PBBFMM3D: a Parallel Black-Box Fast Multipole Method for Non-oscillatory Kernels
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This paper presents PBBFMM3D: a parallel black-box fast multipole method that accelerates kernel matrix-vector multiplications where the kernel is a non-oscillatory function in three dimensions. Such problems arise from a wide range of fields, e.g., computational mechanics, geosciences and machine learning. While a naive direct evaluation has an O(N^2) complexity in time and storage, which is prohibitive for large-scale applications, PBBFMM3D reduces the costs to O(N). In contrast to other fast methods that require the knowledge of the explicit kernel formula, PBBFMM3D requires only the ability to evaluate the kernel. To further accelerate the computation on shared-memory machines, the parallelism in PBBFMM3D was analyzed and implemented using OpenMP. We show numerical experiments on the accuracy and the parallel scalability of PBBFMM3D, as well as its applications to covariance matrix computations that are heavily used in parameter estimation techniques, such as kriging and Kalman filtering.
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