Abstract：

Many problems in physics and engineering require the solution of the heat equation in moving geometry. Integral representations are particularly appropriate in this setting since they satisfy the governing equation automatically and, in the homogeneous case, require the discretization of the space-time boundary alone. In this talk, we present a new method for solving the 2D heat equation in moving geometry that makes use of a spatially adaptive mesh, a new version of the fast Gauss transform that allows for volume and boundary sources, and a new hybrid asymptotic/numerical method for local-in-time quadrature.

Short Bio:

Jun Wang joined Simons Foundation in 2017 as a research fellow at the Flatiron Institute’s Center for Computational Biology.Before coming to the foundation, she obtained her Ph.D. from the Courant Institute at New York University, where she carried out research in fast algorithms and integral equation methods for elliptic and parabolic PDEs. In 2016, she was awarded the Sandra Bleistein Prize from New York University. She obtained her B.S. from Peking University. As a member of the Numerical Algorithms group, she now develops new methods for the simulation of fluid dynamics and diffusion, with a particular focus on moving geometries, biophysical applications and diffusion magnetic resonance imaging.