An Adaptive Wienant Shift Acceleration Method for Solving Neutron Transport Eigenvalues

Abstract

This invention belongs to the technical field of particle transport and nuclear reactors, and discloses an adaptive Viranger shift acceleration method and system for solving neutron transport eigenvalues. The method includes the following steps: S1 Constructing the neutron transport equation, initializing eigenvalues ​​and neutron flux density, and setting the outer iteration number n; S2 Calculating the Viranger shift and corrected fission source; S3 Setting the inner iteration number. l= 0. Using the current eigenvalues, the corrected fission source term, and the Krylov subspace basis vectors, calculate the matrix-vector product; update the Krylov subspace basis vectors and the neutron flux density, and determine whether the neutron flux density converges: if it does not converge, l=l +1, return to S3; if convergence is achieved, update the eigenvalues, n=n+1, return to step S2, until the external iteration convergence criterion is met. This invention can solve the problems of slow iterative convergence speed and long computation time in advanced reactor design and optimization.

Description

Technical Field

[0001] This invention belongs to the technical field of particle transport and nuclear reactors, and more specifically, relates to an adaptive Villander shift acceleration method and system for solving neutron transport eigenvalues. Background Technology

[0002] The refined design and safety analysis of modern nuclear reactors have created an urgent need for high-fidelity neutronics simulations of the entire reactor core. For example, the design and development of advanced reactors such as small modular reactors, high-temperature gas-cooled reactors, and molten salt reactors are currently cutting-edge hot topics in the nuclear energy field. Accurate neutronics simulation of these advanced reactors is a prerequisite for achieving refined design and structural optimization. The core of such simulations is solving the neutron transport equations to obtain eigenvalues ​​and neutron flux density distribution. Currently, the power iteration method is a commonly used approach to solve this problem. This method is a nested outer-inner iteration method, where the outer iteration updates the fission source distribution and eigenvalues ​​using the neutron flux density obtained from the previous step. Each outer iteration requires a complete set of inner iterations to solve a fixed-source transport problem. Although the power iteration method is easy to implement, its convergence rate is affected by the system's dominance ratio. For large advanced reactor systems like these, the dominance ratio is typically close to 1, leading to an extremely slow convergence speed for the power iteration method. Furthermore, the novel materials and complex energy spectrum problems commonly found in advanced reactors often lead to strong self-scattering and inter-group scattering, which slows down the convergence speed of internal iterations. These two factors together constitute the computational bottleneck restricting the efficiency of advanced reactor design and optimization.

[0003] To accelerate convergence, the Viranger shift method has been proposed in existing technologies. This method introduces a shift to change the eigenvalue spectrum of the original problem, thereby effectively reducing the dominance ratio. However, the application of the traditional Viranger shift method heavily relies on the user providing an accurate prior estimate of the true eigenvalues. When facing novel, no-reference advanced reactor designs, the lack of such prior knowledge often makes the selection of the shift a challenge. An inappropriate selection may lead to slower convergence or even divergence, which greatly limits the robustness and versatility of this method in the advanced reactor design process. Furthermore, the application of the Viranger shift method inevitably enhances the coupling effect between neutron energy groups. This strong coupling characteristic between energy groups causes a sharp decrease in efficiency, or even failure, of traditional source-based internal iterative solvers. Therefore, to effectively support the research and design of advanced reactors, there is an urgent need for a comprehensive solution that can adaptively determine the shift and efficiently handle self-scattering and full-group coupling characteristics, so as to overcome both the convergence bottleneck of external iteration and the efficiency problem of internal iteration, and provide a reliable and efficient numerical simulation tool for the design optimization of advanced reactors. Summary of the Invention

[0004] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides an adaptive Villante shift acceleration method and system for solving neutron transport eigenvalues, thereby solving the problems of slow iterative convergence speed and long computation time in advanced reactor design and optimization.

[0005] To achieve the above objectives, according to one aspect of the present invention, an adaptive Wienant shift acceleration method for solving neutron transport eigenvalues ​​is provided, the method comprising the following steps:

[0006] S1 constructs a neutron transport equation using the geometry, materials, and boundary conditions of the nuclear reactor core, initializes the eigenvalues ​​and neutron flux density in the neutron transport equation, and sets the number of external iterations n=0.

[0007] S2 calculates the Wienant offset using the eigenvalues ​​at the current outer iteration number; and calculates the modified fission source in the neutron transport equation using the current Wienant offset and neutron flux density.

