Finite difference and finite volume methods for wave-based modelling of room acoustics

Wave-based models of sound propagation can be used to predict and synthesize sounds as they would be heard naturally in room acoustic environments. The numerical simulation of such models with traditional time-stepping grid-based methods can be an expensive process, due to the sheer size of listening environments (e.g., auditoriums and concert halls) and due to the temporal resolution required by audio rates that resolve frequencies up to the limit of human hearing. Finite difference methods comprise a simple starting point for such simulations, but they are known to suffer from approximation errors that may necessitate expensive grid refinements in order to achieve sufficient levels of accuracy. As such, a significant amount of research has gone into designing finite difference methods that are highly accurate while remaining computationally efficient. The problem of designing and using accurate finite difference schemes is compounded by the fact that room acoustics models require complex boundary conditions to model frequency-dependent wall impedances over non-trivial geometries. The implementation of such boundary conditions in a numerically stable manner has been a challenge for some time. Stable boundary conditions for finite difference room acoustics simulations have been formulated in the past, but generally they have only been useful in modelling trivial geometries (e.g., idealised shoebox halls). Finite volume methods have recently been shown to be a viable solution to the problem of complex boundary conditions over non-trivial geometries, and they also allow for the use of energy methods for numerical stability analyses. Finite volume methods lend themselves naturally to fully unstructured grids and they can simplify to the types of grids typically used in finite difference methods. This allows for room acoustics simulation models that balance the simplicity of finite difference methods for wave propagation in air with the detail of finite volume methods for the modelling of complex boundaries. This thesis is an exploration of these two distinct, yet related, approaches to wave-based room acoustic simulations. The overarching theme in this investigation is the balance between accuracy, computational efficiency, and numerical stability. Higher-order and optimised schemes in two and three spatial dimensions are derived and compared, towards the goal of finding accurate and efficient finite difference schemes. Numerical stability is analysed using frequency-domain analyses, as well as energy techniques whenever possible, allowing for stable and frequency-dependent boundary conditions appropriate for room acoustics modelling. Along the way, the use of non-Cartesian grids is investigated, geometric relationships between certain finite difference and finite volume schemes are explored, and some problems associated to staircasing effects at boundaries are considered. Also, models of sound absorption in air are incorporated into these numerical schemes, using physical parameters that are appropriate for room acoustic scenarios

Code generation for 3D partial differential equation models from a high-level functional intermediate language

Partial Differential Equation (PDE) modelling is an important tool in scientific domains for bridging theory with reality; however, they can be complex to program and even more difficult to abstract. The evolving parallel computing landscape is also making it increasingly difficult to write and maintain codes (such as PDE models) which retain performance across different parallel platforms. Computational scientists should be able to focus on their science instead of also having to become high performance computing experts in order to take advantage of faster parallel hardware. Current methods targeting this problem either concentrate on very niche applications, are too simplistic for real world problems or are too low-level to be easily programmable. Domain Specific Languages (DSLs) are a popular approach, but they have two opposing goals: improving programmability, while also providing high performance. This thesis presents a solution for developing performance portable 3D PDE models, using room acoustics simulations as a case study, by raising the abstraction level in the existing hardware-agnostic, intermediary language LIFT. This functional language and compiler is designed for DSLs to compile into and provides a separation of concerns for developing parallel applications. This separation enables DSL writers to focus on developing high-level abstractions providing productivity to the user, while LIFT turns the intermediary parallel representation these abstractions compile down to into hardware-optimised code. A suite of composable, algorithmic primitives enables LIFT to reuse functionality across domains and an exploratory search space provides a way to find the best optimisations for a given platform. As this thesis shows, room acoustic simulations are expressible in LIFT with only a few small changes to the framework. These expressions are able to achieve comparable or better performance to original hand-written benchmarks. Furthermore, such expressions enable room acoustics models to run across multiple platforms and easily swap in optimisations. Being able to test out what optimisations give the best performance for a given platform — without rewriting or retuning — allows computational scientists to focus on their own work. Optimisations previously inaccessible in LIFT are developed that target 3D stencils generally, including 3D PDE models. In particular, 2.5D Tiling and compiler passes to inline private arrays and structs are added to the LIFT ecosystem, giving high performance to various 3D stencil codes. The 2.5D Tiling optimisation is coded functionally for the first time in LIFT and is selected automatically by additional rewrite rules. These rewrite rules, such as the one for 2.5D Tiling, are explored in a search space to find the best set of optimisations for an application on a given platform. Building on previous work, LIFT is extended to enable complex boundary conditions and room shapes for room acoustics models. This is the first intermediate representation in a high-level code generator to do so. Additionally, it is also the first high-level framework to support frequency-dependent boundary handling for room acoustics simulations. Combined, these contributions show that high-level abstractions for 3D PDE models are possible, enabling computational scientists to optimise and parallelise their codes more easily across different parallel platforms

