When high-speed moving bodies such as landslides, debris flows, and glaciers enter the water and impact water bodies in enclosed waters such as reservoirs, lakes, rivers, and bays, swells will be induced, and large-scale disasters will be produced. A representative example is a large-scale monolithic rock landslide that occurred on the bank of the Vaian Reservoir in Italy in 1963. The landslide body was 2 km long, 1.6 km wide, the landslide volume was 240 million m3, and the sliding speed was 15–30 m/s. When the landslide body breaks into the reservoir, a surge of up to 90–130m is generated, causing destructive damage to the reservoir bank and the market town downstream of the dam [1]. During the typhoon on July 6, 2011 in Japan, a large amount of debris flowed into the upper reaches of the Naban Igawa Pingguo Dam, causing swells exceeding 5m in height, causing damage to the dam gate and creating a flooded roof. At the same time, the Pingguo suspension bridge upstream of the dam was damaged. The Zipingpu Dam is a concrete face rockfill dam with a height of 158m and a storage capacity of 1.11 billion m3. It is only 17km away from the epicenter of the Wenchuan earthquake that occurred on May 12, 2008. The Wenchuan earthquake triggered the Zipingpu landslide. The height difference between the center of the landslide and the water surface of the reservoir was 700m. About 450,000 m3 of landslide rock mass rushed into the reservoir at high speed, generating swells as high as 25m, and about 70 lakeside fishermen were swarmed. Waves swept into the reservoir causing death, and 10 cars were swept into the lake [2].

The big data computer system is an important modern system supporting equipment. The traditional big data computer system is composed of special big data computer equipment. It receives the information of atmospheric static pressure, total atmospheric pressure, and total atmospheric temperature through the external interface, and then calculates it through the internal calculation, output absolute pressure altitude, relative pressure altitude, true airspeed, indicated airspeed, Mach number, atmospheric density, atmospheric density ratio, atmospheric static temperature and other related parameters required by peripherals. The traditional big data computer is cumbersome and takes up space. Wang Liangliang et al. [3] conducted in-depth research on the principle composition, architecture interface, flight parameters, etc. of the big data computer system, and carried out a model based on the latest model-based system engineering modeling tools Modeling, and taking full advantage of the advantages, a lot of simulation work has been done in the model stage. After the simulation is completed, the source code of the model is automatically generated, loaded into the new avionics display, and the actual test is carried out through the air pump test equipment. The model passed the test perfectly, successfully replaced the traditional big data computer system, and further realized the high integration of avionics display functions. Tian Lirong et al. [4] replaced big data computer equipment with models, reducing the weight of peripherals, which has important engineering practical significance for precision instruments whose weight is calculated in grams. Liu Wenxue et al. [5] implemented it based on the latest model-based systems engineering method. The model-based systems engineering method changed the traditional development model, and took the model as the core to separate the model from the platform, so that the model can be replicated on different platforms. It can effectively improve the development efficiency and reliability. Wang Xiaoyang et al. [6] compared the development process of modern technology and traditional technology. The model-based system engineering method has the following advantages: First, the code is automatically generated, and the generated code meets the D0178C-3 standard, eliminating the need for manual coding. hassle and possible errors, increasing efficiency. Secondly, the model is separated from the platform, which improves the reusability of the functional model and has strong portability.

In order to prevent surge disasters, a prediction method capable of establishing surge characteristics and magnitudes is required. The shallow water long wave equation is often used as the governing equation for swell. Because the displacement flow term is included in the shallow water long-wave equation, the stability of numerical calculation is very poor, and it is necessary to solve the stability problem of numerical calculation. In addition, the total coefficient matrix obtained by the finite element discretization is asymmetric. Therefore, in order to shorten the calculation time in large-scale surge analysis, it is necessary to develop a multi-core and multi-thread parallel solution method for linear equations. The classical process of computer modeling is shown in Figure 1 [7]. In this study, a sparse linear equation solver implemented on a shared memory machine provided by Intel MKL is used to develop a high-performance finite element analysis program for surge, and some theoretical solutions and experimental results are used to verify the developed program.

The shallow water long-wave equations expressed in terms of vertical mean flow velocity include the continuity equation (1), and the motion equations (2) and (3) in the x and y directions:

In the formula,

Considering the water surface elevation and the flux vectors in the x and y directions of the two states tn+1 and tn with a time interval of Δt, the time differential of the water surface elevation and the flux vectors in the x and y directions can be expressed as:

The water surface elevation at time _{n+θh} and the time differential of the beam vectors in the x and y directions at time _{n+θu} can be expressed as:

In the formula, _{h}_{u}_{h}_{u}_{h}_{u}

Where:

The flow velocities ũ and

In the formula, Δ_{n−1} and Δ_{n} are the time step lengths of time steps n-1 and n, respectively. When the two time steps are equal, formula () can be simplified to the Adams-Bashforth method of equal time steps.

