feat:inner products for mixed method

[chauj96]

No description provided.

[castelletto1]

Suggested change

	for( localIndex i = 0; i < NF; ++i )
	{
	for( localIndex j = 0; j < NF; ++j )
	{
	M[i][j] = 0.0;
	}
	}
	LvArray::tensorOps::fill< NF, NF >( M, 0.0 );

[castelletto1]

Suggested change

	// 4) U = I - Q Q^T
	real64 U[ NF ][ NF ] = {{0}};
	LvArray::tensorOps::addIdentity< NF >( U, -1.0 );
	LvArray::tensorOps::Rij_add_AikAjk< NF, 3 >( U, Qmat );
	LvArray::tensorOps::scale< NF, NF >( U, -1.0 );
	// 5) A^{-1} * U * A^{-1}
	real64 invA[ NF ];
	for( localIndex i = 0; i < NF; ++i )
	{
	invA[i] = 1.0 / A[i];
	}
	// temp = A^{-1} * U
	real64 temp[ NF ][ NF ];
	for( localIndex i = 0; i < NF; ++i )
	{
	for( localIndex j = 0; j < NF; ++j )
	{
	temp[i][j] = invA[i] * U[i][j];
	}
	}
	// Usc = A^{-1} * U * A^{-1}
	real64 Usc[ NF ][ NF ];
	for( localIndex i = 0; i < NF; ++i )
	{
	for( localIndex j = 0; j < NF; ++j )
	{
	Usc[i][j] = temp[i][j] * invA[j];
	}
	}
	// 6) M = CKCt + (v / t) * Usc
	real64 tParam = 2.0 * ( elemPerm[0] + elemPerm[1] + elemPerm[2] );
	real64 scale = elemVolume / tParam;
	for( localIndex i = 0; i < NF; ++i )
	{
	for( localIndex j = 0; j < NF; ++j )
	{
	M[i][j] = CKCt[i][j] + scale * Usc[i][j];
	}
	}
	// 4) M = CKCt + (v / t) * A^{-1} * ( I - Q Q^T ) * A^{-1}
	real64 invA[NF];
	for (localIndex i = 0; i < NF; ++i)
	{
	invA[i] = real64(1) / A[i];
	}
	// scale = elemVolume / tParam, where tParam = 2 * trace(K)
	real64 const tParam = real64(2) * (elemPerm[0] + elemPerm[1] + elemPerm[2]);
	real64 const scale = elemVolume / tParam;
	for (localIndex i = 0; i < NF; ++i)
	{
	real64 const invAiScaled = scale * invA[i];
	real64 const qi0 = Qmat[i][0];
	real64 const qi1 = Qmat[i][1];
	real64 const qi2 = Qmat[i][2];
	for (localIndex j = i; j < NF; ++j)
	{
	// qdot = (Q Q^T)_{ij} = sum_k Qik * Qjk, with k in [0,2]
	real64 const qdot = qi0*Qmat[j][0] + qi1*Qmat[j][1] + qi2*Qmat[j][2];
	real64 const u = (i == j ? real64(1) : real64(0)) - qdot;
	real64 const mij = CKCt[i][j] + (invAiScaled * invA[j]) * u;
	M[i][j] = mij;
	M[j][i] = mij; // symmetry fill
	}
	}

[castelletto1]

Let's use a consistent nomenclature across inner products, e.g.:

• fCenter vs faceCenter
• fNormal vs faceNormal
• vec_cf vs cellToFaceVector
• ...

Let's keep in mind when refactoring nomenclature, that kernels will eventually be used also for flow within surfaces (faults, fractures). Cell seems appropriate. Instead of faces (or edges), we should probably use the term facets.