LNorms.hpp File Reference

Header file containing functions for computing the error and the L_2 / L_infinity norm. More...

#include <iostream>
#include <typeinfo>
#include <cmath>
#include <cstdio>
#include <stdlib.h>
#include "Vector/vector_dist.hpp"
#include "Grid/grid_dist_id.hpp"
#include "util/PathsAndFiles.hpp"
#include "level_set/redistancing_Sussman/HelpFunctions.hpp"

Go to the source code of this file.

Data Structures
class	LNorms< lnorm_type >
	Class for computing the l2/l_infinity norm for distributed grids and vectors based on given errors. More...

Functions
template<size_t PropNumeric, size_t PropAnalytic, size_t Error, typename gridtype >
void	get_absolute_error (gridtype &grid)
	At each grid node, the absolute error is computed and stored in another property.
template<size_t PropNumeric, size_t PropAnalytic, size_t Error, typename gridtype >
void	get_relative_error (gridtype &grid)
	At each grid node, the relative error is computed and stored in another property.

Detailed Description

Header file containing functions for computing the error and the L_2 / L_infinity norm.

The L_2 and L_inf norm are useful for verification by convergence testings / plots.

Author

Justina Stark

Date

May 2020

Definition in file LNorms.hpp.

Function Documentation

get_absolute_error()

template<size_t PropNumeric, size_t PropAnalytic, size_t Error, typename gridtype >

void get_absolute_error

(

gridtype &

grid

)

At each grid node, the absolute error is computed and stored in another property.

The absolute error is computed as:

\[ Error_{abs} = | numerical solution - analytical solution | \]

Template Parameters

PropNumeric	Index of grid property that contains the numerical value.
PropAnalytic	Index of grid property that contains the analytical (exact) value.
Error	Index of grid property where the computed error should be written to.
gridtype	Template type of the input grid.

Parameters

grid	Input OpenFPM grid. Can be of any dimension.

Definition at line 43 of file LNorms.hpp.

get_relative_error()

template<size_t PropNumeric, size_t PropAnalytic, size_t Error, typename gridtype >

void get_relative_error

(

gridtype &

grid

)

At each grid node, the relative error is computed and stored in another property.

The relative error is computed as:

\[ Error_{rel} = | 1 - \frac{numerical solution}{analytical solution} | \]

\[ Error_{rel} = | \frac{numerical solution - analytical solution}{analytical solution + machine epsilon} | \]

Template Parameters

PropNumeric	Index of grid property that contains the numerical value.
PropAnalytic	Index of grid property that contains the analytical (exact) value.
Error	Index of grid property where the computed error should be written to.
gridtype	Template type of the input grid.

Parameters

grid	Input OpenFPM grid. Can be of any dimension.

Definition at line 75 of file LNorms.hpp.