Dr. Xin Cui, postdoctroal associate in MIT ERL/EAPS, presesnts "Exploration of efficient and robust algorithms to solve simultaneous Partial Differential Equations" as part of the EAPS Geophysics Seminar.

"Many numerical simulations of the physical world boil down to solving a system of Partial Differential Equations (PDEs).  For example, the thermo-hydro-mechanical coupling effect underlying geothermal exploitation, nuclear waste disposal and CO2 storage, is governed by a set of PDEs extracted from energy conservation, mass conservation and stress equilibrium. Today’s scientific research and engineering applications require large-scale simulations more than ever, which poses challenges in efficiently solving PDEs. Although high-performance computing can significantly improve the efficiency of simulations and machine learning is very promising to quickly predict the solutions of PDEs after training, designing an appropriate algorithm to convert PDEs to linear equations and then solve them is of fundamental importance. In this talk, I will share my experience in solving PDEs with a monolithic approach or dividing them into subsets. In the latter case, different numerical methods and linear solvers can be applied to each subset, which may enhance the efficiency and robustness of the algorithms. The strengths and limitations of the two approaches are analyzed, and their applicability turns out to be associated with the degree of coupling between PDEs. This talk is helpful for those who are interested in developing tailored codes to efficiently solve PDEs, especially in the field of multiphysics simulation."

Seminar in Geophysics (12.571) is a class for EAPS graduate students in geophysics. All members of the MIT Community are welcome to join for presentations by guest speakers which will take place approximately every two weeks during the spring semester on Tuesday mornings 10am in 54-209 and on Zoom. Titles and abstracts for talks will be posted here when available.