基于加权CVT的一个微分方程的降阶模型(英文)

Reduced-order Modeling of a Partial Differential Equation Based on Weighted CVT

基于加权CVT的Burgers方程的降阶模型,研究了由非均匀密度确定的近似子空间基元素.并利用有限元方法比较了由CVT-uniform,CVT-nonuniform方法和POD方法得到的相关数值.

In this paper, we consider a weighted CVT-based reduced-order modeling for Burgers equation. So far, the CVT（centroidal Voronoi tessellation） was researched with uniform density （p（y） = 1） to determine the basis elements for the approximating subspaces. Here, we shall investigate the technique of CVT with nonuniform density as a procedure to determine the basis elements for the approximating subspaces. Some numerical experiments including comparison of two CVT（CVT-uniform and CVT-nonuniform）-based algorithm with numerical results obtained from FEM（finite element method） and POD（Proper Orthogonal Decomposition） based algorithm are reported.