Non-uniform grid builder that uses hyperbolic sine function. More...

#include <hsineGridBuilder.hpp>

Inheritance diagram for marian::HSineGridBuilder:

Public Member Functions
	HSineGridBuilder (double c)
	Constructor.

std::vector< double >	buildGrid (double low, double upp, int N, double concentration) const override
	builds non-uniform grid More...

	~HSineGridBuilder ()
	Destructor.

Public Member Functions inherited from marian::DCGridBuilder< HSineGridBuilder >
virtual GridBuilder *	clone () const
	Virtual copy constructor.

Public Member Functions inherited from marian::GridBuilder
virtual	~GridBuilder ()
	destructor

Private Attributes
double	c_
	Control parameter. Must be greater then 0.0. If the value of parameter is smaller, grid become more concentrated around concentration point.

Detailed Description

Class is used to generate non-uniform grid. The algorithm is basing on method proposed by Tavella & Randall [3] and Kluge [15] and briefly described and discussed by Hout & Foulon in [8].

The grid build on interval $(x_{min},x_{max})$ with a concentration point $x_K$ and c control parameter is constructed in following steps:

1) We define uniform grid

$t_i = arcsinh\big(\frac{-k}{c} + i \delta t\big)$

where $k = \frac{x_K-x_{min}}{x_{max} - x_{min}}$ and $\delta t = \frac{1}{M} \Big(arcsinh\big(\frac{t_{max}-k}{c}\big) - arcsinh\big(\frac{-k}{c}\big)\Big)$ :

$s_i = x_{min} + (k + c \times sinh(t_i))$

Below plot presents the construction of non-uniform grid for different control parameters

Plots below visualize the uniform grid for different values of control parameter and different concentration points.

Examples:: convergenceExample.cpp.

Member Function Documentation

std::vector< double > marian::HSineGridBuilder::buildGrid	(	double	low,
		double	upp,
		int	N,
		double	concentration
	)		const

overridevirtual

Parameters

low	Lower bound
upp	Upper bound
concentration	Concentration point
N	Number of grid points (N-1 intervals between lower and upper bound)

Implements marian::GridBuilder.

The documentation for this class was generated from the following files:

C:/Unix/home/OEM/fdm/src/FDM/gridBuilders/hsineGridBuilder.hpp
C:/Unix/home/OEM/fdm/src/FDM/gridBuilders/hsineGridBuilder.cpp

Public Member Functions

Private Attributes

Detailed Description

Member Function Documentation