The solution of the first-order simultaneous linear equation system Ax=b with the large-scale sparse matrix obtained by space and time discretization as the coefficient is one of the central tasks of the finite element analysis of the surge, so the high-speed and robust solution suitable for the sparse linear equation system is adopted device is very important [9]. The direct method can also solve the problem that the iterative method does not converge, especially if the matrix is symmetric positive timing, it can be solved if there is no numerical error. Because of these specialties, the direct method has been widely used. By considering the zero elements inside the one-dimensional storage of the variable bandwidth of the matrix, the direct solution method of the sparse linear equation system, which can further reduce the calculation amount and save memory, has now become the mainstream. The calculation steps of the direct method solvers of sparse linear equations including PARDISO generally include sequential calculation of four steps, such as reordering, symbol decomposition, LU decomposition, and forward and backward substitution. The calculation of each step is briefly described below.

Reordering is to use a suitable permutation matrix P, so that the elements filled in when LU decomposes PAPT are as few as possible. Filled elements here refer to elements that are zero before LU decomposition but non-zero after decomposition. Reordering methods include equal-scale reduction (minimum degree method, Reverse Cuthill-McKee method), triangulation (Markowitz method, Tewarson method), block (Stewart method, Nested Dissection method) and many other algorithms [10]. PARDISO uses the minimum order algorithm or the Nested Dissection algorithm in the METIS algorithm package for reordering. Symbol decomposition does not perform the decomposition calculation of specific elements, but only focuses on the distribution form of non-zero elements in the LU decomposition of matrix A, and finds the positions of non-zero elements after LU decomposition. From this, the amount of memory and calculation required for LU decomposition is calculated, and the memory required to save non-zero elements after LU decomposition is ensured, and the position of non-zero elements is recorded. In order to perform symbolic decomposition efficiently, the concept of column elimination tree is used to classify the problem as a path exploration problem of efficient graphs, thus making high-speed computation possible [11]. The actual LU factorization is performed with the amount of memory guaranteed during symbolic factorization. As the main LU decomposition method, refer to the right-looking algorithm on the right side of the update column, and the left-looking algorithm on the left side is widely known. The multi-core and multi-thread parallel solver PARDISO used in this program utilizes left-looking and right-looking algorithms to achieve efficient parallel computation.

The solution x can be obtained by forward substitution with the lower triangular matrix L decomposed by LU, and backward substitution with the upper triangular matrix U. If the first-order simultaneous linear equation system with the same coefficient matrix A is solved repeatedly (for example, when one loading step is calculated by the modified Newton-Raphson method), the solution can be solved by iteratively performing forward and backward substitution calculations. If the construction of the non-zero elements of the coefficient matrix is the same, then the calculation must be returned to the LU decomposition. Changes such as boundary conditions or analysis range then have to resynthesize the coefficient matrix and start the solution process from the reordering.

Another important concept in the solver is called a super node. The so-called super node is a set of columns in the upper triangular matrix L that are all non-zero, and each column has the same non-zero structure. For example, {1, 2}, {3, 4}, {5}, {6, 7, 8} are super nodes of order 2, 2, 1, and 3, respectively. After the left-looking algorithm is introduced into the super node, it can promote the partitioning, that is, the localization of data access, which can greatly improve the computing speed of the hierarchically structured memory computer. Assuming the zero elements of different non-zero constructs to be non-zero elements, generate super nodes, and in some cases more efficient super nodes can be obtained.

The multi-core and multi-thread parallel computing sparse linear equation solver PARDISO realizes parallelization in three levels: parallelization of tree elimination, parallelization of node level, and parallelization of data channel processing.

When PARDISO is used for surge finite element calculation, it needs to generate a list of the positions of the non-zero elements of the coefficient matrix A of the linear equation system. PARDISO uses a row-based storage method, that is, the deformed CSR (compressed sparse row) form, and the symmetric matrix only stores the upper half triangular elements. This method stores each non-zero data in row units. The storage of a sparse matrix A by PARDISO includes three arrays [12]:

values - non-zero elements of matrix A. The non-zero data of matrix A is mapped to the values array by the following columns and rowindex.

the column of the matrix where each element in columns-values is located.

rowindex - gives the position of each row's element in values.

Data preprocessing is responsible for preprocessing the initially obtained raw data into data files that can be easily parsed. The data preprocessing module in this system is divided into three processes: data batch decompression, data cleaning and preliminary analysis of data files. The batch decompression operation is because the original data exists in the form of multi-layer data compression packages, so it is necessary to realize the A large number of packets do batch deep decompression operations. The data parsing operation is to perform preliminary data parsing on the decompressed data files (xml format files and text files), and then obtain text data files stored in the form of key-value pairs. The data cleaning part is to perform corresponding operations after the data parsing process. Ensure the correctness and consistency of the data The final processed data will be stored in a specific directory for subsequent use. The data preprocessing function is provided by an independent PC-side application software. Here, we focus on the advantages of PC-side applications compared with web applications in performance and data processing efficiency, avoiding browser compatibility issues and network environment limitations in web applications. The influence of factors gives users a better immersive interactive experience.

