An O(N) Helmholtz Solver by Time-Filtering the Wave Equation

Explore an advanced computational mathematics seminar presentation that introduces the WaveHoltz algorithm, a novel approach for solving Helmholtz problems with optimal computational efficiency. Learn about this innovative method that achieves time-harmonic solutions by time-filtering the wave equation, requiring only five time-steps per period regardless of mesh size. Discover how the algorithm combines implicit time-stepping with multigrid techniques to achieve O(N) scaling - linear cost with respect to grid points at fixed frequency - making it optimal for both CPU time and memory usage as mesh refinement increases. Examine the implementation details using overset grids within the Overture framework for handling complex geometries, and understand how Krylov space solvers like GMRES accelerate the basic fixed-point iteration while eigenvector deflation further enhances convergence. Review comprehensive numerical results demonstrating second and fourth-order accuracy across two and three-dimensional problems, showcasing the method's potential for solving large-scale Helmholtz problems across diverse applications in computational physics and engineering.