72 results about "Galerkin method" patented technology

The invention relates to an object deformation real-time simulation graphic processing technique, particularly a soft tissue deformation simulation method based on coupling of mesh-free Galerkin and mass spring, which comprises the following steps: in the pretreatment process, establishing a linear viscoelasticity biomechanical model for soft tissues; in the deformation computation process, dynamically partitioning a mesh-free region and a mass spring region according to the load carried by the soft tissues, establishing a transitional unit of the connection region between the mesh-free region and mass spring region, and constructing a transitional unit approximation displacement function, thereby implementing self-adapting coupling of a mesh-free Galerkin method and a mass spring method;and in the after-treatment process, outputting the state of the mass or node of each time step in the deformation process onto a screen, carrying out illumination rendering, and finally displaying the real-time deformation process of the soft tissue organ under stressed conditions on the screen, thereby implementing visualization effect of dynamic deformation. By utilizing the advantage of high efficiency in the mass spring method and the advantages of high precision and no need of mesh reconstruction in the mesh-free Galerkin method, the invention overcomes the defect that the Galerkin method is not suitable for solving a large-scale problem, thereby effectively lowering the complexity of computation in the soft tissue deformation simulation and enhancing the operation efficiency.

The invention discloses a grid-free Galerkin method structural topology optimization method based on GPU parallel acceleration. The grid-free Galerkin method structural topology optimization method mainly comprises the steps of 1 reading data into a host machine memory, arranging integral points through a CPU, establishing the relation of nodes, the integral points and local lattice searching, computing node influence domain radiuses and the integral point definition domain radiuses, confirming the relation of the nodes and the integral points and then copying the data into a GPU global memory; 2 setting different GPU thread blocks and the thread number according to different calculating data; 3 performing asynchronous assembly through the CPU and a GPU and solving a grid-free Galerkin method global discrete system equation to obtain a displacement approximate solution; 4 performing structural topology optimization calculation in the GPU and judging whether iteration is finished or not and a result is output or not according to residual errors of design variables. The grid-free Galerkin method structural topology optimization method is low in hardware cost and good in universality and can reduce a large amount of time consumption on the premise that the engineering accuracy requirement is met.

The invention discloses a Yeh-multi-scale finite element method for simulating water flow Darcy velocity of a porous medium, comprising the steps of: performing variation on the problem which needs resolution by a Galerkin method; subdividing a research area into coarse grid cells and subdividing all the coarse grid cells into fine grid units; resolving a degradation elliptic equation on each coarse grid cell to construct a basis function; resolving variational form by applying the basis function to obtain a total rigidity matrix; obtaining a right-hand term according to the source sink term and the boundary condition of the research area; performing simultaneous operation to obtain a waterhead equation set; resolving the equation set by an effective numerical method to obtain the node waterhead of the research area; and resolving a Darcy equation directly in the research area by combining a Galerkin finite element model of Yeh and applying the constructed basis function and the waterhead value of the research area to obtain continuous Darcy permeating velocity on the coarse-scale node, and linearly expressing the fine-scale Darcy permeating velocity by the basis function. Compared with the prior art, the method has similar precision and higher efficiency.

The invention relates to a method for determining the protection space between an ultra-high-voltage DC (direct current) transmission line and a wireless station. The method comprises the methods of constructing a passive jamming line-surface model of an ultra-high-voltage DC transmission line and solving an electric field integral equation corresponding to the model. The method comprises the following steps: firstly, constructing a passive jamming simulation surface model of the line according to the real space truss structure of transmission towers of the line, and constructing the passive jamming line-surface model of the transmission line in combination with the line model of an overhead wire and ground wire; solving induced current of each part of the ultra-high-voltage DC transmission line by using a moment method checked by RWG (Rao-Wilton- Glisson) basis function and Galerkin method, and calculating secondary radiation intensity vector generated by the induced current; and superposing the vector with a source electromagnetic filed to obtain the jamming level of the ultra-high-voltage DC transmission line to the wireless station. Comparison of test data obtained through the test proves that the method provided by the invention has higher accuracy, and can be used for accurately determining the passive jamming protection space between high-voltage transmission line and adjacent wireless stations in the future.