Data transfer management is the “data porter” of the system, mainly responsible for the transfer and migration of system data. The data transmission management module includes two functions of data import and distributed storage. The data import function provides data to the user. The theoretical value calculation is based on reference materials and theoretical formulas, importing the data of major surge disasters in history into local files and relational databases. In the model system designed by text, the distributed storage function provides users with the function of migrating system data from relational database to h-base database of distributed storage, realizing distributed storage of large amounts of data, and calculating the surging generated by landslides. The high theoretical values are shown in Table 1:

Theoretical calculation of swell rise from historic landslides or partially underwater landslides

Date | Location | Landslide material | landslide volume/×106m^{3} |
Death toll | Theoretical value of surge rise/m |
---|---|---|---|---|---|

1756 | Tjelle Granite | gneiss | 15 | 38 | 46.883 |

1792 | Yuan Island Volcanic | debris | 500 | >15000 | 10.282 |

1883 | Krakatau | Pyroxene | -- | 36000 | 35.426 |

1888 | Ritter Island | Basalt | 5000 | >100 | 20.732 |

1905 | Disench.Bay | Glacier ice | 29 | 0 | 35.217 |

1934 | Tafjord | Gneiss | 2~3 | 41 | 62.784 |

1936 | Ravnefjell | Gneiss | 0.451 | 73 | 74.225 |

1958 | |||||

1971 | Yanahuin Lake | Limestone | 240 | >2500 | 270.377 |

1980 | M.St.Helens | Rock | 430 | 0 | 200.082 |

2008 | Zipingpu R. | Rock | 0.45 | >70 | 524.362 |

2010 | 513 Lake, Peru | Glacier ice | 0.5 | 1 | 30.683 |

Using the developed software, the wave propagation with a water level difference of 0.8m in the 20m-long tank shown in Figure 3 was first calculated. This calculation example is the phenomenon of instantaneous collapse and discharge of a stationary dam. In order to compare with the theoretical solution of complete fluid, the average eddy viscosity coefficient of water depth ε=0 is assumed in the calculation, and the side wall of the water tank is assumed to be a slip condition. Figure 4 shows the theoretical solution of the water depth and flow velocity 1 s after the dam collapses.

Observing the curves and data in Figure 3 and Figure 4, it can be concluded by calculation that the normalized error of the flow rate obtained by the two is only between 5.2% and 6.8%, which is within the allowable error range specified by the D0178C-3 standard. It shows that the calculated results are basically consistent with the theoretical values, which verifies the correctness of the algorithm and model.

In order to confirm the calculation accuracy of the moving boundary problem, the trough is 10m long, the water level is 0.2m high on the left side of the center, and the instantaneous collapse of the dam in the anhydrous dry-bed trough is calculated on the right side. As in the previous example, in the calculation, it is assumed that the average water depth eddy viscosity coefficient ε=0, and the sidewall of the water tank is a slip condition. Through the comparison of the water depth calculation results and theoretical solutions after the dam collapsed for 1s. It can be seen that the calculation results and the theoretical solutions are also very consistent under the condition of dry-bed sink.

Prediction of swells generated when high-speed-moving landslides, debris flows, and glaciers impact water bodies in enclosed waters such as reservoirs, lakes, rivers, and bays is often a large-scale computational problem. In order to shorten the calculation time of large-scale surge analysis, this research uses PARDISO, a sparse linear equation solver implemented on a shared memory machine provided by Intel MKL, to develop a high-performance finite element analysis program for surge, and use some theoretical solutions and experimental results. The developed program is verified. The theoretical solution and numerical calculation results of vertical dam failure, as well as the comparison of laboratory experimental results and numerical calculation results, show that the developed high-performance finite element software for swell can quickly obtain reliable calculation results.

#### Theoretical calculation of swell rise from historic landslides or partially underwater landslides

Date | Location | Landslide material | landslide volume/×106m^{3} |
Death toll | Theoretical value of surge rise/m |
---|---|---|---|---|---|

1756 | Tjelle Granite | gneiss | 15 | 38 | 46.883 |

1792 | Yuan Island Volcanic | debris | 500 | >15000 | 10.282 |

1883 | Krakatau | Pyroxene | -- | 36000 | 35.426 |

1888 | Ritter Island | Basalt | 5000 | >100 | 20.732 |

1905 | Disench.Bay | Glacier ice | 29 | 0 | 35.217 |

1934 | Tafjord | Gneiss | 2~3 | 41 | 62.784 |

1936 | Ravnefjell | Gneiss | 0.451 | 73 | 74.225 |

1958 | |||||

1971 | Yanahuin Lake | Limestone | 240 | >2500 | 270.377 |

1980 | M.St.Helens | Rock | 430 | 0 | 200.082 |

2008 | Zipingpu R. | Rock | 0.45 | >70 | 524.362 |

2010 | 513 Lake, Peru | Glacier ice | 0.5 | 1 | 30.683 |

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Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate Differential equation model of financial market stability based on Internet big data 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Children’s cognitive function and mental health based on finite element nonlinear mathematical model Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Research on threat assessment problems of island air defence system based on the leader-follower model Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model