Domenico Lahaye Knihy

This edited volume provides a comprehensive overview of advanced solvers for the Helmholtz equation, structured into three parts: developments and analysis of Helmholtz solvers, practical implementation methods, and industrial applications. The Helmholtz equation is crucial in various fields such as seismic inversion, ultrasound medical imaging, sonar detection, and wave behavior in harbors. Despite its seemingly simple form, the equation poses significant challenges in solving. Numerical methods are essential for approximating solutions, starting with discretization through various techniques like Finite Difference, Finite Element, Discontinuous Galerkin, and Boundary Element Methods. The resulting linear systems are large, with complexity increasing at higher frequencies, necessitating more detailed seismic images and leading to larger-scale numerical challenges. Fast and robust iterative solvers are required to tackle these three-dimensional problems, but standard methods often involve excessive iterations. Consequently, new methods have been developed to address these issues. This book targets researchers from academia and industry, as well as graduate students, with a prerequisite understanding of partial differential equations and numerical linear algebra.