El-WaveHoltz : A time-domain iterative solver for time-harmonic elastic waves

• We consider the application of the WaveHoltz iteration to time-harmonic elastic wave equations with energy conserving boundary conditions. The original WaveHoltz iteration for acoustic Helmholtz problems is a fixed-point iteration that filters the solution of the wave equation with time-harmonic forcing and boundary data. As in the original WaveHoltz method, we reformulate the fixed point iteration as a positive definite linear system of equations that is iteratively solved by a Krylov method. We present two time-stepping schemes, one explicit and one (novel) implicit, which completely remove time discretization error from the WaveHoltz solution by performing a simple modification of the initial data and time-stepping scheme. Numerical experiments indicate an iteration scaling similar to that of the original WaveHoltz method, and that the convergence rate is dictated by the shortest (shear) wave speed of the problem. We additionally show that the implicit scheme can be advantageous in practice for meshes with disparate element sizes.

Ämnesord

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Nyckelord

Elastic wave equation

Helmholtz equation

Time-harmonic scattering

Acoustics

Convergence of numerical methods

Elastic waves

Harmonic analysis

Iterative methods

Linear systems

Shear flow

Time domain analysis

Elastic wave equations

Energy-conserving

Fixed-point iterations

Helmholtz problems

Helmholtz's equations

Iterative solvers

Time domain

Time-harmonic

Time-stepping schemes

Wave equations

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