partitionofunity.hh File Reference

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Functions
template<class X , class GFS , class CC >
X	standardPartitionOfUnity (const GFS &gfs, const CC &cc)
	Compute a simple partition of unity.
template<class X , class GFS , class LFS , class CC >
X	sarkisPartitionOfUnity (const GFS &gfs, LFS &lfs, const CC &cc, int cells_x, int cells_y, int overlap, int partition_x, int partition_y)
	Compute a partition of unity according to Sarkis.

Function Documentation

sarkisPartitionOfUnity()

template<class X , class GFS , class LFS , class CC >

X sarkisPartitionOfUnity	(	const GFS &	gfs,
		LFS &	lfs,
		const CC &	cc,
		int	cells_x,
		int	cells_y,
		int	overlap,
		int	partition_x,
		int	partition_y
	)

Compute a partition of unity according to Sarkis.

The resulting partition of unity interpolates linearly where two subdomains overlap and extends consistently to more overlapping subdomains. It is strictly bound to the subdomain arrangement as provided by YaspGrid and only supports the 2D case. The number of subdomains is assumed to divide the number of cells in each dimension.

Template Parameters

X	Vector type

Parameters

gfs	Grid function space.
lsf	Local function space.
cc	Constraints container of the problem to be solved.
cells_x	Number of cells in x direction.
cells_y	Number of cells in y direction.
partition_x	Number of partitions in x direction.
partition_y	Number of partitions in y direction.

Returns

A vector representing the partition of unity.

standardPartitionOfUnity()

template<class X , class GFS , class CC >

X standardPartitionOfUnity	(	const GFS &	gfs,
		const CC &	cc
	)

Compute a simple partition of unity.

The resulting partition of unity is defined as 1/k on each DOF, where k is the number of subdomains covering that DOF. Subdomain boundaries are not counted here provided the constraints container has Dirichlet constraints on subdomain boundaries.

Template Parameters

X	Vector type

Parameters

gfs	Grid function space.
cc	Constraints container of the problem to be solved.

Returns

A vector representing the partition of unity.