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Novel Acceleration Strategies for Acoustic Boundary Element Method and Other Non-Affine Parametric Linear Systems

Book - Dissertation

Sound is everywhere in our environment. We continuously perceive acoustic stimuli, which can either be pleasant such as good music, or annoying such as the traffic noise persisting in modern societies. Recently, it has been widely accepted that excessive exposure to sound can cause major health issues, leading to the definition of noise pollution as a term. Although most of the noise found in modern cities is emitted due to the interactions of vehicles and machines with their surrounding environment, it is neither possible but also nor desirable to eradicate every such sound. In fact, the acoustic information included in this noise can provide useful feedback about their usage and performance. For example, the noise emitted by an approaching vehicle not only warns the surrounding environment about its presence, but also experienced listeners can detect potential faults in its operation. Therefore, instead of eliminating any noise emitted by vehicles and machines, the need to control it has been increasingly prioritized. In that way, any noise negatively affecting public health needs to be abated, but in the same time it also needs to be translated to useful information about the operation conditions of the noise-emitting machine or vehicle. Nevertheless, controlling sound is not a simple task and cannot be performed without the use of powerful tools. Numerical physics-based models can play such a role as they are able to provide accurate predictions about the acoustic behavior of vehicles and machines. Although such models are widely used in engineering practice, they are often accompanied by a high numerical cost. This is especially pronounced in case of acoustic numerical models, since the acoustic behavior constitutes a system and not a component level property and thus the entire acoustic system needs to be modeled. Indeed, acoustic simulations of vehicles or machines might require days or even weeks to solve! To mitigate the cost associated with acoustic models, Model Order Reduction (MOR) techniques have recently arisen. Such techniques act by reducing the size of respective models and thus facilitate the fast computation of acoustic predictions. However, their broad applicability is limited, as most of the already developed techniques only accommodate the reduction of models arising by the use of the Finite Element Method. Moreover, most of these techniques have been developed for one-off applications and, commonly, they either lack generalization or they are based on heuristics for their calibration. In that context, the goal of this dissertation is to increase the applicability of MOR within acoustics by enabling its application to BEM acoustic models and in the same time provide algorithms that are able to accelerate the solution of generic systems with similar properties.
The first contribution of the research presented in this dissertation is the proposal of a framework for the deployment of MOR in acoustic BEM models. This framework consists of an approximation of the BEM system by an affine expression and the construction of a reduction basis by recycling Krylov subspaces on a fixed-spacing grid of frequencies. The proposed framework is accompanied by a cheap error estimator that indicates the expected accuracy of the obtained reduced order model. Employing the proposed technique, the computational efficiency of traditional BEM models is greatly improved by accelerating both their assembly and solution. Next, striving for a general applicability of the proposed framework towards non-affine systems with similar properties, the Automatic Krylov subspaces Recycling (AKR) algorithm is proposed that enables the construction of global solution bases for generic non-affine systems. The proposed algorithm automates the construction of the solution basis by adaptively recycling Krylov subspaces within a predefined parameter interval. Employing this algorithm in the offline stage of the proposed MOR framework minimizes the number of full order BEM systems to be assembled and solved. Furthermore, addressing any concerns about the size of the reduced order models, the memory-constrained version of the AKR algorithm is proposed. Moving in the same direction of improving the efficiency of the reduction method, the basic framework is combined with additional reduction steps to provide highly efficient reduced order models. Moreover, aiming for the broad applicability of the proposed MOR framework, it is extended to accommodate multi-parametric systems by distinguishing among right hand-side dependencies and affine - non-affine parametrizations of the system matrix. Employing this technique, source position, material and shape parametrizations can be efficiently modeled with acoustic BEM models. Finally, the range of applications of such MOR techniques is broadened by providing a general MOR-inspired framework to efficiently construct high quality deflation based preconditioners for parametric systems.
Publication year:2022