98 results about "Finite element method" patented technology

The invention discloses a fluid distribution dynamic regulation and control method and device based on a shale reservoir microstructure, and relates to the technical field of oil and gas exploitation. The method comprises the steps that microstructure parameters of a target shale reservoir are obtained through a core experiment, and a multi-scale model is constructed based on the microstructure parameters; determining control equations of different physical fields of the multi-scale model; coupling the control equations of different physical fields, and resolving through a finite element method; performing a numerical simulation experiment based on the multi-scale model and the resolving result to determine regulation and control parameters; the regulation and control parameters are input into the multi-scale optimization model to optimize the regulation and control parameters, and a regulation and control strategy is obtained. The problems that an existing displacement experiment is single, the complex interaction process under the actual mining environment is not comprehensively considered, and the guiding effect on mining work is limited are solved. Business personnel can be guided to formulate a development scheme more scientifically and accurately, the mining efficiency and the success rate are improved, the development cost can be reduced, and meanwhile economic benefits are improved.

The invention discloses a digital twinborn model construction and life prediction method for pressure vessel defect data, and belongs to the technical field of pressure vessel safety assessment, and the method comprises the following steps: a defect topological graph construction and feature extraction step: converting defect space distribution into a graph structure, and extracting features by adopting a graph attention network; a crack propagation physical constraint modeling step: predicting a defect propagation behavior by adopting a physical information constraint neural network; an uncertainty quantification and reliability evaluation step: calculating a confidence interval and a failure probability of the residual life by adopting a Monte Carlo Dropout method; the model parameters are dynamically adjusted through an online learning mechanism, high-precision real-time prediction of defect evolution and reliability evaluation of the residual life are achieved, and the calculation efficiency is improved by more than two orders of magnitude compared with a traditional finite element method.

The invention relates to a finite element method for calculating temperature distribution of a steel strip in a continuous hot galvanizing process, and belongs to the technical field of hot galvanizing methods. According to the technical scheme, the method comprises the steps that relevant sizes and technological parameters of a continuous hot galvanizing production line are obtained; model establishment and grid division are conducted, a three-dimensional model is established according to the related size, the model comprises molten zinc and a steel belt, and the molten zinc and the steel belt are set to be solid models; and setting boundary conditions, performing heat exchange calculation, and processing a calculation result. The method has the beneficial effects that the method is used for analyzing the temperature distribution of the steel strip in the hot galvanizing process and analyzing the flow field and the temperature field of molten zinc; and the change of working condition parameters such as the temperature of the steel brought into the zinc pot, the moving speed of the steel strip, the thickness and width of the steel strip, the temperature and depth of molten zinc and the like is accurately responded, so that the optimization of the continuous hot galvanizing process is guided.

The invention provides a mining electric shovel working device health detection method based on multidisciplinary digital twinning, and the method comprises the steps: obtaining attitude data through employing a Latin hypercube sampling method; performing electric shovel simulation by using discrete element and finite element methods, and further obtaining a data set required for neural network training; training and testing the LSTM neural network and the RBF neural network by using the data set, and constructing a mining load prediction model and a mining stress prediction model; constructing a digital twinborn model by using a tilt angle sensor, a stay wire encoder and the virtual model; a laser radar is used for scanning the terrain, the material mass is calculated and obtained, the load and stress of data are sequentially predicted through a neural network model, the stress is transmitted to a digital twinborn model, and real-time monitoring is achieved in a color rendering mode. According to the mining electric shovel, the stress change of the working device is displayed in real time in the working process of the mining electric shovel, and the early warning capacity of the mining electric shovel when excavation exceeds the stress safety range in the complex working environment is improved.

The invention provides a method and a system for predicting the frictional wear residual size of a transmission line connection fitting, and the method comprises the steps: calculating the maximum wind speed and swing angle of the connection fitting through the data of a meteorological database and an engineering design data database, and simulating the wear process of the transmission line fitting through a finite element method. The method comprises the steps of obtaining a change relation of the abrasion loss of the connection hardware fitting along with the abrasion frequency, determining the average swing frequency of the hardware fitting according to the current operation and maintenance result of the connection hardware fitting, and predicting the remaining size of the hardware fitting after n years on the basis of the assumption that the connection hardware fitting operates according to the same swing frequency. The method and the system can scientifically and reasonably evaluate the service life of the power transmission line connection hardware fitting, and avoid careless mistakes caused by the fact that the worn hardware fitting is found only through sense organs of people in a traditional manual inspection mode.

