Massively parallel nodal discontinous Galerkin finite element method simulator for room acoustics

Abstract

We present a massively parallel and scalable nodal discontinuous Galerkin finite element method (DGFEM) solver for the time-domain linearized acoustic wave equations. The solver is implemented using the libParanumal finite element framework with extensions to handle curvilinear geometries and frequency dependent boundary conditions of relevance in practical room acoustics. The implementation is benchmarked on heterogeneous multi-device many-core computing architectures, and high performance and scalability are demonstrated for a problem that is considered expensive to solve in practical applications. In a benchmark study, scaling tests show that multi-GPU support gives the ability to simulate large rooms, over a broad frequency range, with realistic boundary conditions, both in terms of computing time and memory requirements. Furthermore, numerical simulations on two non-trivial geometries are presented, a star-shaped room with a dome and an auditorium. Overall, this shows the viability of using a multi-device accelerated DGFEM solver to enable realistic large-scale wave-based room acoustics simulations.

Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operators

“…The 3D data were generated using a DG-FEM solver ( 4 ), whereas the 2D data were generated using an SEM solver ( 3 ). Ensuring good accuracy at interpolation locations is crucial for the applications of interest.…”

“…4 and N = 4 k=1 N k , N k ∈ Z + . We then train four DeepONets N N k , each on the full source function space u, but restrict the location where we evaluate the operator at one of the partitions  i .…”

“…Wave phenomena are precisely described by solving partial differential equations (PDEs) with their approximate solutions found using numerical methods. Many methods exist, such as finite-difference time-domain methods ( 1 ), finite-volume time-domain methods ( 2 ), finite/spectral element methods ( 3 ), discontinuous Galerkin methods (DG-FEM) ( 4 ), boundary element methods ( 5 ), and pseudo-spectral Fourier methods ( 6 ), and are all part of the standard toolbox used to successfully solve a variety of real-world physical problems over the last decades. All these methods require recalculating solutions for different conditions, including initial and boundary conditions, geometry, and specified source and receiver positions.…”