FDTD/K-DWM simulation of 3D room acoustics on general purpose graphics hardware using compute unified device architecture (CUDA)

The growing demand for reliable prediction of sound fields in rooms have resulted in adaptation of various approaches for physical modeling, including the Finite Difference Time Domain (FDTD) and the Digital Waveguide Mesh (DWM). Whilst considered versatile and attractive methods, they suffer from dispersion errors that increase with frequency and vary with direction of propagation, thus imposing a high frequency calculation limit. Attempts have been made to reduce such errors by considering different mesh topologies, by spatial interpolation, or by simply oversampling the grid. As the latter approach is computationally expensive, its application to three-dimensional problems has often been avoided. In this paper, we propose an implementation of the FDTD on general purpose graphics hardware, allowing for high sampling rates whilst maintaining reasonable calculation times. Dispersion errors are consequently reduced and the high frequency limit is increased. A range of graphics processors are evaluated and compared with traditional CPUs in terms of accuracy, calculation time and memory requirements

Steklov Spectral Geometry for Extrinsic Shape Analysis

We propose using the Dirichlet-to-Neumann operator as an extrinsic alternative to the Laplacian for spectral geometry processing and shape analysis. Intrinsic approaches, usually based on the Laplace-Beltrami operator, cannot capture the spatial embedding of a shape up to rigid motion, and many previous extrinsic methods lack theoretical justification. Instead, we consider the Steklov eigenvalue problem, computing the spectrum of the Dirichlet-to-Neumann operator of a surface bounding a volume. A remarkable property of this operator is that it completely encodes volumetric geometry. We use the boundary element method (BEM) to discretize the operator, accelerated by hierarchical numerical schemes and preconditioning; this pipeline allows us to solve eigenvalue and linear problems on large-scale meshes despite the density of the Dirichlet-to-Neumann discretization. We further demonstrate that our operators naturally fit into existing frameworks for geometry processing, making a shift from intrinsic to extrinsic geometry as simple as substituting the Laplace-Beltrami operator with the Dirichlet-to-Neumann operator.Comment: Additional experiments adde

Direct immersogeometric fluid flow analysis using B-rep CAD models

We present a new method for immersogeometric fluid flow analysis that directly uses the CAD boundary representation (B-rep) of a complex object and immerses it into a locally refined, non-boundary-fitted discretization of the fluid domain. The motivating applications include analyzing the flow over complex geometries, such as moving vehicles, where the detailed geometric features usually require time-consuming, labor-intensive geometry cleanup or mesh manipulation for generating the surrounding boundary-fitted fluid mesh. The proposed method avoids the challenges associated with such procedures. A new method to perform point membership classification of the background mesh quadrature points is also proposed. To faithfully capture the geometry in intersected elements, we implement an adaptive quadrature rule based on the recursive splitting of elements. Dirichlet boundary conditions in intersected elements are enforced weakly in the sense of Nitsche\u27s method. To assess the accuracy of the proposed method, we perform computations of the benchmark problem of flow over a sphere represented using B-rep. Quantities of interest such as drag coefficient are in good agreement with reference values reported in the literature. The results show that the density and distribution of the surface quadrature points are crucial for the weak enforcement of Dirichlet boundary conditions and for obtaining accurate flow solutions. Also, with sufficient levels of surface quadrature element refinement, the quadrature error near the trim curves becomes insignificant. Finally, we demonstrate the effectiveness of our immersogeometric method for high-fidelity industrial scale simulations by performing an aerodynamic analysis of an agricultural tractor directly represented using B-rep

MFA-DVR: Direct Volume Rendering of MFA Models

3D volume rendering is widely used to reveal insightful intrinsic patterns of volumetric datasets across many domains. However, the complex structures and varying scales of volumetric data can make efficiently generating high-quality volume rendering results a challenging task. Multivariate functional approximation (MFA) is a new data model that addresses some of the critical challenges: high-order evaluation of both value and derivative anywhere in the spatial domain, compact representation for large-scale volumetric data, and uniform representation of both structured and unstructured data. In this paper, we present MFA-DVR, the first direct volume rendering pipeline utilizing the MFA model, for both structured and unstructured volumetric datasets. We demonstrate improved rendering quality using MFA-DVR on both synthetic and real datasets through a comparative study. We show that MFA-DVR not only generates more faithful volume rendering than using local filters but also performs faster on high-order interpolations on structured and unstructured datasets. MFA-DVR is implemented in the existing volume rendering pipeline of the Visualization Toolkit (VTK) to be accessible by the scientific visualization community