We propose a new numerical algorithm to construct a structured numericalelliptic grid of a doubly connected domain. Our method is applicable to domainswith boundaries defined by two contour lines of a two-dimensional function. Theresulting grids are orthogonal to the boundary. Grid points as well as theelements of the Jacobian matrix can be computed efficiently and up to machineprecision. In the simplest case we construct conformal grids, yet with the helpof weight functions and monitor metrics we can control the distribution ofcells across the domain. Our algorithm is parallelizable and easy to implementwith elementary numerical methods. We assess the quality of grids byconsidering both the distribution of cell sizes and the accuracy of thesolution to elliptic problems. Among the tested grids these key properties arebest fulfilled by the grid constructed with the monitor metric approach.
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