A fast numerical method for the Cauchy problem for the Smoluchowski equation

作者：Matveev S A^*; Smirnov A P; Tyrtyshnikov E E

来源：Journal of Computational Physics, 2015, 282: 23-32.

DOI：10.1016/j.jcp.2014.11.003

• Smoluchowski coagulation equation
• Predictor-corrector scheme
• Cross matrix interpolations
• Fast algorithms of linear algebra

A new solution technique is proposed for one-dimensional Smoluchowski equations. It is based on the finite-difference predictor-corrector scheme and is faster than other methods using this kind of scheme. The new technique capitalizes on low-rank approximations of matrices arising after discretization of the coagulation kernel and includes a new fast convolution algorithm with the trapezoidal quadrature rule. For the grids with N nodes, the complexity of the new method is O(NlogN) for each step with time instead of O(N-2) operations required by the standard implementation of the predictor-corrector scheme.

• 出版日期2015-2-1