dg::DefaultSolver< ContainerType > Struct Template Reference

PCG Solver class for solving $(y-\alpha \hat{I}(t,y))=\rho$. More...

Public Types
using	container_type = ContainerType
using	value_type = get_value_type<ContainerType>

Public Member Functions
	DefaultSolver ()
	No memory allocation.
template<class Implicit >
	DefaultSolver (Implicit &im, const ContainerType &copyable, unsigned max_iter, value_type eps)
template<class ... Params>
void	construct (Params &&...ps)
	Perfect forward parameters to one of the constructors.
void	set_benchmark (bool benchmark)
	Set or unset performance timings during iterations.
void	operator() (value_type alpha, value_type time, ContainerType &y, const ContainerType &ys)

Detailed Description

template<class ContainerType>
struct dg::DefaultSolver< ContainerType >

PCG Solver class for solving $(y-\alpha \hat{I}(t,y))=\rho$.

for given t, alpha and rho. $\hat{I}$ must be linear self-adjoint positive definite as it uses a conjugate gradient solver to invert the equation.

Note

This struct is a simple wrapper. It exists because self-adjoint operators appear quite often in practice and is not actually the recommended default way of writing a solver for the implicit time part. It is better to start with the following code and adapt from there

auto solver = [&eps = eps, &im = im, pcg = dg::PCG<ContainerType>( y0, 1000)]
    ( value_type alpha, value_type time, ContainerType& y, const
        ContainerType& ys) mutable
{
   auto wrapper = [a = alpha, t = time, &i = im]( const auto& x, auto& y){
       i( t, x, y);
       dg::blas1::axpby( 1., x, -a, y);
   };
   dg::blas1::copy( ys, y); // take rhs as initial guess
   Timer t;
   t.tic();
   unsigned number = pcg.solve( wrapper, y, ys, im.precond(), im.weights(), eps);
   t.toc();
   DG_RANK0 std::cout << "# of pcg iterations time solver: "
         <<number<<"/"<<pcg.get_max()<<" took "<<t.diff()<<"s\n";
};

See also

In general it is recommended to write your own solver using a wrapper lambda like the above and one of the existing solvers like dg::PCG, dg::LGMRES or dg::AndersonAcceleration

Template Parameters

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system

ImExMultistep ImplicitMultistep ARKStep DIRKStep

Member Typedef Documentation

container_type

template<class ContainerType >

using dg::DefaultSolver< ContainerType >::container_type = ContainerType

value_type

template<class ContainerType >

using dg::DefaultSolver< ContainerType >::value_type = get_value_type<ContainerType>

value type of vectors

Constructor & Destructor Documentation

DefaultSolver() [1/2]

template<class ContainerType >

dg::DefaultSolver< ContainerType >::DefaultSolver ( )

inline

No memory allocation.

DefaultSolver() [2/2]

template<class ContainerType >

template<class Implicit >

dg::DefaultSolver< ContainerType >::DefaultSolver ( Implicit & im, const ContainerType & copyable, unsigned max_iter, value_type eps )

inline

it does not matter what values copyable contains, but its size is important; the solve method can only be called with vectors of the same size)

Template Parameters

Implicit

The self-adjoint, positive definite implicit part of the right hand side. Has signature void operator()(value_type, const ContainerType&, ContainerType&) The first argument is the time, the second is the input vector, which the functor may not override, and the third is the output, i.e. y' = I(t, y) translates to I(t, y, y'). The two ContainerType arguments never alias each other in calls to the functor. Also needs the WeightType weights() and PreconditionerType precond() member functions.

Parameters

im	The implicit part of the differential equation. Stored as a std::function.

Attention

make sure that im lives throughout the lifetime of this object, else we'll get a dangling reference

Parameters

copyable	forwarded to constructor of dg::PCG
max_iter	maximum iteration number in cg, forwarded to constructor of dg::PCG
eps	relative and absolute accuracy parameter, used in the solve method of dg::PCG

Member Function Documentation

construct()

template<class ContainerType >

template<class ... Params>

void dg::DefaultSolver< ContainerType >::construct ( Params &&... ps )

inline

Perfect forward parameters to one of the constructors.

Template Parameters

Params

deduced by the compiler

Parameters

ps	parameters forwarded to constructors

operator()()

template<class ContainerType >

void dg::DefaultSolver< ContainerType >::operator() ( value_type alpha, value_type time, ContainerType & y, const ContainerType & ys )

inline

set_benchmark()

template<class ContainerType >

void dg::DefaultSolver< ContainerType >::set_benchmark ( bool benchmark )

inline

Set or unset performance timings during iterations.

Parameters

benchmark

If true, additional output will be written to std::cout during solution

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The documentation for this struct was generated from the following file:

• implicit.h