We propose several immersed interface hybridized difference methods(IHDMs),combined with the Crank-Nicolson time-stepping scheme,for parabolic interface problems.The IHDM is the same as the hybrid difference method aw...We propose several immersed interface hybridized difference methods(IHDMs),combined with the Crank-Nicolson time-stepping scheme,for parabolic interface problems.The IHDM is the same as the hybrid difference method away from the interface cells,but the finite difference operators on the interface cells are modified tomaintain the same accuracy throughout the entire domain.For themodification process,we consider virtual extensions of two sub-solutions in the interface cells in such a way that they satisfy certain jump equations between them.We propose several different sets of jump equations and their resulting discrete methods for one-and two-dimensional problems.Some numerical results are presented to demonstrate the accuracy and robustness of the proposed methods.展开更多
基金supported by the National Research Foundation of Korea under the grant NRF 2018R1D1A1A09082082.
文摘We propose several immersed interface hybridized difference methods(IHDMs),combined with the Crank-Nicolson time-stepping scheme,for parabolic interface problems.The IHDM is the same as the hybrid difference method away from the interface cells,but the finite difference operators on the interface cells are modified tomaintain the same accuracy throughout the entire domain.For themodification process,we consider virtual extensions of two sub-solutions in the interface cells in such a way that they satisfy certain jump equations between them.We propose several different sets of jump equations and their resulting discrete methods for one-and two-dimensional problems.Some numerical results are presented to demonstrate the accuracy and robustness of the proposed methods.
