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Geometric integration over irregular domains with application to level-set methods. (English) Zbl 1125.65021
Summary: We present a geometric approach for calculating integrals over irregular domains described by a level-set function. This procedure can be used to evaluate integrals over a lower dimensional interface and may be used to evaluate the contribution of singular source terms. This approach produces results that are second-order accurate and robust to the perturbation of the interface location on the grid. Moreover, since we use a cell-wise approach, this procedure can be easily extended to quadtree and octree grids. We demonstrate the second-order accuracy and the robustness of the method in two and three spatial dimensions.

MSC:
65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
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