scholarly journals Applying the R-solution method for designing a tsunami observational system

2021 ◽  
Vol 2099 (1) ◽  
pp. 012063
Author(s):  
T A Voronina ◽  
A V Loskutov
Keyword(s):  
Wave Propagation ◽  
Numerical Solution ◽  
Least Squares Method ◽  
Tsunami Wave ◽  
Singular Value Decomposition Method ◽  
Spatial Modes ◽  
The Matrix ◽  
Wave Heights ◽  
Value Decomposition ◽  
Tsunami Energy

Abstract One of the promising methods of the early warning of a tsunami is obtaining data of the wave heights based on the numerical solution of the inverse tsunami problem by using the truncated singular value decomposition method as a variant of the least-squares method. The problem is considered within the framework of the linear theory of wave propagation. The technique proposed allows one to avoid the inevitable instability of the numerical solution. It is possible to choose the most informative directions for the placement of the observation stations, which is based on the analysis of the energy transfer by the spatial modes generated by each right singular vector. As it has turned out, the best location of the stations is closely related to the directions of the most intense distribution of the tsunami energy. One of the significant advantages of the approach presented is the possibility, without additional calculations of the tsunami wave propagation from a reconstructed source, to obtain the tsunami wave heights at the points at which there are no observations but which are associated when calculating the matrix of the direct problem operator. The implementation of the approach proposed of the actual event of the Chilean Illapel Tsunami of September 16, 2015, is presented.

scholarly journals Fast Modelling of Tsunami Wave Propagation using PC with Hardware Computer Code Acceleration

2001 ◽  
Vol 14 (4) ◽  
pp. 433-444
Author(s):  
Mikhail M. Lavrentiev ◽  
Keyword(s):  
Wave Propagation ◽  
Tsunami Wave ◽  
Hardware Acceleration ◽  
Source Area ◽  
Computer Code ◽  
Analytic Solutions ◽  
Tsunami Source ◽  
Computational Domain ◽  
Field Programmable ◽  
Wave Heights

The field programmable gates array (FPGA) microchip is applied to achieve considerable performance gain in simulation of tsunami wave propagation using personal computer. The two-step Mac-Cormack scheme was used for approximation of the shallow water equations. An idea of PC-based tsunami wave propagation simulation is described. Comparison with the available analytic solutions and numerical results obtained with the reference code show that developed approach provides good accuracy in simulations. It takes less then 1 minute to compute 1 hour of the wave propagation in computational domain that contains 3000 × 2500 nodes. Using the nested greed approach, it is possible to decrease the size of space step from about 300 meters to 10 m. Using the proposed approach, the entire computational process (to calculate the wave propagation from the source area to the coast) takes about 2 min. As an example the distribution of maximal heights of tsunami wave along the coast of the Southern part of Japan is simulated. In particular, the interrelation between maximal wave heights and location of tsunami source is studied. Model sources of size 100 × 200 km have realistic parameters for this region. It was found that only selected parts of the entire coast line are exposed to tsunami wave with dangerous height. However, the occurrence of extreme tsunami wave heights at some of those areas can be attributed to the local bathymetry. The proposed hardware acceleration to compute tsunami wave propagation can be used for rapid (say, during few minutes) evaluation of danger from tsunami wave for a particular location of the coast

AN EFFICIENT NUMERICAL METHOD FOR SOLVING AN INVERSE WAVE PROBLEM

2013 ◽  
Vol 10 (03) ◽  
pp. 1350009 ◽  
Author(s):  
REZA POURGHOLI ◽  
AMIN ESFAHANI
Keyword(s):  
Inverse Problem ◽  
Numerical Method ◽  
Auxiliary Problem ◽  
Linear Wave ◽  
Singular Value Decomposition Method ◽  
The Matrix ◽  
Uniqueness Of The Solution ◽  
The Stability ◽  
Stability And Accuracy ◽  
Value Decomposition

