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Citations since 2017
5 Research Items
My research interests fall in the broad areas of scientific computing and numerical analysis. Recently, I'm working on machine learning methods for scientific computing, specifically the data-driven modeling and uncertainty quantification of physical systems governed by (stochastic) differential equations.
Skills and Expertise
We present a computational technique for modeling the evolution of partial differential equations (PDEs) with incomplete data. It is a significant extension of the recent work of data driven learning of PDEs, in the sense that we consider two forms of partial data: data are observed only on a subset of the domain, and data are observed only on a su...
In this article, we develop a Taylor-Hood immersed finite element (IFE) method to solve two-dimensional Stokes interface problems. The P2-P1 local IFE spaces are constructed using the least-squares approximation on an enlarged fictitious element. The partially penalized IFE method with ghost penalty is employed for solving Stoke interface problems....
In this article, we introduce a new partially penalized immersed finite element method (IFEM) for solving elliptic interface problems with multi-domains and triple-junction points. We construct new IFE functions on elements intersected with multiple interfaces or with triple-junction points to accommodate interface jump conditions. For non-homogene...
In this article, we introduce a new partially penalized immersed finite element method (IFEM) for solving elliptic interface problems with multi-domain and triple-junction points. We construct new IFE functions on elements intersected with multiple interfaces or with triple-junction points to accommodate interface jump conditions. For non-homogeneo...
Interface problems have wide applications in modern scientific research. Obtaining accurate numerical solutions of multi-domain problems involving triple junction conditions remains a significant challenge. In this paper, we develop an efficient finite element method based on non-body-fitting meshes for solving multi-domain elliptic interface probl...