Controllability methods for the computation of time-periodic solutions; application to scattering
Journal of Computational Physics
Multigrid
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
The Ultra-Weak Variational Formulation for Elastic Wave Problems
SIAM Journal on Scientific Computing
Algebraic multigrid for higher-order finite elements
Journal of Computational Physics
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Controllability method for acoustic scattering with spectral elements
Journal of Computational and Applied Mathematics
Controllability method for the Helmholtz equation with higher-order discretizations
Journal of Computational Physics
Discontinuous Galerkin Methods: Theory, Computation and Applications
Discontinuous Galerkin Methods: Theory, Computation and Applications
A damping preconditioner for time-harmonic wave equations in fluid and elastic material
Journal of Computational Physics
Time-harmonic solution for acousto-elastic interaction with controllability and spectral elements
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Hi-index | 31.46 |
The time-harmonic solution of the linear elastic wave equation is needed for a variety of applications. The typical procedure for solving the time-harmonic elastic wave equation leads to difficulties solving large-scale indefinite linear systems. To avoid these difficulties, we consider the original time dependent equation with a method based on an exact controllability formulation. The main idea of this approach is to find initial conditions such that after one time-period, the solution and its time derivative coincide with the initial conditions. The wave equation is discretized in the space domain with spectral elements. The degrees of freedom associated with the basis functions are situated at the Gauss-Lobatto quadrature points of the elements, and the Gauss-Lobatto quadrature rule is used so that the mass matrix becomes diagonal. This method is combined with the second-order central finite difference or the fourth-order Runge-Kutta time discretization. As a consequence of these choices, only matrix-vector products are needed in time dependent simulation. This makes the controllability method computationally efficient.