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This paper proposes a method for synthesizing local robust multivariable controllers such that the interaction between the grid nodes is explicitly considered.
Numerical calculations show that the resolution of strong gradient flow fields can significantly be improved by using the grid adapted to the solution, while the number of grid nodes is the same.
Even though the degrees of freedom increase initially, reach maximum, and decrease before the system arrives to the steady state, only a small fraction of the full grid nodes is employed at each point of time.
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During the transient calculations, grid nodes are moved while keeping the mesh topology.
The location of the grid nodes was determined, using a consumer-grade handheld GPS device.
The values of the level set functions at the other grid nodes are obtained by linear interpolation.
Since we focus on tremor signals associated with eruptions and lahars, grid nodes are positioned over the volcano surface.
The extrapolation may become unstable in the sense that some of the extrapolation coefficients increase rapidly when the grid nodes are getting closer to the boundary.
Grid spacing in the horizontal direction is 0.1°, and grid nodes are set up at depths of 0, 5,15, 15, 25, 40, and 60 km.
Grid nodes were placed with a separation smaller than the spatial resolution, with smoothing performed in order to stabilize the solution.
Grid nodes were positioned at horizontal (EW and NS) and vertical intervals of 0.25° and 10 km, respectively (Fig. 1(a)).
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