Coated target electromagnetic scattering modeling method based on multi-core heterogeneous parallel computing

Abstract

The invention discloses a coated target electromagnetic scattering modeling method based on multi-core heterogeneous parallel computing, and belongs to the field of computational electromagnetism and high-performance computing. The method comprises the steps that an MPI + OpenMP + DSP three-level heterogeneous parallel framework is constructed, and optimal configuration of computing resources is achieved through one-to-one binding of an MPI process and a DSP acceleration card and one-to-one mapping of an OpenMP thread and a CPU core; dispersing a to-be-solved coating target by adopting a triangular grid, and defining an RWG primary function to expand surface current; substituting the surface current approximate expansion into an electric field integral equation based on impedance boundary conditions; carrying out impedance matrix calculation by adopting a process-based parallel filling strategy, and carrying out parallel solution on a matrix equation based on a ScaLAPACK library; and finally, calculating a far-region scattering field and a radar scattering sectional area according to the solved current coefficient. According to the method, through an innovative heterogeneous parallel architecture and a calculation task scheduling strategy, the problems of insufficient memory and low calculation efficiency during processing of an electrically large coated target in a traditional method are effectively solved, and an efficient and reliable technical means is provided for electromagnetic stealth design of a complex target.

Description

Technical Field

[0001] This invention belongs to the fields of high-performance computing and computational electromagnetics, and relates to a method for modeling electromagnetic scattering of coated targets based on multi-core heterogeneous parallel computing. Background Technology

[0002] In recent years, with the increasing demands for stealth performance in modern weaponry, structures coated with radar-absorbing materials have been widely used in aerospace and other fields. These composite structures, by applying functional coatings to the substrate surface, can effectively control the electromagnetic scattering characteristics of targets. However, traditional integral equation methods face challenges in analyzing such structures: directly discretizing the coating medium in three dimensions leads to a dramatic increase in computational load, severely impacting solution efficiency.

[0003] To overcome this challenge, the Electric Field Integral Equation (EFIE) method based on Impedance Boundary Conditions (IBC) has emerged. This method introduces the concept of surface impedance, equating the volume effect of the coated medium to the boundary conditions of the conductor surface. While maintaining computational accuracy, it reduces the problem dimension from three to two, significantly improving computational efficiency. This innovation makes the IBC-EFIE method an effective tool for analyzing the electromagnetic properties of coated structures, demonstrating significant value in engineering practice.

[0004] However, the IBC-EFIE method still faces significant challenges when dealing with electrically large coated structures. The number of unknowns generated by discretization increases with the square of the electrical size, leading to an exponential increase in computational complexity and memory requirements. Traditional serial computing methods often require days or even weeks to solve such problems, severely limiting engineering design efficiency. Although the introduction of multi-core parallel and heterogeneous computing technologies has alleviated the computational pressure to some extent, existing methods still have many shortcomings in task scheduling, memory access, and load balancing, making it difficult to fully utilize the performance potential of modern computing hardware.

[0005] Therefore, there is an urgent need to develop a new parallel computing method to achieve a qualitative leap in the efficiency of electromagnetic modeling of coated structures through innovative algorithm design and architecture optimization. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention proposes a method for modeling electromagnetic scattering of coated targets based on multi-core heterogeneous parallel computing. This invention designs a three-level parallel architecture of "MPI+OpenMP+DSP," which perfectly matches the parallel computing method with the node hardware configuration, effectively improving the solution efficiency of large-scale electromagnetic problems.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A method for modeling electromagnetic scattering of coated targets based on multi-core heterogeneous parallel computing, characterized by the following steps:

[0009] Step 1: Establish a heterogeneous parallel framework: adopt the heterogeneous parallel strategy of "MPI+OpenMP+DSP". Each MPI process controls one DSP card, and each MPI process uses OpenMP to ensure that each MPI process has 4 threads (4 CPU cores) to meet the load balancing requirements.

[0010] Step 2: Divide the coating target model to be solved using a triangular mesh to obtain all triangular mesh information; define RWG basis functions based on the triangular mesh information to expand and approximate the surface current.

