Most phytoplankters face opposing vertical gradients in light versus nutrient supplies but have limited capacities for vertical habitat choice. We therefore explored a dynamical model of negatively buoyant algae inhabiting a one-dimensional water column to ask how water column depth and turbulence constrain total (areal) phytoplankton biomass. We show that the population persistence boundaries in water column depth-turbulence space are set by sinking losses and light limitation but that nutrients are most limiting to total biomass in water columns that are neither too shallow or too weakly mixed (where sinking losses prevail) nor too deep and turbulent (where light limitation prevails). In shallow waters, the most strongly limiting process is nutrient influx to the bottom of the water column (e.g., from sediments). In deep waters, the most strongly limiting process is turbulent upward transport of nutrients to the photic zone. Consequently, the highest total biomasses are attained in turbulent waters at intermediate water column depths and in deep waters at intermediate turbulences. These patterns are insensitive to the assumption of fixed versus flexible algal carbon-to-nutrient stoichiometry, and they arise irrespective of whether the water column is a surface layer above a deep water compartment or has direct contact with sediments.

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In engineering practice quite simple algebraic multigrid (AMG) methods with inexpensive coarse-grid selection and constant interpolation are frequently found to be the method of choice to solve systems of linear equations where accurate solutions of these systems are not needed.In a case study we analyze the poor parallel performance of such algorithms on common multicore cluster architectures and suggest using a class of algorithms with hybrid coarse-grid selection featuring a superior parallel performance.

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