The Immersed Interface Method for Elasticity Problems with Interfaces
NORTH CAROLINA STATE UNIV AT RALEIGH DEPT OF MATHEMATICS
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An immersed interface method for solving linear elasticity problems with two phases separated by an interface has been developed in this paper. 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 interface 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. Numerical results are presented to show that the method is second-order accurate.