# A Cartesian Grid-Based Boundary Integral Method for an Elliptic Interface Problem on Closely Packed Cells

@article{Ying2018ACG, title={A Cartesian Grid-Based Boundary Integral Method for an Elliptic Interface Problem on Closely Packed Cells}, author={Wenjun Ying}, journal={Communications in Computational Physics}, year={2018}, volume={24} }

In this work, we propose a second-order version and a fourth-order version of a Cartesian grid-based boundary integral method for an interface problem of the Laplace equation on closely packed cells. When the cells are closely packed, the boundary integrals involved in the boundary integral formulation for the interface problem become nearly singular. Direct evaluation of the boundary integrals has accuracy issues. The grid-based method evaluates a boundary integral by first solving an…

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