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• W2113251641 abstract "Elliptic problems with sharp-edged interfaces, thin-layered interfaces and interfaces that intersect with geometric boundary, are notoriously challenging to existing numerical methods, particularly when the solution is highly oscillatory. This work generalizes the matched interface and boundary (MIB) method previously designed for solving elliptic problems with curved interfaces to the aforementioned problems. We classify these problems into five distinct topological relations involving the interfaces and the Cartesian mesh lines. Flexible strategies are developed to systematically extends the computational domains near the interface so that the standard central finite difference scheme can be applied without the loss of accuracy. Fictitious values on the extended domains are determined by enforcing the physical jump conditions on the interface according to the local topology of the irregular point. The concepts of primary and secondary fictitious values are introduced to deal with sharp-edged interfaces. For corner singularity or tip singularity, an appropriate polynomial is multiplied to the solution to remove the singularity. Extensive numerical experiments confirm the designed second order convergence of the proposed method." @default.
• W2113251641 created "2016-06-24" @default.
• W2113251641 creator A5040426930 @default.
• W2113251641 creator A5042015157 @default.
• W2113251641 creator A5087381881 @default.
• W2113251641 date "2007-06-01" @default.
• W2113251641 modified "2023-10-11" @default.
• W2113251641 title "Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces" @default.
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• W2113251641 doi "https://doi.org/10.1016/j.jcp.2006.10.030" @default.
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