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

Adaptive Mesh Fluid Simulations on GPU

We describe an implementation of compressible inviscid fluid solvers with block-structured adaptive mesh refinement on Graphics Processing Units using NVIDIA's CUDA. We show that a class of high resolution shock capturing schemes can be mapped naturally on this architecture. Using the method of lines approach with the second order total variation diminishing Runge-Kutta time integration scheme, piecewise linear reconstruction, and a Harten-Lax-van Leer Riemann solver, we achieve an overall speedup of approximately 10 times faster execution on one graphics card as compared to a single core on the host computer. We attain this speedup in uniform grid runs as well as in problems with deep AMR hierarchies. Our framework can readily be applied to more general systems of conservation laws and extended to higher order shock capturing schemes. This is shown directly by an implementation of a magneto-hydrodynamic solver and comparing its performance to the pure hydrodynamic case. Finally, we also combined our CUDA parallel scheme with MPI to make the code run on GPU clusters. Close to ideal speedup is observed on up to four GPUs.Comment: Submitted to New Astronom

Exponential Integrators on Graphic Processing Units

In this paper we revisit stencil methods on GPUs in the context of exponential integrators. We further discuss boundary conditions, in the same context, and show that simple boundary conditions (for example, homogeneous Dirichlet or homogeneous Neumann boundary conditions) do not affect the performance if implemented directly into the CUDA kernel. In addition, we show that stencil methods with position-dependent coefficients can be implemented efficiently as well. As an application, we discuss the implementation of exponential integrators for different classes of problems in a single and multi GPU setup (up to 4 GPUs). We further show that for stencil based methods such parallelization can be done very efficiently, while for some unstructured matrices the parallelization to multiple GPUs is severely limited by the throughput of the PCIe bus.Comment: To appear in: Proceedings of the 2013 International Conference on High Performance Computing Simulation (HPCS 2013), IEEE (2013

Finite Element Integration on GPUs

We present a novel finite element integration method for low order elements on GPUs. We achieve more than 100GF for element integration on first order discretizations of both the Laplacian and Elasticity operators.Comment: 16 pages, 3 figure

Simulation of reaction-diffusion processes in three dimensions using CUDA

Numerical solution of reaction-diffusion equations in three dimensions is one of the most challenging applied mathematical problems. Since these simulations are very time consuming, any ideas and strategies aiming at the reduction of CPU time are important topics of research. A general and robust idea is the parallelization of source codes/programs. Recently, the technological development of graphics hardware created a possibility to use desktop video cards to solve numerically intensive problems. We present a powerful parallel computing framework to solve reaction-diffusion equations numerically using the Graphics Processing Units (GPUs) with CUDA. Four different reaction-diffusion problems, (i) diffusion of chemically inert compound, (ii) Turing pattern formation, (iii) phase separation in the wake of a moving diffusion front and (iv) air pollution dispersion were solved, and additionally both the Shared method and the Moving Tiles method were tested. Our results show that parallel implementation achieves typical acceleration values in the order of 5-40 times compared to CPU using a single-threaded implementation on a 2.8 GHz desktop computer.Comment: 8 figures, 5 table