InternalModesAdaptiveSpectral

Solve the vertical EVP on an adaptive WKB grid with coupled Chebyshev blocks.

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Declaration

classdef InternalModesAdaptiveSpectral < InternalModesWKBSpectral

Overview

InternalModesAdaptiveSpectral extends InternalModesWKBSpectral using the adaptive multi-region strategy described in Section 4.4 of Early, Lelong, and Smith (2020). The solver keeps the WKB stretched coordinate but partitions it into oscillatory and evanescent regions, then couples separate Chebyshev blocks across the turning points.

This is most useful at fixed frequency, where the turning points of \(N^2(z) - \omega^2\) can leave large regions that are exponentially decaying rather than oscillatory.

im = InternalModesAdaptiveSpectral(rho=rho, zIn=zIn, zOut=zOut, latitude=latitude, nEVP=257);
[F, G, h, k] = im.modesAtFrequency(2*pi*1e-3);

Topics

• Create and initialize modes
  • InternalModesAdaptiveSpectral Initialize the adaptive WKB spectral solver.

Developer Topics

These items document internal implementation details and are not part of the primary public API.

• Developer topics
  • Diff1_xChebFunction Differentiate a vector in the coupled Chebyshev basis.
  • DistributePointsInRegionsWithMinimum Distribute collocation points across adaptive regions.
  • FindWKBSolutionBoundaries Estimate adaptive-region boundaries from turning points and WKB decay.
  • Lxi Length of each coupled subdomain in the adaptive coordinate.
  • N_zCheb Chebyshev coefficients of \(N(z)\) on the reference grid.
  • RemoveRegionAtIndex Merge neighboring adaptive regions by removing one boundary.
  • T_xCheb_xLobatto Transform coupled Chebyshev coefficients onto the adaptive Lobatto grid.
  • T_xCheb_zOutFunction Transform coupled Chebyshev coefficients onto the public output grid.
  • T_xCheb_zOut_Transforms Per-region transforms from Chebyshev coefficients to zOut.
  • T_xCheb_zOut_fromIndices Source indices in coefficient space for each output transform.
  • T_xCheb_zOut_toIndices Target indices in zOut for each output transform.
  • T_xLobatto_xCheb Transform adaptive-grid values into the coupled Chebyshev basis.
  • WKBDecaySolution Evaluate the Airy-based WKB decay envelope used for pruning regions.
  • eqIndices Row indices for each coupled subproblem.
  • nEquations Number of coupled Chebyshev subproblems.
  • polyIndices Column indices for each coupled Chebyshev block.
  • x_zLobatto Adaptive stretched-coordinate grid sampled on the public Lobatto grid.
  • xiBoundaries WKB-coordinate values of region boundaries and turning points.
  • xiIndices Grid-point indices into the unique adaptive Lobatto grid.
  • zBoundaries Physical depths of region boundaries and turning points.

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