The tidal power available for electricity generation from in-stream turbines placed in the Minas Passage of the Bay of Fundy is examined. A previously derived theory is adapted to model the effect of turbine drag on the flow through the Minas Passage and the tidal amplitude in the Minas Basin. The theoretical maximum power production over a tidal cycle is determined by the product of the amplitude of the forcing tide in the Bay of Fundy and the undisturbed volumetric flowrate through the Minas Passage. Although the extraction of the maximum power will reduce the flowrate through the Minas Passage and the tides in the Minas Basin by over 30 per cent, a significant portion of the maximum power can be extracted with little change in tidal amplitude as the initial power generation causes only an increase in the phase lag of the basin tides. Two-dimensional, finite-element, numerical simulations of the Bay of Fundy-Gulf of Maine system agree remarkably well with the theory. The simulations suggest that a maximum of 7 GW of power can be extracted by turbines. They also show that any power extraction in the Minas Passage pushes the Bay of Fundy-Gulf of Maine system closer to resonance with the forcing tides, resulting in increased tidal amplitudes throughout the Gulf of Maine. Although extracting the maximum power produces significant changes, 2.5 GW of power can be extracted with a maximum 5 per cent change in the tidal amplitude at any location. Finally, the simulations suggest that a single turbine fence across the Minas Passage can extract the same power as turbines throughout the passage but that partial turbine fences are less efficient.

For many expensive deterministic computer simulators, the outputs do not have replication error and the desired metamodel (or statistical emulator) is an interpolator of the observed data. Realizations of Gaussian spatial processes (GP) are commonly used to model such simulator outputs. Fitting a GP model to n data points requires the computation of the inverse and determinant of n × n correlation matrices, R, that are sometimes computationally unstable due to near-singularity of R. This happens if any pair of design points are very close together in the input space. The popular approach to overcome nearsingularity is to introduce a small nugget (or jitter) parameter in the model that is estimated along with other model parameters. The inclusion of a nugget in the model often causes unnecessary over-smoothing of the data. In this article, we propose a lower bound on the nugget that minimizes the over-smoothing and an iterative regularization approach to construct a predictor that further improves the interpolation accuracy. We also show that the proposed predictor converges to the GP interpolator.

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Abstract. Moving mesh methods based on the equidistribution principle are powerful techniques for the space-time adaptive solution of evolution problems. Solving the resulting coupled system of equations, namely the original PDE and the mesh PDE, however, is challenging in parallel. We propose in this paper several Schwarz domain decomposition algorithms for this task. We then study in detail the convergence properties of these algorithms applied to the nonlinear mesh PDE in one spatial dimension. We prove convergence for classical transmission conditions, and optimal and optimized variants for the generation of steady equidistributing grids. A classical, parallel, Schwarz algorithm is presented and analysed for the generation of time dependent (moving) equidistributing grids. We conclude our study with numerical experiments.

The efficient generation of meshes is an important step in the numerical solution of various problems in physics and engineering. We are interested in situations where global mesh quality and tight coupling to the physical solution is important. We consider elliptic PDE based mesh generation and present a method for the construction of adaptive meshes in two spatial dimensions using domain decomposition that is suitable for an implementation on parallel computing architectures. The method uses the stochastic representation of the exact solution of a linear mesh generator of Winslow type to find the points of the adaptive mesh along the subdomain interfaces. The meshes over the single subdomains can then be obtained completely independently of each other using the probabilistically computed solutions along the interfaces as boundary conditions for the linear mesh generator. Further to the previously acknowledged performance characteristics, we demonstrate how the stochastic domain decomposition approach is particularly suited to the problem of grid generation -generating quality meshes efficiently. In addition we show further improvements are possible using interpolation of the subdomain interfaces and smoothing of mesh candidates. An optimal placement strategy is introduced to automatically choose the number and placement of points along the interface using the mesh density function. Various examples of meshes constructed using this stochastic-deterministic domain decomposition technique are shown and compared to the respective single domain solutions using a representative mesh quality measure. A brief performance study is included to show the viability of the stochastic domain decomposition approach and to illustrate the effect of algorithmic choices on the solver's efficiency.