Transient Fokker-Planck Equation With SPH Method - Application in Seismic Design

Abstract

Abstract. In reliability theory, the knowledge of the time evolution of the probability density function (pdf) of the response of a diffusive random system may be required. The time evolution of this pdf is described by the transient Fokker-Planck-Kolmogorov (FPK) Numerical implementation shows notable advantages of SPH method for solving FPK equation in an unbounded state-space compared with mesh-based method : (i) the conservation of total probability is explicitly written, (ii) no artefact is required in low density zones, (iii) the positivity of the pdf is ensured, (iv) the formalism offers straightforward extension to higher dimension systems, (v) the method is adapted for a large kind of initial conditions, even slightly dispersed distributions.In