Advacement: A Jacobian-Free Newton-Krylov Implicit Method with Preconditioning for Solving PDEs

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.