Simulating the dynamics and interactions of flexible fibers in Stokes flows
Journal of Computational Physics
A kernel-independent adaptive fast multipole algorithm in two and three dimensions
Journal of Computational Physics
The black-box fast multipole method
Journal of Computational Physics
Fast and accurate numerical methods for solving elliptic difference equations defined on lattices
Journal of Computational Physics
A fast, robust, and non-stiff Immersed Boundary Method
Journal of Computational Physics
A Fourier-series-based kernel-independent fast multipole method
Journal of Computational Physics
Journal of Computational Physics
Second kind integral equation formulation for the modified biharmonic equation and its applications
Journal of Computational Physics
A fast solver for Poisson problems on infinite regular lattices
Journal of Computational and Applied Mathematics
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We present a modification of the fast multipole method (FMM) in two dimensions. While previous implementations of the FMM have been designed for harmonic kernels, our algorithm works for a large class of kernels that satisfy fairly general conditions, amounting to the kernel being sufficiently smooth away from the diagonal. Our algorithm approximates appropriately chosen parts of the kernel with "tensor products" of Legendre expansions and uses the singular value decomposition (SVD) to compress the resulting representations. The obtained singular function expansions replace the Taylor and Laurent expansions used in the original FMM. The algorithm requires O(N) operations and is stable and robust. The performance of the algorithm is illustrated with numerical examples.