Fast Convolutional Reproducing Kernel Particle Method for Efficient Meshfree Simulations

The fast-convolving reproducing kernel particle method (FC-RKPM) is introduced, which is hundreds to millions of times faster than the traditional RKPM for 3D meshfree simulations by expressing the meshfree discretizations with RK approximation in terms of convolution sums and using fast Fourier transform (FFT) to efficiently compute the convolutions.