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. Currently I am focused on threshold dynamics and its extensions. I am interested in exploring new ways of designing efficient and more accurate algorithms and in extending the current convergence results. During my PhD I worked in building numerical methods, together with efficient solvers, for degenerate elliptic partial differential equations using 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

Latest Articles

The Role of Surface Tension and Mobility Model in Simulations of Grain Growth

Authors: Tiago Salvador and Selim Esedoglu

We explore the effects of surface tension and mobility models in simulations of grain growth using threshold dynamics algorithms that allow performing large scale simulations, while naturally capturing the Herring angle condition at junctions and automatically handling topological transitions. The results indicate that in two dimensions, the different surface tension / mobility models considered do not play a significant role in the stationary grain size distribution. However, in three dimensions, there is a substantial difference between the distributions obtained from the same three models, depending on whether the reduced mobilities are isotropic or anisotropic. Additional results show that in three dimensions, the misorientation distribution function of a grain network with random orientation texture returns to the close vicinity of the Mackenzie distribution even if started very far from it.

Read More » A Partial Differential Equation Obstacle Problem for the Level Set Approach to Visibility

Authors: Adam Oberman and Tiago Salvador

We explore the effects of surface tension and mobility models in simulations of grain growth using threshold dynamics algorithms that allow performing large scale simulations, while naturally capturing the Herring angle condition at junctions and automatically handling topological transitions. The results indicate that in two dimensions, the different surface tension / mobility models considered do not play a significant role in the stationary grain size distribution. However, in three dimensions, there is a substantial difference between the distributions obtained from the same three models, depending on whether the reduced mobilities are isotropic or anisotropic. Additional results show that in three dimensions, the misorientation distribution function of a grain network with random orientation texture returns to the close vicinity of the Mackenzie distribution even if started very far from it.

Read More »