[0011] Step 3: Substitute the approximate expansion of the surface current into the electric field integral equation based on impedance boundary conditions (IBC-EFIE) to establish the matrix equation for solving the current, expressed as:

[0012] ZI = V

[0013] Where Z is the impedance matrix, I is the current coefficient vector to be solved, and V is the excitation term on the right side.

[0014] Step 4: Solve the matrix equation to obtain the current coefficient vector, then calculate the far-field scattering electric field based on the current coefficient vector, and finally calculate the target radar cross-section of the coating structure model to be solved.

[0015] Furthermore, the specific process of step 1 is as follows:

[0016] Step 1.1, Hardware Architecture and Parallelism Strategy: For a supercomputing node with a hardware configuration of 16-core CPU + 4 DSP cards, a collaborative computing framework is built based on MPI process-level parallelism. Step 1.2, MPI Process Allocation and Device Binding: Global process management is performed through MPI_COMM_RANK() and MPI_COMM_SIZE(). Each node is allocated 4 MPI processes, and a strategy of taking the MPI process number modulo 4 is used to achieve static binding between MPI processes and DSP accelerator cards.

[0017] Step 1.3, Intra-node thread-level parallelism: Within each MPI process, OpenMP is used to create 4 threads for parallelism, realizing a one-to-one mapping between OpenMP threads and CPU physical cores.

[0018] Through steps 1.1 to 1.3, a three-level parallel architecture of "MPI+OpenMP+DSP" is finally formed: four MPI processes manage four DSPs respectively, and the four OpenMP threads of each MPI process drive the corresponding CPU cores, ensuring that all computing units are fully utilized.

[0019] Furthermore, the specific process of step 2 is as follows:

[0020] Step 2.1: Geometrically discretize the target surface S to be coated using a triangular mesh, and define the RWG basis function f based on this triangular mesh. n (r), whose expression is:

[0021]

[0022] Where n represents the index of the basis function, and Represents two adjacent triangles. and Represent and The area of ​​the triangle, l n Let be the length of the common side of two adjacent triangles. represent The vector from the vertex of the middle triangle to the field point r. represent The vector from midpoint r to the vertex.

[0023] Step 2.2: Expand the surface current J(r) using RWG basis functions. The expansion is as follows:

[0024]

[0025] Among them, a n This represents the current coefficient of the unknown quantity, where N is the number of unknown quantities.

[0026] Furthermore, the specific process of step 3 is as follows: Step 3.1, Filling the impedance matrix:

[0027] 3.1.1 Matrix Distribution Strategy: Based on the ScaLAPACK parallel computing framework, a two-dimensional block cyclic distribution mode is adopted to dynamically divide the impedance matrix into multiple sub-matrices and distribute them to different MPI processes according to a preset two-dimensional process grid topology, thereby achieving distributed data storage. Since the size of the impedance matrix is ​​known during the establishment of the matrix equations, the distribution of the impedance matrix is ​​planned in advance to ensure balanced computational load.

[0028] Step 3.1.2, Local Calculation Range Determination: Each MPI process determines its own calculation range; specifically, by determining the global coordinates of the impedance matrix elements to be calculated and the jurisdiction area of ​​the MPI process in the grid, the local impedance matrix elements to be calculated are located to avoid repeated calculations and storage redundancy.

[0029] Step 3.1.3, In-process parallel acceleration: OpenMP thread-level parallelism is adopted within each MPI process; specifically, the task of calculating the local impedance matrix is ​​decomposed into multiple parallel subtasks, and the loop calculation is executed in parallel by multiple threads to make full use of the computing advantages of the multi-core CPU architecture.

[0030] Step 3.2: Fill in the right-hand stimulus terms:

[0031] The filling method for the right-hand excitation terms is the same as the filling method for the impedance matrix. Each MPI process calculates the corresponding right-hand excitation terms by determining whether they belong to the information of this process, and fills them into the corresponding positions.

[0032] Furthermore, the specific process of step 4 is as follows:

[0033] Step 4.1, Heterogeneous Porting of Mathematical Library: Replace the standard CPU mathematical library with a DSP-specific mathematical core library to ensure that some mathematical library calculations are executed on the DSP, thereby achieving efficient execution of computational tasks.

[0034] Step 4.2, Cooperative scheduling of computational tasks: The parallel LU decomposition method is used for solving the problem; during the parallel LU decomposition process, computationally intensive tasks are scheduled to be executed by the DSP.

