Time: 9h30, Tuesday, December 8, 2015
Location: Room 4, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi
Abstract: In this talk, we present homogenization for Helmholtz equations. After studying the existence and uniqueness of solutions of Helmholtz equations at small scales $\eta$, using multiscale convergence method we show that the homogenized solution satisfies the homogenized variational problem, which is proven to have a unique solution as well. Then, we present the full tensor finite element method (FTFEM) and the sparse tensor finite element method (STFEM) for solving this homogenized variational problem. The convergence rate of discretized solutions to the solution of the homogenized variational problem is obtained under some smoothness conditions. Finally, we illustrate FTFEM and STFEM in some numerical examples. The  advantage of STFEM compared with FTFEM is pointed out in these numerical examples.