[0008] S3 sets the number of iterations within the system. l= 0, using the current eigenvalues, the corrected fission source term, and the Krylov subspace basis vectors. The matrix-vector product of the neutron transport equation is calculated; the vector obtained by orthogonalizing and normalizing the matrix-vector product is used as the updated Krylov subspace basis vector. ;Will l= A linear combination of the Krylov subspace basis vectors from 0 to the current value is performed, and the result is used as the neutron flux density for the current inner iteration number. The convergence of this neutron flux density is then determined.

[0009] If it does not subside l=l +1, return to S3;

[0010] If convergence is achieved, update the eigenvalues ​​according to the preset method, n=n+1, and return to step S2 until the external iteration convergence criterion is met.

[0011] Furthermore, in step S1, the formula for the neutron transport equation is as follows:

[0012]

[0013] in, It is the identity matrix; Operators that represent the conversion of neutron angular flux density to neutron standard flux density; For differential input operators; It is the inverse of the differential input operator; These are the eigenvalues ​​of the transport equation; This is the Vilant offset; Operators that represent the conversion of neutron standard flux density to neutron angular flux density; For scattering cross section operator; For fission spectrum operators; For fission cross-section operators; denoted as neutron standard flux density.

[0014] Further, in step S2, the formula for calculating the Villante offset is as follows:

[0015]

[0016] in, This is the Virant offset in the nth outer iteration; The scaling factor for the eigenvalues; To represent the deviation scaling factor; Indicates the offset conservation factor; , These are the eigenvalues ​​in the nth and (n-1)th outer iterations, respectively.

[0017] Further, in step S2, the formula for calculating the modified fission source is as follows:

[0018]

[0019] in, For the nth outer iteration, the modified fission source term is used. This is the Virant offset in the nth outer iteration; Operators that represent the conversion of neutron angular flux density to neutron standard flux density; For differential input operators; It is the inverse of the differential input operator; Operators that represent the conversion of neutron standard flux density to neutron angular flux density; For fission spectrum operators; For fission cross-section operators; Let be the neutron standard flux density in the nth outer iteration.

[0020] Furthermore, the formula for calculating the matrix-vector product is as follows:

[0021]

[0022] in, Let be the Jacobian matrix of the nth outer iteration; For the first l Krylov subspace basis vectors for the nth inner iteration and the nth outer iteration; It is the identity matrix; Operators that represent the conversion of neutron angular flux density to neutron standard flux density; For differential input operators; It is the inverse of the differential input operator; These are the eigenvalues ​​in the nth outer iteration; This is the Virant offset in the nth outer iteration; Operators that represent the conversion of neutron standard flux density to neutron angular flux density; For scattering cross section operator; For fission spectrum operators; This is the fission section operator.

[0023] Furthermore, the Krylov subspace basis vectors The calculation formula is as follows:

[0024]

[0025]

[0026]

[0027] in, Let be the next basis vector in the Krylov subspace. For vectors The Euclidean norm, For basis vectors Orthogonal vectors For vectors In basis vectors Projection coefficients in the direction, For the nth outer iteration l The first iteration i Krylov subspace basis vectors is the index of the basis vector of the Krylov subspace; This is the result vector corresponding to the matrix-vector product.

[0028] Furthermore, the formula for calculating the neutron flux density is as follows:

[0029]

[0030] in, , These are the nth outer iteration and the... l+ Neutron flux density in the first inner iteration and neutron flux density in the nth outer iteration and the 0th inner iteration. For the first i A linear combination coefficient, For the nth outer iteration l The first iteration i Krylov subspace basis vectors.

[0031] Furthermore, the formula for solving the linear combination coefficients is as follows:

[0032]

[0033]

[0034] in, The initial residual vector, For the nth outer iteration, the modified fission source term is used. It is the identity matrix; This is an operator for converting neutron angular flux density to neutron standard flux density; For differential input operators; It is the inverse of the differential input operator; These are the eigenvalues ​​in the nth outer iteration; This is the Virant offset in the nth outer iteration; This is an operator for converting neutron standard flux density to neutron angular flux density; For scattering cross section operator; For fission spectrum operators; For fission cross-section operators; Let n be the neutron standard flux density of the nth outer iteration and the 0th inner iteration; Let be the Jacobian matrix of the nth outer iteration; It is a matrix composed of all basis vectors of all Krylov subspaces; It is a vector of linear combination coefficients.

