16 results about "Linear algebraic equation" patented technology

The invention discloses a semi-analytic solution-based energy flow calculation method and system for an electricity-gas integrated energy system, and the method comprises the steps: firstly building an ordinary differential-algebraic model of an electricity-gas network based on a numerical boundary extrapolation and semi-discrete method; based on a semi-analytical theory of differential transformation, establishing a linearized electricity-gas network model; carrying out block calculation on a matrix and self-adaptive adjustment on a time window; and finally solving the model to obtain an energy flow calculation result. According to the method, the original nonlinear partial differential equation of the gas network is converted into the linear algebraic equation, the complex nonlinear problem in traditional gas network modeling is simplified, errors caused by local linearization and time difference are avoided, the calculation scale is reduced, and the calculation robustness is improved.

The invention discloses a method and a system for evaluating the bearing capacity of the lower part of a scouring damage bridge under the action of multiple loads. The method comprises the following steps: constructing a pier-bearing platform-pile-soil system model; introducing a vehicle load, a flood load, a pier top additional bending moment, a bridge scouring depth and a pier submerging depth into the system model as working conditions to obtain a mechanical model; calculating a total potential energy function of the system, establishing a horizontal displacement curve function containing undetermined parameters of the system, and setting boundary conditions of the system; constructing a linear algebraic equation of the to-be-determined parameters based on a potential energy stationary value principle; the undetermined parameters are solved, and pier top displacement is obtained; calculating a pier top drift rate, wherein the pier top drift rate is used for evaluating the bearing capacity of the lower part of the bridge; and constructing a lower structure bearing capacity evaluation model, inputting the working condition parameters influencing the lower bearing capacity of the bridge, and outputting the pier top displacement and the pier top drift rate. According to the method, the bearing capacity of the lower part of the bridge under the flood-vehicle multi-load combined action can be quickly and accurately evaluated.

The invention belongs to the technical field of pressure vessel structure analysis, and particularly relates to an intelligent reduced basis finite element method for rapidly analyzing the deformation behavior of a pressure vessel. According to the method, a finite element method is improved by adopting a reduced basis method, an online and offline combined solution mode is developed, after design parameters such as a structure size, a load type and size, material attributes and the like are preset, a reduced basis space is obtained by adopting an offline solution mode, and then a mapping relation between a reduced basis solution and a finite element solution is established; according to the method, order reduction of a finite element model is achieved, the degree of freedom of a problem is reduced, the calculation amount needed by solving a linear algebraic equation set through a traditional finite element method is greatly reduced while the precision is guaranteed, a Gaussian process regression method is further introduced to describe the elastic-plastic deformation behavior of the pressure vessel, and therefore the deformation behavior of the pressure vessel is rapidly solved.

The application provides a sound flow coupling calculation method and device based on a Galbrun equation. The method provided by the application comprises the following steps: obtaining a Galbrun equation based on Euler equations of an ideal fluid under no external force, in combination with Euler disturbance, Lagrange disturbance and mixed disturbance relationship; the Galbrun equation represents the coupling effect of a flow field and a sound field; obtaining flow field data of a non-uniform flow field based on Navier-Stokes equations, in combination with a k-ε turbulence model in a RANS model; introducing a perfect matched layer for sound wave propagation simulation in an unbounded region, and constructing boundary conditions suitable for the Galbrun equation through geometric transformation, complex variable definition and coordinate conversion; performing weak transformation on the Galbrun equation, embedding the boundary conditions, combining the flow field data, adopting triangular finite elements for discretization processing, constructing a global linear algebraic equation group and solving, and obtaining discrete solutions of sound field parameters.

The invention discloses a pile body torsion dynamic response analysis method and system based on a virtual soil pile in the technical field of pile foundation dynamic response analysis. The method comprises the following steps: constructing a total energy function of the pile-soil coupling system; variation is conducted on the total energy function of the pile-soil coupling system on the basis of the variation principle, and a pile periphery soil body radial control function in a general solution form and a Bessel function form of a pile body control differential equation is obtained; according to the general solution form of the pile body control differential equation and the built-in boundary conditions of the bottom of the virtual soil pile section, an equivalent complex impedance function of the top of the virtual soil pile section is constructed; according to the continuity condition and the boundary condition of the pile body and the equivalent complex impedance function of the top of the virtual soil pile section, a system response linear algebraic equation set is constructed; and iteratively updating the control variable of each layer of soil body to obtain the converged control variable of each layer of soil body, further calculating a torsion power response value at the pile top, and obtaining a torsion impedance function of the pile body based on the torsion power response value at the pile top.

