Speeding up the Computation of the Transient Richards’ Equation with AMGCL

Abstract

The Richards’-equation is widely used for modeling complex soil water dynamics in the vadose zone. Usually, the Richards’-equation is simulated with the Finite Element Method, the Finite Difference Method, or the Finite Volume Method. In all three cases, huge systems of equations are to be solved, which is computationally expensive. By employing the free software library AMGCL, a reduction of the computational running time of up to 79% was achieved without losing accuracy. Seven models with different soils and geometries were tested, and the analysis of these tests showed, that AMGCL causes a speedup in all models with 20,000 or more nodes. However, the numerical overhead of AMGCL causes a slowdown in all models with 20,000 or fewer nodes.