Numerical Analysis and Scientific Computing Seminar
WaveHoltz: Wave Based Iterative Scheme for Helmholtz Problems
Speaker: Fortino Garcia, Courant, NYU
Location: Warren Weaver Hall 1302
Date: Oct. 29, 2021, 10 a.m.
Designing efficient iterative solvers for the Helmholtz equation is notoriously difficult, with the two main difficulties being the resolution requirements and the highly indefinite character of the discretized system of equations. The dependence of the number of degrees of freedom on the frequency of the problem requires high frequency Helmholtz solvers to be: (1) parallel, memory lean, and scalable, (2) high order accurate to overcome the penalty due to pollution/dispersion errors.
In this talk we will introduce the WaveHoltz iteration (WHI) which makes use of time-domain methods for wave equations to design Helmholtz solvers. We show that the WaveHoltz iteration is symmetric and positive definite in the continuous setting for energy conserving boundary conditions. Numerical examples using various discretization techniques that demonstrate the method can be used to solve problems with rather high wave numbers in a memory lean and scalable fashion will be presented, as well as recent extensions to problems in elastic media.