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XFEM
The extended finite element method (XFEM), is a numerical technique based on the generalized finite element method (GFEM) and the Partition of unity, partition of unity method (PUM). It extends the classical finite element method (FEM) approach by enriching the solution space for solutions to differential equations with discontinuous functions. History The extended finite element method (XFEM) was developed in 1999 by Ted Belytschko and collaborators, to help alleviate shortcomings of the finite element method and has been used to model the propagation of various discontinuities: strong (Fracture, cracks) and weak (material interfaces). The idea behind XFEM is to retain most advantages of meshfree methods while alleviating their negative sides. Rationale The extended finite element method was developed to ease difficulties in solving problems with localized features that are not efficiently resolved by mesh refinement. One of the initial applications was the modelling of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Element Method
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. Computers are usually used to perform the calculations required. With high-speed supercomputers, better solutions can be achieved and are often required to solve the largest and most complex problems. FEM is a general numerical method for solving partial differential equations in two- or three-space variables (i.e., some boundary value problems). There are also studies about using FEM to solve high-dimensional problems. To solve a problem, FEM subdivides a large system into smaller, simpler parts called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