Influence of Crossover Frequency on a Hybrid Acoustic Model for Room Impulse Response Synthesis

Room impulse responses (RIRs) of arbitrary enclosures may be synthesized using acoustic modelling methods that all offer advantages and limitations in terms of accuracy and efficiency. The use of a hybrid model, which combines a finite difference time domain (FDTD) approach for the low frequency range, and geometric methods for the mid-high frequency range has been shown to provide appropriate results in the past. This thesis is concerned with the optimisation of such a method by reducing the crossover frequency between the two mixed models to improve its efficiency and cost. To that end, hybrid models are implemented to generate synthesized RIRs with various crossover frequencies. These RIRs are compared with real measurements from two different rooms in the time domain, in the frequency domain, and with the use of acoustic parameters

Efficient Light and Sound Propagation in Refractive Media with Analytic Ray Curve Tracer

Refractive media is ubiquitous in the natural world, and light and sound propagation in refractive media leads to characteristic visual and acoustic phenomena. Those phenomena are critical for engineering applications to simulate with high accuracy requirements, and they can add to the perceived realism and sense of immersion for training and entertainment applications. Existing methods can be roughly divided into two categories with regard to their handling of propagation in refractive media; first category of methods makes simplifying assumption about the media or entirely excludes the consideration of refraction in order to achieve efficient propagation, while the second category of methods accommodates refraction but remains computationally expensive. In this dissertation, we present algorithms that achieve efficient and scalable propagation simulation of light and sound in refractive media, handling fully general media and scene configurations. Our approaches are based on ray tracing, which traditionally assumes homogeneous media and rectilinear rays. We replace the rectilinear rays with analytic ray curves as tracing primitives, which represent closed-form trajectory solutions based on assumptions of a locally constant media gradient. For general media profiles, the media can be spatially decomposed into explicit or implicit cells, within which the media gradient can be assumed constant, leading to an analytic ray path within that cell. Ray traversal of the media can therefore proceed in segments of ray curves. The first source of speedup comes from the fact that for smooth media, a locally constant media gradient assumption tends to stay valid for a larger area than the assumption of a locally constant media property. The second source of speedup is the constant-cost intersection computation of the analytic ray curves with planar surfaces. The third source of speedup comes from making the size of each cell and therefore each ray curve segment adaptive to the magnitude of media gradient. Interactions with boundary surfaces in the scene can be efficiently handled within this framework in two alternative approaches. For static scenes, boundary surfaces can be embedded into the explicit mesh of tetrahedral cells, and the mesh can be traversed and the embedded surfaces intersected with by the analytic ray curve in a unified manner. For dynamic scenes, implicit cells are used for media traversal, and boundary surface intersections can be handled separately by constructing hierarchical acceleration structures adapted from rectilinear ray tracer. The efficient handling of boundary surfaces is the fourth source of speedup of our propagation path computation. We demonstrate over two orders-of-magnitude performance improvement of our analytic ray tracing algorithms over prior methods for refractive light and sound propagation. We additionally present a complete sound-propagation simulation solution that matches the path computation efficiency achieved by the ray curve tracer. We develop efficient pressure computation algorithm based on analytic evaluations and combine our algorithm with the Gaussian beam for fast acoustic field computation. We validate the accuracy of the simulation results on published benchmarks, and we show the application of our algorithms on complex and general three-dimensional outdoor scenes. Our algorithms enable simulation scenarios that are simply not feasible with existing methods, and they have the potential of being extended and complementing other propagation methods for capability beyond handling refractive media.Doctor of Philosoph

Review : Deep learning in electron microscopy

Deep learning is transforming most areas of science and technology, including electron microscopy. This review paper offers a practical perspective aimed at developers with limited familiarity. For context, we review popular applications of deep learning in electron microscopy. Following, we discuss hardware and software needed to get started with deep learning and interface with electron microscopes. We then review neural network components, popular architectures, and their optimization. Finally, we discuss future directions of deep learning in electron microscopy