I am a Post-Doctoral Assistant Professor in the Department of Mathematics at University of Michigan. My mentor is Selim Esedoglu.
I received my Ph.D. in Mathematics from McGill University in 2017. My advisor was Adam Oberman.
My research interests are in numerical analysis. My work so far has consisted in building numerical methods, together with efficient solvers, for degenerate elliptic partial differential equations using monotone schemes. On the theory side, I am also interested in viscosity solutions which are the prevalent framework and correct notion of weak solution to prove convergence of monotone schemes.
Contact details
Address: | Department of Mathematics, |
University of Michigan, | |
530 Church Street, | |
Ann Arbor, MI 48109 | |
Office: | 3831 East Hall |
Email: | saldanha[at]umich[dot]edu |
We present a simplified version of the threshold dynamics algorithm given in the work of Esedoglu and Otto (2015). The new version still allows specifying N-choose-2 possibly distinct surface tensions and N-choose-2 possibly distinct mobilities for a network with N phases, but achieves this level of generality without the use of retardation functions. Instead, it employs linear combinations of Gaussians in the convolution step of the algorithm. Convolutions with only two distinct Gaussians is enough for the entire network, maintaining the efficiency of the original thresholding scheme. We discuss stability and convergence of the new algorithm, including some counterexamples in which convergence fails. The apparently convergent cases include unequal surface tensions given by the Read & Shockley model and its three dimensional extensions, along with equal mobilities, that are a very common choice in computational materials science.
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