The application belongs to the technical field of pressure vessel structure analysis, and specifically relates to an intelligent reduced basis finite element method for fast analysis of pressure vessel deformation behavior. The application improves the finite element method by using the reduced basis method, and develops an online and offline combined solving mode. After design parameters such as structure size, load type and size, material properties and the like are preset, the reduced basis space is obtained by using the offline solving mode, and then a mapping relationship between the reduced basis solution and the finite element solution is established, so that the finite element model is reduced, the degree of freedom of the problem is reduced, the calculation amount required for solving the linear algebraic equation set by the traditional finite element method is greatly reduced while the accuracy is ensured, and further, the Gaussian process regression method is introduced to describe the elastic-plastic deformation behavior of the pressure vessel, so that the fast solution of the pressure vessel deformation behavior is realized.

The invention discloses an aquifer hydraulic diffusion coefficient solving method based on a semi-analytical collocation method, belongs to the technical field of groundwater seepage analysis, and aims to solve the problems that an existing finite element method is tedious and time-consuming in grid division when processing is complex, and a finite difference method depends on regular grids and is difficult to adapt to irregular boundaries and the like. The method comprises the following steps: constructing a mathematical model of a two-dimensional seepage problem under a polar coordinate system, solving a groundwater seepage control equation through a variable separation method under a space-time coordinate system to obtain a complete primary function, establishing a space-time collocation constraint system, forming a linear algebraic equation set about an unknown coefficient, and solving the linear algebraic equation set. Establishing an objective function taking a hydraulic diffusion coefficient as an unknown parameter, and combining boundary conditions to form a mathematical expression of a nonlinear optimization problem; according to the method, point collocation calculation is directly carried out in a time-space domain through a Trefftz time-space point collocation method, and the calculation process is remarkably simplified. The method is suitable for complex geometric boundary problems, and the application range of numerical simulation is expanded.

The present invention discloses a method and system for assessing the bearing capacity of the substructure of a scour-damaged bridge under multiple loads. The method comprises: constructing a pier-cap-pile-soil system model; introducing vehicle load, flood load, additional bending moment at the pier top, bridge scour depth, and pier submergence depth as working conditions into the system model to obtain a mechanical model; calculating the total potential energy function of the system, establishing a horizontal displacement curve function of the system containing undetermined parameters, and setting the system's boundary conditions; constructing a linear algebraic equation for the undetermined parameters based on the principle of stationary potential energy; solving the undetermined parameters to obtain pier top displacement; calculating the pier top drift rate, which is used to assess the substructure bearing capacity of the bridge; and constructing a substructure bearing capacity assessment model with inputs of working condition parameters affecting the substructure bearing capacity of the bridge and outputs including pier top displacement and pier top drift rate. The present invention enables rapid and accurate assessment of the substructure bearing capacity of a bridge under the combined action of flood and vehicle loads.

The present invention relates to a quantum preprocessing method based on Schrödingerization. The method includes: performing finite element discretization of the BPX multilevel preprocessing on the partial differential equation to be solved, constructing a quantum block encoding corresponding to the preprocessing system to obtain a quantum preprocessed linear algebraic equation set; transforming the solution of the quantum preprocessed linear algebraic equation set into the solution of the steady state of a linear ordinary differential equation set; adopting Schrödingerization, and using the dimension elevation method to transform the linear ordinary differential equation set into a Hamiltonian system that can be calculated on a quantum computer; designing a quantum circuit diagram for the Hamiltonian system by using a quantum Hamiltonian simulation algorithm, and obtaining a simulation result by simulating the quantum circuit diagram on a quantum computer. The quantum preprocessing algorithm obtained by using Schrödingerization not only has an exponential acceleration advantage in terms of matrix order and accuracy, etc., but also eliminates the complexity influence brought by the condition number, and the algorithm is simple and efficient.

The invention provides an acoustic streaming coupling calculation method and device based on a Galbrun equation. The method provided by the invention comprises the steps of obtaining a Galbrun equation based on an Euler equation of ideal fluid under the condition of no external force and in combination with Euler disturbance, Lagrange disturbance and a mixed disturbance relation; the Galbrun equation represents the coupling effect of the flow field and the sound field; based on a Navier-Stokes equation, in combination with a k-epsilon turbulence model in the RANS model, solving to obtain flow field data of the non-uniform flow field; a perfect matching layer is introduced for sound wave propagation simulation of an unbounded region, and boundary conditions suitable for the Galbrun equation are constructed through geometric transformation, complex variable definition and coordinate transformation; and carrying out weak transformation on the Galbrun equation, embedding the boundary condition, combining the flow field data, carrying out discretization processing by adopting a triangular finite element, constructing a global linear algebraic equation set, and solving to obtain a discrete solution of sound field parameters.

The application discloses a kind of inland lake ecological water supplement amount prediction analysis method, comprising: obtaining the underwater topographic map of target lake, constructs the plane two-dimensional water flow movement basic equation of lake wind lake current and the plane two-dimensional water quality equation describing salt transport in lake conversion;Obtain the ecological water supplement flow and salt concentration of target lake, fit the plane two-dimensional water quality equation;To the finite difference discrete of continuity equation, momentum equation, the plane two-dimensional water flow movement basic equation is converted into linear algebra equation group;Linear algebra equation group is solved by ADI row-by-row method in time period, direction, and the water level, water depth and salt concentration of output prediction are exported;The water depth of each grid ecological water supplement is calculated, and then the comprehensive water depth of target lake ecological water supplement in future time is calculated, and the ecological water supplement amount of target lake prediction is obtained.