The invention relates to the technical field of hydrographic survey, in particular to a riverway water flow calculation method, which comprises the following steps: acquiring topographic data, hydrological data and roughness data, and constructing a one-dimensional riverway hydrodynamic numerical model; the one-dimensional river channel hydrodynamic numerical model is based on a discontinuous finite element method and a Runge-Kutta time discrete shallow water equation set, and a numerical flux is solved by combining an essential oscillation-free ENO slope limiter and an HLL Riemann solver; aiming at the confluence situation of tributaries in different intervals, the interval flow is calculated by utilizing an iterative method, including initially assuming that the tributary flow is zero, simulating non-tributary outflow by using a one-dimensional river hydrodynamic numerical model, determining the difference between the simulated non-tributary outflow and actual site flow measurement, and adjusting the tributary flow; and iteration is repeated until the error between the simulated outlet flow and the actual outlet flow reaches the preset precision. By constructing a one-dimensional river water power numerical model based on a Runge-Kutta time discrete shallow water equation set, high-precision simulation of river water flow calculation under the condition of branch flow convergence in different intervals is realized.

The invention relates to a method for calculating the power-on and power-off delay time performance of an electromagnetic valve, and the method comprises the following steps: obtaining the mass of a valve element of the electromagnetic valve, the spring stiffness and coil resistance data; establishing an electromagnetic valve equivalent circuit model, and listing a current equation; establishing an electromagnetic valve magnetic circuit mathematical model, and listing a magnetic field equation set; establishing an electromagnetic valve flow field mathematical model, and listing a flow field equation set; establishing a kinematic model of the electromagnetic valve, and listing a kinematic equation; using a finite element method to obtain a valve core electromagnetic force-displacement-current data table and a coil inductance-displacement-current data table; a finite element method is used for obtaining a valve element aerodynamic force-displacement data table; and obtaining the power-on and power-off delay time through data analysis processing and solving of the partial differential equation set. According to the method, prediction of the opening and closing delay response time of the electromagnetic valve is more accurate, visual adjustment in the simulation process is achieved, and the time for obtaining the response time of the electromagnetic valve and the test cost are greatly reduced while the preset precision requirement is met.

The invention discloses a flow-induced noise integration method, device and equipment based on a finite element method and a storage medium, and relates to the technical field of noise integration, and the method comprises the steps: obtaining an aerodynamic noise source based on a sound source type and a time domain flow field file; transmitting an aerodynamic noise source from the fluid grid to the acoustic grid based on the acoustic grid file and a data mapping algorithm to obtain a time domain sound source; converting the time domain sound source into a frequency domain sound source based on a time-frequency conversion strategy; and constructing a numerical model based on the frequency domain sound source, and solving the numerical model to obtain a sound propagation result. The problems that in a traditional mixing method, due to the fact that a plurality of independent modules exchange large-scale intermediate data through a file system, the process is split, reading and writing are time-consuming, and user operation is tedious are solved, integrated solving of aerodynamic noise simulation from sound source extraction to sound field calculation is achieved, user operation steps are simplified, and user experience is improved. Therefore, on the premise that the calculation precision is guaranteed, the overall execution efficiency and the automation level of the simulation process are remarkably improved.

The application relates to a seepage simulation method in a multi-scale fractured medium based on coupling finite elements, which comprises the following steps: 1. acquiring statistical distribution characteristics of related parameters of multi-scale fractures in a simulation domain, and constructing a multi-scale fracture geometric model; 2. respectively performing intersection line detection on each scale fracture in the multi-scale fracture geometric model; 3. simplifying the multi-scale fracture geometric model; 4. adopting coupling units to establish coupling relationships among the each scale fracture models; and 5. simulating a multi-scale discrete fracture-matrix model. The application is based on a coupling finite element method, and couples three scale fracture conceptual models, so that the difficulties in calculation precision, calculation cost and mesh partitioning of a single traditional model in solving multi-scale problems are avoided, and a feasible new way is provided for large-scale complex rock mass underground water flow analysis.

