Abstract Interfaces

Find which grid cell contains the given point

evaluate the mapping h q=(X^1,X^2,zeta) -> (x,y,z)

evaluate total derivative of the mapping sum k=1,3 (dx(1:3)/dq^k) q_vec^k, where dx(1:3)/dq^k, k=1,2,3 is evaluated at q_in=(X^1,X^2,zeta) ,

evaluate sum_ij (qL_i (G_ij(q_G)) qR_j) , where qL=(dX^1/dalpha,dX^2/dalpha ,dzeta/dalpha) and qR=(dX^1/dbeta,dX^2/dbeta ,dzeta/dbeta) and dzeta_dalpha then known to be either 0 of ds and dtheta and 1 for dzeta

evaluate sum_k sum_ij (qL_i d/dq^k(G_ij(q_G)) qR_j) q_vec^k, k=1,2,3 where qL=(dX^1/dalpha,dX^2/dalpha ,dzeta/dalpha) and qR=(dX^1/dbeta,dX^2/dbeta ,dzeta/dbeta) and dzeta_dalpha then known to be either 0 of ds and dtheta and 1 for dzeta

evaluate Jacobian of mapping h: J_h=sqrt(det(G)) at q=(X^1,X^2,zeta)

evaluate derivative of Jacobian of mapping h: sum_k dJ_h(q)/dq^k q_vec^k, k=1,2 at q=(X^1,X^2,zeta)

Evaluate value at x of all basis functions with support in local cell values[j] = B_j(x) for jmin <= j <= jmin+degree

Evaluate value and n derivatives at x of all basis functions with support in local cell derivs[i,j] = (d/dx)^i B_j(x) for 0 <= i <= n and jmin <= j <= jmin+degree

Evaluate derivative at x of all basis functions with support in local cell derivs[j] = B_j'(x) for jmin <= j <= jmin+degree

Free storage

evaluate all second derivatives d^2x(1:3)/(dq^i dq^j), i,j=1,2,3 is evaluated at q_in=(X^1,X^2,zeta),

evaluate all first derivatives dx(1:3)/dq^i, i=1,2,3 , at q_in=(X^1,X^2,zeta),