Qiuqi Li

Hunan University · Department of Mathematics and Applied Mathematics

In this paper, we develop a reduced generalized multiscale basis method for efficiently solving the parametrized groundwater flow problems in heterogeneous porous media. Recently proposed generalized multiscale finite element (GMsFE) method is one of the accurate and efficient methods to solve the multiscale problems on a coarse grid. However, the...

Here, we present some Reduced Basis (RB) methods for fluid infiltration problems through certain porous media modeled as dual-continuum with localized uncertainties. We apply dimension reduction techniques to construct a reduced order model. In the RB methods, to perform the offline-online computation decomposition, the model inputs need to be affi...

In this paper, a local-global model reduction method is presented to solve stochastic optimal control problems governed by partial differential equations (PDEs). If the optimal control problems involve uncertainty, we need to use a few random variables to parameterize the uncertainty. The stochastic optimal control problems require solving coupled...

In this paper, we propose a novel variable-separation (NVS) method for generic multivariate functions. The idea of NVS is extended to to obtain the solution in tensor product structure for stochastic partial differential equations (SPDEs). Compared with many widely used variation-separation methods, NVS shares their merits but has less computation...

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. Mixed generalized multiscale finite element method (GMsFEM) is one of the accurate and efficient approaches to solve multiscale problem in a coarse grid with local mass co...

In this paper, we present some reduced basis methods for elliptic PDEs with parameterized inputs. In the framework of Galerkin projection, dimension reduction techniques are used to construct a reduced order model. If the PDEs have multiscale structures, multiscale finite element method (MsFEM) is one of the efficient approaches to numerically solv...

In this article, we present a reduced order method for modeling and computing Allen–Cahn equations. A global basis method is used in the discretized system of the Allen–Cahn equations and Proper Orthogonal Decomposition (POD) method is utilized to reduce the global basis. To treat the difficulty of nonlinearity for Allen–Cahn equations, we apply Di...