This invention provides an information processing method that can shorten the computation time required to obtain results equivalent to those obtained by a Pareto front using only finite element method calculations in the optimization calculation of design parameters using a genetic algorithm with CAE analysis such as the finite element method. [Solution] An information processing method for optimizing design parameters that define an individual model representing a design object using a genetic algorithm, wherein the computer calculates the response value of the individual model in each generation using a first calculation method or a second calculation method which has a faster calculation speed than the first calculation method. When the computer is calculating the response value of the individual model using the second calculation method, it calculates an optimization progress index that indicates the progress of the design parameters, and determines whether the optimization of the design parameters has stalled based on the amount of change in the optimization progress index with respect to generational progress, and if it determines that the optimization has stalled, it calculates the response value of the individual model using the first calculation method.

The present application relates to the technical field of aircraft engine simulation design, and particularly relates to a method for estimating aircraft engine thrust based on flight parameters. The aircraft engine thrust estimation method provided by the present application estimates the aircraft engine thrust from the perspective of flight parameter data, in combination with aircraft engine design parameters, taking into account task requirements and adopting the finite element method. Compared with the traditional scheme based on data, i.e., relying on a large amount of flight parameter data and combining statistical rules to obtain the aircraft engine thrust spectrum, the aircraft engine thrust estimation formula derived based on the physical formula has more reliable physical meaning and physical constraints, the distortion degree of the obtained aircraft engine thrust spectrum caused by data sampling error is smaller, the trend and characteristics are more in line with the real rules, and the aircraft engine thrust spectrum has more guiding significance and prediction value, thereby providing strong theoretical support for aircraft engine thrust spectrum prediction.

This invention relates to the field of slope stability analysis technology, and in particular to a method, device, and storage medium for measuring the stability of unsaturated soil slopes. The unsaturated soil slope stability measurement method of this invention is based on the soil-water characteristic curve of unsaturated soil and uses the finite element method to solve the Richards equation to obtain the transient seepage field distribution of the unsaturated soil slope. This method is more consistent with reality than the seepage field assumed by empirical formulas in the past. While the SMP criterion proposed by Songgang-Zhongjing considers the influence of intermediate principal stress, the SMP criterion is only suitable for cohesive soil failure criteria. Therefore, this invention modifies the SMP criterion by considering the influence of cohesion, friction angle, and matrix suction, making it applicable to unsaturated cohesive soil slopes. Based on the calculation of the slope's self-weight stress, and using a modified SMP material model, we conduct stability analysis of unsaturated soil slopes using the strength reduction method, considering the influence of the intermediate principal stress of the soil, resulting in more reasonable results.

The application relates to a finite element numerical implementation method of an asphalt mixture fractional viscoelastic model, and belongs to the field of constitutive behaviors of asphalt mixtures. The application aims at the problem that the existing finite element method of the fractional viscoelastic model cannot consider both the calculation efficiency and the accuracy. The application comprises the following steps: obtaining a complex frequency domain modulus expression of the fractional viscoelastic model based on Laplace transformation; constructing a one-dimensional form of a stress-strain minimum-order differential expression of the asphalt mixture fractional viscoelastic model through time domain / complex frequency domain equivalent substitution; constructing a discrete form of a stress updating expression of the asphalt mixture fractional viscoelastic model based on non-classical method discrete fractional derivative terms in the stress-strain differential form; constructing a three-dimensional form of stress updating expressions and Jacobian matrix updating expressions of the fractional viscoelastic model based on common / abnormal Poisson ratio assumptions and an incremental iteration method; and writing a user subroutine UMAT for finite element numerical calculation. The application is used for finite element numerical implementation of the fractional viscoelastic model.

The invention provides a geothermal reservoir fracturing-exploitation integrated numerical simulation method and system, and the method comprises the steps: firstly constructing a strong coupling model covering heat-hole-elastic mechanics, building a heat and mass transfer and mechanical equilibrium equation of a matrix and a crack, and forming a unified calculation framework, secondly, constructing a three-dimensional curved surface crack model and a triangular mesh topology by adopting an extended embedded discrete crack method, and establishing a spatial relationship between cracks and a matrix and a spatial relationship between the cracks; then, based on the geometric model, utilizing a displacement discontinuous method to calculate fracture opening and stress shadow, solving a heat-fluid-solid model through iterative coupling, and completing dynamic evolution simulation of a three-dimensional fracture group in a fracturing stage; and finally, the fracturing result serves as the initial condition of the mining stage, the injection-production cycle process is solved through a finite volume / finite element method, and seamless connection of fracturing and mining is achieved. According to the method, the three-dimensional crack propagation and heat extraction efficiency under the thermal-hole-elastic coupling effect can be accurately predicted.