In this paper, we will first study the existence and uniqueness of the solution of a one-dimensional inverse problem for an inhomogeneous linear wave equation with initial and boundary conditions via an auxiliary problem. Then a stable numerical method consisting of zeroth-, first-, and second-order Tikhonov regularization to the matrix form of Duhamel's principle for solving this inverse problem is presented. The stability and accuracy of the scheme presented is evaluated by comparison with the Singular Value Decomposition method. Some numerical experiments confirm the utility of this algorithm as the results are in good agreement with the exact data.

scholarly journals Distributed Singular Value Decomposition Method for Fast Data Processing in Recommendation Systems

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2284
Author(s):  
Krzysztof Przystupa ◽  
Mykola Beshley ◽  
Olena Hordiichuk-Bublivska ◽  
Marian Kyryk ◽  
Halyna Beshley ◽  
...  
Keyword(s):  
Distributed Systems ◽  
Singular Value Decomposition ◽  
Data Processing ◽  
Message Passing ◽  
Message Passing Interface ◽  
Recommendation Systems ◽  
Singular Value ◽  
Singular Value Decomposition Method ◽  
Value Decomposition ◽  
Svd Method

The problem of analyzing a big amount of user data to determine their preferences and, based on these data, to provide recommendations on new products is important. Depending on the correctness and timeliness of the recommendations, significant profits or losses can be obtained. The task of analyzing data on users of services of companies is carried out in special recommendation systems. However, with a large number of users, the data for processing become very big, which causes complexity in the work of recommendation systems. For efficient data analysis in commercial systems, the Singular Value Decomposition (SVD) method can perform intelligent analysis of information. With a large amount of processed information we proposed to use distributed systems. This approach allows reducing time of data processing and recommendations to users. For the experimental study, we implemented the distributed SVD method using Message Passing Interface, Hadoop and Spark technologies and obtained the results of reducing the time of data processing when using distributed systems compared to non-distributed ones.

scholarly journals FPGA Based Tsunami Wave Propagation Calculator

2021 ◽  
Vol 1789 (1) ◽  
pp. 012011
Author(s):  
M M Lavrentiev ◽  
K F Lysakov ◽  
An G Marchuk ◽  
K K Oblaukhov ◽  
M Yu Shadrin
Keyword(s):  
Wave Propagation ◽  
Tsunami Wave

Aggregation Method of Multi-Criteria Evaluations in New and Renewable Energy Power Plants: A Case Study

2009 ◽  
Author(s):  
Jiang-Jiang Wang ◽  
Chun-Fa Zhang ◽  
You-Yin Jing
Keyword(s):  
Renewable Energy ◽  
Nuclear Power ◽  
Power Plants ◽  
Economic Cost ◽  
Evaluation Result ◽  
Singular Value Decomposition Method ◽  
Multi Criteria Evaluation ◽  
Potential Development ◽  
Value Decomposition ◽  
Grey Relational

The multi-criteria evaluation methods of complex systems such as the new and renewable technologies gradually spring up. The feasibility of energy power plants is evaluated and considered from many aspects, such as technology, economic cost and environment protection. However, the energy power plants’ ranking results in different methods or different weighs can be different. Accordingly, the sequencing results should be aggregated and analyzed, and then an integrated result should be given out. Aiming to get the specific evaluation result, 10 kinds of energy power plants, such as hydro, nuclear, wind, geothermal and biomass plants are considered and evaluated. The singular value decomposition method is employed to aggregate the evaluation results in grey relational method, PROMENTHEE II method, and other results from literature. The integrated evaluation result shows that the hydro and nuclear power plants are located on the first place and the renewable energy power plants have great potential development in the future.

TOTAL LEAST SQUARES FOR ESTIMATION OF THE GROSS OUTPUT VECTOR

2020 ◽  
Author(s):  
Dmitriy Vladimirovich Ivanov ◽  
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Direct Costs ◽  
Total Least Squares ◽  
Test Cases ◽  
Output Vector ◽  
Final Consumption ◽  
The Matrix

The article proposes the estimation of the gross output vector in the presence of errors in the matrix of direct costs and the final consumption vector. The article suggests the use of the total least squares method for estimating the gross output vector. Test cases showed that the accuracy of the proposed estimates of the gross output vector is higher than the accuracy of the estimates obtained using the classical least squares method (OLS).

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