Linear and Nonlinear Acoustic Wave Propagation in the Atmosphere

Hariharan, S. I.; Yu, Ping

doi:10.1137/0910032

Cited by 1 publication

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References 12 publications

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“…The acoustic wave propagation model presented in chapter 2 involves the wave propagation from an initial Gaussian pulse on a two-dimensional square domain with fixed boundaries all around. Future modelling efforts can be directed towards three-dimensional media, nonlinear models [199] and absorbing boundary conditions [49,200]. Moreover, a frequency domain analysis of the acoustic wave is of interest in applications such as electromagnetic waves where uncertainty is an important consideration [201].…”

Section: Pde Modelling Aspectsmentioning

confidence: 99%

Scalable Domain Decomposition Methods for Nonlinear and Time-Dependent Stochastic Systems

Padillath Vasudevan

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Computational modelling is one of the most important tools to understand and predict real-life physical processes. However, the accuracy of their predictions becomes questionable when the uncertainties associated with model parameters, assumptions to the mathematical models and the noise in experimental data are not properly accounted for. Sampling-based approaches to handle these uncertainties become overwhelmingly expensive for large-scale models with high resolution discretizations in space/time. This thesis proposes a sampling-free intrusive stochastic Galerkinbased approach to handle the uncertainties associated with model parameters for time-dependent and nonlinear problems. The increased cost of solving high resolution models using this samplingfree approach is handled using domain decomposition (DD)-based solvers by efficiently distributing the workload to many processes. Developing parallel scalable iterative solvers for uncertainty quantification of these high-resolution models in high performance computing (HPC) environments is the main objective of this thesis.An acoustic wave propagation model with a random field representation of wave speed is handled using a non-overlapping DD method. The symmetric and positive-definite coefficient matrix of the system can be solved using a conjugate-gradient iterative method and associated Neumann-Neumann vertex-based preconditioner in two dimensions. However, the complex spatial coupling and the coupling among the stochastic expansion coefficients can affect the scalabilities of the solver in three dimensions. Hence, a wirebasket-based preconditioner is utilized to enrich the coarse grid allowing better global error propagation and improved scalability for the elastic wave propagation model. For nonlinear stochastic partial differential equations (PDEs), the coefficient matrix of the associated linearized algebraic system is non-symmetric which requires the use of generalized minimum residual (GMRES) method-based iterative solvers. A multilevel Schwarz preconditioner combining DD and algebraic multigrid method is proposed for efficient error reduction for large-scale

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Section: Pde Modelling Aspectsmentioning

confidence: 99%

Scalable Domain Decomposition Methods for Nonlinear and Time-Dependent Stochastic Systems

Padillath Vasudevan

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Linear and Nonlinear Acoustic Wave Propagation in the Atmosphere

Cited by 1 publication

References 12 publications

Scalable Domain Decomposition Methods for Nonlinear and Time-Dependent Stochastic Systems

Scalable Domain Decomposition Methods for Nonlinear and Time-Dependent Stochastic Systems

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