The present application belongs to the technical field of flow field, and particularly relates to a general simulation method of complex particle two-phase flow. The method comprises the following steps: S1: constructing a geometric representation model to represent the geometric information of the complex particle and dividing a grid; S2: on the basis of the grid divided in S1, adopting a characteristic line splitting finite element method to solve the flow field to obtain the flow field velocity at pseudo n+1 time and the flow field pressure at n+1 time; S3: calculating the force and torque of the complex particle; and S4: calculating the attitude of the complex particle through a six-degree-of-freedom model. The present application has the following effects: high calculation efficiency, reduced calculation complexity and cost, and improved simulation efficiency. Strong comprehensiveness, which can accurately describe the translation and rotation motion of the complex particle and provide comprehensive dynamic analysis. Good stability, which realizes stable solution of the coupling of fluid and particle motion and avoids numerical oscillation and instability. Multi-scale simulation capability, which can accurately simulate at different scales and meet the demand of multi-scale numerical simulation.

The invention discloses a rapid flow field prediction method based on cooperation of data driving and CFD calculation, and belongs to the technical field of numerical simulation of aircrafts. Extracting geometric features of the airfoils in the data set; reducing dimensions of flow field variables in the data set; building an off-line data driving model of the airfoil flow field prediction task; an off-line data driving model is adopted to provide an initial solution for a high-order discontinuous finite element method (DGM) of airfoil streaming simulation; and iterating to a steady state based on an initial flow field provided by a data driving model by adopting a high-order discontinuous finite element method. The airfoil flow field rapid prediction method based on cooperation of data driving and CFD calculation is suitable for rapid evaluation of aerodynamic performance of an aircraft airfoil design link, and the simulation efficiency of an original discontinuous finite element method based on far-field free flow initialization can be improved by about three times; and the method is hopefully expanded and applied to rapid pneumatic evaluation of the whole aircraft.

The present invention provides a simulation method for a retaining ring structure in a chemical mechanical polishing process, comprising constructing a CFD model of the chemical mechanical polishing process, dividing a fluid region into discrete grids, wherein the grids are non-repetitive control volumes, and within each control volume, using a momentum equation, a continuity equation, and a VOF model to control the motion of the polishing liquid fluid, and a DPM model to control the motion of the abrasive, integrating the momentum equation, the continuity equation, and the VOF model for each control volume to obtain a discrete equation, solving the discrete equation to obtain simulation data, the simulation data including abrasive motion data, plotting the abrasive distribution and the abrasive aggregation state on the polishing pad and / or the wafer edge based on the abrasive motion data, and having the beneficial effects of visualizing the polishing liquid / abrasive flow through a finite element method, helping to understand the influence of the retaining ring on the polishing liquid flow, providing a retaining ring structure improvement to solve wafer edge over-polishing, conforming to actual production processes, and having high simulation accuracy.

The present application belongs to the technical field of health state evaluation and prediction of mechanical transmission system, and proposes a kind of parallel misalignment state mechanical transmission component wear amount probability prediction method.It includes the following steps: step S1: build the three-dimensional model of mechanical transmission component containing parallel misalignment error;Step S2: considering the random uncertainty of load profile, carry out wear simulation analysis based on grid node iteration;Step S3: considering the cognitive uncertainty of the model itself, train the Bayesian long short-term memory network model;Step S4: predict the expected value of wear and its uncertainty interval.The present application improves the description accuracy of traditional finite element method on mechanical transmission component wear behavior, breaks through the limitation of wear amount deterministic numerical prediction, provides high robustness and high reliability of probability prediction result, and provides scientific basis and data support for transmission system condition-based maintenance decision.

The invention discloses a deep sea land slope well site seabed three-dimensional stability quantitative evaluation method. Comprising the following steps: 1) according to topographic data of a well site area, constructing a seabed three-dimensional finite element discrete model of the well site area; 2) according to the three-dimensional seismic inversion, acoustics and soil mechanics relation model, estimating a three-dimensional space distribution rule of deep sea seabed soil mechanics parameters, and establishing a deep sea three-dimensional seabed slope heterogeneous material model; (3) building a three-dimensional seabed slope stability statics model by considering the accumulation effect of rock debris returned from a well mouth of the drilling well; and 4) calculating the stability of the seabed three-dimensional slope in the well site area by adopting a finite element method, and preferably selecting an optimal drilling well position. The method has the advantages that many induction factors are considered, and the stratum heterogeneity can be reflected more effectively. The method is suitable for deep-sea seabed stability evaluation.

