A Reduced Basis Enrichment for the eXtended Finite Element Method
نویسندگان
چکیده
منابع مشابه
On enrichment functions in the extended finite element method
This paper presents mathematical derivation of enrichment functions in the extended finite element method (XFEM) for numerical modelling of strong and weak discontinuities. The proposed approach consists in combining the level set method with characteristic functions as well as domain decomposition and reproduction technique. We start with the simple case of a triangular linear element cut by o...
متن کاملAdaptive Basis Enrichment for the Reduced Basis Method Applied to Finite Volume Schemes
We derive an efficient reduced basis method for finite volume approximations of parameterized linear advection-diffusion equations. An important step in deriving a reduced finite volume model with the reduced basis technology is the generation of a reduced basis space, on which the detailed numerical simulations are projected. We present a new strategy for this reduced basis generation. We appl...
متن کاملAdaptive reduced basis finite element heterogeneous multiscale method
An adaptive reduced basis finite element heterogeneous multiscale method (RB-FE-HMM) is proposed for elliptic problems with multiple scales. The multiscale method is based on the RB-FE-HMM introduced in [A. Abdulle and Y. Bai, J. Comput. Phys, 2012, in press]. It couples a macroscopic solver with effective data recovered from the solution of micro problems solved on sampling domains. Unlike cla...
متن کاملCover interpolation functions and h-enrichment in finite element method
This paper presents a method to improve the generation of meshes and the accuracy of numerical solutions of elasticity problems, in which two techniques of h-refinement and enrichment are used by interpolation cover functions. Initially, regions which possess desired accuracy are detected. Mesh improvment is done through h-refinement for the elements existing in those regions. Total error of th...
متن کاملIntegration of Singular Enrichment Functions in the Generalized/Extended Finite Element Method for Three-Dimensional Problems
A mapping method is developed to integrate weak singularities which result from enrichment functions in the generalized/extended FEM. The integration scheme is applicable to 2D and 3D problems including arbitrarily shaped triangles and tetrahedra. Implementation of the proposed scheme in existing codes is straightforward. Numerical examples for 2D and 3D problems demonstrate the accuracy and co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Modelling of Natural Phenomena
سال: 2009
ISSN: 0973-5348,1760-6101
DOI: 10.1051/mmnp/20094104