A POD-Based Reduced-Order Stabilized Crank–Nicolson MFE Formulation for the Non-Stationary Parabolized Navier–Stokes Equations

We firstly employ a proper orthogonal decomposition (POD) method, Crank–Nicolson (CN) technique, and two local Gaussian integrals to establish a PODbased reduced-order stabilized CN mixed finite element (SCNMFE) formulation with very few degrees of freedom for non-stationary parabolized Navier–Stokes equations. Then, the error estimates of the reduced-order SCNMFE solutions, which are acted as a suggestion for choosing number of POD basis and a criterion for updating POD basis, and the algorithm implementation for the POD-based reduced-order SCNMFE formulation are provided, respectively. Finally, some numerical experiments are presented to illustrate that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order SCNMFE formulation is feasible and efficient for finding numerical solutions of the non-stationary parabolized Navier–Stokes equations

A Reduced-Order Extrapolation Spectral-Finite Difference Scheme Based on the POD Method for 2D Second-Order Hyperbolic Equations

In this study, a reduced-order extrapolation spectral-finite difference (ROESFD) scheme based on the proper orthogonal decomposition (POD) method is set up for the two-dimensional (2D) second-order hyperbolic equations. First, the classical spectral-finite difference (CSFD) method for the 2D second-order hyperbolic equations and its stability, convergence, and flaw are introduced. Then, a new ROESFD scheme that has very few degrees of freedom but holds sufficiently high accuracy is set up by the POD method and its implementation is offered. Finally, three numerical examples are offered to explain the validity of the theoretical conclusion. This implies that the ROESFD scheme is viable and efficient for searching the numerical solutions of the 2D second-order hyperbolic equations

A non-intrusive model order reduction approach for parameterized time-domain Maxwell's equations

International audienceWe present a non-intrusive model order reduction (NIMOR) method with an offline-online decoupling for the solution of parameterized time-domain Maxwell's equations. During the offline stage, the training parameters are chosen by using Smolyak sparse grid method with an approximation level L (L ≥ 1) over a target parameterized space. This method can deal with the so-called curse of dimensionality in high dimensional space. For each selected parameter, the snapshot vectors are first produced by a high order discontinuous Galerkin time-domain (DGTD) solver formulated on an unstructured simplicial mesh. In order to minimize the overall computational cost in the offline stage and to improve the accuracy of the NIMOR method, a radial basis function (RBF) interpolation method is then used to construct more snapshot vectors at the sparse grid with approximation level L + 1, which includes the sparse grids from approximation level L. A nested proper orthogonal decomposition (POD) method is employed to extract time-and parameter-independent POD basis functions. By using the singular value decomposition (SVD) method, the principal components of the reduced coefficient matrices of the high-fidelity solutions onto the reduced-order subspace spaned by the POD basis functions are extracted. Moreover, a Gaussian process regression (GPR) method is proposed to approximate the dominating time-and parameter-modes of the reduced coefficient matrices. During the online stage, the reduced-order solutions for new time and parameter values can be rapidly recovered via outputs from the regression models without using the DGTD method. The performance of this NIMOR method is illustrated numerically by considering two classical test cases: the scattering of a plane wave by a 2-D dielectric disk and the scattering of a plane wave by a multi-layer heterogeneous medium. The prediction capabilities of the NIMOR method are evaluated by varying the relative permittivity. Numerical results indicate that the NIMOR method is a promising approach for simulating accurately and in fast way parameterized timedomain electromagnetic problems

Twenty-Fourth Lunar and Planetary Science Conference. Part 3: N-Z

Papers from the conference are presented, and the topics covered include the following: planetary geology, meteorites, planetary composition, meteoritic composition, planetary craters, lunar craters, meteorite craters, petrology, petrography, volcanology, planetary crusts, geochronology, geomorphism, mineralogy, lithology, planetary atmospheres, impact melts, K-T Boundary Layer, volcanoes, planetary evolution, tectonics, planetary mapping, asteroids, comets, lunar soil, lunar rocks, lunar geology, metamorphism, chemical composition, meteorite craters, planetary mantles, and space exploration