The invention discloses a hybrid time-domain discontinuous-Galerkin-method-based numerical method of time-domain computational-electromagnetics. The method is applied to the numerical-solving field oftime-domain computational-electromagnetics. A hybrid term is introduced on interface units of adjacent body units, and is used to define numerical flux of electromagnetic fields, an implicit Crank-Nicolson time format is used to disperse three-dimensional time-domain Maxwell equations, after introducing the hybrid term, to obtain a global linear system related only to the hybrid term, and the electromagnetic fields of all the units are obtained through solving for the hybrid term. Therefore, the deficiency of calculation time, memory and precision of existing time-domain electromagnetic-fieldnumerical-methods in processing multi-scale equipment under complex electromagnetic environments can be effectively avoided.

A parametric elastic vibration analysis method of a rotating annular periodic structure comprises the steps of building a rigid-elastic coupling dynamic model of the rotating annular periodic structure according to a Hamilton principle under a global stationary coordinate system; introducing coordinate conversion, and converting the dynamic model to a support follow-up coordinate system so that a parametric item in an original equation is eliminated; performing discrete processing on a partial differential constant coefficient dynamic equation under the rotating support follow-up coordinate system by a Galerkin method to obtain an ordinary differential matrix equation; analyzing a characteristic value of the ordinary differential matrix equation by using a classical vibration theory; and respectively analyzing mode characteristic of the rotating annular periodic structure and a dynamic stability rule of parametric elastic vibration by employing an imaginary part and a real part of the characteristic value of the ordinary differential matrix equation. The parametric elastic vibration analysis method can be used for dynamic analysis of rotating machinery, calculation and solution of the mode characteristic of a system, and analysis on the dynamic stability and the dynamic response of the system.

The invention relates to a numerical simulation method for obtaining aircraft flow fields, wherein an interrupted Galerkin method based on non-structural right angle meshes is used to solve the flow field, and right angle meshes with a quadtree structure are used to disperse a to-be-solved flow field area into a set of meshes; each quadrilateral mesh is processed by dual-linear coordinate conversion, so each mesh under a current physical coordinate system can be mapped onto the next regular mesh in a computational coordinate system, so standard square meshes can be obtained; conservation variables in units under the computational coordinate system are obtained through numerical computation; a front face, a lower face, a left face and a right face of each mesh under the physical coordinate system are determined; according to differences between the left and right vibrations of unit interfaces, an interrupted detector is established; and the conservation variables in each mesh are processed by flow field display on the disperse meshes, so flow field distribution can be obtained. According to the invention, the interrupted Galerkin method based on the non-structural right angle meshes is introduced into flow field computation, so accuracy of the flow field computation is increased, and complicated flow phenomena can be solved.

The invention discloses an efficient decomposition parallel method for time domain finite element regions. The method comprises the following steps of establishing a solution model, conducting discretization, and obtaining tetrahedral node information and unit information of the model; determining the total number of processes to make sub-regions correspond to process numbers in a one-to-one mode,distributing units into all the sub-regions, determining the thickness of a buffering area according to the time step length, and establishing numbering indexes of each sub-region and a global calculation region and communication indexes between every adjacent sub-regions; from a first-order Maxwell's curl equation with electric field intensity and magnetic flux as unknown quantities, adopting aGalerkin method to test the two sides of the equation, using a primary function for expansion, and obtaining a final iterative formula to fill a matrix of each solution sub-region; adopting an iterative formula of time domain finite elements in CN difference schemes to conduct time iteration, and obtaining the electric field value and the magnetic flux in the space. By means of the method, the calculation time is effectively saved, the capability of solving large-scale electromagnetic problems is improved, and the method has great significance in practical application.

The invention relates to a parameterization Thevenin equivalence-based alternating current direct current received end power grid commutation failure fault preventive method. A parameterization received end power grid Thevenin equivalence model is obtained by adopting a generalized Galerkin method according to an alternating current direct current received end power grid short circuit current calculation model by considering a direct current commutation failure and multi-convertor-station concurrence failure caused by the alternating current system faults; and by taking the weight sum for improving the single convertor station commutation failure immune factor and the multi-convertor-station commutation failure immune factor as the optimization target, and by taking the parameterization Thevenin equivalence model as the constraint condition, an optimization model is established, so that the alternating current direct current received end power grid commutation failure fault defensive capability is improved. The method has relatively high applicability and high calculation speed, and can adapt to the alternating current direct current received end power grids in different operationmodes, and can better satisfy the actual demands.

