Level 99: Miscellaneous additions

Collaboration diagram for Level 99: Miscellaneous additions:

Topics
	Timer class
	t.tic(); t.toc(); t.diff();
	Functions and functors
	MPI utility functions
	Lowlevel helper functions and classes

Classes
class	dg::Message
	small class holding a stringstream More...
class	dg::Error
	class intended for the use in throw statements More...
struct	dg::Fail
	Indicate failure to converge. More...
class	dg::NoRoot1d
	Exception class, that stores boundaries for 1D root finding. More...

Functions
void	dg::abort_program (int code=-1)
	Abort program (both MPI and non-MPI)
template<class UnaryOp >
dg::SquareMatrix< std::invoke_result_t< UnaryOp, unsigned > >	dg::create::modal_filter (UnaryOp op, unsigned n)
	Create a modal filter block \( V D V^{-1}\).

Detailed Description

Function Documentation

abort_program()

void dg::abort_program ( int code = -1 )

inline

Abort program (both MPI and non-MPI)

#ifdef MPI_VERSION
    MPI_Abort(MPI_COMM_WORLD, code);
#endif //WITH_MPI
    exit( code);

Parameters

code	The abortion code that will be signalled to the caller (of the program)

modal_filter()

template<class UnaryOp >

dg::SquareMatrix< std::invoke_result_t< UnaryOp, unsigned > > dg::create::modal_filter	(	UnaryOp	op,
		unsigned	n )

Create a modal filter block \( V D V^{-1}\).

where \( V\) is the Vandermonde matrix (the backward transformation matrix) and \( D \) is a diagonal matrix with \( D_{ii} = \sigma(i)\)

See also

A discussion of the effects of the modal filter on advection schemes can be found here https://mwiesenberger.github.io/advection

Note

basically the result is that it is usually not advantageous to use a modal filter

Template Parameters

UnaryOp

Model of Unary Function real_type sigma(unsigned) The input will be the modal number i where \( i=0,...,n-1\) and n is the number of polynomial coefficients in use. The output is the filter strength for the given mode number

Parameters

op	the unary function
n	number of polynomial coefficients for forward and backward transformation

Returns

The product \( V D V^{-1}\)

Note

The idea is to use the result in connection with dg::create::fast_transform() to create a matrix that applies the filter to vectors. For example to create a modal filter that acts in two dimensions:

// create filter:
auto filter = dg::create::fast_transform(
     dg::create::modal_filter( op, grid.nx()),
     dg::create::modal_filter( op, grid.ny()), grid);
//apply filter:
dg::blas2::symv( filter, x, y);