select the heat sink as the starting point in the current thermal topology optimization results (such as Figure 8 (a) The algorithm then evaluates each neighboring pixel based on a pre-set similarity criterion: if the pixel meets the criteria and has not been visited before, it is marked as visited and stored in the data structure for subsequent searches. Figure 8 (b) shows that the three neighboring points of the pink pixel all meet the similarity criteria, and thus all three neighboring points are classified as connected regions. Next, the algorithm uses a breadth-first search strategy, expanding layer by layer, systematically exploring all neighboring pixels with similar attributes from the source point outward. Figure 8The search process shown in (c) starts from the right neighboring pixel and checks all surrounding pixels in reverse order; pixels that meet the conditions are marked with blue arrows and added to the queue, while pixels that do not meet the conditions or are at the boundary are marked with red arrows and excluded. To prevent repeated checks, the indices of all visited pixels are recorded in a dedicated data structure. When there are no new expandable pixels, the algorithm terminates, ensuring that all connected areas are fully identified and marked. Figure 8 In (d), the dark gray cells are the island structures that are not recognized by the Flood Fill algorithm. These structures will be deleted by inverting the signed distance field value. Figure 8 (e) The specific details of the FloodFill algorithm implementation process are further presented in detail, including the starting point selection strategy, node queuing strategy, node connectivity judgment strategy, and algorithm convergence strategy.

[0098] Simply put, the Flood Fill algorithm effectively ensures non-redundant exploration of connected regions by marking visited points. When applied to thermal topology optimization, starting with the heat sink, the algorithm identifies all connected material regions and identifies isolated regions disconnected from the heat sink as invalid material. By deleting or modifying these isolated islands, the structure's manufacturability is improved, ensuring a thermal design that is closer to the global optimality.

[0099] 5. Multi-stage volume relaxation strategy (M-VRS)

[0100] Research by Liu et al. has shown that increasing the number of volume relaxation steps in thermal topology optimization can bring the results closer to the global optimal solution. The linear volume relaxation strategy (L-VRS) employed in this study requires a large number of iterations to ensure the stability of the structural topology evolution, thereby allowing the topology optimization results to approach the global solution. The underlying mechanism is that when the objective function dominates the optimization process and the influence of the volume fraction constraint is relatively weak, the optimization process can remain at the optimal solution for the current volume fraction as the volume fraction decreases. However, an overly robust volume relaxation strategy can significantly increase the computational cost of large-scale optimization problems.

[0101] In response to the above problems, the present invention proposes an innovative method called M-VRS. The core of this method is to decompose the volume constraint into a multi-stage adaptive adjustment process: when the volume fraction in the current stage approaches the constraint threshold, it enters the next optimization stage. Taking the four-stage volume relaxation strategy with a volume fraction constraint of 0.2 and an initial volume fraction of 1 as an example, the constraint values ​​of each stage are set to 0.8, 0.6, 0.4 and 0.2 respectively. Through this progressive constraint mechanism, the "tree-like" local solution generated by the traditional method in the early stage of optimization due to the dominance of the volume constraint can be effectively avoided, ensuring that each stage can approach the global optimal solution.

[0102] In terms of optimization algorithm, this paper adopts the Lagrangian method to transform the constrained optimization problem into an unconstrained form. To address the problem of the traditional method where the Lagrangian multiplier decreases sharply when the volume fraction approaches the constraint value, resulting in a decrease in convergence speed, this section proposes an improved Lagrangian multiplier update strategy:

[0103]

[0104] Where λ k is the Lagrange multiplier of the kth iteration, V is the current volume fraction, V s is the target volume of the current stage, V c is the final target volume, μ k and γ k The parameter update strategy adopts two-stage regulation:

[0105]

[0106] Among them, μ0 and γ0 are initial parameters, Δμ and Δγ are incremental parameters, and γ max is the maximum constraint value. This improved strategy effectively maintains the convergence rate of the optimization process by dynamically adjusting the multiplier value. At the same time, the stage transition relaxation threshold ΔV is introduced. When V–V s – When ΔV < 0, the phase transition is triggered to avoid the optimization process from falling into local stagnation.

