Abstract
In this paper, we propose a reduced-order immersed interface method (RO-IIM) to cope with the parabolic interface problem. Second-order central difference scheme in spatial direction is constructed. In time direction, we proposed a reduced-order method with fewer degree of freedoms. Our work contains the initial study of the combination of the immersed interface method and proper orthogonal decomposition (POD) technique. Numerical examples show that the proposed RO-IIM is feasible and efficiency for solving the parabolic interface problems.
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