[0035] Step 4.3, Performance Parameter Optimization Configuration: Determine the optimal computation parameters through parallel LU decomposition performance testing.

[0036] Based on the above technical solution, the beneficial effects of the present invention are as follows:

[0037] In this invention, a three-tiered parallel architecture of "MPI+OpenMP+DSP" is designed to perfectly match the parallel computing method with the node hardware configuration (1 CPU + 4 DSPs). By having "4 MPI processes per node, and each process bound to 1 DSP," exclusive, conflict-free access to the DSP accelerator card is achieved. OpenMP distributes the computational tasks within each MPI process across the 4 CPU cores, allowing both the CPU and DSP to work simultaneously. The CPU can handle tasks such as task scheduling, data processing, and complex branch decisions unsuitable for DSP computation, while the DSP focuses on highly parallel, computationally intensive kernel functions. For example, replacing the CPU's BLAS with mtblas accelerates matrix solving by more than double. For expansion between nodes, simply add computing nodes in the same pattern; the number of MPI processes increases accordingly, while the framework structure remains unchanged, facilitating large-scale expansion. This invention provides an efficient parallel computing method for modeling electromagnetic scattering of coated targets. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of the parallel algorithm flow of the present invention.

[0039] Figure 2 This is a schematic diagram of a heterogeneous parallel framework of "MPI+OpenMP+DSP".

[0040] Figure 3 This is a schematic diagram of the cyclic distribution of two-dimensional blocks in a matrix.

[0041] Figure 4 This is a schematic diagram of a coated amygdala model.

[0042] Figure 5 The calculation results are for the RCS of the coated amygdala model.

[0043] Figure 6 This demonstrates the positive acceleration effect of the CPU / DSP heterogeneous parallel framework.

[0044] Figure 7 This is a comparison chart of the efficiency of CPU / DSP heterogeneous parallel framework and traditional CPU parallel framework. Detailed Implementation

[0045] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0046] This embodiment provides a method for modeling electromagnetic scattering of coated targets based on multi-core heterogeneous parallel computing. The specific implementation process is as follows: Figure 1 As shown, the main steps include: first, establishing a three-level parallel framework of "MPI+OpenMP+DSP"; then, performing geometric modeling and mesh discretization, and defining RWG basis functions; then, establishing the matrix equation ZI=V; finally, obtaining the current coefficient by solving the equation, and calculating the far-field scattering field and radar cross section (RCS).

[0047] The detailed steps are as follows:

[0048] Step 1: Establish a heterogeneous parallel framework: adopt the heterogeneous parallel strategy of "MPI+OpenMP+DSP". Each MPI process controls one DSP card, and each MPI process uses OpenMP to ensure that each MPI process has 4 threads (4 CPU cores) to meet the load balancing requirements.

[0049] Step 2: Divide the coating target model to be solved using a triangular mesh to obtain all triangular mesh information; define RWG basis functions based on the triangular mesh information to expand and approximate the surface current.

[0050] Step 3: Substitute the approximate expansion of the surface current into the electric field integral equation based on impedance boundary conditions (IBC-EFIE) to establish the matrix equation for solving the current, expressed as:

[0051] ZI=V (1)

[0052] Where Z is the impedance matrix, I is the current coefficient vector to be solved, and V is the excitation term on the right side.

[0053] The formula for calculating the area integral equation of the coating target model is as follows:

[0054]

[0055] Where η0 is the wave impedance in vacuum, J and M correspond to the surface current and magnetic current, respectively, and n represents the normal vector. Represents the normal of the incident wave.

[0056] Operators L and K are defined as follows:

[0057]

[0058] k represents the wavenumber, r′ represents the source point, r represents the field point, j represents the imaginary element, and G(r,r′) represents the Green's function in free space, expressed as:

[0059]

[0060] Here we define R = |rr′|.