[0035] Furthermore, the formula for updating the eigenvalues ​​according to the preset method is as follows:

[0036]

[0037] in, The eigenvalues ​​are the eigenvalues ​​of the (n+1)th outer iteration; The eigenvalues ​​are the eigenvalues ​​of the nth outer iteration; This is the Virant offset in the nth outer iteration; V For the mesh volume; For fission cross-section operators; , These are the neutron standard flux densities for the nth and (n+1)th outer iterations, respectively.

[0038] According to another aspect of the present invention, an adaptive Viranger shift acceleration system for solving neutron transport eigenvalues ​​is provided, the system being used to execute the aforementioned adaptive Viranger shift acceleration method for solving neutron transport eigenvalues.

[0039] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art:

[0040] 1. This invention achieves a significant improvement in the convergence speed, stability, and automation of solving steady-state neutron transport eigenvalue problems while ensuring high accuracy by dynamically adjusting the offset and employing an advanced internal iterative solver. This greatly reduces the total computation time and accelerates the engineering design and optimization process of reactors.

[0041] 2. In this invention Defined as the principal eigenvalues ​​of the Villante offset operator, representing the eigenvalues ​​of the true system. Compared with traditional shift parameters The difference between them, this definition will reduce the computation problem from depending on the predicted parameters. The traditional form is transformed into a direct solution with physical meaning. This eliminates the uncertainty of empirical estimates of the offset. This method is not only more intuitive in its physical interpretation, but also more clearly reveals the essence of the Verant offset—through the appropriate selection of… To maximize the separation between the principal and secondary eigenvalues, thereby minimizing The value of is used to maximize the convergence rate of the outer iteration.

[0042] 3. This invention adaptively adjusts the offset based on the changes in the latest eigenvalues ​​during the iteration process. The Wienant shift method is guaranteed to have good numerical stability and computational efficiency through three parts: basic offset term, error estimation term, and conservative constraint term.

[0043] 4. This invention discloses a highly efficient computational framework and system that synergistically couples an adaptive Wienant shift method with a matrix-free multigroup Krylov subspace method. At the outer iteration level, this framework effectively reduces the advantage ratio through Wienant shift, significantly decreasing the number of costly outer iterations. At the inner iteration level, it introduces a matrix-free multigroup Krylov subspace solution method, achieving efficient convergence without explicitly constructing or storing the system matrix, and robustly handling the strong energy group coupling effect introduced by Wienant shift. The synergistic effect of these two methods fundamentally overcomes the dual convergence bottleneck of outer and inner iterations, resulting in a significant improvement in overall computational efficiency. Attached Figure Description

[0044] Figure 1 This is a flowchart of the adaptive Wienant shift acceleration method for solving neutron transport eigenvalues ​​according to the present invention.

[0045] Figure 2 This is a schematic diagram of the C5G7-3D benchmark example in the embodiment of the present invention applied to multi-group neutron transport.

[0046] Figure 3 The graph shows the calculation results of the C5G7-3D benchmark example applied to the multi-group neutron transport embodiment of the present invention.

[0047] Figure 4 This is a schematic diagram of the IAEA-3D benchmark calculation example applied to the multi-group neutron transport embodiment of the present invention.

[0048] Figure 5 The figure shows the calculation results of the IAEA-3D benchmark example applied to the multi-group neutron transport embodiment of the present invention. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0050] like Figure 1 This embodiment provides an adaptive Wienant shift acceleration method and system for solving eigenvalues ​​of neutron transport equations, specifically including:

[0051] Based on given geometric, material, and boundary conditions, S1 constructs a steady-state multi-group discrete ordinate neutron transport model that satisfies the following form:

[0052]

[0053]

[0054] in, Discrete direction angles; This represents the total number of discrete direction angles. The direction of motion of the neutron; For gradient operators; For energy groups; The total number of energy groups; The neutron angular flux density; The standard flux density of neutrons; , and These are the macroscopic total cross section, the scattering cross section, and the neutron fission cross section, respectively. Neutron fission spectrum; for k Eigenvalues; The orthogonal weights are for discrete direction angles.

[0055] For ease of discussion, the steady-state neutron transport equations are written in operator form:

[0056]

[0057] in, For differential transport operators, it represents the sum of the neutron flow term and the transport term; and These are the neutron angular flux density and the neutron standard flux density, respectively. Operators that represent the conversion of neutron standard flux density to neutron angular flux density; For scattering cross section operator; These are the eigenvalues ​​of the transport equation. ; For fission spectrum operators; This is the fission section operator.