The invention discloses a domain decomposition finite element method for simulating Darcy speed at an underground medium interface. The method comprises the following steps: performing variation on anunderground flow problem by using a Galerkin method, sub-dividing a research domain, and acquiring waterhead by applying the finite element method; decomposing the research domain into a plurality ofsingle-medium sub-domains by applying interfaces of different mediums according to the medium composition of the research domain, and decomposing an underground Darcy speed solution problem on the research domain into sub-problems on the sub-domain by applying the domain decomposition method; selecting one sub-problem, performing variation by using the Galerkin method, and acquiring the Darcy speed by applying a Galerkin model of the Yeh, acquiring the Darcy speed at the other side of the interface of the sub-domain and other sub-domain by combining with the refraction law as the first classof boundary condition of the adjacent sub-problem; selecting the next sub-problem to solve, and repeating this process until all sub-problems are completely solved. By using the method disclosed by the invention, the computing consumption of the Darcy speed is reduced through the domain decomposition method, and the precision of the Darcy speed at the interface is guaranteed by using the refraction law.

The invention discloses an extended smooth meshless Galerkin method, which combines the extended finite element, meshless Galerkin and smooth integration technology, wherein the traditional meshless Galerkin method is modified, and a triangle with stronger topological adaptability is used as a background integration cell, so that the discretization process of a geometric body is more simple and easy to perform. The traditional Gaussian integration method is abandoned and the smooth integration technique is introduced to avoid the tedious derivation process of the shape function, which improvesthe calculation accuracy to some extent. The improved meshless method is applied to the simulation of crack propagation in concrete, and the simulation results are closer to the real situation than the traditional finite element method.

The invention discloses a metal target transient electromagnetic scattering analysis method based on delay laguerre polynomials. A target is subdivided through curved surface triangle surface elements. Spatial dispersion and time dispersion are carried out on a time domain mixed field integral equation through a CRWG primary function and the delay laguerre polynomials. A test is carried out through a galerkin method. An order-stepped matrix equation is finally formed, and the transient electromagnetic scattering characteristic of the target can be obtained through resolution of the equation and post-processing. As a delay item related to the spatial position of the target is introduced into a time primary function, the time primary function contains the spatial phase information of the target is adopted, and the target can be subdivided with less curved surface triangle surface elements. The unknown calculation amount is greatly reduced, consumption of an inner storage is effectively reduced, the calculation time is shortened, and important reference documents are provided for accurate analysis of the transient electromagnetic scattering characteristic of an electric large-size metal target.

The invention relates to a complex frequency domain calculation method for a converter transformer alternating current and direct current composite electric field, which comprises the following steps:obtaining a finite element equation by combining a Galerkin method based on a full current density continuity equation of a lossy medium; expressing each periodic variable in the equation under the AC/DC composite excitation by using a complex stage number; obtaining a unit matrix equation by using the equal harmonic coefficients, and superposing all the units to obtain a system matrix equation;introducing fixed-point conductivity, and converting an iterative equation into distribution according to harmonic frequency by performing row and column change on the matrix; and selecting fixed point conductivity, carrying out iterative solution according to a set convergence criterion, and carrying out convergence to obtain a potential value. According to the method, the finite element stiffness matrix of each iteration is decomposed according to the harmonic frequency by adopting a fixed-point method, so that the memory consumption of a harmonic balance algorithm is reduced, and the calculation cost for analyzing a nonlinear alternating-current and direct-current composite electric field can be effectively reduced.

The invention discloses a lithium battery hot process space time modeling method based on dual-LS-SVM. The method comprises the steps that S1, a lithium battery charge/discharge control platform is set up; S2, space time data of a lithium battery under a cyclic charge/discharge condition is obtained, wherein according to the space time data, temperature distribution changes along with time; S3, anupper computer learns a set of space primary functions representing space nonlinear characteristics, through utilization of a PCA algorithm (namely, a principal component analysis algorithm); S4, theupper computer decomposes an ordinary differential equation ai(t) into two nonlinear modules g(.) and h(.) through utilization of a Galerkin method; and S5, the upper computer carries out series connection on two least squares support vector machines (LS-SVMs) to form a dual-LS-SVM model, thereby approaching to the nonlinear modules g(.) and h(.). The method is used for online estimation of LIBs temperature distribution. The two least squares support vector machines (LS-SVMs) are connected in series to form the dual-LS-SVM model, thereby simulating a distributed parameter system comprising two inherent coupling nonlinearities. The method is relatively effective in the performance approximate aspect of the two inherent coupling nonlinearities. The model precision is high.