[0061] The relationship between J and M is:

[0062]

[0063] M=-η0η S n×J (7)

[0064] η0 represents the wave impedance in vacuum, η s Let J represent the relative surface impedance of the coating material. Replacing M with J in Formula 2, and employing the Galerkin test with the RWG basis function as the test function, the impedance matrix is ​​then discretized and calculated using the following formula:

[0065]

[0066] In the above formula, Z mn Let denote the element in the m-th row and n-th column of the impedance matrix, and the superscript ++ indicates that it is formed by a triangle. and triangle The calculated impedance matrix elements, with superscripts + and - indicating triangular shapes. and triangle The calculated impedance matrix elements, with superscripts -+ indicating triangular... and triangle The calculated impedance matrix elements, with the superscript -- indicating a triangle and triangle Calculate the elements of the impedance matrix.

[0067] Consider the first item have:

[0068]

[0069] Here, m represents the test function f. m The number of (r), Represents a triangle area, l m Two adjacent triangles The length of the common edge, These represent the vertices corresponding to the common edge.

[0070] According to formula (9), the calculation of the impedance matrix elements is only related to the triangle. and Therefore, each MPI process only needs to store the corresponding triangular unit to calculate the corresponding impedance matrix element, and there is no need for communication between MPI processes.

[0071] Step 4: Solve the matrix equation to obtain the current coefficient, then calculate the far-field scattering electric field based on the current coefficient, and finally calculate the radar cross-section of the coating structure model to be solved.

[0072] Optionally, the specific process of step 1 includes:

[0073] Step 1.1 Hardware Architecture and Parallelism Strategy: For supercomputing nodes with a hardware configuration of 16-core CPU + 4 DSP cards, a collaborative computing framework is built based on MPI process-level parallelism.

[0074] Step 1.2, MPI process allocation and device binding: Global process management is performed through MPI_COMM_RANK() and MPI_COMM_SIZE(); 4 MPI processes are allocated to each node, and the static binding between MPI processes and DSP acceleration cards is achieved by using the strategy of taking the MPI process number as a remainder of 4.

[0075] Step 1.3, Intra-node thread-level parallelism: Within each MPI process, OpenMP is used to create 4 threads for parallelism, realizing a one-to-one mapping between OpenMP threads and CPU physical cores.

[0076] Through steps 1.1 to 1.3, a three-level parallel architecture of "MPI+OpenMP+DSP" is finally formed: four MPI processes manage four DSPs respectively, and the four OpenMP threads of each MPI process drive the corresponding CPU cores, ensuring that all computing units are fully utilized.

[0077] Optionally, the specific process of step 2 is as follows:

[0078] Step 2.1: Geometrically discretize the surface S of the coated structure model to be solved using a triangular mesh, and define the RWG basis function f based on this triangular mesh. n (r), whose expression is:

[0079]

[0080] Where n represents the index of the basis function, and Represents two adjacent triangles. and Represent and The area of ​​the triangle, l n Let be the length of the common side of two adjacent triangles. represent The vector from the vertex of the middle triangle to the field point r. represent The vector from midpoint r to the vertex.

[0081] Step 2.2: Expand the surface current J(r) using RWG basis functions. The expansion is as follows:

[0082]

[0083] Among them, a n This represents the current coefficient of the unknown quantity, where N is the number of unknown quantities.

[0084] like Figure 3 The coated amygdala model shown is subjected to plane wave incidence at a frequency of 3 GHz and an incidence angle θ = 90°. o φ=0 o The polarization mode is vertical polarization, and the relative permittivity ε of the coating material is... r =9+9j,μ r =9+9j, with a coating thickness of 0.005 times the wavelength, the model is discretized using RWG basis functions, generating a total of 85881 unknowns, and its bistatic RCS is calculated.

[0085] Optionally, the specific process of step 3 is as follows:

[0086] Step 3.1: Fill in the impedance matrix:

[0087] 3.1.1 Matrix Distribution Strategy: Based on the ScaLAPACK parallel computing framework, a two-dimensional block cyclic distribution mode is adopted to dynamically divide the impedance matrix into multiple sub-matrices and distribute them to different MPI processes according to the preset two-dimensional process grid topology to achieve distributed data storage; during the process of establishing the matrix equation, the size of the impedance matrix is ​​known, so the distribution of the impedance matrix in advance can further ensure the balanced computing load.