[0058] Neutron standard flux As the objective to be solved, we have:

[0059]

[0060]

[0061] in, This represents the operator for converting neutron angular flux density to neutron standard flux density.

[0062] After the discrete model is constructed as described above, the initial feature values ​​will be used. and initial neutron flux density Given the conditions, perform an iterative solution.

[0063] At the start of each outer iteration, S2 updates the Virant offset using the following adaptive strategy based on the current iteration state. :

[0064]

[0065] in, Indicates the first Second outer iteration Represents the eigenvalue scaling factor. To represent the deviation scaling factor, This represents the offset conservation factor; in the later stages of iteration, Using the basic offset term, a basic offset is maintained even when the error is extremely small in the later stages of iteration, preventing the linear system from becoming ill-conditioned and improving the numerical stability of the algorithm. This is the error estimation term, which approximates the error of the current iteration using the difference in eigenvalues ​​between two consecutive outer iterations. When the error is large, this term provides a larger offset to ensure computational stability; when the error decreases, this term automatically decreases to ensure computational efficiency and achieve fine-tuning. As a conservative constraint, this item prevents offsets. If it is too large, the convergence will be slow.

[0066] Using the neutron flux density converged in the previous outer iteration Current updated Virant offset and fission cross section Calculate the modified fission source term corresponding to the neutron transport equation after the Wieland shift. .

[0067] S3 sets the number of iterations within the system. l= 0, using the neutron flux density converged in the previous iteration. Current updated Virant offset Current eigenvalues Fission cross section and scattering cross section Calculate the matrix-vector multiplication corresponding to the neutron transport equation after the Wieland shift:

[0068]

[0069] in, For the results obtained based on the transport scanning process and The result of the product .

[0070] Furthermore, the vectors obtained by orthogonalizing and normalizing the matrix-vector product are used as the updated Krylov subspace basis vectors. ;Will l= A linear combination of the Krylov subspace basis vectors from 0 to the current value is performed, and the result is used as the neutron flux density for the current inner iteration number. The convergence of this neutron flux density is then determined.

[0071] If it does not subside l=l +1, return to S3;

[0072] If convergence is achieved, update the eigenvalues ​​according to the preset method, n=n+1, and return to step S2 until the external iteration convergence criterion is met.

[0073] In one embodiment of the present invention, the vector obtained by orthogonalizing and normalizing the matrix-vector product is used as the updated Krylov subspace basis vector. The details are as follows:

[0074] Let the resulting vector corresponding to the matrix-vector product be:

[0075]

[0076] in, This is the result vector corresponding to the matrix-vector product; Let be the Jacobian matrix of the nth outer iteration; For the nth outer iteration l Krylov subspace basis vectors in the inner iteration.

[0077] The result vector corresponding to the matrix-vector multiplication is obtained by using the following formula. Perform orthogonalization:

[0078]

[0079]

[0080] in, is the index of the basis vector of the Krylov subspace; This is the result vector corresponding to the matrix-vector product; For the nth outer iteration l The first iteration i Krylov subspace basis vectors; For vectors In basis vectors Projection coefficient in the direction; For vectors and basis vectors The vector dot product; For basis vectors Orthogonal vectors.

[0081] Subsequently, normalization is performed using the following formula to generate the next basis vector of the Krylov subspace. :

[0082]

[0083] in, Let be the next basis vector in the Krylov subspace. For vectors The Euclidean norm.

[0084] In one embodiment of the present invention, the matrix-free multigroup Krylov subspace method involves linearly combining the Krylov subspace vectors from l=0 to l+1, with the result serving as the neutron flux density. Specifically, the linear combination is performed as follows:

[0085] The optimal linear combination coefficient vector is obtained by solving the following minimization problem. :

[0086]

[0087]

[0088] in, The initial residual vector, For the nth outer iteration, the modified fission source term is used. It is the identity matrix; Operators that represent the conversion of neutron angular flux density to neutron standard flux density; For differential input operators; It is the inverse of the differential input operator; These are the eigenvalues ​​in the nth outer iteration; This is the Virant offset in the nth outer iteration; Operators that represent the conversion of neutron standard flux density to neutron angular flux density; For scattering cross section operator; For fission spectrum operators; For fission cross-section operators; The neutron standard flux density for the nth outer iteration and the 0th inner iteration Let be the Jacobian matrix of the nth outer iteration; It is a matrix composed of all basis vectors of all Krylov subspaces; It is a vector of linear combination coefficients.

