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Session Overview
plenary 7: Anna-Karin Tornberg
Friday, 16/July/2021:
2:10pm - 3:00pm

Session Chair: Jie Shen
Virtual location: Zoom 1

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Partition of unity extension for high-order approximations

Anna-Karin Tornberg

KTH Royal Institute of Technology, Sweden

Partition of unity extension (PUX) is a computational method in which a function on an arbitrary domain is extended outside its support with high global regularity and compact support. The global extension consists of local extensions weighted together with weight functions of a prescribed regularity, which form a partition of unity. These local extensions are the result of interpolating given function data with smooth radial basis functions with a precomputed interpolation matrix. We have used the PUX method to extend the applicability of boundary integral methods for linear elliptic homogeneous PDEs. This includes accurate numerical solutions on complex domains for elliptic inhomogeneous PDE (Poisson equation) and for time dependent PDEs also on time dependent domains (the heat and advection-diffusion equations). We will discuss some of the additional framework needed for these extensions, but will in this talk mainly focus on the properties of this new function extension methodology.

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