| Abstract: |
| In this talk, we present a Cartesian grid-based method for solving mean curvature flows in two and three space dimensions. The mean curvature flows describe the dynamics of a hypersurface whose normal velocity is determined by local mean curvature. The proposed method embeds a closed hypersurface into a fixed Cartesian grid and decomposes it into multiple overlapping subsets. For each subset, extra tangential velocities are introduced such that marker points on the hypersurface only moves along grid lines. By utilizing an alternating direction implicit (ADI)-type time integration method, the subsets are evolved alternately by solving scalar parabolic partial differential equations on planar domains. The method removes the stiffness using a semi-implicit scheme and has no high-order stability constraint on time step size. Numerical examples in two and three space dimensions are presented to validate the proposed method. |
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