[0089] After obtaining the linear combination coefficient vector, the neutron flux density is updated using the following formula:

[0090]

[0091] in, , These are the nth outer iteration and the... l+ Neutron flux density in the first inner iteration and neutron flux density in the nth outer iteration and the 0th inner iteration. For the first i A linear combination coefficient, For the nth outer iteration l The first iteration i Krylov subspace basis vectors.

[0092] The feature values ​​are updated according to a preset method:

[0093]

[0094] in, The eigenvalues ​​are the eigenvalues ​​of the (n+1)th outer iteration; The eigenvalues ​​are the eigenvalues ​​of the nth outer iteration; This is the Virant offset in the nth outer iteration; V For the mesh volume; For fission cross-section operators; , These are the neutron standard flux densities for the nth and (n+1)th outer iterations, respectively.

[0095] Figure 2 A schematic diagram of the C5G7-3D benchmark computation example in a multi-group neutron transport embodiment is shown. The adaptive Wienant shift and matrix-free multi-group Krylov co-coupling algorithm disclosed in this invention, the matrix-free multi-group Krylov algorithm alone, and the traditional power iteration algorithm are applied to the C5G7-3D benchmark computation example, and their performance is tested. The results are as follows: Figure 3 As shown in the table, it is evident that compared to the traditional power iteration algorithm, the adaptive Wienant shift and matrix-free multigroup Krylov cooperative coupling algorithm disclosed in this invention can significantly reduce the number of outer iterations, achieving convergence in only 12 iterations. The relevant convergence count and convergence time are shown in Table 1. Compared to the traditional power iteration algorithm, the adaptive Wienant shift and matrix-free multigroup Krylov cooperative coupling algorithm disclosed in this invention achieves a 6.5-fold iteration speedup and a 4.8-fold time speedup.

[0096] Figure 4 A schematic diagram of the IAEA-3D benchmark calculation in a multi-group neutron transport example is shown. Similarly, the three calculation methods were applied to the IAEA-3D benchmark calculation, and their performance was tested. The results are as follows: Figure 5 As shown in Table 2, it is evident that, compared to the traditional power iteration algorithm, the adaptive Wienant shift and matrix-free multigroup Krylov cooperative coupling algorithm disclosed in this invention significantly reduces the number of outer iterations required for convergence, achieving convergence in only 42 iterations. The relevant convergence count and convergence time are shown in Table 2. Compared to the traditional power iteration algorithm, the adaptive Wienant shift and matrix-free multigroup Krylov cooperative coupling algorithm disclosed in this invention achieves a 17.1-fold iteration speedup and a 15.3-fold time speedup.

[0097] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An adaptive Wienant shift acceleration method for solving neutron transport eigenvalues, characterized in that, The method includes the following steps: S1 constructs a neutron transport equation using the geometry, materials, and boundary conditions of the nuclear reactor core, initializes the eigenvalues ​​and neutron flux density in the neutron transport equation, and sets the number of external iterations n=0. S2 calculates the Wienant offset using the eigenvalues ​​at the current outer iteration number; and calculates the modified fission source in the neutron transport equation using the current Wienant offset and neutron flux density. S3 sets the number of iterations within the system. l= 0, using the current eigenvalues, the corrected fission source term, and the Krylov subspace basis vectors. The matrix-vector product of the neutron transport equation is calculated; the vector obtained by orthogonalizing and normalizing the matrix-vector product is used as the updated Krylov subspace basis vector. ;Will l= A linear combination of the Krylov subspace basis vectors from 0 to the current value is performed, and the result is used as the neutron flux density for the current inner iteration number. The convergence of this neutron flux density is then determined. If it does not subside l=l +1, return to S3; If convergence is achieved, update the eigenvalues ​​according to the preset method, n=n+1, and return to step S2 until the external iteration convergence criterion is met.

2. The adaptive Wienant shift acceleration method for solving neutron transport eigenvalues ​​as described in claim 1, characterized in that, In step S1, the neutron transport equation is as follows: in, It is the identity matrix; Operators that represent the conversion of neutron angular flux density to neutron standard flux density; For differential input operators; It is the inverse of the differential input operator; These are the eigenvalues ​​of the transport equation; This is the Vilant offset; Operators that represent the conversion of neutron standard flux density to neutron angular flux density; For scattering cross section operator; For fission spectrum operators; For fission cross-section operators; denoted as neutron standard flux density.

