Frank Lin | UC Irvine (original) (raw)
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Université de Valenciennes et du Hainaut-Cambrésis (UVHC)
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Papers by Frank Lin
ArXiv, 2021
This article presents an immersed virtual element method for solving a class of interface problem... more This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh methods. A background body-fitted mesh is generated initially. On those interface elements, virtual element spaces are constructed as solution spaces to local interface problems, and exact sequences can be established for these new spaces involving discontinuous coefficients. The discontinuous coefficients of interface problems are recast as Hodge star operators that is the key to project immersed virtual functions to classic immersed finite element (IFE) functions for computing numerical solutions. The proposed method is capable of handling more complicated interface element configuration, and provides better performance than the conventional penalty-type IFE method for the H(curl)-interface problem. It also brings a connection between various methods such as body-fitted methods, IFE methods, and virtual e...
We begin our study of finite difference methods for partial differential equations by considering... more We begin our study of finite difference methods for partial differential equations by considering the important class of partial differential equations called hyperbolic equations. In later chapters we consider other classes of partial differential equations, especially parabolic and elliptic equations. For each of these classes of equations we consider prototypical equations, with which we illustrate the important concepts and distinguishing features associated with each class. The reader is referred to other textbooks on partial differential equations for alternate approaches, e.g., Folland [18], Garabedian [22], and Weinberger [68]. After introducing each class of differential equations we consider finite difference methods for the numerical solution of equations in the class.
ArXiv, 2021
This article presents an immersed virtual element method for solving a class of interface problem... more This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh methods. A background body-fitted mesh is generated initially. On those interface elements, virtual element spaces are constructed as solution spaces to local interface problems, and exact sequences can be established for these new spaces involving discontinuous coefficients. The discontinuous coefficients of interface problems are recast as Hodge star operators that is the key to project immersed virtual functions to classic immersed finite element (IFE) functions for computing numerical solutions. The proposed method is capable of handling more complicated interface element configuration, and provides better performance than the conventional penalty-type IFE method for the H(curl)-interface problem. It also brings a connection between various methods such as body-fitted methods, IFE methods, and virtual e...
We begin our study of finite difference methods for partial differential equations by considering... more We begin our study of finite difference methods for partial differential equations by considering the important class of partial differential equations called hyperbolic equations. In later chapters we consider other classes of partial differential equations, especially parabolic and elliptic equations. For each of these classes of equations we consider prototypical equations, with which we illustrate the important concepts and distinguishing features associated with each class. The reader is referred to other textbooks on partial differential equations for alternate approaches, e.g., Folland [18], Garabedian [22], and Weinberger [68]. After introducing each class of differential equations we consider finite difference methods for the numerical solution of equations in the class.