This invention discloses a simulation method, apparatus, equipment, and medium for an electromagnetic railgun. Compared to constant load parameter values, it employs a finite element method combined with equivalent circuit analysis. The rail is divided into N segments, and the armature is positioned at the end of the i-th segment. The current equivalent load parameters of the rail are updated based on the circuit parameters at each discrete time point, thereby approximating the true value of the equivalent load parameters segment by segment. The current equivalent load parameters are then substituted into the circuit and mechanical equations to calculate the discrete data when the armature is positioned at the end of the i-th segment. If i < N, let i = i + 1, and iterate the above simulation steps; if i = N, then fit all the calculated discrete data between the armature velocity and discrete time points to obtain continuous data between the armature velocity and time. It is evident that this invention corrects the equivalent load parameters whenever the armature moves a certain distance, thus simulating an electromagnetic railgun firing process that more closely approximates the real situation.

Systems and methods to determine a thickness profile of nested metallic pipes can include processing long sections (windows) of induction multi spacing and multi frequency noncollocated sensor measurements (attenuation and phase). The systems and methods also include using an inversion based process to deconvolve the tool transfer function from the surrounding pipe structure and its anomalies by running an axisymmetric finite element method (FEM modeling solver with a model in an inversion loop.

The invention relates to the field of optimization design of permanent magnet synchronous motors, in particular to a high-torque low-vibration built-in permanent magnet synchronous motor optimization method which comprises the following steps: S1, calculating motor electromagnetic field distribution through a finite element method, and determining a key noise source of a motor according to a calculation result; s2, defining an optimization target and constraint conditions, constructing an optimization mathematical model, performing sensitivity analysis on design variables by adopting a random forest algorithm, and dividing design parameters into a strong sensitive level, a middle sensitive level and a weak sensitive level; s3, constructing a multi-layer perceptron neural network agent model for the strong sensitive level parameters, and performing multi-objective optimization by adopting a second-generation non-dominated sorting genetic algorithm; s4, aiming at medium sensitive level parameters, adopting a response surface model for proxy modeling, and performing optimization in combination with a multi-target particle swarm optimization algorithm; s5, aiming at the weak sensitive level parameters, adopting a parameterized scanning method, combining weights of different targets through a weighted summation method, and comprehensively optimizing a target function; and S6, optimizing results are integrated and verified.

The application provides a heavy-load multi-rotor propeller design optimization method, and relates to the technical field of multi-rotor propeller design.The application realizes fine design of the blade shape through parameterized modeling, can flexibly adjust key parameters for different radius positions, and effectively matches the complex working condition requirements.Combining segmented aerodynamic force analysis and blade element momentum theory, the overall thrust and torque of the propeller can be accurately obtained to provide data basis for structure and performance evaluation.Through finite element method, structural static force and vibration modal analysis are carried out to identify stress concentration areas and potential resonance risks, so that system evaluation of multi-target performance is realized.Combining the multi-target optimization model of aerodynamic efficiency and structural safety, the optimal geometric parameters of the blade are automatically iteratively searched, the structural stress and vibration risk are effectively reduced while meeting the heavy-load thrust requirement, and the stability and reliability of the aircraft are improved.

The invention provides a submarine pipeline stability analysis method based on a mathematical optimization particle finite element method, which is used for specially building a set of novel submarine pipeline stability analysis architecture and reflecting the novel submarine pipeline stability analysis architecture by a corresponding numerical model, and can accurately simulate the interaction of wave-pipeline-soil body, so that the stability of the submarine pipeline is improved. Therefore, the stability of the submarine pipeline can be accurately analyzed, high-quality data support is provided for evaluating the stability of the submarine pipeline in a real marine environment, and then work in the aspects of analysis, construction, maintenance and the like of the submarine pipeline can be better carried out.

