Search Results

Dynamic mode decomposition (DMD) describes the dynamical system in an equation-free manner and can be used for the prediction and control. It is an efficient data-driven method for the complex systems. In this paper, we extend DMD to the ...

In this paper, we consider a variable-separation (VS) method to solve the nonlinear partial differential equations (PDEs) with random inputs. The aim of the VS method is to get a sep- arated representation of the Galerkin solution for nonlinear PDEs with ...

In this paper, we propose a Multiscale Virtual Element Method (MsVEM) for elliptic problems in heterogeneous porous media. The use of very general coarse grids has advantages in subsurface simulations since they provide flexibility and can render ...

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 ...

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. A typical application for the elliptic PDEs is the flow in heterogeneous ...

In this paper, we propose a novel variable-separation (VS) method for generic multivariate functions. The idea of the novel VS is extended to obtain the solution in tensor product structure for stochastic partial differential equations (SPDEs). Compared ...

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,...

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 ...