The spectral boundary element method: a new window on boundary elements in rock mechanics

摘要: Abstract This paper describes a novel spectral method based on the FFT for solving boundary integral equations incorporating effect of non-linear material behaviour. The mathematical properties this are developed and illustrated by means simple model problem. element technique is shown to provide new framework volumetric modelling with easy access number interesting features not available spatially implemented algorithms. A fundamental set point Fourier kernels introduced from which variety approximation schemes (including standard piecewise polynomial approximations) can be constructed in frequency domain introducing high filters. implementation these avoids tedious integrations associated spatial discretizations provides considerable flexibility general-purpose user-defined schemes. Techniques described overcome periodicity constraint imposed so that general non-repeating geometries modelled. It how same also exploited repeating geometries. Two iterative methods solve discretized BE efficiently. first uses information provided construct an approximate inverse extremely efficiently use preconditioned conjugate gradient algorithm. reduce operation count solution problem O(N log N) operations. second adaptation Jacobi iteration roughly double convergence rate linear problems help inhibit undesirable simultaneous failure neighbouring elements when brittle rock fracture. appendices containing expressions their transforms provided.