An efficient multigrid algorithm for heterogeneous acoustic media sign‐indefinite high‐order FEM models

Summary Large‐scale scientific computing models are needed for the simulation of wave propagation especially for multiple frequency and high‐frequency models in complex heterogeneous media. Multigrid methods provide efficient iterative solvers for many large sign‐definite systems of equations result...

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Vydané v:Numerical linear algebra with applications Ročník 24; číslo 3; s. np - n/a
Hlavní autori: Ganesh, Mahadevan, Morgenstern, Charles
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Oxford Wiley Subscription Services, Inc 01.05.2017
Predmet:
acoustic wave propagation
Computer simulation
Finite element method
indefinite FEM systems
Mathematical analysis
Mathematical models
Media
multigrid
Solvers
Wave propagation
Wavelengths
ISSN:1070-5325, 1099-1506
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Shrnutí:Summary Large‐scale scientific computing models are needed for the simulation of wave propagation especially for multiple frequency and high‐frequency models in complex heterogeneous media. Multigrid methods provide efficient iterative solvers for many large sign‐definite systems of equations resulting from physical models. Time‐harmonic wave propagation models lead to sign‐indefinite systems with eigenvalues in the left half of the complex plane. Thus standard multigrid approaches applied in conjunction with a low‐order finite difference or finite element method are not sufficient. In this work, we describe a high‐order finite element method model for multiple (low to high) frequency time‐harmonic acoustic wave propagation on general curved, non‐convex, and non‐smooth domains with heterogeneous media using a multigrid approximation of the shifted Laplacian operator as a preconditioner. We implement the model using an efficient geometric multigrid approach with parallel grid transfer operator calculations to simulate the model using the BiCGStab iterative solver. We demonstrate the efficiency and parallel performance of the computational model with multiple low (5 wavelength) to high‐frequency (100 wavelength) input incident waves. Copyright © 2016 John Wiley & Sons, Ltd.
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ISSN:1070-5325
1099-1506
DOI:10.1002/nla.2049