Modern Solvers for Helmholtz Problems

Part I. Algorithms: New Developments and Analysis

1. Recent Results on Domain Decomposition Preconditioning for the High-Frequency Helmholtz Equation Using Absorption
Ivan G. Graham, Euan A. Spence, Eero Vainikko

2. High Order Transparent Boundary Conditions for the Helmholtz Equation
Lothar Nannen

3. On the Optimality of Shifted Laplacian in a Class of Polynomial Preconditioners for the Helmholtz Equation
Siegfried Cools, Wim Vanroose

Part II. Algorithms: Practical Methods and Implementations

4. How to Choose the Shift in the Shifted Laplace Preconditioner for the Helmholtz Equation Combined with Deflation
D. Lahaye, C. Vuik

5. The Multilevel Krylov-Multigrid Method for the Helmholtz Equation Preconditioned by the Shifted Laplacian
Yogi A. Erlangga, Luis García Ramos, Reinhard Nabben

6. A Geometric Multigrid Preconditioner for the Solution of the Helmholtz Equation in Three-Dimensional Heterogeneous Media on Massively Parallel Computers
H. Calandra, S. Gratton, X. Vasseur

Part III. Implementations and Industrial Applications

7. Some Computational Aspects of the Time and Frequency Domain Formulations of Seismic Waveform Inversion
René-Édouard Plessix

8. Optimized Schwarz Domain Decomposition Methods for Scalar and Vector Helmholtz Equations
X. Antoine, C. Geuzaine

9. Computationally Efficient Boundary Element Methods for High-Frequency Helmholtz Problems in Unbounded Domains
Timo Betcke, Elwin ’t Wout, Pierre Gélat

Keywords: Mathematics, Numerical Analysis, Partial Differential Equations, Linear and Multilinear Algebras, Matrix Theory, Difference and Functional Equations