We propose a new reverse time migration method for reconstructing extended obstacles in the planar waveguide using acoustic waves at a fixed frequency. We prove the resolution of the reconstruction method in terms of the aperture and the thickness of the waveguide. The resolution analysis implies that the imaginary part of the cross-correlation imaging function is always positive and thus may have better stability properties.Numerical experiments are included to illustrate the powerful imaging quality and to confirm our resolution results.
Based on the PMHSS preconditioning matrix, we construct a class of rotated block triangular preconditioners for block two-by-two matrices of real square blocks, and analyze the eigen-properties of the corresponding preconditioned matrices. Numerical experiments show that these rotated block triangular pre- conditioners can be competitive to and even more efficient than the PMHSS preconditioner when they are used to accelerate Krylov subspeme iteration methods for solving block two-by-two linear systems with coefficient matrices possibly of nonsymmetric sub-blocks.
Consider a Hamiltonian action of S1 on （Cn^n＋1,ωstd）, we shown that the Hamiltonian Gromov-Witten invariants of it are well-defined. After computing the Hamiltonian Gromov-Witten invariants of it, we construct a ring homomorphism from HS1,CR（X, R） to the small orbifold quantum cohomology of X//rS^1 and obtain a simpler formula of the Gromov-Witten invariants for weighted projective space.
