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**GPU-accelerated boundary element method for Helmholtz’ equation in three dimensions.**
*(English)*
Zbl 1183.76829

Summary: Recently, the application of graphics processing units (GPUs) to scientific computations is attracting a great deal of attention, because GPUs are getting faster and more programmable. In particular, NVIDIA’s GPUs called compute unified device architecture enable highly mutlithreaded parallel computing for non-graphic applications. This paper proposes a novel way to accelerate the boundary element method (BEM) for three-dimensional Helmholtz’ equation using CUDA. Adopting the techniques for the data caching and the double-single precision floating-point arithmetic, we implemented a GPU-accelerated BEM program for GeForce 8-series GPUs. The program performed 6-23 times faster than a normal BEM program, which was optimized for an Intel’s quad-core CPU, for a series of boundary value problems with 8000-128000 unknowns, and it sustained a performance of 167 Gflop/s for the largest problem (1 058 000 unknowns). The accuracy of our BEM program was almost the same as that of the regular BEM program using the double precision floating-point arithmetic. In addition, our BEM was applicable to solve realistic problems. In conclusion, the present GPU-accelerated BEM works rapidly and precisely for solving large-scale boundary value problems for Helmholtz’ equation.

### MSC:

76M15 | Boundary element methods applied to problems in fluid mechanics |

76Q05 | Hydro- and aero-acoustics |

### Keywords:

boundary element method; acoustics; graphics processing unit; GPGPU; multithread computing; high performance computing
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\textit{T. Takahashi} and \textit{T. Hamada}, Int. J. Numer. Methods Eng. 80, No. 10, 1295--1321 (2009; Zbl 1183.76829)

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