[0088] Step 3.1.2, Local Calculation Range Determination: Each MPI process determines its own calculation range; specifically, by determining the global coordinates of the impedance matrix elements to be calculated and the jurisdiction area of ​​the MPI process in the grid, the local impedance matrix elements to be calculated are located to avoid repeated calculations and storage redundancy.

[0089] Step 3.1.3, In-process parallel acceleration: OpenMP thread-level parallelism is adopted within each MPI process; specifically, the task of calculating the local impedance matrix is ​​decomposed into multiple parallel subtasks, and the loop calculation is executed in parallel by multiple threads to make full use of the computing advantages of the multi-core CPU architecture.

[0090] Step 3.2: Fill in the right-hand stimulus terms:

[0091] The filling method for the right-hand excitation terms is the same as the filling method for the impedance matrix. Each MPI process calculates the corresponding right-hand excitation terms by determining whether they belong to the information of this process, and fills them into the corresponding positions.

[0092] like Figure 4 The diagram shows a two-dimensional block cyclic distribution of the matrix. The left image shows the matrix distribution within the MPI process grid, with the numbers on the left and top representing the row and column coordinates of the matrix, respectively. The right image shows the data for each MPI process. When assigning tasks, a global index (i.e., the element's index within the entire matrix) is needed, while when using matrix elements, a local index (i.e., the element's index within the matrix of its current process) is required.

[0093] Optionally, the specific process of step 4 is as follows:

[0094] Step 4.1, Heterogeneous Porting of Mathematical Library: Replace the standard CPU mathematical library at the bottom layer of ScaLAPACK with the DSP mathematical library.

[0095] Step 4.2, Cooperative scheduling of computational tasks: During the parallel LU decomposition process, the matrix block update computation task is automatically scheduled to be executed by the DSP; at the same time, the CPU is responsible for the logical operations of process control, task scheduling and MPI communication, forming a cooperative computing mode between the CPU and the DSP.

[0096] Step 4.3, Performance Parameter Optimization Configuration: The optimal calculation parameters are determined through system performance testing. In this embodiment, the optimal calculation parameters are: the matrix block size is set to 198×198 to achieve a balance between computational efficiency and communication overhead. Simultaneously, a near-square process grid shape (P x Q) is adopted to solve the matrix equation ZI = V to obtain the current coefficient vector I.

[0097] Furthermore, the scattered field is calculated using the following formula:

[0098]

[0099] Find the far-field scattering field E s In the above formula It is called the radial vector, r represents the field point, and r′ represents the source point.

[0100] Furthermore, using the radar cross-section calculation formula:

[0101]

[0102] The radar cross section σ of the coated amygdala model in this embodiment is calculated, where E i This represents the incident excitation electric field.

[0103] The radar cross section curve of the coated amygdala model in this embodiment is shown in the figure below. Figure 5 As shown in the figure, the radar cross section calculated using the method of this invention is in good agreement with the reference result, further proving the correctness of the parallel algorithm.

[0104] In this embodiment, the speedup of solving the matrix equations of the coated amygdala model compared to traditional CPU parallel computing is as follows: Figure 6 , Figure 7 As shown: From Figure 6 As can be seen, the CPU / DSP heterogeneous parallel solution achieves a speedup of more than 2 times compared to CPU-based parallel computing. However, as the number of nodes increases, the proportion of communication overhead gradually rises, leading to a slight decrease in the speedup, which is in line with expectations. Figure 7 It can be seen that the CPU / DSP heterogeneous parallel framework outperforms the traditional CPU parallel framework compared to CPU parallel computing, thus proving the good acceleration effect of the heterogeneous parallel framework.

[0105] The above description is merely a specific embodiment of the present invention. Any feature disclosed in this specification may be replaced by other equivalent or similar features unless otherwise specified. All disclosed features, or steps in all methods or processes, may be combined in any way except for mutually exclusive features or steps.