[0107] and Figure 9 Compared with the L-VRS shown in (a), Figure 9 (b) The M-VRS presented introduces an adaptive stage transition mechanism, which achieves phased management of volume constraints by dynamically adjusting the volume relaxation parameters during the optimization process. In the initial iteration stage, when the volume fraction of the structure is far from the set volume constraint, the strategy appropriately relaxes the volume constraint, which is conducive to fully exploring the design scheme; while in the later iteration stage, the constraint is gradually tightened to meet the volume fraction constraint and optimize the final design performance. M-VRS can significantly shorten the convergence time and improve computational efficiency, while ensuring that the optimization results are not inferior to traditional methods in terms of thermal conductivity and structural stability. In summary, through adaptive stage transition, M-VRS achieves an effective balance between global design and computational cost, providing an efficient and robust solution for topology optimization problems with practical engineering application value.

[0108] like Figure 10 As shown, an embodiment of the present invention provides a multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization system based on implicit identification and Flood Fill algorithm, specifically comprising:

[0109] Implicit recognition model for constructing signed distance fields;

[0110] CPU parallel finite element analysis module, used to achieve multi-core parallel acceleration;

[0111] Flood Fill algorithm module, used to eliminate isolated tip structures;

[0112] The M-VRS module is used to reduce the number of convergence iterations, resulting in a final structure with better performance and manufacturability.

[0113] Application 1: Radiator

[0114] Taking the engineering structure of the radiator as an example, the effects of the pseudo-two-dimensional model optimization and the three-dimensional model optimization of the present invention are tested respectively. For the pseudo-two-dimensional model, three volume constraint strategies (not using volume relaxation strategy, L-VRS, M-VRS) and three Flood Fill strategies (not using Flood Fill algorithm, using Flood Fill algorithm only in the last step of iteration, and using Flood Fill algorithm once every 20 steps in the optimization process) are used for topology optimization respectively. In these three volume constraint strategies, the volume fraction of the material in the optimization is defined as 35%. The optimization design results, final objective function values ​​and number of iteration steps of the three volume constraint strategies are shown in Figure 2. Figure 11 The figure shows the advantages of M-VRS. Figure 12 The topology optimization results and objective functions of three FloodFill strategies are presented, which demonstrates the necessity of adopting the Flood Fill algorithm.

[0115] For the three-dimensional model, two volume constraint strategies (not using volume relaxation strategy, M-VRS) are adopted. The corresponding optimization design results and the final objective function value are as follows: Figure 12 As shown. It can be seen that the use of M-VRS can successfully improve the overall heat transfer performance of the structure. In addition, in order to be able to more comprehensively display the final results, Figure 13 The final topology optimization results are shown from two isometric views.

[0116] The present invention demonstrates its significant technical effectiveness in heat conduction topology optimization through a series of comparative experiments. For the same 200×200×200 grid and three different volume constraint strategies—fixed volume, linear volume relaxation strategy (L-VRS), and multi-stage volume relaxation strategy (M-VRS)—the relaxation weight μ is fixed at 3 in L-VRS, and the Lagrange multiplier γ increases by 0.01 per step until it reaches 5. In M-VRS, the volume relaxation process is divided into 10 discrete stages, with an initial μ0 of 3 and an increment of Δμ = 0.1 per iteration. γ is incremented from 0.01 to 5 in the same step size, while ΔV = 0.1 is maintained constant. Figure 15The results show that both relaxation strategies generate a fine, "hair-like" mesh structure, in stark contrast to the "tree-like" skeletal layout that often occurs when no relaxation strategy is used. This shows that the volume relaxation strategy adopted in this invention not only gives the optimization algorithm greater freedom, allowing it to effectively avoid local optimal traps under relaxed constraints, but also, through comparison, it is found that the objective function values ​​obtained by L-VRS and M-VRS are almost the same, and both are better than the results obtained by the fixed volume strategy, further demonstrating that appropriate relaxation can significantly improve the thermal conductivity of the structure.

