Multigrid methods for the modified elastic transmission eigenvalue problem.

The modified transmission eigenvalue problem of elastic waves arises from inverse scattering theory. In this work we first analyze the well-posedness of the modified transmission problem and accomplish a rigorous error analysis of conforming finite element methods. Then we establish two types of multigrid schemes. Finally, we numerically research the effect of a flaw in the material on the modified elastic transmission eigenvalues and apply the multigrid schemes to perform parallel computing. Numerical experiments are presented to verify the theoretical convergence order and the efficiency of the proposed schemes. [ABSTRACT FROM AUTHOR]