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Computer modeling and numerical analysis of acoustical phenomena have important applications including manufacturing, audio technologies in immersive multimedia, and machine learning systems involving audio. The focus of the present dissertation is the exploration of numerical methods for modeling, simulating, synthesizing, estimating, processing, controlling, and analyzing acoustical phenomena in the physical world as well as its applications to the virtual world, i.e. immersive technologies for creating virtual, augmented, and extended realities.The dissertation is structured as follows. In chapter 1, I introduce some fundamentals and basic concepts of numerical acoustics and discuss existing practical problems in acoustics. In chapter 2 and chapter 3, I propose two novel techniques for three-dimensional sound field capturing end encoding for immersive audio applications, which are both based on (semi-)analytical cancellation of scattering caused by microphone arrays mounted on acoustic scatterers. In chapter 4 and chapter 5, I introduce a fast algorithm for synthesizing acoustic impulse responses in large-scale forests, and use it to predict the performance of acoustic wildlife monitoring systems based on large-scale distributed microphone arrays. In chapter 6, I propose a novel general-purpose individual-agnostic binaural localizer which supports sound source localization from arbitrary directions without a priori knowledge of the process generating the binaural signal. In chapter 7 and chapter 8, I develop frameworks for regularized active sound control, using either point- or mode-control and using either distributed or local worn loudspeaker and microphone arrays with applications including speech privacy, personal active noise control, and local crosstalk cancellation with limited noise injection into the environment. In chapter 9, chapter 10 and chapter 11, three numerical methods for evaluating integrals arising in the (fast multipole accelerated) boundary element method are introduced. In chapter 9, a recursive algorithm is developed which allows efficient analytical evaluation of singular and nearly singular layer potential integrals arising in the boundary element method using flat high-order elements for Helmholtz and Laplace equations. In chapter 10, a differential geometry-based quadrature algorithm is developed which allows accurate evaluation of singular and nearly singular layer potential integrals arising in the boundary element method using smooth manifold boundary elements with constant densities for Helmholtz and Laplace equations. In chapter 11, an algorithm for efficient exact evaluation of integrals of regular solid harmonics over high-order boundary elements with simplex geometries is developed. In chapter 12, I discuss future research directions and conclude the dissertation.