[0117] In further comparison of iteration efficiency, Figure 14 The results of L-VRS and M-VRS show that while both achieve similar final morphologies to the target, M-VRS requires only about 60% of the iterations of L-VRS, achieving significant computational cost savings. This efficiency improvement is particularly critical for heat conduction topology optimization at resolutions of millions or even higher, validating the effectiveness and practicality of the proposed multi-stage volume relaxation strategy within a high-performance solution framework.

[0118] Figure 15 The effectiveness of M-VRS on improving structural thermal performance was further demonstrated. In benchmark tests without any volumetric relaxation strategies, the optimized structures typically exhibited irregular tree-like branches, uneven material distribution, and tortuous flow paths. However, with M-VRS, the branches exhibited a more uniform, linear extension morphology, which not only reduced manufacturing difficulty and improved mechanical strength, but also facilitated a smoother heat conduction path. Quantitative results showed that the M-VRS design achieved an approximately 8% reduction in thermal compliance compared to a no-relaxation strategy, fully demonstrating the effectiveness of progressive relaxation in improving heat conduction efficiency in structural topology optimization.

[0119] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware portion can be implemented using dedicated logic; the software portion can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. Those skilled in the art will appreciate that the above-mentioned devices and methods can be implemented using computer-executable instructions and / or contained in processor control code, for example, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, or can be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0120] The above merely provides the specific implementation of the present application, but the protection scope of the present application is not limited thereto, any modification, equivalent replacement and improvement within the technical range disclosed by the present application and within the spirit and principle of the present application should be covered within the protection scope of the present application.

Claims

1. A parameterized level set heat conduction topology optimization method based on implicit identification and flood fill algorithm with multi-core CPU parallel acceleration, characterized by: The following steps are involved: S1, construct the signed distance field; S2, under the multi-core CPU architecture, divides the computational domain into the local domain and the ghost domain, and performs finite element heat conduction solution; S3, joint evolution of structural boundaries based on parametric design and level set method; S4, setting staged volume constraints and updating optimization variables; S5, apply the Flood Fill algorithm to remove isolated structures.

2. The method according to claim 1, wherein The S1 includes: performing proportional scaling and translation operations on the STL format three-dimensional model, embedding the model into the background grid, calculating the signed distance field of each grid node, and initializing the level set function with the field.

3. The method according to claim 1, wherein In the step of constructing the signed distance field, a compactly supported radial basis function is used to assign a value to each node, and an initial level set function is constructed based on the Euclidean distance between the node and the model boundary.

4. The method according to claim 1, wherein In S2, the local domain is composed of private units managed by the processor core and shared units within the tight support range, which are used to construct the required node neighborhood information in parallel.

5. The method according to claim 1, wherein The level set function uses a narrowband evolution method to update the boundary shape and controls the change of the topological structure by adjusting parameterized variables.

6. The method according to claim 1, wherein The volume relaxation process in S4 is divided into multiple stages, each stage sets a volume fraction limit, and enters the next stage after reaching the target value.

7. The method according to claim 1, wherein The Flood Fill algorithm adopts a breadth-first search method, marking the structural connected areas starting from the heat source connected areas, and performing a clearing operation on the unmarked material nodes.

8. A multi-core CPU parallel accelerated parameterized level set heat conduction topology optimization system based on the method according to any one of claims 1 to 7, characterized in that: include: Recognition module for STL model preprocessing and signed distance field construction; Multi-core finite element calculation module for heat conduction solution; parameterized level set module for structural boundary updates; Flood Fill algorithm module for isolated structure removal; Volume control module for staged volume-constrained scheduling.

9. The system according to claim 8, wherein The recognition module is coupled with the background grid to achieve model scaling, registration and signed distance field initialization.

10. The system according to claim 8, wherein The volume control module is provided with a volume fraction determination threshold for the switching phase, which is used to coordinate the process scheduling of the optimization process.

Images