A new algorithm based on factorization for heterogeneous domain decomposition (Q312190)

The authors present a new algorithm based on factorization for heterogeneous domain decomposition. They first provide their new factorization algorithm for a time-dependent model advection-reaction-diffusion problem in \(d\) spacial dimensions. A detailed analysis of the new factorization algorithm in one spatial dimension is given as well as a proof of asymptotic error estimates when the viscosity is becoming small. Numerical experiments are given to show that in one spatial dimension the theoretical error estimates are sharp and numerical experiments are given in two spatial dimensions to illustrate their new factorization algorithm works beyond the one-dimensional case.