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Zimbabwe's poor are predominantly located in the semi-arid regions (Bird and Shepherd, 2003) and rely on rainfed agriculture for their subsistence. Decline in productivity, scarcity of arable land, irrigation expansion limitations, erratic rainfall and frequent dry spells, among others cause food scarcity. The challenge faced by small-scale farmers is to enhance water productivity of rainfed agriculture by mitigating intra-seasonal dry spells (ISDS) through the adoption of new technologies such as rainwater harvesting (RWH). The paper analyses the agro-hydrological functions of RWH and assesses its impacts (at field scale) on the crop yield gap as well as the Transpirational Water Productivity (WP T ). The survey in six districts of the semi-arid Zimbabwe suggests that three parameters (water source, primary use and storage capacity) can help differentiate storage-type-RWH systems from "conventional dams". The Agricultural Production Simulator Model (APSIM) was used to simulate seven different treatments (Control, RWH, Manure, Manure + RWH, Inorganic Nitrogen and Inorganic Nitrogen + RWH) for 30 years on alfisol deep sand, assuming no fertiliser carry over effect from season to season. The combined use of inorganic fertiliser and RWH is the only treatment that closes the yield gap. Supplemental irrigation alone not only reduces the risks of complete crop failure (from 20% down to 7% on average) for all the treatments but also enhances WP T (from 1.75 kg m -3 up to 2.3 kg m -3 on average) by mitigating ISDS.* Corresponding author. E-mail address: mwengej@ebe.pg.wits.ac.za (J. Mwenge Kahinda).

This paper discusses an element‐by‐element approach of implementing the Boundary Element Method (BEM) which offers substantial savings in computing resource, enables handling of a wider range of problems including non‐linear ones, and at the same time preserves the second‐order accuracy associated with the method. Essentially, by this approach, herein called the Green Element Method (GEM), the singular integral theory of BEM is retained except that its implementation is carried out in a fashion similar to that of the Finite Element Method (FEM). Whereas the solution procedure of BEM couples the information of all nodes in the computational domain so that the global coefficient matrix is dense and full and as such difficult to invert, that of GEM, on the other hand, involves only nodes that share common elements so that the global coefficient matrix is sparse and banded and as such easy to invert. Thus, GEM has the advantage of being more computationally efficient than BEM. In addition, GEM makes the singular integral theory more flexible and versatile in the sense that GEM readily accommodates spatial variability of medium and flow parameters (e.g., flow in heterogeneous media), while other known numerical features of BEM—its second‐order accuracy and ability to readily handle problems with singularities are retained by GEM. A number of schemes is incorporated into the basic Green element formulation and these schemes are examined with the goal of identifying optimum schemes of the formulation. These schemes include the use of linear and quadratic interpolation functions on triangular and rectangular elements. We found that linear elements offer acceptable accuracy and computational effort. Comparison of the modified fully implicit scheme against the generalized two‐level scheme shows that the modified fully implicit scheme with weight of about 1·25 offers a marginally better approximation of the temporal derivative. The Newton–Raphson scheme is easily incoporated into GEM and provides excellent results for the time‐dependent non‐linear Boussinesq problem. Comparison of GEM with conventional BEM is done on various numerical examples, and it is observed that, for comparable accuracy, GEM uses less computing time. In fact, from the numerical simulations carried out, GEM uses between 15 and 45 per cent of the simulation time of BEM.

SUMMARYThis paper discusses an element-by-element approach of implementing the Boundary Element Method (BEM) which offers substantial savings in computing resource, enables handling of a wider range of problems including non-linear ones, and at the same time preserves the second-order accuracy associated with the method. Essentially, by this approach, herein called the Green Element Method (GEM), the singular integral theory of BEM is retained except that its implementation is carried out in a fashion similar to that of the Finite Element Method (FEM). Whereas the solution procedure of BEM couples the information of all nodes in the computational domain so that the global coefficient matrix is dense and full and as such difficult to invert, that of GEM, on the other hand, involves only nodes that share common elements so that the global coefficient matrix is sparse and banded and as such easy to invert. Thus, GEM has the advantage of being more computationally efficient than BEM. In addition, GEM makes the singular integral theory more flexible and versatile in the sense that GEM readily accommodates spatial variability of medium and flow parameters (e.g., flow in heterogeneous media), while other known numerical features of BEM-its second-order accuracy and ability to readily handle problems with singularities are retained by GEM.A number of schemes is incorporated into the basic Green element formulation and these schemes are examined with the goal of identifying optimum schemes of the formulation. These schemes include the use of linear and quadratic interpolation functions on triangular and rectangular elements. We found that linear elements offer acceptable accuracy and computational effort. Comparison of the modified fully implicit scheme against the generalized two-level scheme shows that the modified fully implicit scheme with weight of about 1-25 offers a marginally better approximation of the temporal derivative. The Newton-Raphson scheme is easily incoporated into GEM and provides excellent results for the timedependent non-linear Boussinesq problem. Comparison of GEM with conventional BEM is done on various numerical examples, and it is observed that, for comparable accuracy, GEM uses less computing time. In fact, from the numerical simulations carried out, GEM uses between 15 and 45 per cent of the simulation time of BEM.