Fortino Garcia

Fortino Garcia

NSF Postdoctoral Fellow at the Courant Institute of Mathematical Sciences

Posts by Collection

portfolio

publications

WaveHoltz: iterative solution of the Helmholtz equation via the wave equation

Published in SIAM Scientific Computing, 2020

A new idea for iterative solution of the Helmholtz equation is presented. We show that the iteration which we denote WaveHoltz and which filters the solution to the wave equation with harmonic data evolved over one period, corresponds to a coercive operator or a positive definite matrix in the discretized case.

Download here

Extensions and Analysis of an Iterative Solution of the Helmholtz Equation via the Wave Equation

Published in arXiv, 2022

This paper extends analysis of the WaveHoltz iteration, a time-domain iterative method for the solution of the Helmholtz equation, to problems with impedance boundary conditions in a single spatial dimension. We additionally analyze Helmholtz problems with damping, and we additionally show that it is possible to \textit{completely remove} time discretization error from the WaveHoltz solution through careful analysis of the discrete iteration and updated quadrature formulas.

Download here

El-WaveHoltz: A Time-Domain Iterative Solver for Time-Harmonic Elastic Waves

Published in Computer Methods in Applied Mechanics and Engineering, 2022

We consider the application of the WaveHoltz iteration to time-harmonic elastic wave equations with energy conserving boundary conditions. Numerical experiments indicate an iteration scaling similar to that of the original WaveHoltz method, and that the convergence rate is dictated by the shortest (shear) wave speed of the problem.

Download here

talks

teaching