Explicit Time-domain Finite-element Method Research Articles

Binaural Auralization of Room Acoustics with a Highly Scalable Wave-Based Acoustics Simulation

This paper presents a proposal of an efficient binaural room-acoustics auralization method, an essential goal of room-acoustics modeling. The method uses a massively parallel wave-based room-acoustics solver based on a dispersion-optimized explicit time-domain finite element method (TD-FEM). The binaural room-acoustics auralization uses a hybrid technique of first-order Ambisonics (FOA) and head-related transfer functions. Ambisonics encoding uses room impulse responses computed by a parallel wave-based room-acoustics solver that can model sound absorbers with complex-valued surface impedance. Details are given of the novel procedure for computing expansion coefficients of spherical harmonics composing the FOA signal. This report is the first presenting a parallel wave-based solver able to simulate room impulse responses with practical computational times using an HPC cloud environment. A meeting room problem and a classroom problem are used, respectively, having 35 million degrees of freedom (DOF) and 100 million DOF, to test the parallel performance of up to 6144 CPU cores. Then, the potential of the proposed binaural room-acoustics auralization method is demonstrated via an auditorium acoustics simulation of up to 5 kHz having 750,000,000 DOFs. Room-acoustics auralization is performed with two acoustics treatment scenarios and room-acoustics evaluations that use an FOA signal, binaural room impulse response, and four room acoustical parameters. The auditorium acoustics simulation showed that the proposed method enables binaural room-acoustics auralization within 13,000 s using 6144 cores.

Time Domain Room Acoustic Solver with Fourth-Order Explicit FEM Using Modified Time Integration

This paper presents a proposal of a time domain room acoustic solver using novel fourth-order accurate explicit time domain finite element method (TD-FEM), with demonstration of its applicability for practical room acoustic problems. Although time domain wave acoustic methods have been extremely attractive in recent years as room acoustic design tools, a computationally efficient solver is demanded to reduce their overly large computational costs for practical applications. Earlier, the authors proposed an efficient room acoustic solver using explicit TD-FEM having fourth-order accuracy in both space and time using low-order discretization techniques. Nevertheless, this conventional method only achieves fourth-order accuracy in time when using only square or cubic elements. That achievement markedly impairs the benefits of FEM with geometrical flexibility. As described herein, that difficulty is solved by construction of a specially designed time-integration method for time discretization. The proposed method can use irregularly shaped elements while maintaining fourth-order accuracy in time without additional computational complexity compared to the conventional method. The dispersion and dissipation characteristics of the proposed method are examined respectively both theoretically and numerically. Moreover, the practicality of the method for solving room acoustic problems at kilohertz frequencies is presented via two numerical examples of acoustic simulations in a rectangular sound field including complex sound diffusers and in a complexly shaped concert hall.

Numerically stable explicit time-domain finite element method for room acoustics simulation using an equivalent impedance model

This article presents a numerically stable explicit time-domain finite element method (TD-FEM) for room acoustic simulation using an equivalent impedance model. Performance over a conventional explicit TD-FEM is demonstrated using numerical experiments. Both explicit TD-FEMs were based on simultaneous first-order ordinary differential equations. The conventional method has a stability problem derived from backward difference approximation of time derivative of sound pressure related to a dissipation term for treating absorption at a boundary. The numerically stable explicit TD-FEM avoids the stability problem through the combined use of first-order forward and backward difference approximation. A completely explicit algorithm is obtainable using a lumped dissipation matrix. Numerical results demonstrate that the proposed explicit TD-FEM is stable for changing impedance values at boundary surfaces. In addition, numerical dissipation and dispersion error analyses revealed that both explicit TD-FEMs have small dissipation error. Moreover, the proposed method has slightly lower accuracy than the conventional explicit TDFEM. However, the proposed method is computationally more efficient than the conventional method for acoustics simulation of rooms with smaller impedance values at boundaries.

