A rapid numerical method for the Mullins-Sekerka flow with application to contact angle problems

The Mullins-Sekerka problem is numerically solved in $\mathbb{R}^2$ with the aid of the charge simulation method. This is an expansion of the numerical scheme by which Sakakibara and Yazaki computed the Hele-Shaw flow. We investigate a sufficient condition for the number of collocation points to ensure that the length of the generated approximate polygonal curves gradually decreases. We propose a new benchmark function for the Mullins-Sekerka flow to confirm that the scheme works well. Moreover, by changing the fundamental solutions of the charge simulation method, we are successful to establish a numerical scheme that can be used to treat the Mullins-Sekerka problem with the contact angle condition.