The invention provides a parallel multi-starting-point iterative solution method, which relates to the field of high-performance calculation and comprises the following steps of: discretely generating a linear algebraic equation or a nonlinear algebraic equation according to a physical field problem; analyzing problem features, and selecting an initial value in a solution space or a feasible region; independently iterating each initial value in parallel by adopting a gradient iteration method, calculating a linear algebraic equation or a nonlinear algebraic equation, and searching a minimum residual error; taking the norm of the residual error to judge the convergence; the convergence condition is judged according to the iteration results of all the initial values, if convergence is carried out, solving is ended, otherwise, a new initial value is generated according to the convergence condition of iteration of all the initial values last time, and initial value iteration, residual calculation and convergence judgment are carried out again. The problem that in the prior art, when a gradient-based single-point iteration method is adopted to calculate a large-scale linear equation set, long time needs to be consumed, and therefore the market risk is improved can be solved; the time required for solving a large-scale linear equation set is shortened, so that the market risk is reduced.

This invention relates to the field of capacitance calculation technology and discloses a fast algorithm for extracting parasitic capacitance in large-scale integrated circuits. This method combines the method of moments (MoM), a fast multipole algorithm for layered dielectrics, and overlapping region decomposition preprocessing techniques to construct a complete parasitic capacitance extraction solution. By directly introducing the Green's function for the layered dielectric, the numerical solution strictly satisfies the electric field transport conditions at the dielectric interface, and the electrostatic problem in the layered dielectric is transformed into boundary integral equations defined on the interconnect surface. Subsequently, the MoM is used to discretize these boundary integral equations, resulting in a large-scale dense system of linear algebraic equations. To improve solution efficiency, an efficient preprocessing strategy based on overlapping region decomposition is further designed, and combined with the matrix-free minimum residual iteration method and the layered fast multipole algorithm, achieving efficient solution with low computational and storage overhead.

The invention discloses a rapid solving method for a linear algebraic equation set, and belongs to the technical field of data processing, and the method comprises the steps: determining a precondition matrix according to a coefficient matrix in a to-be-solved linear algebraic equation set, and obtaining a precondition matrix in each iteration solving process; obtaining a solution vector according to the following steps: solving the linear algebraic equation set by using a precondition conjugate gradient algorithm, determining a residual vector in the next iteration process based on the solution vector obtained in the current iteration process, and constructing a precondition equation set in combination with a precondition matrix; performing reduction on the n precondition equations in sequence by using an expansion loop reduction algorithm to obtain an equation only containing a preset number of unknown numbers; and solving the reduced equation to obtain at least one precondition residual vector, and sequentially and reversely substituting the obtained precondition residual vector into n precondition equations before reduction to obtain all precondition residual vectors. The technical problem that the solving speed is low when a linear algebraic equation set is solved in the prior art is solved.

The application discloses a kind of power grid to buried pipe network's electromagnetic interference calculation method, comprising the following steps: conductor is divided into a conductor microsection, conductor microsection outer surface two end potential difference is equal to the potential difference of conductor microsection inside, according to this continuity feature equation group is established, according to leakage current the potential difference of conductor microsection outer surface two ends is solved, the impedance of conductor microsection itself and the product of axial current are then solved the potential difference of conductor microsection inside two ends;According to Kirchhoff's law, the relationship between axial current and leakage current on each conductor microsection is obtained, a set of linear algebraic equations is established, and the leakage current distribution on the conductor is obtained by solving the linear algebraic equations.The results of the application are used to evaluate the influence of electromagnetic interference on buried pipe network, so as to control the risk in advance and realize the harmonious coexistence of power grid and oil and gas pipeline network.

This invention belongs to the field of hypersonic aerodynamics and discloses a method for predicting hypersonic boundary layer transition based on the numerical solution of the frequency domain Navier-Stokes equations. This method, through the assumption of small perturbations, linearly decomposes the hypersonic flow field into a steady flow field and a perturbed flow field. It eliminates the time differential terms in the time-domain Navier-Stokes equations using complex decomposition, transforming the time-domain Navier-Stokes equations into linear algebraic equations in complex space, thereby simplifying the solution and analysis of the time-domain Navier-Stokes equations. Specifically, it includes three stages: preprocessing, solver, and post-processing. The iterative solution of the frequency-domain Navier-Stokes equations in the solver is the core, including spatial discretization of the frequency-domain Navier-Stokes equations, iterative progression, implementation of boundary conditions, parallel data exchange, convergence judgment, and result output. The hypersonic boundary layer transition prediction method based on the numerical solution of the frequency-domain Navier-Stokes equations of this invention can balance computational efficiency and accuracy, and has practical engineering value.