Multi-Method Linear Solvers
I conduct research on multimethod linear solvers, i.e., solvers that combine more than one underlying algorithm to improve the performance of large-scale simulations in collaboration with Sanjukta Bhowmick (Columbia University), Lois McInnes (Argonne), and Padma Raghavan (Penn. State). We have developed adaptive solvers, which use heuristics to select a solution method to better match the changing attributes of linear systems generated in different stages of an application. We have also developed composite solvers, which use a sequence of methods on the same linear system to improve reliability.
The diagram to the right illustrates an example runtime scenario of the components involved in multimethod linear system solution, which is a part of an application, such as the solution of a nonlinear PDE. We have demostrated the effectiveness of composite and adaptive linear solver techniques in a number of applications, such as a driven cavity flow simulation, and simulation of flow around an airfoil.
