scholarly journals Convergence analysis of the Generalized Empirical Interpolation Method

2016 ◽  
Vol 54 (3) ◽  
pp. 1713-1731 ◽  
Author(s):  
Y. Maday ◽  
O. Mula ◽  
G. Turinici
Keyword(s):  
Convergence Analysis ◽  
Interpolation Method ◽  
Empirical Interpolation Method

scholarly journals Sensor placement in nuclear reactors based on the generalized empirical interpolation method

2018 ◽  
Vol 363 ◽  
pp. 354-370 ◽  
Author(s):  
J.-P. Argaud ◽  
B. Bouriquet ◽  
F. de Caso ◽  
H. Gong ◽  
Y. Maday ◽  
...  
Keyword(s):  
Nuclear Reactors ◽  
Interpolation Method ◽  
Sensor Placement ◽  
Empirical Interpolation Method

Numerical Treatment of Nonlinear Stochastic Itô–Volterra Integral Equations by Piecewise Spectral-Collocation Method

2019 ◽  
Vol 14 (3) ◽  
Author(s):  
Fakhrodin Mohammadi
Keyword(s):  
Approximate Solution ◽  
Finite Number ◽  
Convergence Analysis ◽  
Integral Equations ◽  
Lagrange Interpolation ◽  
Interpolation Method ◽  
Approximate Solutions ◽  
Volterra Integral Equations ◽  
Numerical Treatment ◽  
Nonlinear Integral Equations

This paper deals with the approximate solution of nonlinear stochastic Itô–Volterra integral equations (NSIVIE). First, the solution domain of these nonlinear integral equations is divided into a finite number of subintervals. Then, the Chebyshev–Gauss–Radau points along with the Lagrange interpolation method are employed to get approximate solution of NSIVIE in each subinterval. The method enjoys the advantage of providing the approximate solutions in the entire domain accurately. The convergence analysis of the numerical method is also provided. Some illustrative examples are given to elucidate the efficiency and applicability of the proposed method.

scholarly journals The use of POD–DEIM model order reduction for the simulation of nonlinear hygrothermal problems

2020 ◽  
Vol 172 ◽  
pp. 04002
Author(s):  
Tianfeng Hou ◽  
Karl Meerbergen ◽  
Staf Roels ◽  
Hans Janssen
Keyword(s):  
Interpolation Method ◽  
Computational Cost ◽  
Order Reduction ◽  
Illustrative Case ◽  
Hygrothermal Simulation ◽  
Discrete Empirical Interpolation Method ◽  
Empirical Interpolation Method ◽  
Illustrative Case Study ◽  
Volume Method ◽  
Proper Orthogonal

In this paper, the discrete empirical interpolation method (DEIM) and the proper orthogonal decomposition (POD) method are combined to construct a reduced order model to lessen the computational expense of hygrothermal simulation. To investigate the performance of the POD-DEIM model, HAMSTAD benchmark 2 is selected as the illustrative case study. To evaluate the accuracy of the POD-DEIM model as a function of the number of construction modes and interpolation points, the results of the POD-DEIM model are compared with a POD and a Finite Volume Method (FVM). Also, as the number of construction modes/interpolation points cannot entirely represent the computational cost of different models, the accuracies of the different models are compared as function of the calculation time, to provide a fair comparison of their computational performances. Further, the use of POD-DEIM to simulate a problem different from the training snapshot simulation is investigated. The outcomes show that with a sufficient number of construction modes and interpolation points the POD-DEIM model can provide an accurate result, and is capable of reducing the computational cost relative to the POD and FVM.

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