An Efficient Numerical Method for a Mathematical Model of a Transport of Coagulating Particles

摘要

AbstractA new computational algorithm based on a fast way of computing integral operators describing the coagulation process is proposed for a mathematical model of coagulating particles. Using this algorithm, the computational complexity of each timestep of an explicit difference scheme can be substantially reduced. For each step, the complexity of execution is reduced fromO(NM2) arithmetic operations toO(NMRlnM), whereNis the number of mesh points along the physical coordinates of particles,Mis the number of mesh points in a grid corresponding to sizes of coagulating particles, andRis the rank of a matrix corresponding to the values of the function of a coagulation kernel at mesh points. Using this approach, computations can be greatly accelerated, provided that kernel rankRis small.