An optimization-based approach for solving a time-harmonic multiphysical wave problem with higher-order schemes

Abstract

An optimization-based approach for solving a time-harmonic multiphysical wave problem with higher-order schemes Mönkölä, Sanna Mönkölä, S. (2013). An optimization-based approach for solving a time-harmonic multiphysical wave problem with higher-order schemes. Journal of Computational Physics , 242 (1 June), 439-459. doi:10.1016/j.jcp.2013.02 AbstractThis study considers developing numerical solution techniques for the computer simulations of time-harmonic fluid-structure interaction between acoustic and elastic waves. The focus is on the efficiency of an iterative solution method based on a controllability approach and spectral elements. We concentrate on the model, in which the acoustic waves in the fluid domain are modeled by using the velocity potential and the elastic waves in the structure domain are modeled by using displacement.Traditionally, the complex-valued time-harmonic equations are used for solving the time-harmonic problems. Instead of that, we focus on finding periodic solutions without solving the time-harmonic problems directly. The time-dependent equations can be simulated with respect to time until a time-harmonic solution is reached, but the approach suffers from poor convergence. To overcome this challenge, we follow the approach first suggested and developed for the acoustic wave equations by Bristeau, Glowinski, and Périaux. Thus, we accelerate the convergence rate by employing a controllability method. The problem is formulated as a least-squares optimization problem, which is solved with the conjugate gradient (CG) algorithm. Computation of the gradient of the functional is done directly for the discretized problem. A graph-based multigrid method is used for preconditioning the CG algorithm.

Time-harmonic electromagnetics with exact controllability and discrete exterior calculus

“…The exact controllability approach was extensively studied in the late 2000s and early 2010s by Mönkölä et al In particular, higher-order spectral element discretizations and fluid-structure interaction problems were considered in [34][35][36]. The approach was recently extended to threedimensional visco-elastic equations [37].…”

On the Accuracy and Efficiency of Transient Spectral Element Models for Seismic Wave Problems

“…The method is widely used for simulating seismic waves, in both frequency and time domains (see, e.g., [12,13]). We have applied it to time-harmonic acoustoelastic equations in [14,15], while this paper concentrates on the accuracy and efficiency of the time domain solutions.…”