Abstract: Spherical microphone arrays are becoming increasingly important in acoustic signal processing systems for their applications in sound field analysis, beamforming, spatial audio, etc. The positioning of target and interfering sound sources is a crucial step in many of the above applications. Therefore, 3D sound source localization is a highly relevant topic in the acoustic signal processing field. However, spherical microphone arrays are usually composed of many microphones and running signal processing localization methods in real time is an important issue. Some works have already shown the potential of Graphic Processing Units (GPUs) for developing high-end real-time signal processing systems. New embedded systems with integrated GPU accelerators providing low power consumption are becoming increasingly relevant. These novel systems play a very important role in the new era of smartphones and tablets, opening further possibilities to the design of high-performance compact processing systems. This paper presents a 3D source localization system using a spherical microphone array fully implemented on an embedded GPU. The real-time capabilities of these platforms are analyzed, providing also a performance analysis of the localization system under different acoustic conditions.

Abstract: The Scaled Boundary Finite Element Method (SBFEM) can be applied to solve linear elliptic boundary value problems when a so-called scaling center can be defined such that every point on the boundary is \textit{visible} from it. From a more practical point of view, this means that in linear elasticity, a separation of variables ansatz can be used for the displacements in a scaled boundary coordinate system. This approach allows an analytical treatment of the problem in the scaling direction. Only the boundary needs to be discretized with Finite Elements. Employment of the separation of variables ansatz in the virtual work balance yields a Cauchy-Euler differential equation system of second order which can be transformed into an eigenvalue problem and solved by standard eigenvalue solvers for nonsymmetric matrices. A further obtained linear equation system serves for enforcing the boundary conditions. If the scaling center is located directly at a singular point, elliptic boundary value problems containing singularities can be solved with high accuracy and computational efficiency. The application of the SBFEM to the linear elasticity problem of two meeting inter-fiber cracks in a composite laminate exposed to a simple homogeneous temperature decrease reveals the presence of hypersingular stresses.

Abstract: Forward mode algorithmic differentiation transforms implementations of multivariate vector functions as computer programs into first directional derivative (also: first-order tangent) code. Its reapplication yields higher directional derivative (higher-order tangent) code. Second derivatives play an important role in nonlinear programming. For example, second-order (Newtontype) nonlinear optimization methods promise faster convergence in the neighborhood of the minimum through taking into account second derivative information. Part of the objective function may be given implicitly as the solution of a system of n parameterized nonlinear equations. If the system parameters depend on the free variables of the objective, then second derivatives of the nonlinear system’s solution with respect to those parameters are required. The local computational overhead for the computation of second-order tangents of the solution vector with respect to the parameters by Algorithmic Differentiation depends on the number of iterations performed by the nonlinear solver. This dependence can be eliminated by taking a second-order symbolic approach to differentiation of the nonlinear system.