In this research project, we aim to analyse and design a multiscale finite element solver for flow in porous media. The performance of the solver will then be compared against existing finite element software. The multiscale solver will couple local finite element solvers together via a coarse scale set of Lagrange multipliers enforcing continuity of moments. In order to accelerate the simulation, we will consider an off-line phase in which we will create a nonlinear map from the Lagrange multiplier to the coarse scale fluxes in terms of deep neural networks.
Jacob Vandenberg is a second-year student at Monash University, studying a Bachelor of Science Advanced – Research. Due to his passion for helping and teaching others, he currently works as a high school mathematics and physics tutor, and is also involved as a mentor for science students at Monash.
After exploring Algorithms, Data Science, Philosophy and Stochastic Processes, Jacob has found research interests in Numerical Analysis, Physics and Partial Differential Equations.
As an avid climber, Jacob will often be found at rock climbing gyms in his spare time, and has recently taken up endurance running alongside.