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

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
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.

Date:12 Jan 2018 →  25 May 2022
Keywords:Pass-By-Noise, Numerical methods, vibroacoustics
Disciplines:Manufacturing engineering, Other mechanical and manufacturing engineering, Product development, Control systems, robotics and automation, Design theories and methods, Mechatronics and robotics, Computer theory
Project type:PhD project