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inv_geo_trans_derivative.m File Reference

computes entries of a geometry transformation function's inverse transposed jacobian More...

Go to the source code of this file.

Functions

function [ P1res
, P2res ] = 
inv_geo_trans_derivative (model, glob, P1derivates, P2derivates, callerid)
 computes entries of a geometry transformation function's inverse transposed jacobian More...
 
function ind = invgeotransderivative>gethash (Xx, hashes)
 

Detailed Description

computes entries of a geometry transformation function's inverse transposed jacobian

Definition in file inv_geo_trans_derivative.m.

Function Documentation

function [ P1res , P2res ] = inv_geo_trans_derivative (   model,
  glob,
  P1derivates,
  P2derivates,
  callerid 
)

computes entries of a geometry transformation function's inverse transposed jacobian

If model.geometry_transformation is set to spline, this function computes derivatives of the given geometry transformation function \(\Phi : \mathbb{R}^2 \to \mathbb{R}^2\).

Parameters
modelmodel
globmatrix with two columns for the \(x\) and \(y\) coordinates specifying where the derivative should be evaluated.
P1derivatesa cell array of vectors of length one to three filled with scalar values one or two. For each cell entry, a derivative is evaluated, where a value of one means a derivation in \(x\) direction and two a derivation in \(y\) direction. For example { [1, 2, 1] } corresponds to the derivative \(\partial_x \partial_y \partial_x \Phi_1(x,y)\)
P2derivatesa cell array of vectors of length one to three filled with scalar values one or two. For each cell entry, a derivative is evaluated, where a value of one means a derivation in \(x\) direction and two a derivation in \(y\) direction. For example { [1, 2, 1] } corresponds to the derivative \(\partial_x \partial_y \partial_x \Phi_2(x,y)\)
calleridAs this function only depends on the space variable, during the evaluation of an evolution scheme, the same derivatives need to be computed repeatedly. Therefore, the computations done in the first time step are are cached by this function. In order to make sure, the hash function works correctly, all calls of this function with different arguments for P1derivates and P2derivates should pass a unique callerid.
Return values
P1resa cell array of derivative evaluations specified by glob and P1derivates.
P2resa cell array of derivative evaluations specified by glob and P2derivates.
Required fields of model:
  • tstep —  tstep
  • verbose —  flag indicating the verbosity level of informative output
  • geometry_transformation —  geometry transformation

Definition at line 17 of file inv_geo_trans_derivative.m.

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