Browsing by Author "Yang, Xingzhou"
Now showing 1 - 4 of 4
- Results Per Page
- Sort Options
- A priori error estimates for numerical methods for scalar conservation laws. Part III: multidimensional flux-splitting Monotone schemes on non-Cartesian grids(North Carolina State University. Center for Research in Scientific Computation, 1997) Cockburn, B.; Gremaud, Pierre Alain; Yang, Xingzhou
- An immersed FEM for elasticity equations with interfaces(North Carolina State University. Center for Research in Scientific Computation, 2004) Li, Zhilin; Yang, Xingzhou
- Immersed Interface Method for Elasticity Problems with Interfaces(2004-07-20) Yang, Xingzhou; Dr. Mansoor A. Haider, Committee Member; Dr. Kazufumi Ito, Committee Member; Dr. Sharon R. Lubkin, Committee Member; Dr. Zhilin Li, Committee Chair; Computational MathematicsAn immersed interface method and an immersed finite element method for solving linear elasticity problems with two phases separated by an interface have been developed in this thesis. For the problem of interest, the underlying elasticity modulus is a constant in each phase but vary from phase to phase. The basic goal here is to design an efficient numerical method using a fixed Cartesian grid. The application of such a method to problems with moving interfaces driving by stresses has a great advantage: no re-meshing is needed. A local optimization strategy is employed to determine the finite difference equations at grid points near or on the interface. The bi-conjugate gradient method and the GMRES with preconditioning are both implemented to solve the resulting linear systems of equations and compared. The level set method is used to represent the interface. Numerical results are presented to show that the immersed interface method is second-order accurate.
- The immersed interface method for elasticity problems with interfaces(North Carolina State University. Center for Research in Scientific Computation, 2002) Yang, Xingzhou; Li, Bailian; Li, Zhilin