The application belongs to the technical field of aviation structure impact dynamics, and is a kind of crash dynamics modeling method for simplifying fuselage frame section structure of an airplane. A fuselage frame section model is established by corresponding structural characteristics of the fuselage frame section, the position and deformation mode of a large deformation region in the fuselage frame section model are determined, the large deformation region is simulated into a plastic hinge, and torque and axial force performance parameters corresponding to the plastic hinge are determined. Different gravity fields and initial velocities are given to the fuselage frame section, and the response of the plastic hinge of the fuselage frame section structure at different deformation degrees is calculated. Based on the plastic large deformation principle, the advantages of simple connection relationship model, fast calculation efficiency and high calculation accuracy of the finite element method are fully combined, the calculation efficiency of the crash finite element analysis of the fuselage frame section of the airplane is improved, and potential calculation non-convergence problems in the calculation of the plastic large deformation region of the fuselage frame section structure of the airplane can be avoided, the design cycle of the airplane structure adaptability is shortened, and the application prospect is great.

The invention belongs to the technical field of composite material mechanics, and provides a composite material constitutive curve obtaining method considering material dispersibility, and the method comprises the following steps: carrying out a static mechanical property test on a test piece, and obtaining a plurality of test stress-strain curves under given conditions; performing validity test on each test stress-strain curve, and removing invalid curves to obtain a test stress-strain curve set under the given condition; fitting and solving the constitutive model according to the test stress-strain curve set by adopting a gradient descent method to obtain characterization parameters; and adopting the characterization parameters, obtaining a composite material constitutive curve through a finite element method, and carrying out iterative correction on the composite material constitutive curve through the test stress-strain curve set until a final composite material constitutive curve is obtained. According to the method, the constitutive curve representing the composite material can be accurately obtained, and a foundation is laid for performance analysis of the composite material and high-fidelity simulation calculation of the composite material structure.

The application discloses an interpretable prediction method for liquefied stratum pile foundation buckling bearing capacity and related equipment, and the method comprises the following steps: establishing a pile foundation buckling bearing capacity calculation database based on a finite element method, generating a target data sample, and constructing a training set and a test set; a buckling bearing capacity prediction model is constructed, and a target AutoML model is obtained through screening; SHAP values of each input feature are calculated for a prediction result, and a global interpretability analysis result is obtained; a sample instance is randomly selected from the test set, a force diagram and a decision path diagram of the sample instance are generated, a local interpretability analysis result and a decision path analysis result are obtained, and then specific influence mechanisms and decision paths of each input feature on the buckling bearing capacity are determined. The SHAP technology is deeply combined with the AutoML model, end-to-end joint modeling is carried out, the liquefied stratum pile foundation buckling bearing capacity can be quickly and accurately evaluated, and the method can be widely applied to the technical field of machine learning.

To provide a method capable of predicting a change of an object when an action is applied to the object in a relatively short time and with high accuracy.SOLUTION: A prediction method of the present invention is a method of predicting a change of an object when an action is applied to the object, and includes predicting a change of a first object in a region to which the action of the object is applied and a vicinity thereof by a graph neural network, and predicting a change of a second object in at least a part of a region other than the region to which the action of the object is applied and the vicinity thereof by analysis using a finite element method.SELECTED DRAWING: Figure 1

The invention belongs to the field of monitoring, and particularly relates to a gearbox parallelism prediction method based on an NRBO-ELM algorithm. The objective of the invention is to solve the problem of low prediction precision of an existing gearbox parallelism prediction method. The invention provides a gearbox parallelism prediction method based on an NRBO-ELM algorithm. Comprising the steps of S1, calculating distribution data of tooth root bending stress in the tooth width direction when a shaft system is in a deflection state through a finite element method; performing linear normalization processing on the data, and dividing the data into a training data set and a test data set; s2, an extreme learning machine (ELM) model is created, and internal parameters of the model are initialized; step S3, using a Newton-Raphson iteration method in combination with a trap escape algorithm (Newton-Raphson-Based Optimizer, NRBO) to optimize internal parameters of the extreme learning machine model (ELM), and searching for an optimal parameter combination of the ELM prediction model; the problem that an existing gearbox parallelism prediction method is low in prediction precision is solved.

A spiking neuromorphic circuit that instantiates a finite element methods (FEM) mesh is provided. The circuit comprises a number of groups of spiking neurons, wherein each group of spiking neurons represents a mesh node in the FEM mesh, wherein the FEM mesh represents a linear system. A bias current represents conditions in the linear system. Interaction weights between adjacent mesh nodes are proportional to the linear system represented by the FEM mesh. The spiking neurons within each group of spiking neurons spike in a manner that flows to a solution variable for the respective mesh node.