H-matrix methods for linear and quasi-linear integral operators appearing in population balances

In population dynamics, the source term of breakage and the sink term of coagulation are often described by linear and quasi-linear operators, respectively. These operators are characterised by their kernel functions. Naive discretisation leads to full matrices and therefore to quadratic complexity O(n2), if n   denotes the number of degrees of freedom. For several popular kernel functions, e.g. the modified Smoluchowski kernel, an efficient treatment is introduced using the ideas of H-matrices. This approach leads to linear complexity O(n).