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BIRS Workshop Lecture Videos

A target specific QBX method for the accurate computation of boundary integrals with nearly touching interfaces Siegel, Michael


Boundary integral methods are among the most popular methods for computing interfacial fluid flow, and have the advantage that they can be made high-order accurate. Thus, they are useful for investigating phenomena that require high accuracy to resolve features, such as "pinching" or topological singularities that can occur on the interface. However, standard BI methods lose accuracy when two parts of an interface are near touching. In this talk, we present a new algorithm based on the QBX method of Klockner et al. for the accurate computation of boundary integrals with singular or nearly singular kernels in 3D. The QBX method is typically based on a spherical harmonics expansion which when truncated at $\mathcal{O}(p)$ has $\mathcal{O}(p^2)$ terms. This expansion can equivalently be written with $\mathcal{O}(p)$ terms, but paying the price that the expansion coefficients will depend on the target point. Based on this observation, we develop a target specific QBX method. We give error estimates for our method, and illustrate its performance in several examples. This work is joint with Anna-Karin Tornberg.

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