Claims

1. A method for modeling electromagnetic scattering of coated targets based on multi-core heterogeneous parallel computing, characterized in that, Includes the following steps: Step 1: Establish a heterogeneous parallel framework: adopt the heterogeneous parallel strategy of "MPI+OpenMP+DSP". Each MPI process controls one DSP card, and each MPI process uses OpenMP to ensure that each MPI process has 4 threads, thereby satisfying load balancing. Step 2: Divide the coating target model to be solved into triangular meshes to obtain all triangular mesh information; RWG basis functions are defined based on triangular mesh information to expand and approximate the surface current; Step 3: Substitute the approximate expansion of the surface current into the electric field integral equation based on the impedance boundary conditions to establish the matrix equation for solving the current, expressed as: ZI = V Where Z is the impedance matrix, I is the current coefficient vector to be solved, and V is the excitation term on the right side; Step 4: Solve the matrix equation to obtain the current coefficient vector; then calculate the far-field scattering electric field based on the current coefficient vector, and then calculate the target radar cross-section of the coated target model to be solved.

2. The method for modeling electromagnetic scattering of coated targets based on multi-core heterogeneous parallel computing as described in claim 1, characterized in that, The specific process of step 1 includes: Step 1.1, Hardware Architecture and Parallelism Strategy: For a supercomputing node with a hardware configuration of 16-core CPU + 4 DSP cards, a collaborative computing framework is built based on MPI process-level parallelism. Step 1.2, MPI process allocation and device binding: MPI processes are managed globally using MPI_COMM_RANK() and MPI_COMM_SIZE(); each node is allocated 4 MPI processes, and the static binding between MPI processes and DSP acceleration cards is achieved by using the strategy of taking the MPI process number as a remainder of 4. Step 1.3, Intra-node thread-level parallelism: Within each MPI process, OpenMP is used to create 4 threads for parallelism, realizing a one-to-one mapping between OpenMP threads and CPU physical cores.

3. The method for modeling electromagnetic scattering of coated targets based on multi-core heterogeneous parallel computing as described in claim 2, characterized in that... Step 2 includes the following specific steps: Step 2.1: Geometrically discretize the surface of the target model to be coated using a triangular mesh; define the RWG basis function f based on the triangular mesh. n (r), whose expression is: Where n represents the index of the basis function, and Represents two adjacent triangles. and Represent and The area of ​​the triangle, l n Let be the length of the common side of two adjacent triangles. represent The vector from the vertex of the middle triangle to the field point r. represent The vector from the midpoint r to the vertex of the triangle; Step 2.2: Expand the surface current J(r) using RWG basis functions. The expansion is as follows: Among them, a n This represents the current coefficient of the unknown quantity, where N is the number of unknown quantities.

4. A method for modeling electromagnetic scattering of coated targets based on multi-core heterogeneous parallel computing as described in claim 2 or 3, characterized in that, Step 3 includes the following specific steps: Step 3.1: Fill in the impedance matrix: 3.1.1 Matrix Distribution Strategy: Based on the ScaLAPACK parallel computing framework, a two-dimensional block cyclic distribution mode is adopted to dynamically divide the impedance matrix into multiple sub-matrices and distribute them to different MPI processes according to the preset two-dimensional process grid topology to achieve distributed data storage. Step 3.1.2, Local Calculation Range Determination: Each MPI process determines its own calculation range; specifically, by determining the global coordinates of the impedance matrix elements to be calculated and the jurisdiction area of ​​the MPI process in the grid, the local impedance matrix elements to be calculated are located. Step 3.1.3, In-process parallel acceleration: OpenMP thread-level parallelism is adopted within each MPI process; specifically, the task of calculating the local impedance matrix is ​​decomposed into multiple parallel subtasks, and the loop calculation is executed in parallel by multiple threads. Step 3.2: Fill in the right-hand stimulus terms: The filling method for the right-hand excitation terms is the same as the filling method for the impedance matrix. Each MPI process calculates the corresponding right-hand excitation terms by determining whether they belong to the information of this process, and fills them into the corresponding positions.

5. The method for modeling electromagnetic scattering of coated targets based on multi-core heterogeneous parallel computing as described in claim 4, characterized in that, Step 4 includes the following specific steps: Step 4.1, Heterogeneous Porting of Mathematical Library: Replace the standard CPU mathematical library with the DSP mathematical library; Step 4.2, Cooperative scheduling of computational tasks: The parallel LU decomposition method is used for solving the problem; during the parallel LU decomposition process, computationally intensive tasks are scheduled to be executed by the DSP. Step 4.3, Performance Parameter Optimization Configuration: Determine the optimal calculation parameters through parallel LU decomposition performance testing.

Images