An Alternative Explicit and Unconditionally Stable Time-Domain Finite-Element Method for Electromagnetic Analysis

A new method for making an explicit time-domain finite-element method unconditionally stable is developed for general electromagnetic analysis, where the dielectrics and conductors can be inhomogeneous, lossless, or lossy. In this method, for a given time step, we find the unstable modes that are the root cause of instability, and deduct them directly from the system matrix resulting from a time-domain finite-element based analysis. The resultant explicit time-domain simulation is absolutely stable for the given time step no matter how large it is, and irrespective of the space step. The accuracy of the method is also guaranteed when the time step is chosen based on accuracy. In addition to a formulation for lossless problems, formulations for general lossy problems are also presented in detail. Numerical experiments have demonstrated the accuracy, efficiency, and unconditional stability of the proposed new explicit method.

A modified integration rule for an explicit time-domain finite element method using rectangular elements for room acoustics simulations

A modified integration rule for an explicit time-domain finite element method using rectangular elements for room acoustics simulations

An explicit time-domain finite element method for room acoustics simulations: Comparison of the performance with implicit methods

This paper presents the applicability of an explicit time-domain finite element method (TD-FEM) using a dispersion reduction technique called modified integration rules (MIR) on room acoustics simulations with a frequency-independent finite impedance boundary. First, a dispersion error analysis and a stability analysis are performed to derive the dispersion relation and the stability condition of the present explicit TD-FEM for three-dimensional room acoustics simulations with an infinite impedance boundary. Secondly, the accuracy and efficiency of the explicit TD-FEM are presented by comparing with implicit TD-FEM using MIR through room acoustics simulations in a rectangular room with infinite impedance boundaries. Thirdly, the stability condition of the explicit TD-FEM is investigated numerically in the case with finite impedance boundaries. Finally, the performance of the explicit TD-FEM in room acoustics simulations with finite impedance boundaries is demonstrated in a comparison with the implicit TD-FEM. Although the stability of the present explicit TD-FEM is dependent on the impedance values given at boundaries, the explicit TD-FEM is computationally more efficient than the implicit method from the perspective of computational time for acoustics simulations of a room with larger impedance values at boundaries.

Applicability of an explicit time-domain finite-element method on room acoustics simulation

Applicability of an explicit time-domain finite-element method on room acoustics simulation

Explicit Time-Domain Finite-Element Method Stabilized for an Arbitrarily Large Time Step

The root cause of the instability is quantitatively identified for the explicit time-domain finite-element method that employs a time step beyond that allowed by the stability criterion. With the identification of the root cause, an unconditionally stable explicit time-domain finite-element method is successfully created, which is stable and accurate for a time step solely determined by accuracy regardless of how large the time step is. The proposed method retains the strength of an explicit time-domain method in avoiding solving a matrix equation while eliminating its shortcoming in time step. Numerical experiments have demonstrated its superior performance in computational efficiency, as well as stability, compared with the conditionally stable explicit method and the unconditionally stable implicit method. The essential idea of the proposed method for making an explicit method stable for an arbitrarily large time step irrespective of space step is also applicable to other time domain methods.

A New Explicit Time-Domain Finite-Element Method Based on Element-Level Decomposition

A new explicit time-domain finite-element method (TDFEM), which is fundamentally different from traditional explicit TDFEM formulations for solving Maxwell's equations, is introduced. This new explicit TDFEM is derived from a recently developed TDFEM domain-decomposition algorithm by extending domain decomposition to the element level. This method solves dual-field second-order wave equations and computes the electric and magnetic fields in a leapfrog fashion. With the element-level decomposition, no global system matrix has to be assembled and solved as required in the implicit TDFEM, and each element is related to its neighboring elements in an explicit manner. Hence, the computational complexity of the method is reduced to only O(N) for both computer memory and CPU time. A hybrid explicit/implicit scheme is also proposed to alleviate a major disadvantage of the proposed explicit TDFEM formulation. In addition, the convergence behavior of the corresponding higher order algorithms and the stability issues are discussed