Technology for a Changing World

Speaker Name:

Skylar Trigueiro

Speaker Title:

PhD Student

Speaker Organization:

Applied Mathematics & Statistics

Start Time:

Wednesday, December 13, 2017 - 1:30pm

End Time:

Wednesday, December 13, 2017 - 3:30pm

Location:

Engineering 2, Room 553

Organizer:

Dongwook Lee

**Abstract: **In this talk, I will examine the Jacobian-Free Newton-Krylov (JFNK) method and its effectiveness at solving classical scalar partial differential equations such as the heat equation, wave equation, and systems of partial differential equations, specifically the Euler equations. In the first part of the talk, I will discuss the generalized minimal residual algorithm (GMRES) which is an iterative solver for solving large sparse matrix equations that commonly occur when using implicit schemes for solving. In the second part of the talk, I will focus on the JFNK scheme, which is a method that eliminates the need to store the large matrix used in implicit scheme by creating preserves the matrix transformation as vector operations. The third part of the talk will focus on preconditioning, which is used in the GMRES scheme to reduce the number of iterations required to converge to the correct solution or to increase the robustness of our solver! . Finally, I will end with results on the classical partial differential equations mentioned earlier.