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math.NA2026
High-Resolution Solvers for 3D Helmholtz Scattering Problems Using PFFT and Eigenvector-Based Preconditioning
Yury Gryazin, Ron Gonzales, Xiaoye Sherry Li
This paper presents an efficient Krylov subspace iterative solver for the three-dimensional (3D) Helmholtz equation with non-constant coefficients and absorbing boundary conditions…
math.NA2019
Scalable Algorithms for High-Order Approximations on Three-Dimensional Compact Stencils
Ronald Gonzales, Yury Gryazin, Yun Teck Lee
This paper presents an efficient parallel direct algorithm with near-optimal complexity for the compact fourth and sixth-order approximation of the three-dimensional Helmholtz equa…
math.NA2012
Preconditioned Krylov subspace methods for sixth order compact approximations of the Helmholtz equation
Yury Gryazin
In this paper, we consider an efficient iterative approach to the solution of the discrete Helmholtz equation with Dirichlet, Neumann and Sommerfeld-like boundary conditions based…