3. The adaptive Wienant shift acceleration method for solving neutron transport eigenvalues ​​as described in claim 1, characterized in that, In step S2, the formula for calculating the Villante offset is as follows: in, This is the Virant offset in the nth outer iteration; The scaling factor for the eigenvalues; To represent the deviation scaling factor; Indicates the offset conservation factor; , These are the eigenvalues ​​in the nth and (n-1)th outer iterations, respectively.

4. The adaptive Wienant shift acceleration method for solving neutron transport eigenvalues ​​as described in claim 3, characterized in that, In step S2, the formula for calculating the modified fission source is as follows: in, For the nth outer iteration, the modified fission source term is used. This is the Virant offset in the nth outer iteration; Operators that represent the conversion of neutron angular flux density to neutron standard flux density; For differential input operators; It is the inverse of the differential input operator; Operators that represent the conversion of neutron standard flux density to neutron angular flux density; For fission spectrum operators; For fission cross-section operators; Let be the neutron standard flux density in the nth outer iteration.

5. The adaptive Wienant shift acceleration method for solving neutron transport eigenvalues ​​as described in claim 4, characterized in that, The formula for calculating the matrix-vector product is as follows: in, Let be the Jacobian matrix of the nth outer iteration; For the first l Krylov subspace basis vectors for the nth inner iteration and the nth outer iteration; It is the identity matrix; Operators that represent the conversion of neutron angular flux density to neutron standard flux density; For differential input operators; It is the inverse of the differential input operator; These are the eigenvalues ​​in the nth outer iteration; This is the Virant offset in the nth outer iteration; Operators that represent the conversion of neutron standard flux density to neutron angular flux density; For scattering cross section operator; For fission spectrum operators; This is the fission section operator.

6. The adaptive Wienant shift acceleration method for solving neutron transport eigenvalues ​​as described in claim 5, characterized in that, The Krylov subspace basis vectors The calculation formula is as follows: in, Let be the next basis vector in the Krylov subspace. For vectors The Euclidean norm, For basis vectors Orthogonal vectors For vectors In basis vectors Projection coefficients in the direction, For the nth outer iteration l The first iteration i Krylov subspace basis vectors is the index of the basis vector of the Krylov subspace; This is the result vector corresponding to the matrix-vector product.

7. The adaptive Wienant shift acceleration method for solving neutron transport eigenvalues ​​as described in claim 6, characterized in that, The formula for calculating the neutron flux density is as follows: in, , These are the nth outer iteration and the... l+ Neutron flux density in the first inner iteration and neutron flux density in the nth outer iteration and the 0th inner iteration. For the first i A linear combination coefficient, For the nth outer iteration l The first iteration i Krylov subspace basis vectors.

8. The adaptive Wienant shift acceleration method for solving neutron transport eigenvalues ​​as described in claim 7, characterized in that, The formula for solving the linear combination coefficients is as follows: in, The initial residual vector, For the nth outer iteration, the modified fission source term is used. It is the identity matrix; This is an operator for converting neutron angular flux density to neutron standard flux density; For differential input operators; It is the inverse of the differential input operator; These are the eigenvalues ​​in the nth outer iteration; This is the Virant offset in the nth outer iteration; This is an operator for converting neutron standard flux density to neutron angular flux density; For scattering cross section operator; For fission spectrum operators; For fission cross-section operators; Let n be the neutron standard flux density of the nth outer iteration and the 0th inner iteration; Let be the Jacobian matrix of the nth outer iteration; It is a matrix composed of all basis vectors of all Krylov subspaces; It is a vector of linear combination coefficients.

9. The adaptive Wienant shift acceleration method for solving neutron transport eigenvalues ​​as described in claim 1, characterized in that, The formula for updating feature values ​​according to the preset method is as follows: in, The eigenvalues ​​are the eigenvalues ​​of the (n+1)th outer iteration; The eigenvalues ​​are the eigenvalues ​​of the nth outer iteration; This is the Virant offset in the nth outer iteration; V For the mesh volume; For fission cross-section operators; , These are the neutron standard flux densities for the nth and (n+1)th outer iterations, respectively.

10. An adaptive Wienant shift acceleration system for solving neutron transport eigenvalues, characterized in that, The system is used to execute the adaptive Wienant shift acceleration method for solving neutron transport eigenvalues ​​as described in any one of claims 1-9.

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