SIAM Journal on Scientific and Statistical Computing
A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
Fluid-solid interaction: acoustic scattering by a smooth elastic obstacle
SIAM Journal on Applied Mathematics
A domain decomposition method for the Helmholtz equation and related optimal control problems
Journal of Computational Physics
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
An iterative substructuring method for coupled fluid-solid acoustic problems
Journal of Computational Physics
Computational aspects of the ultra-weak variational formulation
Journal of Computational Physics
The Ultra-Weak Variational Formulation for Elastic Wave Problems
SIAM Journal on Scientific Computing
A Discontinuous Galerkin Method for Linear Symmetric Hyperbolic Systems in Inhomogeneous Media
Journal of Scientific Computing
Solving Maxwell's equations using the ultra weak variational formulation
Journal of Computational Physics
Some numerical aspects of the PUFEM for efficient solution of 2D Helmholtz problems
Computers and Structures
Journal of Computational Physics
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We introduce the ultra-weak variational formulation (UWVF) for fluid-solid vibration problems. In particular, we consider the scattering of time-harmonic acoustic pressure waves from solid, elastic objects. The problem is modeled using a coupled system of the Helmholtz and Navier equations. The transmission conditions on the fluid-solid interface are represented in an impedance-type form after which we can employ the well known ultra-weak formulations for the Helmholtz and Navier equations. The UWVF approximation for both equations is computed using a superposition of propagating plane waves. A condition number based criterion is used to define the plane wave basis dimension for each element. As a model problem we investigate the scattering of sound from an infinite elastic cylinder immersed in a fluid. A comparison of the UWVF approximation with the analytical solution shows that the method provides a means for solving wave problems on relatively coarse meshes. However, particular care is needed when the method is used for problems at frequencies near the resonance frequencies of the fluid-solid system.